Magnetic Sensors, Volume 5, Sensors: A Comprehensive Survey

1

Introduction R ICHARD BOLL. Vacuumschmelze GmbH. Hanau. FRG

Contents 1.1 1.2 1.3 1.4 1.4.1 1.4.2 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.6 1.6.1 1.6.2 1.7 1.7.1 1.7.2 1.7.3 1.8 1.8.1 1.8.2 1.8.2.1 1.8.2.2 1.8.3 1.9

. . . . . . . . . . . . Definition of Magnetic Sensors . . . . . . . . . . . . . . . . . . . Magnetic Terms and Units .................... Natural and Technical Magnetic Fields and Their Order of Magnitude . . Introductory Remarks. Historical Background

Natural Magnetic Fields . Technical Magnetic Fields

. . . . . . . . . . . . ............ Soft and Hard Magnetic Materials for Sensors . . Soft Magnetic Materials . . . . . . . . . . . . . Hard Magnetic Materials . . . . . . . . . . . .

Mechanical Properties of Magnetic Materials . Supplementary Remarks . . . . . . . . . . .

. . Magnetic Noise . . . . . . . . . . . . . . . . Thermal and Thermomagnetic Noise . . . . . Barkhausen Noise . . . . . . . . . . . . . . .

. . . . .

. . . . .

. . . . .

. . . . . . . ....... . . . . . . . . ....... . . . . . . .

. . . . . . . . . . ......... . . . . . . . . . . . . . . . . . . . ......... Coil Systems to Produce Definite Magnetic Fields . . . . . . . . . . Coils for Homogeneous DC Fields up to Approximately 100 A/cm . . . Coils for Higher Fields (Electromagnets) . . . . . . . . . . . . . . . Superconducting Coils . . . . . . . . . . . . . . . . . . . . . . . Shielding Magnetic Fields . . . . . . . . . . . . . . . . . . . . . General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Principles of Magnetic Shielding . . . . . . . . . . . . . . . . DC Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . AC Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 3 5

6 6 8 9 10 13 15 16 16 16 19 20 21 23 24

Materials for Magnetic Shieldings and Design

24 24 25 25 26 27

References

29

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

2

1 Introduction

1.1 Introductory Remarks, Historical Background The expression magnet or magnetic originates from the region Magnesia in Thessaly (Greece) where magnetic loadstone (Magnetite, Fe, 0,) is found as a natural resource. The first reports in Europe of the attraction and repulsion forces arising between magnetic loadstones were made by Thales of Miletus around 600 B. C. The expression “sensor” is derived from the Latin “sensus” meaning capable of sensitivity. It is gradually replacing previously used expressions such as “measurement pick-up” and “probe”. The directional compass can really be regarded as the first magnetic sensor since it reacts to the Earth’s magnetic field. Its history stretches back over 4000 years and can be traced to the Chinese who first discovered magnetic loadstone as a natural source of magnetism and used it as a directional aid for orientation [l, 21. Other early sensors can be found in the world of wildlife where nature has equipped certain birds and fish with “magnetic sensors” providing them with the capability to orientate themselves in the Earth’s magnetic field and hence providing them with a sense of direction. The compass became significantly more important in Europe from about 1200 A. D. onwards, and in particular around the time of the great seafaring adventurers and explorers. On his transatlantic voyages Christopher Columbus observed the behavior of the compass as he sailed westward and famous compass-makers are known to have lived in London and Nurnberg around 1500. At that time the production of “steel’’ suitable for compass needles was a closely kept secret. In 1820 Oersted discovered that a current carrying wire deflected a compass needle in its vicinity, and with that the age of electromagnetism had arrived. The first mathematical formula describing the correlation between electric current and magnetism through the deflection of a magnetic needle was Biot-Savart’s law. Then Faraday repeated and extended Oersted’s experiments and while doing so discovered the Law of Induction in 1831. The first magnetometer to be constructed was the bifilar magnetometer built in 1831 by Gauss and Weber and in 1841 the Weber-Bussole compass which included a magnetic needle was used to measure powerful currents. In 1862 Maxwell created the common theoretical basis for electromagnetism with the laws which were named after him [3], though the expression “permeability” can be traced to Lord Kelvin. Throughout the history of this topic it is evident that the availability of different types of sensors operating on a magnetic basis is very closely linked to the development and the availability of special magnetic materials and to the discovery of new physical and magnetic effects. Some of these effects were very soon exploited to make new magnetic sensors, others were not used until much later and some are yet to be utilized in sensors. Table 1-1 gives a brief survey (see also [4]).

1.2 Definition of Magnetic Sensors

3

B b l e 1-1. Magnetic effects for sensors. Year

Effect

Explanation

Technical Use

1842

Joule effect

Change in shape of a ferromagnetic body with magnetization (magnetostriction)

In combination with piezoelectric elements for magnetometers and potentiometers

1846

AE effect

Change in Young’s modulus with magnetization

Acoustic delay line components for magnetic field measurement

1847

Matteucci effect

Torsion of a ferromagnetic rod in a longitudinal field changes magnetization

Magnetoelastic sensors

1856

Magnetoresistance (Thomson effect)

Change in resistance with magnetic field

Magnetoresistive sensors

1858

Wiedemann effect

A torsion is produced in a current carrying ferromagnetic rod when subjected to a longitudinal field

Torque and force measurement

1865

Villari effect

Effect on magnetization by tensile or compressive strength

Magnetoelastic sensors

1879

Hall effect

A current carrying crystal produces a transverse voltage when subjected to a magnetic field vertical to its surface

Magnetogalvanic sensors

1903

Skin effect

Distance sensors, proximity sensors

1931

Sixtus Tonks effect

Displacement of current from the interior of material to surface layer due to eddy currents Pulse magnetization by large Barkhausen jumps

1962

Josephson effect

lbnnel effect between two superconducting materials with an extremely thin separating layer; quantum effect

Wiegand and pulse-wire sensors SQUID magnetometers

1.2 Definition of Magnetic Sensors

The expression “Magnetic Sensors” is not commonly used. However, when the concept for a book series on sensors was formed and the volumes and chapters were being planned it appeared that the term “magnetic sensors” described quite succinctly a clearly defined group of sensors.

4

1 Introduction

This description is sensible when one considers that the category is not limited solely to magnetic-field sensors, but is allowed to include all magnetic sensors some of which have previously fallen into different groups. Here, magnetic sensors are understood to be sensors which in one way or another are associated with the laws and effects of magnetic or electromagnetic fields. The latter group covers those sensors which utilize the laws of induction, whilst the former group includes sensors in which certain material properties are influenced by a magnetic. field. Magnetic materials, i. e., soft and hard magnetic materials and all other materials, which are sensitive to magnetic fields, play a principal role in the nature and operation of magnetic sensors, but at this stage it is not relevant to consider whether metals, metal oxides or semiconductors are concerned or which physical properties are being influenced by the magnetic field. Previous attempts at classification and grouping of sensors have been inconsistent and not uniform. In textbooks on measurements and control, but also from other books on sensors or from review articles sensors have been classified using the following methods [5-141:

-

‘Ijrpes of sensors Physical principles Properties measured Sensor applications Sensor technologies.

For this edition of Volume 5 , a classification system has been selected which is essentially based on physical principles and effects, as follows:

- Magnetogalvanic sensors - Magnetoelastic sensors

-

Magnetic-field sensors: saturation-core magnetometers (flux-gate magnetometers) and induction-coil and search-coil magnetometers Inductive sensors (including eddy-current sensors) Wiegand and pulse-wire sensors Magnetoresistive sensors SQUID sensors.

Each chapter of this volume individually deals with the fundamentals, measurement magnitudes, sensor components and devices, new technologies, and also partially with sensor electronics. In addition, technical design and the main fields of application are also discussed. A more complete survey of applications is presented in Chapter 11, whilst Chapter 12 outlines future trends in the field. This volume does not include sensors based on a magneto-optical basis, i. e., fiber-optic sensors. These are discussed in Volume 6 as their intrinsic physical properties are primarily derived from the field of optics and optical effects (e.g. Faraday effect). Moreover, Volume 5 does not cover magnetic heads of the sort used to read magnetic memories of audio, video and data devices like magnetic tapes, magnetic cards, Winchester disks etc. Strictly speaking though, magnetic heads which react to the stray fields of information carriers are actually magnetic sensors. However, they form a special group which does

1.3 Magnetic Terms and Units

5

not readily fall under the subject matter discussed in this volume, and this applies equally to magnetic heads operating on an induction or magnetoresistive basis as well as to those sensors operating magneto-optically. Also excluded are magnetic sensors using magnetic resonance effects or the Zeeman effect. Some special magnetic sensors based on integrated circuits technology will be covered by Volume 1.

1.3 Magnetic Terms and Units The subject of magnetism generates a number of terms and units which are commonly used, the more important ones being included in Table 1-2. Nowadays, magnetic terms and units are given using the MKSA system, a subsystem of the SI system (Systtme International d’unites), Table 1-2. Magnetic terms and units. Term, quantity

MKSA unit

subunits

CGS unit

conversion

Magnetic field strength H

A/m

1 A/cm = 100 A/m 1 mA/cm = 0.1 A/m 1 kA/m = 1000 A/m

Oe (Oersted)

1 Oe = 79.58 A/m = 0.796 A/cm

Magnetization M Magnetic induction B (flux density)

A/m T (Tesla)

G (Gauss)

v.s --

see field strength 1 mT = T 1 pT = 1 0 - 6 T 1 nT = 1 0 - 9 T 1 pT = T 1 yl) = 1 nT

1G = T 1 kG = 0.1 T 1 mG = iO-’T

Magnetic flux

Wb (Weber)

-

Mx (Maxwell)

1 Mx = lo-* Wb

m2

@

=v*s Magnetic polarization Permeability

T

J

(absolute)

P

= 10-5 G

see induction -

T.m

G -

A

Permeability of vacuum (magnetic constant) ,uo

1 yl)

4n.10-’

-

Oe

T.m

T.cm

- 0 , 4 ~ . 1 0 - ~ -A A

1

-

I) y is a special unit used in geomagnetism, there is a necessity to distinguish between yH and ye (related to H and B )

The most important basic equations are: B =/J~,.(H+M)=P~.H+J

B M = - - H = -

J

PO

PO

P

=

p,, . p r

p , = relative permeability

6

1 Introduction

and they are based on the four basic units of meter, kilogram, second and amptre (see also [ISl). Although the previously used electromagnetic system of dimensions (CGS electromagnetic units - emu), also known as the Gauss system, is officially no longer acceptable it is still sometimes found in the literature and so a conversion table for the CGS units has been included (Table 1-2) [16- 181. Specialized terms pertaining to particular materials are explained in the individual chapters.

1.4

Natural and Technical Magnetic Fields and Their Order of Magnitude

Both our natural environment and our technical surroundings provide magnetic fields of many different types and orders of magnitude. Many magnetic sensors detect such fields either directly or indirectly using diverse principles, hence it is important to take a closer look at the types and magnitudes of the various fields.

1.4.1

Natural Magnetic Fields

The firth’s Magnetic Field The most ubiquitous natural field of all is the magnetic field of the Earth which surrounds us perpetually. It is a dipole field, whose field lines originate at the magnetic poles in the interior of the earth, escaping through the surface and reaching into outer space (Figure 1-1). The Earth’s magnetic field is used everyday by people with compasses to determine direction or at altitudes of several hundred kilometers to stabilize satellites [19], and on the Earth’s sur-

Figure 1-1. Magnetic field of the Earth.

1.4 Natural and Technical Magnetic Fields and Their Order of Magnitude

7

face it can be employed as a constant reference field within certain ranges and times. The precise determination of the parameters of the Earth’s magnetic field, namely its magnitude and direction was one of the great pioneer acts in the field of magnetism and goes back to the works of Gauss and Oersted [20]. Table 1-3 gives examples of data on the Earth’s magnetic field for several towns in the Federal Republic of Germany. As a rough guide we may consider the magnitude of the field or flux density at the poles of the Earth to be approx. 0.5 A/cm (0.06 mT) and at the equator to be roughly 0.25 A/cm (0.03 mT).

Magnetic Fields in Outer Space With the aid of satellites and sensitive magnetic-field sensors, magnetic fields in the vicinity of planets and in outer space can also be determined directly (see Table 1-4 and [21, 221). Table 1-3. Components of the Earth’s magnetic field (values from German Hydrographical Institute, Hamburg, 1986). Town Berlin Dusseldorf Frankfurt Hamburg Munich

H= A/cm

H, A/cm

0.1480 0.1536 0.1580 0.1441 0.1662

0.3590 0.3964 0.3466 0.3375 0.3404

8

go

+ 0.42

61.6 68.8 65.6 66.9 63.9

-2.20 - 1.42 - 1.03 -0.18

H = = Horizontal component, H , = Vertical component, 8 = Declination, r9 = Inclination. Positive declination 8 means a deviation to the east referred to the geographic direction north T = 0.1256mT = 1.256 * lo5 nT in air, respectively in a vacuum. 1 A/cm corresponds to 1.256 .

Table 1-4. Magnetic field strengths of celestial bodies and objects in outer space. Celestial bodies Galaxies Mercury (poles) Jupiter (poles) Mars Saturn (equator) Sun (surface) Earth (poles) A-stars 1 m T a 10 Gauss

Field strength A/cm

Flux density mT

0.15 ... 0.25 * = 3 10-3 up to 6

I :

2.4 ... 16 4 8

0.2 . .. 0.3 * 0.35 . 10-3 up to 0.8 0 0.3 .., 2 0.5 .., I

I :

0.5

0.06

4

.

0 I :

...

up to 28 . lo3 A/cm

up to 3.5 T

8

1 Introduction

Biomagnetic Fields Human beings also produce small magnetic fields which are primarily caused by microcurrents in cardiac, brain, and muscle tissue. They can nowadays be measured with highly sensitive magnetic-field detectors such as flux-gate magnetometers, SQUIDS, and gradiometer coils (see Chapter 10) on the surface of the body, whereas in the past, it has only been possible to measure these currents indirectly by attaching electrodes to the skin and measuring the relevant voltage drops - a technique which forms the basis for the electrocardiogram (ECG). The magnitude of the field strengths and flux densities produced by heart and brain currents are nT and 1 nT, respectively [23, 241. approximately 50 .

-

Magnetic Noise Fields in Magnetic Components Magnetic and thermomagnetic noise fields are caused by thermal fluctuations in every magnetic component, as they are in magnetic cores. In particular, Barkhausen noise is significant in magnetic materials (see Section 1.6).

1.4.2 Technical Magnetic Fields Magnetic Fields in the Vicinity of i7-ansformers and Electric Motors Magnetic fields produced in electrotechnical devices, equipment, and plants are usually in to 1 T). In most cases these would be the field-strength range of 0.1 to lo4 A/cm (ca. AC fields emitted by overhead lines, electrified lines (train or tram lines etc.), transformers and electrically powered machinery. Transformers and machinery are mostly operated near the saturation limit of their iron cores, and as such the polarization in the core material attains a level of about 2 T. Similarly, both flux densities in the air gaps of big choke coils or in the gaps between rotors and stators of electric machinery and the stray fields in the vicinity are, as a rule, not much lower.

Fields of Permanent Magnets With the exception of electromagnets, permanent magnets and magnet systems are frequently used to produce static magnetic fields, particularly in measurement devices. In such cases, the field is mostly concentrated into a specified volume (eg, operating air gap) through appropriate design of the magnet and the magnetic circuit. The magnitude of the field strengths or flux densities attainable depends on both the remanence and the energy density of the magnetic materials as well as on the geometry of the magnetic circuit (see Section 1.5 and [25, 261).

1.5 Soft and Hard Magnetic Materials for Sensors

9

Fields of Conventional and Superconducting Coils Solenoids with a conventional design, iron cored coils (electromagnets), and superconduction (solenoid) coils can produce flux densities in the region of 1 to 100 T depending on their dimensions, their magnitude and their mode of operation [27-291. Superconducting coils in medical scanning machines (NMR systems) with a practical diameter of roughly 1 m can produce fields of 1 to 2 T, and special coils with large diameters are used for specified tasks in elementary particle physics and nuclear fusion producing flux densities anywhere from 2 to 10 T. The schematic diagram in Figure 1-2 presents the entire field strength and flux density scale for natural and technical magnetic fields which extends over 16 to 18 orders of magnitude [30].

Blomagnet ic fields

'FG 'FG I

1

I I

1 1

I

I

;

1 I

1 1

I

10-16

Hi gh-current Convent 1 ona 1 and transmission, superconductive cot 1s short power transformers, Devices chokes, I nith I I motors permanent; II I magnets I

Long distance from earth

:stance

!

I

10-14

I

I

,

10-12

,

I

I

,

,

I

10-l~

,

,

I

,

;

10-~

I

,

,

1

!

,

lo2 T

Figure 1-2. Scale of magnetic field strength and flux density.

1.5 Soft and Hard Magnetic Materials for Sensors Almost all magnetic sensors include magnetic materials in the form of active or passive components, and to a large extent, they determine the concept, construction, and ultimately the sensitivity of the sensors. In view of this, a brief survey of magnetic materials and their most important characteristic is presented in Tables 1-5 and 1-6. These materials are classified according to the IEC system for soft and hard magnetic materials [31, 321. For textbooks on materials refer to 133-451. The magnetic materials listed in Tables 1-5 and 1-6 are closely related to the main classes of magnetic sensors shown in Table 1-7 although some special materials have been added.

10

1 Introduction

Table 1-5. Soft magnetic materials [31]. Group

Code

G

Irons Low carbon mild steel Silicon steel, mainly with 3% Si Other steels Nickel-iron alloys (5 groups E l .. . E5 with 30% Ni) Iron-cobalt alloys (3 groups F1 . . F3 with 23% CO) Other alloys as AlSiFe-alloys

H

Soft ferrites as NiZn and MnZn oxides and others

Amorphous metals

I

Amorphous alloys (Fe-based and Co-based alloys)

Powder composite metals

-

based on Fe and iron alloy powders

Crystalline metals

A B C D E F

Oxides

.

. . . 83% . . . 50%

~

Table 1-6. Hard magnetic materials (31, 321, see also [33, 35, 37, 44,451. Group

Code

~

Crystalline metals

R1 I) R2 R3 R6 R5 I) R7')

Amorphous metals

-

Alloys of AlNiCo-type Platinum-cobalt alloys Iron-cobalt-vanadium (Chromium) alloys Chromium-iron-cobalt alloys Rare earth cobalt alloys Rare earth iron alloys Rare earth iron alloys

Oxides

S1

Hard ferrites as Ba- and Sr-ferrites

T

Other hard magnetic materials, e. g., magnetically semihard metals

I)

also as powder composite materials

1.5.1

Soft Magnetic Materials

Shape of the Hysteresis Loop The most typical characteristic of a soft magnetic materials is its hysteresis loop. The shape of the loop can vary greatly and is determined by the type of material and its structure which can be changed by processing and annealing. This is valid for both metals and oxides. The three main types of loop are shown in Figure 1-3 [36]. As the number of magnetic materials currently available is vast, there seems little point in providing extensive tables of materials data. This information is published in standard monographs and company catalogues. Instead, we have chosen to present the ranges of variation of the most important magnetic material terms found in survey diagrams.

1.5 Soft and Hard Magnetic Materials for Sensors

11

Table 1-7. Magnetic materials for sensors (materials defined in Tables 1-5 and 1-6). magnetically hard

magnetically soft Sensor class magnetogalvanic

material

Ic, E D El, I

magnetoelastic

C, El

useful for

material

useful for

I slotted cores yokes I R1, R5, R7 1 magnetic circuits shafts, surface layers for shafts, laminated core packages, pot-cores

fluxgate

El, H, I

strips and rods, toroidal cores

inductive, eddy-current

C, E2, E3

rods, yokes, laminated cores pot cores, rods

parts magnets as rods for switching

Wiegand, pulse-wire alloys magnetoresistive

resistors NiCo, NiFeCo

R

Z

premagnetizing layers

R2, R5, CoCr

F

Figure 1-3. Shapes of hysteresis loop.

Saturation Polarization J, and Coercivity H, Two of the most important material terms are saturation polarization J , , which gives an idea of the amount of material required for a certain component and coercivity H , , which provides the basis for classification of the magnetic material with regard to its hard and soft

12

1 Introduction

magnetic qualities. Figure 1-4 shows a plot of saturation polarization J, versus the coercivity H, where J, is plotted on a linear scale and H, on a logarithmic scale, since the materials currently available range from extremely soft alloys, such as permalloys, to commercial iron and steel, covering approximately four to five orders of magnitude.

soft magnetic alloys carbon steels alloys

\

0.001

0.1

0.01

10 A/cm 100

1

Coercivity

/f,

Figure 14. Survey on soft magnetic materials.

Initial Permeability pi Another important property of soft magnetic materials is the (relative) initial permeability pi, which in a similar manner to coercivity covers several orders of magnitude and is shown in Figure 1-5. The diagram is subdivided in order to correlate with the material groups shown in Table 1-5. metals amorphous crystalline

ui oxides,

ponder composite materials

ferr 1tes I06

co based

-

I o5 E2

E3

Febased

-c

E4

c

c

1 o4

1o3

A, C. F B,O[

1o2

10

3

-

NiZn ferrltes

NiFe powder and Fe ponder hexagonal cores ferrltes

-

Figure 1-5. Range of initial permeability of soft magnetic materials (materials defined in

Table 1-5).

13

1.5 Soft and Hard Magnetic Materials for Sensors

The highest initial permeability, with a value of more than 100000, is seen in crystalline 72 to 83% NiFe alloys and in cobalt-based amorphous alloys. Mid-range permeabilities in the region of 2000 to 15000 occur in NiFe alloys with 36 to 50% Ni and also in ferrites. Low initial permeability values of 300 to 1500 are typical for iron, silicon-iron, cobalt-iron, and some ferrites. Even lower values, in the region of 50 to 300 occur with powder composite materials and ferrites and very low permeabilites (down to values of 5 to 10) are typical for some special powder composite materials and special ferrites.

Specific Electrical Resistivity p, Curie temperature T, The difference between the specific electrical resistivity of metals and that of ferrites is several orders of magnitude as a result of which, for AC-field applications metals require laminated cores whereas ferrites and powder composites can be used directly as compact cores and parts. Figure 1-6 shows the range of the specific electrical resistivity p for metals, ferrites and powder composites. The Curie point is another important parameter for a magnetic material. At the Curie temperature the saturation polarization decreases to zero and ferromagnetic materials become paramagnetic. Figure 1-7 shows the range of Curie temperatures T, of soft magnetic materials. P

metals

-

R cm 10’0

106

TC

ferrites

1

1000 OC!

.:.:$:

.... :::.

102

....

:.... .: ... .... .... .... .... ,.. ...

1o-2

Figure 1-6. Specific electrical resistivity p of soft magnetic materials.

1.5.2

10-6

a

Figure 1-7. Curie points of soft magnetic materials.

O t

Hard Magnetic Materials

In a similar manner to Figure 1-4 for soft magnetic materials Figure 1-8 shows a separate survey of permanent magnetic materials. Since in this case, however, the coercivity H,, and the remanence B, are the most important terms, both of these values have been included in

1 Introduction

14

1.5

1.5 FeNiCo

NdFeB

FeCoCr

T

I'

Qc

1.0

1 .o

E

/

FeCoVCr

I

Y

a

0

.-

0

Y

a

f

c

AlNlCo

0.5

L

PtCO

1

I

1

10

3

100

3

Coercivity

HCI

-

3

0.5

I

1000 A/m

0

Figure 1-8. Survey diagram of permanent magnetic materials.

NdFeB V = 0,32 cm3

Sm Co5 V = 0,86 cmS

Al Ni Co 500

H

5mm

Figure 1-9. Magnets which produce a field of 0.1 T at a distance of 5 mm from the face.

15

1.5 Soft and Hard Magnetic Materials for Sensors

the diagram. The maximum energy density ( B H),,,= depends on B, and H, and also on the shape of the demagnetization curve. The schematic representation in Figure 1-9 illustrates the significance of the energy density with respect to the volume V of a magnet by showing the volume of various magnetic materials that is required to achieve a flux density of 0.1 T, at a distance of 5 mm from the face of the magnet. The differences in magnet volume required are quite marked.

1.5.3

Mechanical Properties of Magnetic Materials

In certain sensor types, the mechanical properties of materials are also important, for example, in magnetoelastic sensors the hardness, yield strength, compressive strength, Young’s modulus etc. must all be considered. Several of the mechanical properties of soft and hard magnetic materials have been compiled in Table 1-8.

’Pable 1-8 Mechanical Properties of magnetic materials I). _____

~

Vickers hardness HV

Material Group

80 800

Yield strength N/mm

... 200 ., , 1000

150 1500

Magnetically soft

100

... 230

ca. 150

compressive strength N/mm2 soft ferrites powder composite metals

malleable alloys like FeCoCr, FeCoV Magnetically hard

800

75 60

-

450

... 950

1

... loo

... 250

150

ca. 50

Yield strength N/mm2 1000

... 1500

245

... 255

compressive strength N/mm2 metals, cast AlNiComagnets RE magnets (SmCo, NdFeB) hard ferrites

I)

... 500 . . . 2000

Young’s modulus kN/mm

in the magnetically optimized state

110 ... 150 150

16

I Introduction

1.5.4 Supplementary Remarks Section 1.5 provides a short review of essential background information on magnetic materials. Each chapter of this volume deals with a particular class of magnetic sensors discussing the specific materials and material properties which are practically important to the mode of operation of each group of sensors, e. g., thin-film materials and semiconductor materials.

1.6 Magnetic Noise The sensitivity limits of measurement and detection are determined by the noise effect of the electronic components. Noise in electronic components and devices is a reflection of fundamental statistical fluctuations and results from a number of different physical effects. These limitations are equally encumbered on magnetic sensors, and for this reason the phenomenon of magnetic noise, i.e., noise in magnetic materials, is considered here.

1.6.1 Thermal and Thermomagnetic Noise Resistance noise is the best known form of this and was first calculated by Nyquist [46]. He discovered that every effective resistance must be considered as a source of noise regardless of the degree of complexity of the circuitry involved. The most practical method for the investigation of noise in a magnetic material is to use an equivalent circuit diagram in which a coil is considered to be a pure inductance and a resistance [47]. Thermomagnetic noise is actually created by directional fluctuations in the magnetization which result from thermal effects that cause the magnetic moments to perform a type of Brownian molecular movement, i. e., small torsional movements around their position of equilibrium. This gives rise to local fluctuating fields which cause wall movements and jumps. These processes give rise to losses in the material due to eddy currents, after-effects etc. Nee1 has shown theoretically that such fields are the result of thermal fluctuations [48]. Macroscopically, the external magnetization or polarization of a magnetic sample is basically constant, and it can also be zero. However, this is not valid on a microscopic scale. There are constant minute temporal fluctuations of the overall magnetization or polarization which produce stray fields on the surface of the sample. Although the sample is not externally magnetized, these fields will create a noise voltage in a winding around the sample, and the noise voltage itself, in turn, generates a noise current. Figure 1-10 shows the equivalent circuit diagram of a noise voltage source feeding resistance R (a) and a coil with pure inductance L and resistance R (b). The noise voltage source can I”, since it consists of statistical fluctuations about the arithmetical be described by (2) mean value zero. Similarly, the noise current is described by (2)”’.

1.6 Magnetic Noise

17

Figure 1-10. Resistance and coil with a noise voltage source U, and noise current I,.

According to Nyquist [46] the spectral distribution of the noise voltage of a resistance R (Figure 1-10a) is given by:

where k ,

=

Boltzmann’s constant = 1.38

.

W . s/K, T = absolute temperature, and

w = 2 x f , circular frequency.

In the frequency interval dw the noise current in Figure 1-10a is given by: ti; d o iidw = R2 *

For a coil (Figure 1-lob) with an impedance Z,

Z 2 = R 2 + w 2 *L 2 .

(1-7)

Thus, it follows that the noise current in dw is

The noise now must not only be considered for the frequency interval d o , but also for the entire frequency range of 0 + 03; it is therefore necessary to integrate. From Equation (1-8) we obtain for the noise current in [O,w]: w

This integral has the solution (see also [49]):

.

2 k,*T wL R (arc tan x), R . R R L

= -

~

(1-10)

18

I Introduction After inserting the boundary values ultimately, we obtain: (1-11)

Now L (at low excitation) can be replaced by (1-12) where A , = iron core cross section, lFe= magnetic path length, N = number of windings, and pi = initial permeability. Introducing the noise field strength Hn

(1-13)

-

we obtain, after elimination of N and L and introduction of the core volume VFe = lFe A , for a constant temperature of the specimen: (1-14)

The same result can also be obtained from an energy calulation, where the magnetic field energy Em in the volume VFe equals the thermal energy Ethper degree of freedom [50]:

Eth =

I 2

- * k, T .

(1-16)

From Equations (1-15) and (1-16) it is possible to obtain Equation (1-14) directly. A summary interpretation of these results is that the higher the permeability of the core, the smaller the fluctuating stray fields arising on the surface of the specimen because the magnetic flux is almost entirely contained in the interior of the material. With larger specimens, it is worth noting that the volume of the specimen close to the surface where the fluctuating stray fields arise is a smaller portion of the whole volume of the specimen. For a core made of Permalloy with pi = 50000, VFe = 1 cm3, and T = 295 K (room temperature), the numerical value for Equation (1-14) is:

H,,=

* 295 A2 1.38 * 1.256 lo-* . 50 lo3 1 cm2

-

=

2.55

- 10-gA/cm.

1.6 Magnetic Noise

Near the surface of the specimen (in air) this corresponds to a noise induction of B,,

19 =

po * H,, = 0.32 fl.

The noise field strength H,, within the core material itself is equivalent to an induction of B = ,uo. pi H,, = 16 nT. If the specimen is cooled to the temperature of liquid helium (4 K), then H,, is reduced to 0.29 10 -9 A/cm, i. e., reduced by one order of magnitude. In this example, this corresponds to the minimum thermomagnetic noise field strength which cannot be further reduced. An alternative method for reducing H,, is to increase the permeability of the specimen or to enlarge the volume. If a thermomagnetic specimen is not kept at a constant temperature but rather subjected to temperature variations, then additional noise effects known as “excess noise” will occur in addition to the normal thermomagnetic noise which will be present [SO]. Mechanical vibrations of the material are a similar source of excess noise. In both cases additional noise is caused by inherent mechanical stress in the material which becomes noticeable with temperature variations and vibrations and in turn give rise to Bloch wall jumps.

-

1.6.2 Barkhausen Noise After the discovery of Barkhausen noise in the year 1917 it became clear that the existence of Weiss domains and spontaneous change of magnetization were the factors responsible for magnetic noise. Since these domains have a finite magnitude, change of magnetization of a ferromagnetic material is an unstable process on a microscopic level, thus a magnetization curve is not ideally smooth but rather shows steps. Figure 1-11 shows the hysteresis loop of an AlFe alloy as an example from [51].

Figure 1-11. Hysteresis loop of a 12% AlFe alloy.

As soon as the magnetization of a ferromagnetic material is no longer characterized by reversible (elastic) wall displacements, which only occurs with very low field strengths, but is in the form of step-like irreversible wall displacements, then Barkhausen noise becomes clearly noticeable. It is most pronounced in the region of coercivity, i. e., in the steep parts of the magnetization curve, and it depends strongly on the nature of the material. It is, however,

20

I Introduction

nearly independent of the velocity of remagnetization as long as quasi static conditions are fulfilled. This behavior can be described by a model where the Bloch walls are located in energy minima which are a result of the structure of the material, and as such they act as pinning centers. An externally applied magnetic field will lift the Bloch wall over the nearest energy barrier where it falls into another (higher potential) energy minimum. This process causes a spontaneous step-like Bloch wall movement which contributes to the Barkhausen noise. In the quantitative treatment of Barkhausen noise its energy spectrum is considered a function of the frequency. Figure 1-12 is an example of the energy spectrum (energy density) for a narrow strip approximately 300 mm . 2 mm 0.1 mm of 3% SiFe, for an extremely slow cycle of the hysteresis loop (roughly 2 hours) after [50]. There is a relatively constant energy density in the range of 0.1 Hz to 10 Hz, then this drops proportionally to f - 1 . 6 .

Figure 1-12. Energy spectrum of Barkhausen noise for 3% SiFe [501.

(q)”2

From Figure 1-12 a noise voltage of V,,= = 80 pV is obtained for the frequency 10 Hz with a band width of 1 Hz and for a coil with 3860 turns, i.e., 20 nV per turn, with a core volume V,, = 0.06 cm3. It should be noted that the purely resistive noise voltage according to Equation (1-5) for a resistor of 100 SZ at 295 K and with a band width of 1 Hz is approximately 1.3 nV. Barkhausen noise is a very complex phenomenon on which extensive literature is available. It is strongly dependent on the material itself, the state of the material, and the shape of the specimen. The reader should refer to review articles, papers and books for further details [50-551.

1.7 Coil Systems to Produce Standard Magnetic Fields Standard magnetic fields - whether homogeneous or gradient fields - are frequently required to allow comparable measurements to be made and to enable calibration of magnetic sensors. Such fields are produced most effectively with pure air-cored coils, since in this case the inhomogeneities caused by nonlinearity in the magnetic curves of iron cores do not arise. Depending on the configuration and the dimensions of the coils, in some limited areas relatively high homogeneity in the range of 10 - 2 to 10 - 4 can be achieved.

1.7 Coil Systems to Produce Standard Magnetic Fields

21

Larger air-cored coils, with diameters of some meters, are used to compensate for the Earth's field in situations where a space free of a magnetic field is required but shielding cannot be used for some reason. Examples of some of the better-known coil systems are described below. Initially, simple air-cored coils will be discussed, and also coil systems for field strengths with magnitudes up to 100 A/cm which can be produced without any special provisions such as water cooling etc. will be considered. Also more recent data is provided on coils for high fields including the superconducting coils.

1.7.1

Coils for Homogeneous DC Fields up to Approximately 100 A/cm

The best-known coil arrangement for homogeneous fields is the Helmholtz coil. It ideally consists of two circular rings with radius r, which are arranged concentrically and parallel to each other with a separation distance r (Figure 1-13a). As a rule, flat multi-layer coils are used (Figure 1-13b) and the magnetic fields of Helmholtz coils are described in detail in the literature [56].

Figure 1-W. Helmholtz coil schematically.

The following equations are derived from the ideal arrangement as shown in Figure 1-13a, for the field components H, and H, at the point P with the coordinates x, z, at a distance r' from the center of the coil:

H,

=

Hz0 * - - -

(1-18)

22

I Introduction

At the center of the axis:

H,,

= 0.715

*

I r

-,

(1-19)

where I is the current in the coil. The situation is slightly more complex for the arrangement shown in Figure 1-13b (multilayer winding with cross section a x b) where in order to avoid impairing the high degree of homogeneity certain relationships with respect to a and b must be maintained [57]. In multi-coil arrangements such as the one shown in Figure 1-14 where the radius decreases towards the outside, the region of high homogeneity can be made larger than that achievable by Helmholtz coils [58].

Figure 1-14. Multi-coil arrangement.

Relatively homogeneous fields can also be created in the coil center of longer cylindrical coils. The following mathematical formulas are applied along the axis for evenly wound cylindrical coils such as that shown in Figure 1-15 [56]: (1-20) Thus, for the coil center (x = 112): (1-21) and for the coil ends (x = 0 and x = 1, respectively) (1-22)

23

1.7 Coil Systems to Produce Standard Magnetic Fields

-

+.-

-

---

-.+L

H-

I

I

Figure 1-15. Cylindrical coil.

The smaller the ratio r/l, the more homogeneous is the field. It follows that for r/l 5 1/80 the field is constant within +0.1%0 over 2/3 of the length of the coil. Fields up to approximately 0.5 T can also be produced with cylindrical coils in which the winding density increases towards the ends (Figure 1-16), once again, when compared to the fields generated with Helmholtz coils, this kind of coil produces both higher field strengths and improved homogeneity [60].

I

Figure 1-16. Production of homogeneous fields in a cylindrical coil where the winding density increases towards the ends; (a) linear, (b) quadratically increasing winding density.

I

.. U

Refer to references [61] and [62] for more information on circular coils with very high homogeneous magnetic fields. Finally, in addition to the simple cylindrical coil it is worth mentioning an arrangement which involves two additional moveable coils (Figure 1-17). For further details and more information on the mathematical formulas involved see [58, 591.

Figure 1-17. Production of homogeneous coil fields in a cylindrical coil with adjustable additional coils at each end.

1.7.2 Coils for Higher Fields (Electromagnets) Magnetic fields of up to about 3 T are produced in the air gap of electromagnets since, in this case, the magnetic field strength is concentrated primarily along the relatively short length of the air gap, whilst the iron return circuit of the magnet system only requires a small part

24

I Introduction

of the field strength. By mounting pole shoes made of CoFe alloys and using computer-aided calculations to select the shape of the pole shoe, it is possible to generate relatively high homogeneous fields whilst still only creating low stray fields. Before the advent of superconducting coils, it was necessary to use specially constructed Bitter coils in order to generate stationary fields with flux densities of up to 15 T [61-641. Under pulse operation, these are capable of producing flux densities of the order of 50 to 100 T over brief periods (milliseconds) [65].

1.7.3 Superconducting Coils Magnetic fields in the range of 10 to 20 T can only be continuously produced using superconducting coils which actually, in principle, are air-cored coils. Currently the only suitable conducting materials for such coils are the hard Q p e 111 superconductors which are capable of carrying the high critical field strengths that are required. The most commonly used materials are NbTi alloys (up to 10 T) and Nb,Sn alloys (up to approximately 20 T). These materials must be cooled to approximately 4 K to be effective [61, 621. Currently, new superconducting materials of metallic oxides capable of achieving superconductivity above 90 K are under investigation. The superconducting wires are either embedded in a metallic matrix, i. e., of Cu or surrounded with Cu to ensure that in the event of failure the high currents can still be carried even if only for a brief time. In order to improve the dynamic behavior of the coils, using a special twisted cable conductor construction the conductors are made up into filaments [66, 671. Figure 1-18 shows a schematic design for a superconducting coil [68].

Superconduct ing coi 1 Liauid Helium

Figure 1-18. Superconducting magnetic coil in a cryostat (for NMR spectrometer, outside diameter ca. 1 m).

1.8 Shielding Magnetic Fields 1.8.1 General In order to ensure that accurate measurement and calibration can be achieved it is often necessary to exclude magnetic interference fields or at least to eliminate them as far as possible. This can be achieved in several different ways:

1.8 Shielding Magnetic Fields

25

- by maintaining sufficient distance between the source of interference and the object of interest,

- by ensuring suitable orientation of critical objects with respect to the direction of the interference field, e. g., orientation perpendicular to the Earth’s field,

- by using different types of compensation, i.e. coil systems or permanent magnet arrangements, - by using gradiometer coils as sensing coils, - by use of magnetic and electromagnetic shielding.

The methods given above are all limited in some way or cannot be always fully realized. For instance, it is easier to compensate a constant static magnetic field than to compensate fluctuating AC fields of different field strengths, frequencies and directions. Similarly, compensation of spatially homogeneous fields is much easier in small volumes than in large volumes, and for multi-sensor configurations. The most effective method is electromagnetic shielding, where either the object or the source of interference is shielded. The basic principles and possible applications of shielding are described below [69-721.

1.8.2

Basic Principles of Magnetic Shielding

1.8.2.1 DC Fields

The use of soft magnetic materials for shielding of static magnetic fields is based on the fact that these materials possess an extremely high magnetic permeability: their magnetic permeability is in fact higher by a factor of between lo3 and lo5 than that for either air or a vacuum. Shielding made of soft magnetic materials provides very effective shunts for the magnetic interference field which will preferentially concentrate in the walls of the shielding leaving the interior space effectively free of magnetic field (Figure 1-19).

Figure 1-D. Shielding static magnetic fields.

26

I Introduction The shielding factor Sin a static field is defined as the ratio of the external interference field

Heto the residual field Hiin the interior of the shielding. That is: (1-23) The shielding attenuation a, is often used instead of S:

.

a, = 20 log S

(1-24)

,

These shielding factors can be fairly accurately calculated for simple geometric shapes (closed housing) [69-71, 731. Several examples illustrating the use of high permeability material and small wall thicknesses are stated below:

- Hollow sphere: 4 Pr*d s = -3

0

+,

p r : relative permeability of shielding material, usually denoted as pi or p4

d : wall thickness

(1-25)

D: diameter

- Cube:

a : edge length of cube (1-26)

- long cylinder

N : demagnetization factor dependent on

perpendicular to axis:

s,

Pr*d =-

+

1

(1-27)

D

parallel to axis: =

L/D

L : length of cylinder

- 1) + 1 + D/2 . L

4N(S 1

(1-28)

- Double cylinder

S,, Sz shielding factors S, of cylinder 1 and

S = S, * Sz * [1 - (D2/D1)2] +

+s, +s,+

1

2 according to Equation (1-27)and D, > D, (1-29)

The above formulas apply to entirely closed shieldings or infinitely long cylinders. The shielding factors of short cylinders and housings with openings are smaller and, moreover, the calculations are more complex [73-751.

1.8.2.2 AC Fields When AC fields are being shielded, field displacement in the shielding wall plays a major role due to the eddy currents which are induced in the material as a result - the so-called skin effect. The penetration depth 6 is significant and is calculated as follows [69-731:

1.8 Shielding Magnetic Fields

p = specific electrical resistivity ,uo= magnetic constant

f

(1-30)

= frequency.

For a 75% nickel iron alloy with p = 0.55 serted in Hz as

6=

27

a mm2/m 6 is obtained in mm when f is in-

f-. 139400 Pi

*f

Example: when pi = 50000 and f = 50 Hz follows 6 = 0.24 mm. For a closed magnetic shield, e. g. a sphere or a long cylinder the shielding factor s, in an AC field is given by [69, 701: (1-31)

With open shielding, the formulas are again more complex [74+751, but for shielding with small homogeneously distributed openings, e. g., braided shielding, cable wrapping etc., the equation is: (1-32)

In this case the permeability pr from Equation (1-26) is replaced by the modulus of the complex permeability lp 1. The important difference between Equations (1-31) and (1-32) is the fact that in the closed shielding case the shielding factor increases exponentially with the frequency, whereas in shielding with openings it decreases at a rate of l / f l [69, 711. Thus, it can be concluded that static magnetic fields can only be shielded with soft magnetic materials. These materials are also extremely effective at shielding in AC fields, especially in the lower frequency range. Shielding with soft magnetic materials is limited to fields or flux densities up to 0.5 T due to the onset of saturation effects above this value. Pure conducting shielding (copper and aluminium) can be used for higher frequencies, and indeed, in many cases a combination of magnetic and conducting shielding is recommended.

1.8.3 Materials for Magnetic Shieldings and Design The materials most commonly used for magnetic shielding are crystalline nickel-iron alloys, followed closely by silicon-iron and iron. The full shielding effect is only obtained from these materials in their final annealed state after which the shielding must not be mechanically deformed. The group of suitable materials has recently been extended by the advent of the amorphous alloys, in particular the low magnetostriction Co-rich alloys which can be exposed to mechanical stress without impairing their shielding effect. A survey of suitable materials is given in Table 1-9.

28

I Introduction

Table 1-9. Materials for magnetic shielding [73]. Group

Alloy

crystalline

77% 50% 36% 3% Iron

amorphous

NiFe NiFe NiFe SiFe

Co-based

Code

BUi

J. (TI

El E3 A

30000 to 50000 6000 3000 1000 300

0.8 1.55 1.3 2.0 2.1

I

25 000

0.55

E4 c2

To complete the picture it should be pointed out that superconductors can also be used to shield against magnetic fields. Superconductors can force magnetic fields out of the interior of the material (Meissner-Ochsenfeld effect), and it, therefore, follows that the interior of a superconducting hollow sphere is absolutely free of magnetic field. Superconductors are suitable for use in high field strengths, such as flux densities up to 10 T. Magnetic shieldings are available in many diverse designs, e. g. as round or square shaped cans, cylindrical and conical housings as well as in flexible metal hose and foil forms. A further variant is the use of multi-layer shielding. Table 1-10 gives several examples of the shielding factors of simple housings.

Table 1-10. Shielding factors of different housings [73];(material 77% NiFe with pi = 30000; 6 = 0.30 mm at 50 Hz;6 = 0.11 mm at 400 Hz). Design

Diameter D Wall thickness d

Sphere

D = 100mm d = d =

Double cylinder

400

1000

> 105

300

900

> 105

lmm

D,= 150 mm D, = 100 mm d =

400 Hz

lmm

D = 100mm

Single cylinder

Shielding factor 50 Hz

static

= 34000

lmm

A design which arouses particular interest in biomedical and industrial circles is the socalled “walk-in” magnetically shielded room which has interior measurements of approx. 2.5 m 2.5m 2.5 m. Depending on the required degree of suppression or shielding factor, either single or multi-layer shields can be used [76-791.The latter are used in diagnostics to facilitate interference free measurement of the magnetic fields produced by the human body using SQUIDS which are a highly sensitive family of magnetic field sensors (see Chapter 10). As an example Figure 1-20 shows the measured shielding factors as a function of frequency for five different designs of shielded room.

-

-

29

1.9 References

120

106

dB lo5

100

104

8o

S

t

as

lo3

60

100

40

10

20

1

0

0.01

1

0.1

10

1000

100

No.

Number of shields (Shells) Total Magnetic Conducting shields shields

1 2 3 4 5

2 2 3 6 7

2 1 2 3 6

1 1 2 x 3 1

Hz

References [781 1731 [731 [791 [771

Figure 1-20. Shielding factor S and shielding attenuation a, of different shielded rooms; interior measurements approx. 2.5 m x 2.5 m x 2.5 m.

1.9 References [l] Meyer, H.W., A History of Electricity and Magnetism; CambridgdMass.: The MIT Press, 1971. [2] Enz, U.; “From loadstone to ferrite: A survey of the history of magnetism!’ In: Wohlfarth, E. P. (ed.), Ferromagnetic Materials, Vol. 3; Amsterdam, New York, Oxford: North Holland Publishing Co., 1982, pp. 3-36. [3] Krafft, F., (Ed.), GroJe Nuturwissenschaftler. 2nd Edition; Dttsseldorf: VDI Verlag, 1986. [4] Schubert, J., Dictionary of Effects and Phenomena in Physics; Weinheim: VCH Verlagsgesellschaft, 1987.

30

1 Introduction

[5] Rohrbach, C. Handbuch fur elektrisches Messen mechanischer GriJen; Dtisseldorf VDI-Verlag, 1967. [6] Profos, P. (Ed.), Handbuch der industriellen MeJtechnik. 4th Edition; Essen: Vulkan-Verlag, 1987. [7] Bently, J. P., Principles of Measurement Systems; London, New York: Longman, 1983. [8] Heywang, W., Sensorik (Halbleiter-Elektronik 17); Berlin, Heidelberg, New York, Tokyo: Springer Verlag, 1981. [9] Seippel, R. G., Transducers, Sensors and Detectors; Reston/Virginia: Reston Publishing Co. Inc., 1983. [lo] Schanz, G. W., Sensoren - Fuhler der MeJtechnik: Heidelberg: Huthig-Verlag, 1986. [ll] Hederer, A. et al., Dynamisches Messen (Kontakt + Studium, Band 32); Grafenau: Lexika-Verlag, 1979. [12] Bonfig, K. W., Bartz, W. J., Wolff, J. (Ed.), Das Handbuch fur Zngenieure. Sensoren, MeJauJ nehmer. 2nd Edition; Ehningen: expert verlag, 1988. [13] Usher, M. J., Sensors and Transducers; London: Macmillan Publishers Ltd. 1985. [14] Fiz-technik, In,formationsdienst Sensoren; Berlin: ZDENDE-Verlag, 1988. [15] Recommendations in the Field of Quantities and Units Used in Electricity; IEC Publication 164, 1964. [16] German, S., “Das internationale Einheitensystem”. In: Kohlrausch, F., Praktische Physik, Vol. 1, 23rd Edition; Stuttgart: B.G. Teubner, 1985, pp. 6-13. [17] Chen, C. W.: “Magnetism and Metallurgy of Soft Magnetic Materials”. In: Wohlfarth, E. P.: Selected topics in Solid State Physics, Vol. V, Appendix I; Amsterdam: North-Holland Publishing Co., 1977. [l8] “Units for magnetic quantities”, Magnets in your Future 1/6 (1986) 15. [19] Mager, A., “Diimpfungsstilbe fur magnetfeldstabilisierte Satelliten”, Z. Flugwiss. 15 (1967) 91 -98. [20] Fanselau, G. (Ed.), Geomagnetische Instrumente und MeJmethoden; Berlin: VEB Deutscher Verlag der Wissenschaften, 1960. [21] Parker, E. N., Kosmische Magnetfeder, Spektrum der Wissenschaft 10 (1983) 82-94. [22] Acuna, M. H., “Fluxgate magnetometers for outer planets exploration”, ZEEE Trans. Magn. MAG10 (1974) 519-523. [23] Ern& S. N., Hahlbohm, H. D., Lllbbig, H. (Ed.), Biomagnetism; Berlin, New York: de Gruyter, 1981. [24] Williamson, S. J., Kaufman, L., “Biomagnetism”, J Magn. Magn. Mat. 22 (1981) 129-201. [25] Schuler, K., Dauermagnete. Werkstoffe und Anwendungen; Heidelberg: Springer, 1970. [26] McCaig, M., Permanent Magnets in Theory and Practice; Plymouth: Pentech Press, 1977. [27] Parkinson, D. H., Mulhall, B. E., The Generation of High Magnetic Fields; London: Plenum Press, 1967. [28] Zijlstra, H.: Experimental Methods in Magnetism. Part 1: Generation and computation of magnetic fields; Amsterdam: North-Holland Publishing Co., 1967. [29] Montgomery, D. B., Solenoid Magnet Design, New York: Wiley-Interscience, 1969. [30] Boll, R., “Magnetische Schirmung, eine wichtige MaBnahme zum Schutz gegen StBrungen und Umweltbelastung durch elektromagnetische Felded’ In: Jahrbuch fur Ingenieure; Grafenau: expert verlag, 1981, pp. 436-447. [31] “Magnetic materials”. Part 1: “Classification”, ZEC Publication 404-1(1979). [32] “Magnetic materials”. Part 8: “Specifications for individual materials!’ Section 1: “Standard specifications for magnetically hard materials”, ZEC Publication 404-8-1(1986). [33] Bozorth, R. M., Ferromagnetism; Toronto, New York, Londong: Van Nostrand Co. Inc., 1955. [34] Heck, C., Magnetic Materials and their Applications; New York: Crane, Russack & Co. Inc., 1974. [35] Kneller, E., Ferromagnetismus. Berlin, Gdttingen, Heidelberg: Springer Verlag, 1962. [36] Boll, R. (Ed.), Soft Magnetic Materials; Berlin, Miinchen: Siemens A G London: Heyden, 1979. [37] Wohlfarth, E. P. (Ed.), Ferromagnetic Materials. A Handbook on the Properties of Magnetically Ordered Substances. Vol. 2; Amsterdam: North-Holland Publishing Co., 1980.

1.9 References

31

[38] VDEh (Ed.), Werkstoffkunde Stahl. Vol. 2: Anwendung; Berlin, Heidelberg: Springer Verlag, 1985, Sec. D 20. [391 Chen, H. S., “Glassy metals”, Rep. Prog. Phys. 43 (1980) 353-432. 1401 Luborsky, F. E. (Ed.), Amorphous Metallic Alloys; London: Butterworth, 1983. [411 Smit, J., Wijn, H. P. J., “Ferrites”, Philips Tech. Rev. (1962). 1421 Snelling, E. C., Soft Ferrites; London: Iliffe Books Ltd. 1962. [43] Kampczyk, W., Rdss, E., Ferritkerne. Berlin, MUnchen: Siemens AG, 1978. [44] Schlller, K., Brinkmann, K., Dauermagnete. Werkstoffe und Anwendungen; Heidelberg: Springer Verlag, 1970. [45] Tebble, R. S., Craig, D. J., Magnetic Materials; London, New York, Sydney, Toronto: Wiley-Interscience, 1969. [46] Nyquist, H., Thermal agitation of electric charge in conductors, Phys. Rev. 32 (1928) 110-113. [47] Nonnenmacher, W., Schweizer, W., “Die Bestimmung der Permeabilittit ferromagnetischer Stoffe aus der thermischen Rauschspannung von Spulen”, Z. Angew. Phys. M (1957) 239-243. [48] Ntel, L., Theorie du trainage magnktique des substances massives dans la domaine de Rayleigh, J. Phys. Radium ll/8 (1950) 49-61. [49] Kleen, W., Pdschl, K., “Rauschen”, in: Meinke, M., Gundlach, F. W. (Eds.), Taschenbuch der Hochfrequenztechnik, 3. Aufl.; Berlin: Springer Verlag, 1968, pp. 1242- 1244. [50] Bittel, H., Storm, L., Rauschen; Berlin, Heidelberg, New York: Springer Verlag 1971. [51] Lambeck, M., Barkhausen-Effekt und Nachwirkung in Ferromagnetika; Berlin: de Gruyter, 1971. [52] Hdhler, G. (Ed.), Der magnetische Barkhausen-Effekt (Springer Tracts in Modern Physics, Vol. 40); Berlin: Springer Verlag, 1966. [53] McClure, J. C., Schrdder, K., “The magnetic Barkhauseneffect”, CRC Crit. Rev. Solid State Mater. Sci. Jan. 1976, 45-83. [54] Heiden, C., Storm, L., GrundsBtzliches zur Bestimmung der GrbRenverteilung der Barkhausenvolumina in Ferromagnetika. Z. Angew. Phys. 21 (1966) 349-354. [55] Bertotti, G., Fiorillo, F., Sassi, M. P., Barkhausen noise and domain structure dynamics in SiFe at different points of the magnetization curves, J. Magn. Magn. Mater. 23 (1981) 136-148. [56] Braun, E., “Erzeugung und Messung magnetischer Felder”, in: Kohlrausch, F., Praktische Physik, Vol. 2, 23rd Edition, Stuttgart: B. G. Teubner, 1985, pp. 399-401. [57] Berger, W., Butterweck, H. J., “Die Berechnung von Spulen zur Erzeugung homogener Magnetfelder und konstanter Feldgradienten”, Arch. Elektrotechnik XLII (1956) 216-222. [58] Neumann, H., “Herstellung raumlich und zeitlich konstanter Magnetfelder fur MeRzwecke”, Part 11, ATM Z 60-2 (1940). [59] Fanselau, G., “Die Erzeugung weitgehend homogener Magnetfelder durch Kreisstrdme”, Z. Phys. 54 (1929) 260-269. [60] Heddle, T. A., “A method of designing compensated solenoids giving approximately uniform field”, BZ Appl. PhyS. 3 (1952) 95-97. [61] Parkinson, D. H., Mulhall, B. E., The Generation of High Magnetic Fields; London: Plenum Press, 1967. [62] Zijlstra, H., Experimental Methods in Magnetism, Part 1: Generation and Computation of Magnetic Fields; Amsterdam: North-Holland Publ. Co., 1967. [63] Montgomery, D. B., Solenoid Magnet Design; New York: Wiley-Interscience, 1969. [64] Braun, E., “Elektromagnete”, in: Kohlrausch, F., Praktische Physik, Vol. 2, 23rd Edition, Stuttgart: B. G. Teubner, 1985, pp. 405-407. [65] Knoepfel, H., Pulsed High Magnetic Fields; Amsterdam, London: North-Holland Publ. Co., 1970. [66] Hillmann, H., “High Field Superconductors”. Lecture Notes in Physics 177, in: Landwehr, G. (Ed.); Berlin, Heidelberg: Springer Verlag, 1983, pp. 517-530. [67] Krauth, H., “Multifilamentary NbTi and Nb,Sn superconductors for pulse magnets and electrical machines”, Cigre symposium 05-87, Vienne 1987, Sec. 1, 100-08, 2-6.

32

1 Introduction

[68] VACUUMSCHMELZE GMBH, “High field superconductors”, IB SLOl; Hanau, 1986. [69] Kaden, H., Wirbelstr6me und Schirmung in der Nachrichtentechnik, 2nd Edition; Berlin, Heidelberg: Springer Verlag; Miinchen: J. F, Bergmann, 1959. [70] Mager, A., “Magnetic shields”, IEEE Trans. Magn. MAG4 (1970) 67-70. [71] Boll, R., Borek, L., “Elektromagnetische Schirmung”, NTG-Fachber. 76 (1980) 187-204. [72] Mager, A., Magnetostatische Abschirmfaktoren von Zylindern mit rechteckigen Querschnittsformen, Physica SOB (1975) 451-463. [73] VACUUMSCHMELZE GMBH, Magnetic Shielding, FS-M9; Hanau, 1989. [74] Kaden, H., “Die Ausbreitung elektrischer und magnetischer Wechselfelder in offenen Abschirmrohren”, Frequenz 24 (1970) 27-32. [75] Mager, A., “Magnetic shielding efficiencies of cylindrical shells with axis parallel to the field”, J. Appl. Phys. 39 (1968) 1914. [76] Mager, A.: “The Berlin magnetically shielded room (BMSR) Section A. Design and construction”, in: Erne, S. N., Hahlbohm, H. D., Liibbig, H. (Eds.), Biomagnetism; Berlin, New York: de Gruyter, 1981, pp. 51-78. [77] Cohen, D. et al., “Magnetocardiogram taken inside a shielded room with a superconducting pointcontact magnetometer”, Appl. Phys. Lett. 16/7 (1970) 278-280. [78] Cohen, D., “Large volume conventional magnetic shields”, Rev. Phys. Appl. 5, (1970) 53-58. [79] KelhB, V. A., “Construction and performance of the Otaniemi magnetically shielded room”, in: Erne, S. N., Hahlbohm, H. D., Liibbig, H. (Eds.), Biomagnetism; Berlin, New York: de Gruyter, 1981, pp. 33-50.

2

Physical Principles KENNETH J. OVERSHOTT. Brighton Polytechnic, Brighton. UK

Contents 2.1 2.2 2.3 2.4 2.5 2.6 2.1

........................... Galvanomagnetic Effects . . . . . . . . . . . . . . . . . . . . . . Magnetostriction and Magnetoelastic Effects . . . . . . . . . . . . Electromagnetic Systems . . . . . . . . . . . . . . . . . . . . . . Movement of Domain Boundaries . . . . . . . . . . . . . . . . . Josephson Effect . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction

34

35 36 38

39 42 42

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

34

2 Physical Principles

2.1 Introduction The basic principle of all sensors is transduction - that is, the transmission of energy from one system to another. In general, an electric signal is produced by the change of a physical property induced by the applied change of a second parameter (see Figure 2-1). In the case of magnetic sensors either the property or the parameter would have a magnetic context. For example, in a magnetoresistive device the induced change of a physical property, resistance, caused by the applied change of a magnetic field is used to produce an electrical signal (see Figure 2-2). The linearity, magnitude, sensitivity, repeatability, etc, of the relationship between the electrical output, E, and the physical property defines the quality of the sensor

E

=

f(R, H ) .

Ease of measurement and processing makes an electrical signal the preferred output. APPLIED second parameter

1

1-

kb

INPUT

OUTPUT

physical property

in general: electrical signal

Figure 2-1. Schematic diagram of sensor.

field

R

resistance

Figure 2-2. Schematic representation of a magnetoresistive sensor.

The physical effects useful for magnetic sensors have been developed over 120 years with the Joule effect being discovered in 1842, the latest discovery being the Josephson effect in 1962. Over these 120 years many other physical effects suitable for magnetic sensors have been investigated, as shown in Figure 2-3. These physical effects can be classified into four categories, although the position of magnetostrictive effects in c. below and not b. is debatable: a. electromagnetic systems ; b. effects of magnetic fields on material properties, eg, Hall, galvanic, resistance ; c. interrelationship of stress and magnetic properties, eg, magnetostriction and magnetoelastic ; d. superconductivity, eg, Josephson effect.

2.2 Galvanomagnetic Effects

Figure 2-3. Physical effects useful for magnetic sensors and year of discovery.

35

W 1865

It would be logical to describe the physical effects used in magnetic sensors under these four categories. However, the description of the physical principles used in magnetic sensors will be presented in the same order as the later chapters to facilitate cross-referencing. In addition, the description of these physical effects presented here is brief in order not to duplicate the information included in later chapters.

2.2 Galvanomagnetic Effects One group of magnetic sensors is based upon the galvanomagnetic effects that occur in semiconductors. These galvanomagnetic effects are caused by the interrelationship that occurs between the electrical currents flowing in a material which is being subjected to a magnetic field. The two most important galvanomagnetic effects are the magnetoresistive (or Thomson) effect [l] and the Hall effect [2]. The effects can only be exploited in semiconductor materials in which a high carrier mobility and a low free carrier concentration is achieveable. However, sensors based upon the magnetoresistive effect in thin ferromagnetic films are also of commercial importance. Under the influence of a magnetic field, an increase in the resistivity of a material occurs and this phenomenon is called the magnetoresistive effect. The exploitation of this effect in sensors has only been worthwhile since the development of III/V semiconductors. A free charge carrier in a semiconductor is deflected by the Lorentz force which acts perpendicular to the direction of the motion and the magnetic flux density. The charge carrier even-

36

2 Physical Principles

tually collides with the crystal lattice and the rotation of the current direction occurs which results in an increase in the length of the path of the current flow. This increase in the path length produces an increase in the resistivity of the material, magnetoresistance, which is the physical basis of a family of magnetic sensors. If a very long strip of strongly extrinsic and homogeneous semiconductor material carries a current, I,, in the x direction and when the strip plane is in the xy plane then an applied field in the z direction, manifested as a flux density, B,, produces a transverse electric field in the y direction, the Hall field (see Figure 2-4).

Figure 2-4. Schematic diagram of Hall effect.

The Hall voltage, U,, is approximately proportional to the product of the flux density perpendicular to the strip plane, B,, and the current I,.

The theoretical basis of the Hall effect - that is, the effect of the Lorentz force on the charge-carrier transport phenomenon occuring in condensed matter - is well described in Chapter 3.

2.3 Magnetostriction and Magnetoelastic Effects In 1842 Joule observed that when a magnetic rod was subjected to a longitudinal magnetic field then the length of the rod changed. This longitudinal magnetostrictive (change of dimensions due to effect of the magnetic field) phenomenon is called the Joule effect [3]. If there is an increase in length in the longitudinal direction then a decrease in dimensions takes place in the transverse direction and, in general, a change in the volume of the material occurs. Four years after the initial discovery of magnetostriction it was found the Young’s modulus, E, of a material is changed by the application of the magnetic field to a material. Young’s modulus is the ratio of stress to applied strain and hence this A E effect is a ramification of the property that a change of stress in a material occurs when it is magnetized and is dependent on the magnetostrictive properties of a ferromagnetic material.

2.4 Magnetostriction and Magnetoelastic Effects

37

The magnetostrictive change in dimensions is caused by rotation of the magnetization or displacement of 90" walls. When a mechanical stress is applied to a demagnetized ferromagnetic, two kinds of strain are produced : (i) mechanical elastic strain, I , , which occurs in any material, and (ii) magnetoelastic strain, A,, due to the reorientation of domains by the applied stress, n. The Young's modulus for this demagnetized state is given by

For a saturated sample the magnetoelastic strain is zero because no domain reorientation can occur. therefore

Hence it follows:

The magnetoelastic strain, I , , depends on the applied stress and the magnitude of the anisotropy present. The latter half of the nineteenth century saw the discovery of other magnetoelectric effects which are often in contemporary literature described as obscure magnetostrictive effects. The best known of these effects are named after their discoverers - that is, the Matteucci effect, the Wiedemann effect and the Villari effect. Villari [4] found that an elastic elongation of a ferromagnetic material produces a permeability change in the direction of the applied tension. Materials which have a positive magnetostriction increase their permeability under tensile stress and conversely materials with negative magnetostriction reduce their permeability under the influence of a tensile stress. The Matteucci effect [ 5 ] and the Wiedemann effect [6] are closely related. The Matteucci effect was discovered in 1847 when Matteucci stated that the torsion of a ferromagnetic rod in a longitudinal field changes the magnetization of the rod. Wiedemann stated this effect more precisely by saying that if a ferromagnetic rod is subjected to a longitudinal magnetic field (produced by a solenoid) and a current is passed through the rod (producing a circular field) then the rod will twist (see Figure 2-5). There are obviously two inverse Wiedemann effects such that : (a) when the circularly magnetized ferromagnetic rod is twisted a longitudinal magnetic field is produced, (b) when a longitudinally magnetized ferromatic rod is twisted a circular magnetic field is produced. This latter inverse Wiedemann effect can be seen to be essentially similar to the Matteucci effect. It has been shown [7] that the Wiedemann effect is a consequence of the tensorial relationships of magnetostriction in a material. The theoretically-derived formula for the angle of a twist, 8, of a rod has been related to the longitudinal and transverse magnetostriction con-

38

2 PhysicaWrinciples solenoid producing longitudinal magnetic field 00000000000000000000000000000000

n

current producing circular magnetic field OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO~

twist

Figure 2-5. The Wiedemann effect.

stants, I , and I , , of the materials and the magnitude of the longitudinal and circular magnetic fields, H, and Hci,. I 9= - 2( A , I r

- A,)

4 Hcir H : + Hf,, '

where 1 is length of rod and r is radius of rod. This theoretical derivation has been experimentally verified [8] and further work on the effect has recently been performed [9].

2.4 Electromagnetic Systems The most simple type of magnetic sensor is based upon electromagnetic principles. Faraday's Law states that a voltage is induced in a closed electric circuit when the rate of flux linkage, N@,is changed with time:

U = - d 0") dt

The most important aspect of Faraday's Law of electromagnetic induction is that it is the rate of flux linkage in a sensing coil which produces the induced voltage. Hence, the flux linkage can be changed with respect to time by changing the flux linking with a stationary coil or by changing the flux linking with a coil by moving the coil. The former method of changing the flux linking with a stationary coil can be achieved in two principal ways: (a) the generation of a flux which changes periodically with time (b) the magnetic flux varying within a magnetic circuit due to variation of an air gap or changes in the direction of magnetization. The most common use of system (a) above is the generation of a sinusoidal flux by exciting a primary coil with a sinusoidal current and using a search (secondary) coil to measure the flux density in a specific area. The electromagnetic induction equation can be then used to calculate the peak flux density, B, in Tesla, for the specific area of search coil, A in m2, when the flux is changing at a frequency off in Hz . The rms voltage U (in Volt) induced in a search coil of N turns is given by

U

= 4.44

-

B, A N * f .

2.5 Movement of Domain Boundaries

39

One has to make sure carefully that the impedance of the search coil does not load the measuring system. However, the search coil, being the most simple magnetic sensor, has many advantages and, in fact, whole careers in magnetism have been founded upon its extensive use [lo]. An alternative method of changing the flux linkage in the coil is to change the magnetic domain structure in the region of the magnetic material close to the search coil and is described in Section 2.5. Variable reluctance sensors also use a change of the configuration of the magnetic flux in a magnetic circuit to induce voltage in a coil. A permanent magnet is used in variable reluctance sensors to produce a magnetic flux in a magnetic circuit. A change in the length of an air gap in the circuit or some other method of producing a change in the reluctance of the magnetic circuit causes a change in the magnetic flux in the circuit. This change of flux generates a voltage in a search coil by electromagnetic induction. The second family of electromagnetic sensors is based upon moving a coil so that the flux linkage of the winding changes with time. This necessary change of flux linkage can be made to occur by

- moving the coil in a controlled method or by taking the coil into and completely out of a DC field - varying the electromagnetic coupling between coils - changing the inductance of coils by the relative motion of coils or by moving a soft

magnetic core within the coils. A secondary method of utilizing electromagnetics in a sensor is the use of eddy currents. If the conducting material is subjected to an alternating magnetic field then emf’s are induced in the material which cause eddy currents to circulate in the material because of resistive property of the material. These eddy currents produce a secondary magnetic field in the material. The interaction of this secondary magnetic field with the original alternating magnetic field can be used as the basic principle of magnetic sensors. These devices, which can also be based upon the detection of the eddy currents, are generically called eddy current sensors, see Chapter 7, Section 7.5.

2.5 Movement of Domain Boundaries In 1931 Sixtus and Tonks [ll] performed a classic experiment which showed that hard-drawn nickel-iron wires, having between 10% and 20% nickel, positive magnetostriction and relatively low magnetic anisotropy, when magnetized and under tension would form a single domain with the saturation magnetization along the axis of the wire. Reversal of the magnetization field produced no effect on the single domain until a critical value H,, was exceeded. For greater fields it was possible to start a reversal of the domain magnetization at one end of the wire by means of a local magnetizing coil. Figure 2-6a shows the experimental scheme, D is the starting coil while coils C and F were used to determine the velocity with which the domain boundary passed along the wire, and also to give some information about the shape of the advancing domain boundary.

40

2 Physical Principles

wire in tension

H

-

main coil

V

a

IB

b

C

Sixtus-Tonks experiment.

Figure 2-6b shows an hysteresis loop for the unstressed multi-domain condition and a loop when the wire is stressed. The high rate of change of flux density with field, dB/dH, corresponds to the reversal of magnetization produced by the movement of the domain wall from one end of the wire to the other. The travelling wall was deduced to have a trumpet shape, as shown in Figure 2-6c [12]. The discontinuous magnetization reversal of a small magnetic specimen, which in the ideal case comprises a single magnetic domain, can be used for sensing purposes if the resulting induced voltage pulse in a coil associated with the reversal is utilized. This magnetic switching effect is due to large reproducible Barkhausen jumps in ferromagnetic wires under tensile stress. The most common practical use of the Sixtus-Tonks phenomenon was proposed by Wiegand [13] who twisted wires made of Vicalloy (Co 52, V 10, Fe 38). These Wiegand wires, which have a soft magnetic inner core and a harder magnetic outer zone, supply high reproducible pulse-voltages. In the initial status, it is ensured that the inner core and outer zone are magnetized to saturation in mutually opposite directions (Figure 2-7a). The hard magnetic outer zone keeps the magnetization of the inner core under a magnetic strain. If an

41

2.5 Movement of Domain Boundaries

additional field is generated - for example, using a permanent magnet - in the direction of the magnetization of the outer zone, then after a particular threshold value has been exceeded (threshold field strength > coercive field strength H , ) a domain wall propagation is triggered in the inner core which induces a voltage of several volts if a 1000 turn coil is used. At the end of this procedure, the inner core and outer zone are magnetized in the same direction (Figure 2-7b). For the next reversal procedure the wire is reset to its original status (Figure 2-7a) by a magnetic field of the correct magnitude. In the ideal case the amplitude and shape of the voltage pulse are only dependent on the velocity of the moving domain wall propagation (Sixtus-Tonks wave), but not on the rate of change, dH/dt, of the driving field. For an induced voltage, generally the relation holds

where A B is the flux density change of a large Barkhausen jump, v is the velocity of the domain wall propagation and n is the number of domain walls. Figure 2-7c explain the magnetization reversal mechanism using the hysteresis loop and shows a typical voltage pulse. The use of these physical principles of domain wall propagation is used in Wiegand sensors and pulse-wire sensors as described in Chapter 8.

I

I

a

b

B

/-

I

large I Barkhausen

I

t IAB

*

C

Figure 2-7. The Wiegand effect.

H

42

2.6

2 Physical Principles

Josephson Effect

A whole new family of magnetic sensors has been developed over the last 25 years. These sensors are called SQUIDs (Superconducting Quantum Interference Devices) and are based upon a superconducting phenomenon named the Josephson Effect. SQUIDs are the most sensitive magnetic sensors and have achieved a magnetic field resolution in the order of several femto-Tesla (fT). The operation of these sensors is based upon the properties of the superconducting state - namely, flux quantization and the Josephson effect. The superconducting state which occurs in materials at low temperature (approaching 0 K) - although superconduction at higher temperatures (circa 100 K) has been reported - is categorized by perfect conduction of current without power loss, the expulsion of magnetic flux (Meissner effect) and the quantization of flux with the occurence of an energy gap, etc. In 1962, Josephson [14] published a theoretical prediction that it should be possible for electron-pairs to tunnel between closely spaced superconductors even with no potential difference. An experimental demonstration of the effect was made in 1964 [15]. The theoretical basis and application of the Josephson effect in sensors, SQUIDs, are described in Chapter 10.

2.7 References [l] Thomson, W., “On the effects of magnetization on the electric conductivity of metals”, Philos. Trans. R. SOC.London A 146 (1856) 736-751. [2] Hall, E. H., “On a new action of the magnet on electric current”, Am. J. Math. 2 (1879) 287-292. [3] Joule, J. P., “On a new class of magnetic forces”, Ann. Electr. Mugn. Chem. 8 (1842) 219-224. [4] Villari, E., “Change of magnetization by tension and by electric current”, Ann. Phys. Chem. 126 (1865) 87-122. [5] Matteucci, C. H. ,“Memoire sur le magnetisme developpi par la courrant electrique”. Comptes Rendus 24 (1847) 301-302. [6] Wiedemann, G . , Lehre von der Elektrizitut 3 (1883) 680-684. [7] Yamamoto, M., Sci. Rep. Tohoku Univ. /AJ 10 (1958) 219-239. [8] Smith, I. R. and Overshott, K. J., “The Wiedemann effect, a theoretical and experimental comparison”, Brit. J, Appl. Phys. 16 (1965), No. 12, 47-50. [9] Ruzek V. J., “Untersuchung des Wiedemann’schen Effektes zur Kraft- und Drehmomentmessung”, Feinwerktechnik & Messtechnik 92 (1984) 415-416. [lo] Overshott, K. J., Private communication (1989). [ll] Sixtus, K. J., and Tonks, L., “Propagation of large Barkhausen discontinuities”, . Phys. Rev. 37 (1931) 930-958. [12] Brailsford, F., “Physical Principles of Magnetism”, New York: Van Nostrand 1966, pp. 183f. [13] Wiegand, J. R . , “Switchable Magnetic Device”, U S. Patent No 4247601, 1981. [14] Josephson, B. D., “Possible new effects in superconductive tunnelling”, Phys. Lett. 1 (1962) 251 -253. [15] Anderson, P. W., and Rowell, J. M., “Probable observation of the Josephson superconducting tunnelling effect”, Phys. Rev. Lett. 10 (1963) 230-232.

3

Magnetogalvanic Sensors RADNOJEPOPOVIC. Landis & Gyr. Zug. CH WOLFGANG HEIDENREICH. Siemens AG. Regensburg. FRG

Contens 3.1 3.2 3.2.1 3.2.2 3.2.3 3.3 3.3.1 3.3.2 3.3.3 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.5 3.5.1 3.5.2 3.5.3 3.6 3.6.1 3.6.2 3.6.3 3.6.4 3.7 3.8

. . . . . . . . . . . . . . . . . . . . . . . . . . . Galvanomagnetic Effects . . . . . . . . . . . . . . . . . . . . . . The Hall Effect . . . . . . . . . . . . . . . . . . . . . . . . . . The Hall Coefficient . . . . . . . . . . . . . . . . . . . . . . . Magnetoresistance . . . . . . . . . . . . . . . . . . . . . . . . . Hall Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structures and Technology . . . . . . . . . . . . . . . . . . . . . Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetoresistors . . . . . . . . . . . . . . . . . . . . . . . . . Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetoresistor Technology . . . . . . . . . . . . . . . . . . . . Properties of Magnetoresistors . . . . . . . . . . . . . . . . . . . Differential Magnetoresistors . . . . . . . . . . . . . . . . . . . . Other Semiconductor Devices as Magnetic Sensors . . . . . . . . . . Magnetodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetotransistors . . . . . . . . . . . . . . . . . . . . . . . . Carrier-Domain Magnetic Sensors . . . . . . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic Measurement . . . . . . . . . . . . . . . . . . . . . . Noncontact Position Sensing . . . . . . . . . . . . . . . . . . . . Selected Examples . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction

44 45 46 48 51 52 54 56 57 61 61 64 67 68 71 72 73 74 75 75 76 81 87 91

92

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

44

3 Magnetogalvanic Sensors

3.1 Introduction

This chapter is devoted to magnetic field sensors whose operating principle is based on the galvanomagnetic effects that occur in semiconductors. Galvanomagnetic effects are the physical phenomena that arise in matter which is carrying an electrical (galvanic) current whilst at the same time being exposed to a magnetic field. The best known fundamental galvanomagnetic effects are the Hall effect and the magnetoresistive effect. These effects are most conveniently exploited in materials that possess a high carrier mobility and a relatively low free carrier concentration, and since these two criteria are best met in a number of semiconductors, only the semiconductor galvanomagnetic sensors are of practical importance. The only exception are the sensors based on the magnetoresistive effect in thin ferromagnetic films (see Chapter 9). Hall discovered the effect which was subsequently named after him in 1879 [l]. The magnetoresistive effect, however, was discovered even earlier in 1856 by Thomson [2], but was little known until the advent of Hall’s discovery. For a long time, both effects were used in solid-state physics as powerful tools for studying carrier transport phenomena [3, 41, and it was only the developments occurring in semiconductor technology that enabled the additional use of the galvanomagnetic effects for sensor applications. In 1948, Pearson proposed a germanium Hall device as a magnetic sensor [5], and it was then only a few years after the discovery of the high-mobility compound semiconductors [6], that Hall devices and magnetoresistive sensors became readily available commercially. A detailed account of the early work done on the galvanomagnetic semiconductor sensors can be found in references [7-91. The current microelectronic revolution still strongly influences and stimulates further development of new galvanomagnetic sensors, because, generally, sensors that show as high a performance-to-price ratio as the microelectronic circuits themselves are highly desirable [lo]. This also applies, of course to magnetic-field sensors and similarly determines trends in their development. An obvious way to achieve the goal then, is to make use of an available mainstream technology. Accordingly, most new developments in the field of galvanomagnetic sensors take advantage of the availability of high-quality materials and the well-established sophisticated fabrication methods that are used in integrated circuit production. Such a trend has been further motivated by the possibility of being able to integrate a magnetic-field sensor and some signal-processing circuitry on the same chip. These integrated sensors, with “on chip”-signal processing, are called smart sensors [ll]. It is interesting to note, however, that only the semiconductor magnetic-field sensors have the potential to be fully compatible with contemporary integrated circuits [12], and thus they are the natural choice for the realization of smart magnetic sensors. The first directly integrated galvanomagnetic sensor, an MOS-Hall element, was proposed by Gallagher and Corak in 1966 [13]. In 1968, Bosch proposed the incorporation of a Hall device into a standard silicon bipolar integrated circuit [14], and this idea formed the basis of a number of commercially successful products [15, 161. By 1980, over 150 million smart Hall sensors had been manufactured and put to use as position or current sensors [15]; the new results on such integral semiconductor galvanomagnetic sensors will form one of the main topics of this chapter.

’

3.2 Galvanomagnetic Effects

45

Another way in which microelectronics has influenced the development of galvanomagnetic sensors is through the full employment of the abundance of physical effects available in semiconductor devices. The basic galvanomagnetic effects may be combined in any number of ways with the well-known phenomena inherent to semiconductor devices, such as carrier drift, diffusion, injection, recombination, etc., thus producing new, combined galvanomagnetic effects. In 1949, for example, Suhl and Shockley studied the carrier transport phenomena in point-contact transistors exposed to an external magnetic field [17] and discovered a combined galvanomagnetic effect, which is now called the magnetoconcentration effect or Suhl effect. Many interesting magnetic sensors have been proposed over the last 30 years which exploit such combined galvanomagnetic effects in somewhat modified conventional semiconductor devices such as transistors, diodes, and thyristors. They are now referred to as magnetotransistors, MagFETs, magnetodiodes, and carrier-domain magnetometers for more information refer to the review papers [12] and [MI. A part of this chapter also deals with these promising devices.

3.2 Galvanomagnetic Effects In this section, we have summarized the most important theoretical ideas and experimental results concerning the two basic galvanomagnetic effects, the Hall effect and the magnetoresistive effect, concentrating on the issues which are the most important for magnetic-field sensors. More detailed treatments of the subject can be found in many textbooks, for example references [19-211, monographs [3, 41, and review papers [22-251. Isothermal conditions have been assumed for this theoretical consideration and only the basic effects have been dealt with here. The combined effects will be discussed in Section 3.6, along with the corresponding devices. Generally, galvanomagnetic effects are manifestations of the charge-carrier transport phenomena occurring in condensed matter, when the carriers are subject to the action of the Lorentz force F :

F = eE

+ e[u x

B]

.

(3-1)

Here e denotes the carrier charge (for electrons e = -4, and for holes e = q, where q = 1.6 10-l9C and represents the magnitude of the electron charge), E denotes the electrical field, u the carrier velocity and B the magnetic induction. For nondegenerate semiconductors exposed to transverse electrical and magnetic fields, ie, (E * B) = 0, the carrier transport equation for one type of carrier reads (after [19]):

where j denotes the total current density. The term j , = aE

- eDVn

(3-3)

46

3 Magnetogalvanic Sensors

is the current density due only to the electric field and the carrier-concentration gradient V n ; ie, j , does not depend explicitly on the magnetic field. However, j , # j ( B = 0), since a magnetic field generally influences the electric potential and carrier-concentration distributions. Equations (3-2) and (3-3) take into account both carrier drift and diffusion phenomena (the terms proportional to E and V n , respectively), and also the transverse transport caused by the magnetic field (the term proportional to B ) . The transport coefficients pH (the Hall mobility), 0 (the conductivity), and D (the diffusion coefficient) are determined by the carrier scattering processes and generally depend on electric and magnetic fields. Both the galvanomagnetic effects we are interested in can be derived from the solutions of Equation (3-2) subject to the appropriate boundary conditions. The Hall mobility is given by

where r is the Hall scattering factor and p is the drift mobility. The Hall mobility has the sign of the corresponding carriers, ie, pHp > 0 and p H n < 0, p and n denoting holes and electrons, respectively. The Hall scattering factor, a number close to unity, is defined by

where tion.

( 7 )denotes

the average value of the carriers relaxation time over their energy distribu-

3.2.1 The Hall Effect Let us now consider a special case of carrier transport in a very long strip of a strongly extrinsic and homogeneous (Vn = 0) semiconductor material (Figure 3-1). For simplicity we assume that the strip axis is along the x-axis, the strip plane is in the xz-plane, and that B = (0, By, 0). If we expose the strip to an external electric field E,,, = (Ex, 0, 0) a current Z will flow through it with current densityj = ( j x ,0, 0). Since j , = 0, an internal transverse electric field EH must build up in order to counteract the “magnetic” part of the Lorentz force (the second term in Equation (3-1)). The field EH is called the Hall field and can be determined from Equation (3-2), by substituting E = E,,, + EH , under the condition that the transverse current density vanishes, ie:

Figure 3-1. The Hall effect in a long sample. If a strip of conducting material, placed in the xz-plane along the x-axis, is exposed to an electric field Ex and magnetic induction B y , a transverse electric field E, appears.

3.2 Galvanomagnetic Effects

47

A macroscopic and tangible consequence of the existence of the Hall field is the appearance of a measurable transverse voltage, namely the Hall voltage:

where w denotes the strip width. The generation of the transverse Hall electric field and the consequent Hall voltage under conditions similar to those in Figure 3-1 is usually collectively referred to as the Hall effect. Another way to characterize the Hall effect is by the angle of inclination of the total electric field in the sample with respect to the external field. This angle 0, is called the Hall angle and is given by Ez = - p , ~ . tan@, = EX

(3-9)

In weak magnetic fields, the Hall voltage is proportional to the Hall angle (Equations (3-8) and (3-9)). The intensity of the Hall effect in a material is best characterized by the Hall coefficient. By definition, the Hall coefficient R H is given by: EH RH = - [ j x B ]

(3-10) *

However, in our case:

[J

X

Bl = (O,O,j , B )

(3-11)

so that now: (3-12) Sincej = aE, we can obtain within the limit of B = 0: RH - pH c 7

=-

en

(3-13)

using Equation (3-4) and the relation a = q p n . It is thus possible to express the Hall voltage (3-8) as UH = R , j x B w

where the negative sign has been omitted.

(3-14)

48

3 Magnetogalvanic Sensors

Consider now another form of the galvanomagnetic effect, arising in an unlimited sample. For the sake of ease, an arrangement such as that shown in Figure 3-1 has been used, but with w 03, see Figure 3-2a). If an electric field E = (Ex, 0, 0) is applied, the current density (Equation (3-2)) becomes +

j x = aEx

(3-15)

j, = p H B a E x .

(3-16)

Since there are no boundaries, the current is not solely confined to the field direction. Consequently, the total current density vector rotates with respect to the applied electric field. The angle of rotation is the Hall angle, given by tan@, = p H B .

(3-17)

Exept for the opposite sign, this is the same as in the conventional Hall effect (Equation (3-9)). In infinite samples the Hall effect is sometimes referred to as the carrier deflection effect. The essential condition for its appearance is obviously the nonexistence of the Hall field. This condition also can be realized approximately in a short sample, using highly conductive contact electrodes on the larger faces (see Figure 3-2 b), which provide a partial short-circuiting of the Hall voltage.

= b)

Figure 3-2. The Hall effect in an unlimited sample - the carrierdeflection effect. a) If a plate of conducting material, placed in the xz-plane, is exposed to an external electric field Ex and magnetic induction By, the current density vector j covers with Ex the Hall angle 0,.b) The same effect can be obtained in a short sample with highly conducting contacts at the large faces.

3.2.2 The Hall Coefficient The Hall coefficient is the proportionality factor relating the Hall field or the Hall voltage to the current-magnetic field product in a Hall-effect experiment (Equations 3-10 and 3-14).

3.2 Galvanomagnetic Effects

49

The value and stability of the Hall coefficient directly determines the magnitude and the stability of the sensitivity of the sensors based on the Hall effect. For a material with both types of carriers, ie, electrons and holes, the Hall coefficient is given by RH =

1 r p p - b2r,n 4 (p + b n ) 2

(3-18) (3-19)

Here rp and r, denote the Hall scattering factors, ,upand p, are the mobilities, and p and

n are the concentration of holes and electrons, respectively. The coexistence of both types of carriers reduces the Hall voltage: the carriers tend to accumulate at the same side of the plate and partially compensate each other’s fields. This situation arises in two cases, namely, in intrinsic semiconductor materials and under high-injection conditions. In the intrinsic semiconductors, p = n = n, , where n,is the intrinsic carrier density, given by: -

ni = A T 2 e

-~E8

(3-20)

2kgT

and where A is a coefficient, dependent on the carriers’ effective masses and the energy bands’ structures, A = (0.2/4) . 10’’ m - 3 K -3’2, T is the absolute temperature, Eg is the band-gap energy and k, is the Boltzmann constant. The high-mobility semiconductors, such as InSb and InAs, tend to have small band gaps and are nearly intrinsic at room temperature. The Hall coefficient (Equation (3-18)) thus becomes: 1 I rp - b 2 r , RHi = -q n, (I + b ) 2

(3-21)

and is highly temperature dependent. High-injection conditions arise in a sample if a strong nonthermal carrier-generation mechanism supplies the nonequilibrium carriers to the sample. Such mechanisms may, for example, be the internal photoeffect or carrier injection via a p-n junction. In an extreme case, p = n, Equation (3-21) applies again, with n + n,; the carrier concentration, however, is now Z [26], then defined predominantly by the generation rate. For example, n

-

RHinj

C

-

zinj

rP-b2rn (1+b)2

(3-22)

where Zinj denotes the injection current and C is a coefficient, which depends on the recombination process. Should the higher mobility carriers strongly prevail, eg, if

50

3 Magnetogalvanic Sensors

then Equation (3-18) reduces to

R,, = --rn

(3-24)

9n

which is the same as Equation (3-13). The condition (3-23) is best fulfilled in strongly extrinsic semiconductors, when n&p, n =Nd

(3-25)

where Nd is the donor density. Both of these equations are valid only within the saturation temperature range [26]. The values of the Hall scattering factors rp and rn in Equations (3-18) and (3-24) are always close to unity. However, their exact values depend on many parameters, such as temperature, magnetic field and mechanical stress, and so they are important determinants of the performance of the galvanomagnetic sensors. In the simple case of semiconductors with spherical constant-energy surfaces in weak magnetic fields (defined by p 2 B 2 4 1) the Hall scattering factor is given by the ratio of the appropriate relaxation-time averages (Equation (3-5)). For acoustic phonon scattering, this expression gives r = 1.18, and for ionized impurity scattering r = 1.93. In strong magnetic fields, defined by p 2 B 2 %- 1, or in degenerate semiconductors and metals, r = 1. Generally, in weak magnetic fields, the Hall scattering factor may be represented by [27] r

= ro(l - a p c B 2 )

(3-26)

where r, = r ( B = 0) and a is a parameter, a complicated function of the scattering process. For lightly doped silicon, r,, = 1.15 and rop = 0.7, for electrons and holes, respectively, at 300 K [28, 291. Within the temperature range 200 K to 400 K, r,, varies approximately linearly with temperature, the temperature coefficient being (l/ron) (8ro,/i3 T ) = 10 - 3 K - I . The nonlinearity coefficient a for n-type silicon is a, t: 0.3 to 1 [27], the lower values being found in more highly doped samples (Nd = 10l6 cm-3) and at lower temperatures ( T = 250 K). A value of a = 1 was found in low-doped samples (Nd = 1.7 . 1014 ~ m - at ~ higher ) temperatures ( T = 400 K), a result corroborating the theoretical predictions for the case involving the phonon scattering process. For n-type GaAs with electron concentrations in the range from lOI5 to lo1' cm-3, it was found that r,, = 1.1 to 1.2 at T = 300 K and l(l/ron) (aro,/aT)I < 0.5 also a, = 0.1 for n < 1015 cm-3 at 300 K (extracted from [30]). Semiconductors such as silicon, with many-valley band structures and anisotropic energy minima, generally exhibit piezo effects in the carrier-transport phenomena. A change in the Hall coefficient occurring as a function of the mechanical stress X i s referred to as the piezoHall effect. For lowdoped n-type silicon, the coefficients relating to piezoresistance and the piezo-Hall effect are of almost equal size and sign and depend strongly on the crystal orientation [31]. For example, A R , , / ( R H , X ) = 0.45 . bar-' for a device in the (100) plane, bar-] for a current along the ( 1 1 1 ) directions in the (110) and A R , , / ( R , , X ) < 0.1 . plane.

3.2 Galvanomagnetic Effects

51

3.2.3 Magnetoresistance Under the influence of a magnetic field, an increase in material resistivity is generally observed and this phenomenon is called the magnetoresistive effect. In weak magnetic fields, the change in resistivity is proportional to the square of the magnetic-field component perpendicular to the current-density vector, ie. CJB

=

CJO

1

+ HB:

(3-27)

where po is the resistivity at B = 0, CJ = l/p, gois the conductivity at B = 0, and H i s the coefficient of magnetoresistance. The coefficient of magnetoresistance can be obtained by solving the general transport equation (3-2), subject to the appropriate boundary conditions. For example, for an infinite sample of the type discussed at the end of Section 3.2.1, Figure 3-2a, in small magnetic fields [19] one obtains: (3-28)

In the case of the long strip (see Figure 3-1): HL = p2(C - r2)

(3-29)

where r is the Hall scattering factor, Equation (3-5). For spherical energy surfaces and acoustic phonon scattering, C = 1.77, r = 1.18, so that H,, P h = 1.77 p 2 and HL,P h = 0.38 p 2 ; for ionized impurity scattering, C = 5.89, r = 1.93, so that H,, = 5.89 p 2 and HL,= 2.17 p 2 . The increase in resistivity of the carrier transport under the influence of a magnetic field arises because of the shorter distance which a carrier can travel between two successive collisions, along the direction of the external electric field. An obvious macroscopic consequence of this observation is that the current-density vector is rotated with respect to the electric field (Figure 3-2). Since the current lines in a short sample like the one in Figure 3-2b become longer when a magnetic field is present, the magnetoresistive effect under such conditions is sometimes referred to as the geometrical magnetoresistive effect. However, even if the pure in Figure 3-l), the geometrical effect vanishes, such as occurs in the long strip (i 1 magnetoresistive effect generally still exists, Equation (3-29). This is a consequence of the fact that the Hall field compensates for the action of the magnetic field only in average, while the carriers are spread over all energies, and they generally travel along curved lines. The magnetoresistive effect will only vanish (to a first approximation) in a long sample and in degenerate materials if the relaxation time does not depend on energy: C = r = 1, and HL = 0 (Equation (3-29). Since the Hall field diminishes the magnetoresistive effect, it is common practice to design the magnetoresistive sensor in such a way that the generation of a Hall field therein is inhibited. To this end, the most effective design is that of the Corbino disc [32] (Figure 3-3) which is a practical realization of an effectively infinite sample. Other such practical realiza-

,

,

52

3 Magnetogalvanic Sensors

0

Figure 3-3. The Corbino disk is a round plate of semiconductor material with one electrode at the center and the other round the circumference. As there are no nonconducting boundaries, the Hall field cannot build up, and the electric field E is always radial. The current density j covers everywhere with E an equal Hall angle 0,.

tions are based on the short-circuiting effect of the Hall voltage in short samples such as the one in Figure 3-2 b. The coefficients of magnetoresistance are proportional to the square of the carrier-mobility term, Equations (3-28) and (3-29). Therefore, high mobility materials are strongly preferred for magnetoresistive sensor applications. (At T = 300 K, ,u: (in m2/V2 s2) is 0.022 for Si, 0.15 for Ge, 0.72 for GaAs, 10.9 for InAs and 64 for InSb.) The intrinsic behavior of small bandgap materials at around room temperature is not of great importance to the magnetoresistive effect. Indeed, the presence of both types of charge carrier even helps to reduce the Hall field, see Equation (3-21), and simplifies realization of magnetoresistive sensors with H = H a .

3.3 Hall Sensors A Hall sensor is a magnetic-field sensor based on the Hall effect much in the form as Hall discovered it. Usually, such a sensor composes of a thin rectangular plate of a semiconductor material, fitted with four electrical contacts (Figure 3-4). A bias current I is supplied via two of the contacts (the current contacts, CC, and CC,), and the other two contacts (the sense contacts, SC, and SC,) are placed on two equipotential points at or close to the plate boundary. If a magnetic field is applied to the device, the Hall voltage, which is the sensor output signal, appears between the sense contacts. The Hall voltage is approximately proportional to the product of the component of the magnetic induction perpendicular to the plate plane B, and the bias current I.

Figure 3-4. Rectangular Hall plate. CC, and CC, are the current contacts, SC, and SC, the sense contacts, Z the bias current, U the voltage drop over the plate and U, the Hall voltage.

In the ideal case o f a very long plate, such as the strip described in Figure 3-1, with very small sense contacts, the Hall voltage is given by Equation (3-14). Since the current density j is given by j = I/tw

(3-30)

53

3.3 Hall Sensors

where t is the plate thickness and w is its width, Equation (3-14) can be rewritten as: U,, =

3 BI t

(3-31)

where the suffix L stands for long plate. In the general case of a plate with finite dimensions and a finite contact size, the Hall voltage is given by: U , = -RG,B I t

(3-32)

where G is the geometrical correction factor. By definition, the geometrical correction factor is the ratio of the Hall voltage in an idealized, point-contact device to that of an actual device: G = UH/UHL,

(3-33)

It accounts for the diminution of the Hall voltage due to the short-circuiting effect caused by the finite current and sense contacts. Obviously, the geometrical correction factor may vary between 0 (for a device with large contacts, covering its whole periphery) and 1 (for the above described very long or point-contact device). In most practical realizations of Hall sensors, the electron conductivity is strongly prevalent, ie, condition (3-23) is fulfilled. Thus it is possible to substitute for the Hall coefficient in Equation (3-32) with R , = R,, (see Equation (3-24)) and obtain:

rn G B I

IuHl

(3-34)

This Equation explains why Hall sensors are usually thin plates and are made of a low-carrier-concentration material, since the Hall voltage is inversely proportional to both the plate thickness t and the carrier concentration n. However, a thin plate with a low carrier concentration generally has a high sheet resistance. Using such a material for the sensor may cause the voltage drop across the sensor current contacts

U = RI

(3-35)

to become unacceptably high. (R denotes the resistance between the current contacts.) For example, for a rectangular plate, like in Figure 3-4,

I

1

1

R = p- = -wt q p n wt

(3-36)

where p is the resistivity of the plate material. By substituting Equations (3-35) and (3-36) into (3-34), the Hall voltage can be expressed in terms of the voltage U applied between the current contacts: (3-37)

54

3 Magnetogalvanic Sensors

Combining equations (3-34) and (3-37), it is possible to obtain the Hall voltage in terms of the power P = U s Z dissipated in the plate: (3-38) It is important to note in both of the last equations the dependence on the mobility. For a given Hall voltage, both the voltage drop and the dissipated power will be minimized if a high-mobility material is used for the Hall plate.

3.3.1

Geometry

A Hall device does not have to have a rectangular shape such as the example shown in Figure 3-4, or indeed any other regular shape. Actually, any finite plate, provided with a least three contacts, may be used as a Hall device. (The fourth contact may be replaced by a potentiometer [33].) Some examples of Hall-plate shapes are shown in Figure 3-5. Using conformal mapping theory, Wick [34] demonstrated the invariance of Hall plate electrical efficiency with respect to geometry (“. . . there are no properties . . . that cannot be obtained from a circle, square, or any other simple shape by proper size and position of the electrodes!’) That said however, some of the shapes may have some technological or application advantages over the others. For example, a vertical Hall device [35] is much easier to fabricate in IC technology if all contacts are situated on one side of the plate, as shown in Figure 3-5 h. Alternatively, achieving a high value for the geometrical factor G in small-size devices is much easier in a cross-shaped configuration (Figure 3-5 c) than in a rectangular one (Figure 3-5 a) [36]. Still another example is the application of devices which are invariant under rotation through

sc/cc

O b

GCed SC/CC

SC/CC

rnf sc cc sc cc

Fieure 3-5. Some shapes of Hall plates. CC represents the current contact, SC the sense contact, and S C K C indicates that the current and sense contacts are interchangeable.

3.3 Hall Sensors

55

90°, such as those in Figure 3-5b, c, and d, for cancelling the offset voltage [15] (see Section 3.3.3). The influence of the Hall-plate shape on its efficiency is summarized in the geometrical correction factor G (Equations (3-32) and (3-33)). The problem has been studied using conformal mapping technique and numerical simulation [34, 37-42] and for some conventional shapes of Hall plates, the following approximate analytical expressions were found: For relatively long rectangular Hall plates, with I/w > 1.5, small sense contacts, s/w CO.18, and small Hall angles 0, (Equation (3-9)) the geometrical correction factor can be approximated by [38]

2 s O H ] n w tan@,

G = [t - + enx p ( - + $ ) + ] . [ i

(3-39)

with an accuracy better than 4%. Here I, w, and s are the characteristic dimensions of the plate, as defined in Figure 3-4. The function (3-39) approaches unity if I/w > 3 and s / w < 1/20. For short rectangular Hall plates, with vanishingly small sense contacts, it was found [37] that: 1

W

+ 2.625 - 3.257

W

This expression is accurate to within 1% if the plate length-to-width ratio I/w + 0 and 0 , + 0,

(3-40)

< 0.35 and

0, < 0.45. In the limit of I/w G

I

0.742 -

(3-41)

W

By substituting this expression into Equation (3-37), the maximum value for the Hall voltage

U,, = 0.742pH,BU

(3-42)

that can be obtained in a Hall sensor biased by a given voltage U. For Hall plate shapes which are invariant under a rotation through 90°, such as a square (Figure 3-5 b), cross (Figure 3-5 c), circle, and octagon, the geometrical correction factor can be approximated by the following function [40]: (3-43) Here g(1) is a function of the ratio A of the (all) contacts length and the total length of the plate boundary. The approximation is valid for small Hall angles and small ratios A. For example, for a symmetrical octagon,

g(1) = 1.940

(

1 1

+ 0.4141)

2

(3-44) *

56

3 Magnetogalvanic Sensors

This leads to an accurate value of G (A, OH)to within 0.5% if A I0.73, ie, g (A) I0.61, and OH = 0.016. If the term @,/tan OH in Equation (3-43) is expanded into a series and only the first two terms are retained, it leaves us with [27]:

After some rearrangements, the geometrical correction factor can be described by:

G = Go(l + p , u i B 2 ) ,

(3-46)

ie, in the same form as Equation (3-40). Here Go = 1 - g (A) is the value of the geometrical correction factor at B = 0, and is a numerical coefficient dependent on the plate geometry. For devices with a weak short-circuiting effect, using Equations (3-45) and (3-46) one can obtain an expression for /3:

p z - . 1 - Go

(3-47)

3 GO

For devices with a strong short-circuiting effect such as a short rectangular plate, one finds from Equations (3-40) and (3-46) that:

p

%

0.604 - 0.732Go

.

(3-48)

In view of the equivalency of Hall plates with different shapes [34], it was concluded in [27] that expressions (3-46), (3-47) and (3-48) are generally valid. In particular, according to Equations (3-40) and (3-44), they are accurate to within 1% if Go I 0.260 or Go 2 0.39, respectively.

3.3.2 Structures and Technology The fabrication technology of Hall sensors has always been influenced by the state of the art of semiconductor technology. Early devices were made as bulk or thin-film discrete components [5, 7, 81; later, with the development of integrated-circuit technology, devices were proposed based on the silicon MOS process [13], the silicon bipolar process [14], GaAs epitaxy [43], and, recently, a superlattice structure fabricated by molecular beam epitaxy [44]. Most of the currently available commercial Hall sensors are based on the bipolar integrated circuit process [15, 161, as shown in Figure 3-6. The active region of the plate is realized as a part of the n-type epitaxial (collector) layer, its planar geometry being defined by the deep p-(isolation)-diffusion regions and the n -(emitter)-diffusion regions. The n + layers are used to provide good ohmic contacts between the low-doped n-type active region and the metal layer (the contacts). The isolation between the Hall plate and the rest of the chip is achieved using reverse-biased p-n junctions surrounding the plate, a technique commonly employed in monolithic integrated circuits. +

3.3 Hall Sensors

sc

57

cc

Figure 3-6. Rectangular Hall plate in bipolar IC technology. The notation for the contacts is the same as that used in Figure 3-4. D L denotes the depletion layer surrounding the n-type active device region.

Typical electron densities and thicknesses for the epitaxial layer are n = 10l5 to 10I6cm - 3 and t = 5 to 10 pm, respectively, yielding an nt product (see Equation (3-34)) of 5 10" cm-2 to 1013cm -2. The active n-type layer can also be created by ion implantation, which provides better control and uniformity of doping density than epitaxy. The typical implantation dosages correspond to the nt products given above. Typical planar dimensions for integrated Hall plates are about 200 pm, but devices with submicron active-region dimensions have also been demonstrated [45]. The devices described so far have had the form of a discrete plate or an integrated plate merged into the chip surface. They are sensitive therefore, to the magnetic field perpendicular to the chip plane. For applications where sensitivity to the magnetic field parallel to the device surface is preferred, a so called vertical Hall device was devised [35]. In the vertical Hall device (Figure 3-7) the general plate shape is chosen in such a way that all contacts become available on the top surface of the chip, as in Figure 3-5 h. The active device volume is part of the n-type substrate material, surrounded by a deeply defused p-type ring. The sensitivity of the device is not affected by the unusual geometry, corroborating the considerations discussed in Section 3.3.1. A version of the vertical Hall device in bipolar technology [46] has been made successfully and a three-contact device [47] has also been realized. Figure 3-7. Vertical Hall device (see also Figure 3-5 h). The bias current Z flows between the two peripheral contacts, each carrying a half of the current (1/2), and the central contact. The Hall voltage appears between the two sense contacts SC, and SC,.

3.3.3 Performances Sensitivity: In modulating transducers, such as Hall sensors, absolute and relative sensitivities can be distinguished. Absolute sensitivity of a Hall sensor is defined as:

S, = I 8UH/i3BI I

=

Const

(in V/T = Volt/Tesla)

.

(3-49)

58

3 Magnetogalvanic Sensors

-

-

However, since in a Hall-effect device U, BZ and UH BU, (see Equations (3-34) and (3-37), a more useful feature is its relative sensitivity. Supply-current-related sensitivity of a Hall sensor is defined as: (in V/AT = volt/ampere

- tesla) .

(3-50)

From Equations (3-32) and (3-34) one can obtain:

(3-51) Current-related sensitivity depends solely on the plate-surface carrier density, nt, and the geometry. Its typical values range between 80 V/AT [16] and 400 V/AT [35], but the value becomes rather high in small-contact devices, where G = 1, if the nt product is made small. However, in integrated Hall devices, the minimum value of nt is limited by the junction field-effect. The highest sensitivity reported so far is S, = 3100 U/At, corresponding to nt = 2 10" cm-' [481. Analogously, supply-voltage-related sensitivity can be defined as:

(3-52) For a rectangular device, using Equation (3-37) one obtains:

(3-53) Typical values of voltage-related sensitivities are 0.07 T for silicon [16] and 0.2 T for GaAs devices [49]. The maximum value is obtained in short Hall plates, the physical limit derived from Equations (3-42) and (3-52), being:

Sum, = 0 . 7 4 2 ~ ~ " .

(3-54)

This yields, at room temperature, 0.128 T - ' and 0.725 T - ' for low-doped n-type silicon and GaAs respectively. Noise: The noise-voltage spectral density across the Hall sensor contacts is given by [50]:

(3-55) where S,, stands for l/f noise and S,, for thermal noise. Two useful figures with respect to noise are: firstly, the equivalent input magnetic-field noise spectral density, which is defined as

(3-56)

59

3.3 Hall Sensors

where S, denotes the absolute sensitivity, Equation (3-49); and secondly, the detection limit, determined by 1

(3-57) in the frequency range between fland f2.The detection limit corresponds to a signal-to-noise ratio of SNR = 1. A low detection limit can be achieved in large devices, if they are made of a high-mobility material with a low Hooge a-parameter, operated at a high power level [12]. The detection limit of a Hall element made of a material with p H = 6 m2/Vs and operated at P = 0.5 W for a high frequency signal with Af = 1 Hz was assessed theoretically to be Bmin= 4 10 -I1 T [50]. The experimentally obtained SNB values of a silicon Hall device biased at Z = 0.5 mA are: 3 . 10 -I3 T*/Hz at 100 Hz (l/f noise) and 10 -I5 T2/Hz at 100 kHz (thermal noise) [51]. Cross-sensitivity can be defined as the undesirable sensitivity of the sensor to other environmental parameters or signals, such as temperature, pressure, light, etc. A convenient way to characterize the cross-sensitivities of a Hall device is to use relevant secondary sensitivities,

-

(3-58) where P denotes a parameter, such as temperature ( P = T ) or pressure ( P = p ) , and S, denotes a prime sensitivity, Equations (3-49), (3-50) and (3-52). For example, by taking S, = S,and P = T, it is possible to derive an important secondary sensitivity known as the temperature coefficient of current-related sensitivity. For a Hall plate made of strongly extrinsic n-type material, Equation (3-25), one can obtain from equation (3-51) and (3-58) the function:

(3-59) Similarly, the pressure coefficient of current-related sensitivity can be expressed as:

(3-60) Some experimental data on the temperature sensitivity of the Hall scattering factor, (3-59), and the pressure sensitivity of the Hall coefficient, (3-60), are quoted in Section 3.2.2. Offset of a sensor can be defined as a static or very slowly varying output signal in the absence of a measurand. The major causes of offset in Hall sensors are imperfections in the fabrication process and also piezoresistive effects producing an asymmetry voltage U, f (B) at the sense contacts [12, 521. Offset is usually characterized by an equivalent (offset) magnetic induction B, corresponding to the offset voltage U,, such that:

*

B, = Uo/S, , where S, denotes the absolute sensitivity (Equation 13-49)).

(3-61)

60

3 Magnetogalvanic Sensors

If a static magnetic field is to be measured with a Hall sensor, the application of an offsetreduction technique is usually required. Conventionally, offset can be reduced by trimming or calibration [7-91. Devices with a shape which is invariant under a rotation through 90" allow the application of the connection commutation technique, where diagonally situated contacts are alternately used as the current and sense contacts [15, 531. Since the Hall voltage rotates with the bias current and the offset voltage does not, the offset voltage can be cancelled out from the output voltage. A similar effect is obtained if two matched integrated Hall elements are biased orthogonally and their outputs connected in parallel [15]. Combining this idea with a buried active layer design, an equivalent offset induction as low as 1 mT has been achieved in silicon-integrated Hall elements [54]. Recently, an attempt was also made to apply the sensitivity variation method for offset reduction [55] on integrated Hall devices [52]. Nonlinearity is the ratio:

where U, is the measured Hall voltage and UHois a best linear fit to the measured values. Since UH = S, BZ, Equation (3-62) can be rewritten as:

(3-63) where S, (B,I) denotes the current-related sensitivity as a function of magnetic field and current. If one of the terms determining the sensitivity, namely RH , G, and t in Equation (3-51), varies with magnetic field or current, the sensor will exhibit a non-linearity, which is respectively called material, geometrical, or junction field-effect non-linearity [27]. Material non-linearity stems from the magnetic-field dependence of the Hall scattering factor (Equation (3-26)). It is characterized by the parameter a, whose value ranges between 0.1 and 1, (refer to the notes following (Equation (3-26)). Geometrical non-linearity is a consequence of the magnetic-field dependence of the geometrical factor G, see Equation (3-46). The coefficient p can vary from 0 (in devices with no short-circuit effect) to 0.604 (in devices with Go = 0, see Equation (3-48)) [27]. Junction field-effect nonlinearity is due to a feedback modulation of the Hall-plate thickness (t in Equation (3-51)) by the generated Hall voltage. It plays an important role in high-sensitivity integrated Hall devices, where it may be as high as a few percent [48]. The linearity of Hall sensors can be improved in several ways. Geometrical non-linearity can be compensated for by loading the sensor output with a resistor [7-91. More efficiently, material and geometrical nonlinearities can be made to mutually cancel in devices where a = 8, see Equations (3-26) and (3-46) [27]. Nonlinearity due to the junction field-effect can be compensated for using the very same effect in a feedback circuit [48], [27]. One of the lowest experimental nonlinearity values, N L = + 3 . at B c 1 T and room temperature, was reported for an ion-implanted, cross-shaped GaAs Hall device [43].

3.4 Magnetoresistors

61

3.4 Magnetoresistors 3.4.1 Fundamentals Magnetoresistors (MR) are passive semiconductor sensors which are based on the increase in resistance which occurs when they are exposed to a magnetic field. Although Thomson [2] observed the effect in metals in 1856, the effect only found a technical application after the discovery of III/V semiconductors by Welker [6]. The principle of Magnetoresistance has already been described in Section 3.2.3 and the following summary serves to recall the basis of the phenomenon. Magnetoresistive sensors which are based on the anisotropic magnetoresistive effect in thin films of ferromagnetic transition metals are the topic of Chapter 9. A free charge carrier experiences a deflection by virtue of the Lorentz force (Equation (3- l)), which acts perpendicular to the direction of the velocity v and the magnetic induction B. In a semiconductor material the charge carrier eventually collides with the crystal lattice, whereby it loses velocity and hence establishes the so called Hall angle 0, between the electric field Ex and the direction of the current. The Hall angle 0, as given in (3-17) is proportional to , , and to the magnetic induction B. the Hall mobility U This rotation of the current direction results in an increase in the length of the path of the current flow, which manifests itself as an increase in the resistance of the material. This magnetoresistive effect is exploited to produce MR devices. Further descriptions of the Magnetoresistive effect and components based on it are given in [8, 9, 79-82].

3.4.1.1 Basic Equations Equations (3-27) and (3-28) are valid for infinite geometries with low magnetic fields. They show a quadratic characteristic between specific resistance and magnetic field B. At large magnetic fields (0,--$ d 2 ) the function shows a linear dependence. Lippmann and Kuhrt [83] have reported the resistance of a square semiconductor plate in relation to Hall angle and to the geometry ratio I/w, where I is the length and w the width of the plate. For small Hall angles 0, 5 0.45 the quadratic dependence is valid, ie,

PB (1 + c,( P H B ) 2 )

RB -Ro

(3-64)

Po

where Ro is the resistance at B = 0, p B / p ois the relative specific resistance of an infinitely long rod (see Equations (3-27) and (3-29)) and C, is a geometry-dependent constant. For large Hall angles, 0, + d 2 , the linear relationship is valid, ie, RB PB = -(C,,U,B

Ro

Po

+ C3)

where C, and C3 are both geometry-dependent factors.

(3-65)

62

3 Magnetogalvanic Sensors

The resistance characteristic is symmetrical about the R, /R,axis and thereby independent of the magnetic field direction. In order to produce components which work by using the magnetoresistive effect it is necessary to optimize the geometry-dependent factors C, , C,, C, , and also the semiconductor material which determines p,, the Hall mobility.

3.4.1.2 Influence of Geometry If one considers the current paths in a real isotropic semiconductor plate when it is subjected to a perpendicular magnetic field, then it can be shown that the effects of the Hall angle OH are only significant in the region close to the contact electrodes. The supply-current terminals stretch over the full width w of the plate as is represented in Figure 3-8.

1

1 Y

H

O

X -

I

-

F

Figure 3-8. Rectangular semiconductor plate in a magnetic field perpendicular to the plane of the page. - represents current paths, -- represents equipotentials.

W

The current paths in the center of the plate run parallel to the edges and here, as already discussed in 3.2.3, the Hall field tends to reduce the magnetoresistive effect. The equipotentials are therefore rotated through the Hall angle OH,ie, a Hall voltage can be measured. The magnetoresistive effect is magnified as the ratio of the electrode separation along the length I to the electrode width w decreases. Figure 3-9 shows the relative resistance change for various length to width relations I/w as a function of the magnetic field B from tests made on similar doping grades of InSb [84]. //w =0 Korbino disk)

20

1

d \ d

15 I / w = 0.33

10 //w=l

5 1

0

I

I 0.1 0.2 0.3 0.4 0.5 0.6 03 0.8 0.9T1.0 1

I

B-

//w

10

Figure 3-9. Dependence of the relative resistance R , / R , on a magnetic field B, for various length-to-width ratios.

63

3.4 Magnetoresistors

From the results of [83] the geometry-dependent factors C,, C 2 , C3 (from Equations (3-64) and (3-65)) can be expressed in order to define the characteristic curve. For I/w 5 0.35 (3-66)

C, = 1 - 0 . 5 4 1 / ~ ,

hence the Equation for Hall angles 0, 5 0.45 can by using Equation (3-64) be given by: RB PB = -(1

Ro

Po

+ ( p H B)’(l - 0.541/~))

(3-67)

If I/w = 0 then the largest possible relation is obtained. This can only be practically realized in the form of the Corbino disc [32] (see Figure 3-3).

c2= w/l

(3-68)

using (3-65) the following expression for large Hall angles 0, + n/2 can be obtained: RB =

Ro

PB @H B w/l Po

+ C3) .

(3-69)

The dependence of the geometry factor C3 in on I/w gives the characteristic curve in Figure 3-10 after [83]. In Equation (3-69) the ratio w/l gives the gradient of the asymptote and C3 the point where it cuts the axis. 1 0 -1 -2 -3

5 \

z

-4

-5 -6

-7

Figure 3-10. Constant C, in Equation (3-69) showing its dependence on the length/width ratio I/w; from [83].

-8 -9

-10

0

05

1

1.5 I/

2

25

3

W

3.4.1.3 Selection of Material The influence of the material is strongly manifest in the Hall mobility pH and this is of special importance for the magnetoresistive effect. Table 3-1 shows a selection of suitable semiconductor materials. InSb shows the highest absolute value for mobility and is therefore the preferred material for magnetoresistive components. The very small band gap possessed

64

3 Magnetogalvanic Sensors

Table 3-1. Physical properties of some suitable semiconductor materials. unit cm2V-' s eV

P E8

ni(RT) a(RT)

InSb

-'

P@T)

Rn

3 . lo4 0.45 6 ' 1014 + i s 10-3 - 1 . 10-~ 100

7.7 104 0.24 2 * 10'6 -2 * 10-2 -1.5 . 380 +

K-' K-' cm3A-I s - '

Si

Ids

1.5. 103 1.12 1.5 * 10" + 5 . 10-~ +1.2. 1 0 - ~ 3000')

GaAs

8 * lo3 1.43

10' +8 - 5 . 10-4 60 I )

depending on doping

by InSb leads, even at room temperature (20°C), to a high temperature coefficient of resistance, a = -2%/K. This disadvantage can be overcome by the addition of foreign atoms, ie, doping, which shifts the intrinsic conductivity range to higher temperatures. The accompanying reduction in the gradient of the characteristic curve can usually be tolerated. The temperature dependence of the normalized internal resistance R,/R,, (0:Celsius temperature) of various semiconductor materials is shown in Figure 3-11.

,8.10-&

'

0-20 0

I

I

20

60

I

100 Temperature E

GaAs

I

I

140

180

-

'C

Figure 3 4 . Temperature dependence of the normalized resistance R,/R,, of various semiconductors.

3.4.2 Magnetoresistor Technology 3.4.2.1 Production of InSb Semiconductor Material InSb material for magnetoresistors is produced as a polycrystalline bar in a zone-melting process. The elements Indium, In, and Antimony, Sb, are purified and powdered and then melted together in stoichiometric proportions in an inert atmosphere. The melting point of InSb lies at 525 "C. The InSb bar is then refined to the required purity by zone melting, and then the pure material is doped as required with tellurium to about 2 loz2to 2 1023m- 3 [7].

3.4.2.2 Technology of Short-circuit Straps The basic requirement for the effective use of the magnetoresistive effect is the smallest possible ratio of I/w, Equations (3-67) and (3-69). Intrinsic or doped InSb has a very

3.4 Magnetoresistors

65

high specific conductivity, ie, 0 = 200-800 (SZcm)-'. The ideal form of the Corbino disc is therefore not a practical proposition. In order to obtain resistances in the range 100 - 1000 ohms a large number of I/w ratios must be connected in series, and the principle behind short circuit straps is shown in Figure 3-12.

Figure 3-U. Semiconductor plate with shortcircuit straps and current paths in a magnetic field acting perpendicular to the plane of the page.

3.4.2.2.1 Gridded Magnetoresistor Thin films of InSb are prepared either by grinding or by evaporation techniques. Short circuit straps of highly conductive metals are deposited perpendicular to the direction of the supply current flow either by evaporation or by galvanic growth into pre-prepared grooves [8], [91. The basic resistance R, can be determined to a reasonable degree by controlling the crosssection and length of the MR system, Figure 3-13 showing a possible configuration. Due to the high production effort required and the relatively small scale of the desired effect, the short circuiting process is restricted to the surface. This type of MR has been of little significance and as a result will not be considered further.

Figure 3-W. Connection example of a gridded magnetoresistor.

3.4.2.2.2 Magnetoresistors with NiSb Needles Using a process developed by Weiss and Wilhelm [76], highly conductive NiSb needles are built into the polycrystalline InSb rod. Formally, 1.8% mass fraction NiSb is added to the InSb rod which is then remelted far above the InSb melting point. At this point an eutectic exists, and on recrystallization of this eutectic the NiSb forms as long thin needles of approximately 1 pm diameter. As the growth of the needles extends perpendicular to the liquidholid phase boundary, a homogeneous distribution of needles is produced parallel to the axis of the bar by a specially designed temperature profile. The conductivity of NiSb is more than two orders of magnitude greater than that of InSb at room temperature and as such produces a very good short-circuiting effect. The average length of the needles is about 50 pm and they are separated by about 5 10 pm, so that throughout the entire cross section the resulting I/w ratio is about 50.2. Figure 3-14

66

3 Magnetogalvanic Sensors

a

b

c

Figure 3-14. Cross-section photograph of the InSb/NiSb eutectic a) parallel to needle direction, and b) perpendicular to needle direction; c) current path through the InSb/NiSb eutectic under the influence of a magnetic field directed into the plane of the page.

shows a cross-sectional view of the material parallel and perpendicular to the direction of the NiSb needles.

3.4.2.3 Construction of Magnetoresistors with NiSb Needles The bar of semiconductor material is sliced parallel to the NiSb needles, and the wafers are subsequently reduced to a thickness of 25 pm. In order to produce a resistance which is of practical value, the resistors are etched with a meander path using photolithography and acidetching processes. Some examples of this are shown in Figure 3-15. ,

Figure 3-15. Layout and contact pad examples of meander paths.

Indium is galvanically deposited onto the contact areas, the resistance meander is glued onto a soft iron or ceramic carrier and wire contacts are soft soldered onto the pads. Figure 3-16 shows the configuration of such a system. The systems are then covered in lacquer in order to provide some protection.

Figure 3-16. Layout and connection example of a magnetoresistor on a carrier using leadwires as connectors.

3.4 Magnetoresistors

67

In a newly developed production process the semiconductor wafers are coated with an insulating layer and bonded to a large ferrite substrate. The resistor meander paths are then produced by a similar photolith/etch process as before after which the chips can be separated by dicing on a wafer saw. The contacts are made using a modified impulse solder process whereby the InSb/NiSb resistance meanders are bonded directly to the Micropack frame. A ferrite system and a complete Micropack package are shown in Figure 3-17. The system is protected from mechanical damage by a protective lacquer, as above. Using special high temperature adhesives and lacquers and also pure tin solder contacts, the Micropack component can be implemented at operating temperatures up to 180°C [77].

Figure 3-17. Layout and connection example of a magnetoresistor on a ferrite substrate using Micropack as the connector.

3.4.3 Properties of Magnetoresistors R , is the basic resistance at B = 0 and is determined by the geometry and conductivity of the system. The cross-section of the resistance paths is constant with a width of 80 pm and a thickness of 25 pm. The desired resistance is obtained by varying the length of the resistor (see Figure 3-15). The conductivity of InSb can be varied by adjusting the doping level. In practice three doping levels have found use [78, 71:

o o o

200 (C2 cm)-' 550 (a cm)-' = 800 (C2 cm)-'

=

=

-

undoped n = 2 loz2m - 3 D-type Te-doped n = 6 . loz2m - 3 Ltype Te-doped n = 2 . loz3m - 3 N-type

R , is the resistance of the element when it is subjected to a magnetic field. With small magnetic fields it takes a quadratic form (3-67) and at larger magnetic fields it is almost linear as defined by Equation (3-69). At increasing levels of doping the specific resistance and Hall mobility pH decrease, as can be seen in Figure 3-18, and this is manifested as a decrease in the sensitivity of the sensor. a is the temperature coefficient of the InSb which in its undoped form shows intrinsic conductivity at room temperature, and hence shows a very strong temperature coefficient of resistance of approximately - 2%/K. Increasing the levels of doping causes the point of tran-

68

3 Magnetogalvanic Sensors

Figure 3-18. The magnetic field dependence of the normalized resistance R,/R, of magnetoresistors in the InSb/NiSb eutectic for three different doping grades.

B-

sition to intrinsic conductivity to be raised to a higher temperature, although it simultaneously gives rise to a reduction in the magnetic field dependence as shown in Figure 3-19.

R

1

2 103

e d 5 n *

.D

2

LL

10'

5 2'

-20

I

0

I

20

1

I

40 60 Temperature 8

1

80

1

I

100 'C 120

Figure 3-19. The temperature dependence of the resistance of a magnetoresistor in the InSb/NiSb eutectic for two standard doping grades (D and N) shown with B = OT a n d B = 1T.

3.4.4 Differential Magnetoresistors

3.4.4.1 Magnetic Biasing The temperature dependence of InSb/NiSb magnetoresistors can be compensated for to a greater extent by placing them in a differential configuration. Differential sensors are described in [85, 86, 871. The magnetoresistors are arranged in pairs with a definite separation so that the field gradient produces a difference in their resistances which, when the arrangement is completed into a Wheatstone-bridge circuit, can be picked off as a voltage (Figure 3-20). The error arising from the asymmetry of the two resistors R , , R, when uninfluenced

69

3.4 Magnetoresistors

Figure 3-20. Signal conditioning of a differential magnetoresistor using a Wheatstone bridge arrangement; R , , R, : magnetoresistors, R,, R,: fixed resistors, Ui,: operating voltage, U,,,:

R1

output voltage; M = R 1 - R2 100%: middle symmetry. ~

ov

R,

by an external magnetic field gradient is called the middle symmetry A4 and shows up as an offset voltage U, in the bridge output. The output voltage Uo,,of a differential configuration of the type shown in Figure 3-20, depends not only on the magnitude of the effective magnetic field gradient AB but also on the value of the magnetic biasing field Bb due to the strong nonlinear R , characteristic, as shown in Figure 3-21.

Figure 3-21. Control of a biased differential magnetoresistor; B, : magnetic biasing level, A& actuation level, R,: resistance at working point, R , , R,: resistance of the MRs with an actuation of AB. With no actuation the resistances R , = R, = R,.

*

B-

The following is valid for low levels of actuation: B , = Bb

+ AB;

B2 = B,

- AB

dR dB

R,=Rb+AR=Rb+-AB

dR R, = Rb - AR = Rb - dB R,

=

(3-70) (3-71)

AB

R,

(3-72) (3-73)

and as (3-73) can be used to equate the output voltage (3-74) Thus together with (3-71) and (3-72) (3-75)

70

3 Magnetogalvanic Sensors

So then the sensitivity can be defined as: (3-76) The sensitivity Uo,, /AB is proportional to the relative magnetic-resistance change (dR/(R dB)), which itself is dependent on the level of magnetic bias and on the temperature. Figure 3-22 represents the dependence of the relative change in resistance on the level of magnetic biasing, the influencing parameters here being doping level and temperature.

D: 6 = 200 (Run)-’ N: 6 800 (Run)-’

-

1 dR R dB

0

0.2

0.4 Induction B

-

0.6

T

0.8

Figure 3-22. Dependence of the relative magnetic sensitivity on magnetic field at two temperatures and two standard doping grades (D and N).

Using (3-64) and C, = 1 it is possible to calculate the relative change in resistance for small Hall angles: (3-77)

As long as pH B I 0.45, then a proportional increase in the relative resistance change can be recognized, whereas when p H . B s- 1 a reduction proportional to 1/B is noticeable (Figure 3-22). The maximum lying between these values occurs at B i+ l/pH. If the Hall mobility p H is reduced through an increase in temperature or in doping level, then this maximum is shifted to higher field levels. It is necessary to choose a working point as close as possible to the maximum (see Figure 3-22) to produce the highest sensitivity in a differential system, and in order to obtain the smallest temperature dependence it should be subjected to a high level of bias field. The required levels of magnetic field are produced by permanent magnets which influence the magnetoresistors with a homogeneous magnetic field perpendicular to their plane. Rare earth/Cobalt magnets are the preferred biasing magnets, since as a result of their high energy density and small volume they can be used in open magnetic circuits to generate field strengths of 0.2 - 0.4 T on their pole faces. Differential MR systems then, have two advantages in addition to their improved temperature dependence in that the required magnetic bias does not

71

3.5 Other Semiconductor Devices as Magnetic Sensors

reflect itself in the output of the bridge circuit and the sensor therefore only reacts to a magnetic field gradient.

3.4.4.2 Temperature Compensation of Differential Sensors A differential sensor configuration only compensates for the individual magnetoresistors when they are both under the exact same conditions. However, when each MR is experiencing a different level of magnetic field strength then a difference in their temperature coefficients will be noted (Figure 3-22). In the simplest case, the temperature characteristic of the internal resistance itself is used as compensation. Figure 3-23 shows the relevant circuit arrangement for this mode of operation. The operational amplifier equates the output current from the bridge: (3-78) where U , is the open-circuit output voltage and Ri the internal resistance of the bridge. R,R2 R3R4 R. = ‘ R, + R, R, + R, +

(3-79)

R , and R , are independent of temperature, so that the temperature course of Ri is determined only by R , and R , . As the open-circuit output voltage U , and the internal resistance Ri decrease with increasing temperature, the quotient i in Equation (3-78) remains approximately constant. The output voltage U,,, can be stabilized over a defined range by the addition of a compensation resistor R, (Figure 3-23). The optimal value of R , is calculated empirically for the required temperature range and ( R , + R , ) / 2 can be taken as a good starting value for this.

3.5 Other Semiconductor Devices as Magnetic Sensors Generally, all “nonmagnetic” semiconductor devices, such as diodes and transistors, are sensitive to a magnetic field: via the Lorentz force, Equation (3-1), a magnetic field will modify the carrier-transport conditions in these devices and produce changes in their electrical output

72

3 Magnetogalvanic Sensors

characteristics. Normally, these changes are negligible. If, however, the device design and operating conditions are optimized with respect to the magnetic field sensitivity of the device characteristics, some useful magnetic sensors can be obtained. In this section we shall discuss the main operating mechanisms and design features of such devices. Additional details concerning various devices can be found in references [12] and [18].

3.5.1

Magnetodiodes

The operating principle of magnetodiodes is based on a combined galvanomagnetic effect (see Section 3.1) called the magnetoconcentration effect or Suhl effect [17]. It is a combination of three basic phenomena: carrier injection, Hall effect (in the form of carrier deflection, see Section 3.2.1), and surface recombination or generation of carriers. The general structure of a magnetodiode is shown in Figure 3-24. It is a long and thin semiconductor slab doped in such a way that a p-i-n structure along the long axis is formed. The two opposite surfaces of the slab S, and S,, have very different surface recombination velocities s, and s, say s, s,. In operation, the carriers are injected from the n + - and p +-contacts into the i-region, and drift there due to the electric field E along the long axis. If the device is exposed to a magnetic induction B parallel to S, and S, and perpendicular to E, both electrons and holes are deflected towards the same surface, S, or S,. If they are deflected towards the S, surface, their concentration at this surface increases, as does the generation rate, and the conductance between n and p increases. With the Lorentz force acting in the opposite direction, the carriers are deflected towards the S, surface where they recombine, the recombination rate and the resistance increase being roughly proportional to the magnetic induction [56]. +

p-or n - l i )

*

+

Figure 3-24. Basic magnetodiode structure. It is a long and thin p-i-n diode, with both low-recombination (S,) and high-recombination (S,) surfaces. .

I

I

52

In practical realizations, the low-recombination surface is prepared by polishing and surface passivation, for example by growing thermal SiO, on silicon. The high recombination surface can be effected via surface roughness (by grinding) [57], by use of surface crystal defects at the interface with another crystal (silicon-on-sapphire) [58], or by use of a reverse-biased p-n junction, where recombination is replaced by the collection of minority carriers [59]. Typical relative sensitivities of magnetodiodes are about 5 V/mA T at bias currents of 1 mA to 10 mA. Noise characteristics [60] are similar to those of the Hall devices (see Section 3.3.3).

3.5 Other Semiconductor Devices as Magnetic Sensors

73

3.5.2 Magnetotransistors Magnetotransistors are bipolar transistors whose structures and operating conditions are optimized with respect to the magnetic-field sensitivity of the collector current Z, . There are at least four effects which are fundamental to magnetotransistor operation: carrier deflection, injection modulation, modulation of the base-transport factor, and the magnetoconcentration effect. Usually, all these effects coexist, and understanding the operation of a specific magnetotransistor is rather involved. In the following discussion therefore some examples are considered where only a single magnetotransistor effect prevails. A semiconductor structure exhibiting a strong carrier deflection in a magnetic field was proposed originally as a model [61]. Later, a similar device, shown in Figure 3-25, was used as a magnetic sensor [62]. It is a drift-aided lateral double-collector bipolar transistor. Its base region (the large square), an isolated island in a bipolar integrated circuit, is obviously reminiscent of a Hall plate. As a result of the Hall field generated in the base region due to the drift of the majority carriers, the total electric field E in the base region is inclined with respect to the x-axis through a Hall angle of OH,,Equation (3-9). However, the current density vectorj, of the (injected) minority carriers rotates through an additional Hall angle OHp, Equation (3-17), with respect to E. As a result the upper collector C, receives more current than the lower one, the current difference being proportional to the total deflection angle: Mc

=

bHn

+ PHp) BzE

(3-80)

where K is a coefficient and ZE the emitter current.

Figure 3-25. Drift-aided lateral double-collector magnetotransistor. B, and B, are the contacts to the base region (n), E is the emitter, and C, and C, are the collectors.

The same double deflection phenomenon plays a key role in another lateral magnetotransistor devised for the CMOS process [63]. Relative sensitivities IZ;' . 8 Z C / 8 B I of up to 1.5 T were obtained in this device, and recently a relative sensitivity as high as 30 T - I was achieved in a similar structure [64]. Devices where only single deflection takes place generally show more moderate sensitivities of about 0.05 T - I [65, 661. The current-deflection mechanism can also be exploited in split-drain MOS transistors, called MagFETs. By incorporating a complementary Mag FET pair in a CMOS circuit, a sensitivity of 1.2 V/T has been achieved [67]. The injection modulation mechanism of magnetotransistor operation can be better understood with reference to Figure 3-26, which shows the cross-section of a lateral doublecollector magnetotransistor. Consider the Hall voltage generated in the base region between the two points A and B situated close to the emitter sidewalls, opposite to the collectors. The

74

I

3 Magnetogalvanic Sensors

c1

IE

cz

I Figure 3-26. Illustrating the injection-modulation mechanism in a lateral double-collector magnetotransistor. E denotes the emitter, N is the base region and C , and C , are the collectors.

Hall voltage is equal to the line integral over the Hall field along a line AB (see first part of Equation (3-8)). Assuming a very low emitter efficiency, ie, ZE t: ZB , ZE and ZB denoting the emitter and the base currents, respectively, one obtains [68]:

where t denotes the devices thickness (perpendicular to the figure plane). The Hall voltage (Equation (3-81)) produces an asymmetrical emitter-base bias, which leads to asymmetrical injection of the minority carriers. The resulting collector currents are

where I, denotes the collector saturation current, and U the emitter-base bias voltage. The corresponding relative sensitivity at B t: 0 reads

(3-83) The sensitivity is proportional to the emitter current, see Equations (3-81) and (3-82) as long as the device works at low injection levels. At high injection levels, the Hall coefficient of the base region drops (Equation (3-22)), as does the sensitivity. The relative sensitivities of magnetotransistors reported hitherto cover a surprisingly wide range, from 10 - 2 T - I to as high as 30 T - I . However, the high-sensitivity devices tend to require a large bias current not accounted for in the sensitivity definition, so that a fair comparison to other devices is not easy. In addition, low-frequency noise characteristics of some magnetotransistors seem to be superior to that of Hall plates [69]. In all other respects however, (offset, linearity, temperature coefficient), Hall plates are still better than magnetotransistors.

3.5.3 Carrier-Domain Magnetic Sensors A carrier domain in a semiconductor is a region of high nonequilibrium carrier density. It consists of an electron-hole plasma, where the carriers are permanently generated by a suitable mechanism, such as injection over a barrier or impact ionization. The formation of a carrier domain has been demonstrated in bipolar transistors [70], thyristor-like structures [71], and transistor-like structures operating in breakdown mode [72].

3.6 Applications

75

Figure 3-27 shows a vertical four-layer (n-p-n-p) device which can operate as a carrier-domain magnetic sensor [73]. It is a bipolar transistor with split-collector buried n +-contacts, and can be fabricated using bipolar IC technology. In operation, both emitter(1)-base(2) and substrate(4)-collector(3) junctions are forward-biased. Due to the lateral voltage drops, carrier injection occurs in two opposite small spots at the emitter-base and the substrate-collector junctions, and thus, a carrier domain forms which consists of electrons and holes moving in opposite directions. A magnetic field perpendicular to the figure plane produces a displacement of the domain, which in turn causes a change in the currents I, and I p . These variations in the base and collector currents can be interpreted as the sensor output signals. A variation in the current as large as 3 mA/T at 10 mA total current bias has been measured [73].

Figure 3-27. Cross-section of a vertical four-layer carrier-domain magnetic sensor. (1) is the emitter, (2) the base, (3) the collector, (4) the substrate, and the buried n +-regions, together with the two small n +-regions at the top, are the collector contacts.

In circular four-layer [74, 751 and three-layer [72] structures the carrier domain can travel around the circumference of the device, the rotation frequency being proportional to the magnetic field. A drawback of these devices, however, is a large offset: in the four-layer devices, the domain does not rotate unless the magnetic field exceeds a threshold value, which is between 0.1 and 0.4 T, but in the three-layer structure the domain rotates spontaneously even at B = 0. Moreover, these devices require rather large bias currents and are very sensitive to temperature changes.

3.6 Applications 3.6.1 Introduction Galvanomagnetic sensors convert a magnetic field value into an electrical signal. The major application for direct measurement of magnetic-field strength using Hall-effect probes is in instrumentation, and to fulfill the many types of function required of them, their packaging and also internal construction are matched to the necessary criteria. By measuring their magnetic-fields, electrical currents can be measured noninvasively using these devices,

76

3 Magnetogalvanic Sensors

and as a result of the multiplication factor characteristic inherent in Hall-effect generators, they can be used additionally to measure power. By suitable arrangement of the magnetic circuit, small physical movements of permanerlt magnets or of ferromagnetic materials can be detected by galvanomagnetic sensors via the field changes produced. As a result, these components find universal application in noncontact position sensing and are characterized by their reliability, high noise immunity and also their independence of actuating speed (contrary to inductive type sensors). Both areas of application, instrumentation measurement and position sensing, will be described in detail along with examples of practical applications.

3.6.2 Magnetic Measurement 3.6.2.1 Measurement of Magnetic Fields Hall-effect generators are used almost exclusively for the precise measurement of magnetic fields due to their linear and point-symmetrical characteristics. In addition they fulfill thc essential requirements of a small temperature coefficient, small and stable offset voltage as well as good linearity with sufficient sensitivity (see Section 3.3.3). When measuring alternating magnetic fields great care should be taken in the layout of the connection leads so that disruptive inductive components in the output signal are minimized, ie, avoiding loops, or twisted leads. The probes themselves are compensated internally to give a minimum residual component. Hall-effect generators are operated with a constant supply current so that the linear relationship U, B is used (as shown in Equation (3-32)). As the output signal U, of Hall-effect generators can be very small, they are often amplified by accurate voltage amplifiers or instrumentation amplifiers, usually coupled with temperature sensors to compensate for the temperature coefficient. Extensive application directions are given in [7, 8, 50, and 791. As mentioned above the internal construction and also the outer shape of Hall-effect probes are often matched to their use so that, for example, axial probes are constructed to measure axial fields in radial holes, tangential probes, and extremely thin probes for measuring in very small airgaps. Probes are also available which have a small active area so they can be used to give almost point measurements in magnetic fields and others have been developed for low temperature measurements in liquid helium [78].

-

3.6.2.2 Noninvasive Current Measurement Every electric current has an associated magnetic field. Hall-effect sensors are the preferred method for measurement of this magnetic field, since they can obtain a measurement of the current flowing yet remain potentially isolated from the current-carrying circuit. The current waveform is repeated identically in the output voltage of the Hall-effect sensor.

Measuring the tangential field strength of an electrical conductor A simple tangential field measurement produces a linear relationship between the measuring current Z and the magnetic induction B, as there are no nonlinear constituents like, for

3.6 Applications

77

Induction Liner

Figure 3-28. Principle of noninvasive current measurement in a circular conductor by measuring the tangential field strength at a distance r from the center of the conductor.

example, iron cores present. To effect such a measurement, a Hall effect probe is required which has its active area very close to the edge of the package. Figure 3-28 shows an example of a round conductor where:

I = $H*ds.

(3-84)

In a closed loop around the conductor the following is valid: I = H2nr; H = -

I 2nr

(3-85)

and in air: B=pO-

I 2711.

(3-86)

-'

where po is the permeability of vacuum and equals 4n * 10 H m - I . From (3-86) it can be seen that sufficiently large values of B will only be given for large values of I, the advantage of this method of current sensing being the good linearity obtainable in addition to its simple construction. A special application is described in [107].

Direct measurement using a core with an air gap Very large sensitivities can be obtained using a magnetic conductive core around the conductor [88],the sensor being located in an air gap in the core. Using multiple winding, an increased signal level can be obtained, such an arrangement being shown in Figure 3-29. Here:

In = Q H . ds

(3-87)

In = H L B + HFeIFe

(3-88)

where n is the number of windings, I , the mean path length of the iron and 6 the air gap.

78

3 Magnetogalvanic Sensors

Hall sensor

6 Figure 3-29. Arrangement for noninvasive current measurement using an iron core. The current to be measured produces a proportional magnetic field which can be measured in the air gap.

If the influence of stray magnetic fields are neglected then BFe = BFe =

and as: (3-89)

Pr PO

BL6 BL'Fe , then In=-+-

PO

BL =

BL,

(3-90)

Pr Po

PO In

(3-91)

'Fe

6+PI

Wh re B, is the air-gap induction nd p1the p rmeability of the core material. If pr is chosen to be sufficiently large (uI > 1000) then the following approximation can be used.

(3-92) The result of measurements with the arrangement in Figure 3-29 using an air gap of 6 = 1 mm is shown in Figure 3-30.

I

-30

-15

0 1.n

-

I

15

AW

Figure 3-30. Characteristic curve produced by the current measuring arrangement of Figure 3-29, where B = f ( I . n) with an air gap = 1 mm, and where n is the number of turns.

3.6 Applications

19

When large current values are being measured the nonlinear characteristic of the iron core must be taken into account as well as the occurrence of remanence effects. Using ferrite flux concentrators built into the sensor housing, Hall-effect sensors can be produced in GaAs or in InSb with effective air gaps of 6 = 0.2 to 1 mm, typical applications being current measurement probes in the range of 10 A to some kA.

Indirect measurement using the compensation method For very accurate measurements and also for very small measurand currents the compensation method, as represented in Figure 3-31, is employed. The iron core is kept free of induction by injecting a reverse current into the windings n, of the compensation coil. The current I2 required to compensate is then proportional to the measurand current I , . The Hall-effect sensor acts to indicate the null point, ie, B = 0, whereby the null voltage stability of the sensor is the determining parameter in the total accuracy of the measuring arrangement. When the field is zero, then

I , n,

+ I, n,

=

0,

(3-93)

and the output voltage is thus, given by

(3-94) whereby the strongly linear dependence between the measurand current and the output voltage can be seen. Hall-effect sensors in GaAs and InSb are used.

Figure 3-31. Arrangement for indirect noninvasive current measurement using the compensation principle. An iron core as represented in Figure 3-29 is held field free by injecting a current into a compensating coil wound on the core which offsets the field generated by the current being measured. The Hall effect sensor in the air gap serves as a null indicator.

“out

3.6.2.3 Noninvasive Power Measurement It is the multiplicative nature of Hall-effect sensors which is exploited in noninvasive power measurement (3-32). The load current consumption is measured using an arrangement like that shown in 3.6.2.2 with a magnetically soft-iron core. The load voltage is converted into a proportional control current from the AC supply using a transformer (Figure 3-32).

iL

-B

(3-95)

UL

-

(3-96)

‘in

80

3 Magnetogalvanic Sensors

T'

AC net

ure 3-32. Circuit diagram for AC-power measurement using a Hall effect sensor.

"out " PL

so using (3-32): UH

=

R H ii, B -

t

=

cuLi, = cp,

(3-97)

where c is a system constant. The arithmetic mean value is derived in the signal-conditioning circuit, ie, in a low pass filter, so that the disruptive offset voltage u,, of the Hall-effect sensor is eliminated. For resistive loads: u,(t) =

0,cos w t

(3-98)

i L ( t ) = 1, cos w t

uo(t) = UH

=

(3-99)

U0cos a t , then CU,

(t) i, (t)

(3-100)

+ u0 (t)

(3-101)

together with (3-98) through (3-IOO), then cos w t

.

(3-102)

Figure 3-33. Circuit diagram for DC-power measurement using a Hall effect sensor.

3.6 Applications

81

The term oocos w t does not contribute to the arithmetic mean. In reference [lo51 a complete application has been described. In DC systems, the supply current Ii, proportional to the load voltage U, is read directly from a high impedance, eg, impedance convertor, this principle being shown in Figure 3-33.

3.6.3 Noncontact Position Sensing Position sensors based on galvanomagnetic components detect the position of a permanent magnet by a localized measure of its magnetic field strength. To determine the position of a magnetically conductive material (eg, iron, ferrite etc.) the sensor is mounted directly onto a permanent magnet, which generates a constant bias field at the sensor, and by moving the magnetically conducting target within the field, localized changes in the magnetic field are produced which are converted by the sensor into electrical signals, and with suitable output circuitry the signal can then be further processed in analogue or in digital form. In silicon sensors this signal conditioning is integrated monolithically on the same chip (smart sensors). Figure 3-34 is a representation of the various configurations used with their respective output signal forms; a-d show sensors which are actuated by permanent magnets while e-f show those which are magnetically biased and are actuated by magnetically conductive materials. In each case the single and differential sensor configuration is represented. In arrangement a), actuation can take place along two axes. In one case the magnitude of the air gap can be changed by A d or the displacement As. This configuration is suitable for use in conjunction with electronic switching circuits to produce digital position sensors, limit switches etc. Arrangement b) shows the basic principle used in the construction of a brushless DC motor using a diametrically magnetized cylindrically formed permanent magnet, which is described below in more detail. In arrangement c), a linear position sensor with a range of up to 2 mm is shown. The arrangement can be optimized for each application by selecting suitable values for the air gap and the magnet dimensions. The differential arrangement shown in d) produces the same output waveform as in c). Arrangement e), where the sensor is magnetically biased and can therefore be actuated by magnetically conductive target materials, has the inherent disadvantage in both axes of actuation, that the usable nonlinear output signal is much smaller than that produced by the biasing magnetic field. Arrangement f) avoids the disadvantages of arrangement e) and produces an output signal with a linear portion similar to that obtained by c) and d). It is, however, a bit more difficult to realize due to the vertical assembly required. An additional area of application for this type of arrangement besides linear position sensing, is in the detection of cams and gearwheels, eg, in revolution measurement. The output signal which is similar to a sinusoid produced by each geartooth is digitalized as a square wave by a comparator. An example of a closed magnetic circuit is shown in arrangement g). Using a slotted disc as an actuator, one element is alternately short-circuited so that the opposing element effectively becomes field free. When combined with a comparator this arrangement can be used as a digital-output orientation/position indicator.

82

3 Magnetogalvanic Sensors

Arrangement

Preferred sensors

Output signal form

a1

Active area Sensor

s = constant = 0

Permanent magnet

Hall sensor Magnetoresistor

, -

d

5

bI

A,

E; I

-

dI

+ + d = constant

Hall sensor

5

d i constant

Hall sensor Magnetoresistor

Figure 3-34. Galvanomagnetic components for sensing the position of permanent magnets and magnetically conductive materials.

3.6 Applications

Arrangement

Preferred sensors

Output sigaal form

el

1

I

Unut

d = constant

s =constant

Hall sensor Magnetoresistor

d

fl I I I

E L

Magnetically conductive materiai

% d = constant

Hall sensor

Iron core /

Hall sensor

hI

+ d = constant

Hall sensor Magnetoresistor

83

84

3 Magnetogalvanic Sensors

Arrangement h) shows the classical construction used to detect magnetically conductive materials. As a result of its differential construction there is no electrical offset and an additional advantage is that the assembly is also realized with little effort. The output signal corresponds to that of arrangements c), d) and f) described above and the applications are identical to those described in f). When designing magnetic circuits it must always be kept in mind that the magnetic induction of permanent magnets falls off very rapidly with increasing distance from the pole face. For cubic magnets such as Figure 3-35, the relationship for the fall-off in the z-axis is given as follows (this is valid for rare earthkobalt magnets which are recommended for the applications mentioned above) [104]:

(3-103)

where the magnetization M lies in the z-direction.

Z-

Figure 3-35. Cuboid permanent magnet with square pole faces (a . a). The magnetic axis is along the length c.

The characteristic curve for Equation (3-103) is shown in Figure 3-36. The magnet geometry can be fixed for optimal effectiveness by choosing the magnetic length c to be about half as large as the diagonal of the poleface. As Equation (3-103) shows, an increase in the magnetic length will not produce a corresponding increase in magnetic induction since the contribution from magnetic length is approximately proportional to its square root and as such can be regarded as negligible for higher values of length. The strong dependence of the air gap on magnetic induction, which can also be seen from arrangement a) in Figure 3-34 implies that movements perpendicular to the axis of operation are to be avoided. When designing magnetic circuits, the air gap 6 should be kept as small as possible, or flux linking parts such as concentrators shoud be used, to help obtain as large an output signal as possible.

85

3.6 Applications

1 4

0.35 T

0.30 0.25 0.20 0.15

0 .lo 0.05

Figure 3-36. Fall-off in magnetic induction found with increasing distance z from the pole face of a cuboid magnet of SmCo (Vacomax) as represented in Equation (3-103).

0

mm

5

10

z-

Even for analogue position indication, nonlinear output signals are often used, if they are well reproducible. With modern electronics and with the availability of microprocessors for signal processing, such characteristics can be linearized very easily, hence the usable range of the galvanomagnetic position sensor can be significantly increased, eg, by using the arrangement in Figure 3-34a. A brief study of the collection of arrangements in Figure 3-34 will show that a great many of the configurations can be realized using either Hall-effect or MR sensors. Hall-effect sensors can be completed in the form of a differential system, as shown by Figure 3-37, and such components are also currently available. Iin

0

Figure 3-37. Connection of two Hall-effect sensors for use as a differential sensor.

The following discussion aims to help decide which sensor type is best suited to a given application. MR sensors of an InSb/NiSb eutectic mixture (see Section 3.4) connected as differential sensors have the advantage that they produce a large output signal when operated in the steep

86

3 Magnetogalvanic Sensors

portion of their characteristic curve (Figure 3-21). Differential MR sensors are therefore usually offered with a built-in permanent magnet. Their major applications are in digital position detection, e. g. presence indicators, limit switches, revolution/speed detectors, and also incremental angular encoders using magnetically conductive gearwheels or cams, in arrangements such as those shown in Figure 3-34h. The high temperature package (Micropack) designed for use up to +18O"C has already been described in 3.4.2 and plastic package devices with built-in permanent magnets are usable up to +150"C. Hall-effect sensors can be produced very economically using standard semiconductor processes such as epitaxy, ion implantation, or evaporation, and together with the choice of available materials a whole new area of applications can be addressed. Although silicon is not an ideal material in which to produce galvanomagnetic effects it can be integrated monolithically with signal conditioning electronics to give analogue or digital outputs [12, 14-16, 18, 94, 951. Gallium arsenide with its large bandgap of Eg = 1.43 eV presents itself as an ideal candidate for use up to temperatures in excess of 200°C and the relatively low output signal can be amplified by building a magnetic flux concentrator into the package [loll. Indium antimonide can be deposited in very thin layers onto ferrite or ceramic substrates by evaporation, or can be worked from bulk material by grinding. Very high output signals can be achieved with small magnetic fields if the active material is sandwiched between a ferrite substrate and a ferrite flux concentrator. Hall-effect sensors offer the user the opportunity of realizing a cost-effective sensor system for his individual 'use, simply by using a suitable arrangement of magnetic circuit (Figure 3-34). Due to their good stability over temperature (ie, GaAs) and their linear characteristics, Hall-effect sensors are amongst the most suitable components available for analogue position detection, and in addition to simple detection of position, other physical parameters such as force, pressure, flow, torque, acceleration etc. can be measured as a function of continuous displacement sensing. Further details of these are given in [89-92, 1061. A summary of the range of the magnetic induction for galvanomagnetic semiconductor sensors is given in Table 3-2. lsble 3-2. Range of the magnetic induction for semiconductor sensors. Magnetic induction B

Hall-effect sensors - measurement applications, open loop: with linearization:

-

0 0

position sensors with biasing, open magnetic circuit: bias : levels of actuation closed magnetic circuit: bias : levels of actuation

0.1 0 0.3 0

Magnetoresistors bias levels of actuation The detection limit (SNR = 1) for Af = 1 Hz: Bmi, s

0.2 0

T

... 1 T

... > 2 T

... 0.4 T

... 0.1 T

... 0.8 T

... 0.3 T ... 0.4 T ... 0.2 T

3.6 Applications

81

3.6.4 Selected Examples The following is a more detailed description of four of the applications mentioned earlier.

3.6.4.1 Revolution Counter Using a Differential MR Sensor The principle of the differential MR sensor has been described already in Section 3.4.4. Using the arrangement shown in Figure 3-34 h, magnetically soft gearwheels can be used to produce output signals as shown in Figure 3-38. In the construction of these differential sensors two magnetoresistors are mounted onto a magnetically conductive flux linking base of ferrite or soft magnetic alloys. The magnetic bias field is delivered by a rare earthkobalt permanent magnet. Magnetic materials for sensors have already been described in Chapter 1.5. If the sensor is completed into a Wheatstone bridge configuration such as in Figure 3-20 and actuated by a ferromagnetic gearwheel then a signal of the type in Figure 3-38 would be generated.

Gearwheel

material

$,_I

',>I

Permanent magnet Position:

I

I1

I11

"out

Position:

I

I1

I11

Figure 3-38. Sensing of a gearwheel using a differential MR sensor for revolution sensing or angular rotation measurement, showing also the corresponding output waveform.

The optimal signal amplitude is achieved when the intercenter separation x of the individual MRs corresponds to exactly half of the tooth period I (maximum value of AB). At present sensors are available with intercenter separations of x = 0.4 mm to x = 2.4 mm. However, the exact dimension of x / l = 0.5 is not always required, for a mismatch of up to

88

3 Magnetogalvanic Sensors

25% produces a reduction in the maximum obtainable signal of only 10%. Note that in cases

where x / l c 0.5, sharp tooth flanks should be used. The sinusoidal output waveform from the bridge is usually digitized by a comparator, either at the zero crossover or at a predetermined switching level, and the impulses are counted over a set time period. Figure 3-39 shows the principle block diagram of a suitable signal conditioning circuit. If two differential sensors phase shifted by 90" to each other are used then it is also possible to determine the sense of the rotation by combining the output signals. Rotation sensors based on MRs for automotive applications are also described in [93].

I

I

Figure 3-39. Block diagram showing the output signal conditioning of a differential MR sensor for revolution sensing as shown in Figure 3-38. The sinusoidal output is digitized, the impulses counted over time, and the output displayed numerically.

3.6.4.2 Noncontact Interrupter for Automotive Use, based on a Silicon Hall-Effect IC The potential for silicon to be monolithically integrated gives rise to the interesting possibility of being able to produce smart sensors. Using a Hall-effect sensor as the basic element, intelligent sensors in the form of magnetic switches [94] have been produced, some with additional temperature compensation or with analogue outputs [95], see also [96]. Digital sensors which latch on reaching a predetermined flux level and which have built-in hysteresis so that they release at a lower flux level are especially suitable for use in position detection, eg, as noncontact switches or as wear-free contact breaker points in automotive applications. The block diagram in Figure 3-40 shows the separate units which are required: constant voltage supply, Hall-effect sensor, amplifier, Schmitt trigger, output stage with open collector and protection circuitry. The Hall-effect IC is packaged together with a permanent magnet into a closed magnetic circuit as shown in Figure 3-34g, and is used extensively in automotive applications as a contact breaker (magnetic vane switch [97]). The sensor is actuated by a magnetically conductive vane with four slots which is passed through the air gap of the magnetic circuit. The switching

89

3.6 Applications

I I I I

I

-

Protection Us I t

circuit

- Regulator -

I

Hall genera tor

-

-

Protection circuit

-

-

I 1 L---,--------------------------------------~

0

1output I I

, t

I I

I I

signal of the sensor is then distributed at the required ignition point to each of the four spark plugs in the cylinders. Figure 3-41 is a schematic representation of this device. One arm of the core comprises the permanent magnet the other arm contains the digital Hall IC, and the actuating vane moves in between the two arms. When there is no vane present the Hall IC sees the maximum undisturbed magnetic-field level and its open collector output is conducting (low), Figure 3-41 a. Once the vane is inserted into the magnetic circuit, the circuit is effectively short-circuited and the arm of the magnetic circuit containing the Hall IC becomes field free, at which point its output is nonconducting (high), Figure 3-41 b. Due to the mode of operation the sensor still produces sharp edges even at low speeds of operation.

Package Hall

IC

Magnetically conductive material

b

Perrnan'ent magnet

Figure 3-41. Functional representation of a magnetic vane switch, a) without, b) with the actuating vane.

3.6.4.3

Brushless DC Motors

A brushless DC motor is based on a diametrically magnetized permanent-magnet rotor with coils in the stator [98, 991. The position of the rotor relative to the stator coils is detected by two Hall-effect sensors, and the four stator coils are then powered via the resultant Hall-effect

90

3 Magnetogalvanic Sensors

voltages from the sensors, so that a torque is produced by the magnetic field of the rotor. As a result of the polarity dependence of the Hall voltage, two Hall-effect sensors, displaced through 90°, suffice to control four stator coils. The operation principle is represented in Figure 3-42.

Control range

I

I

I

I

I

*

Figure 3-42. Representation of a brushless electronic motor using Hall-effect sensors. W, . . . W, are the stator coils, H , , H, are Hall-effect sensors, T, .. . T, are transistors, and U2... U8are typical characteristics of the control voltages for the coils belonging to the Hall voltages.

The two Hall-effect sensors are located either directly in the air gap between rotor and stator and are acted on directly by the magnetic field of the permanent-magnet rotor, or they are located outside the motor windings, eg, on a printed circuit board (PCB), and are acted upon by a control magnet mounted directly onto the motor shaft. By using Hall-effect sensors, smooth current change over in the windings is possible as the stator fields are reduced proportionally; this gives these motors good rotational characteristics. In noncritical cases where digital change over is sufficient, silicon Hall-effect ICs can be used without seriously affecting the rotational behaviour. At present Hall-effect sensors based on InSb or GaAs are being used. The advantage of these brushless motors lies in their long life, which is limited only by the lifetime of the bearings. Also worth mentioning is their low noise level, the absence of disruptive brush sparking and their good controllability. In addition to the obvious industrial applications, eg, in drive units, this form of electric motor is also used in commercial equipment, eg, HiFi and video machines etc.

3.6.4.4 Pressure Can Bused on Hall-Effect Sensing In a pressure can a Hall-effect sensor is actuated by a permanent magnet mounted onto a pressure sensitive diaphragm. The diaphragm flexes under pressure and thereby moves the magnet relative to the Hall-effect sensor, so that a change in pressure is effectively measured through a change in position. This application is described by the arrangements shown in Figure 3-34a and c. The characteristic curve W H = f(p) does not need to be linear but must be reproducible to the required level. Using the microelectronics that is currently available, it

3.7 Conclusions

91

is a relatively simple procedure to linearize a curved output characteristic through signal conditioning. The principle of the pressure can is shown in Figure 3-43. Electromechanical pressure sensing cans using Hall-effect sensors are a cost effective alternative to piezoresistive silicon pressure sensors, especially for automotive applications [loo]. The mechanical diaphragm affords complete separation between the media being measured and the electronic circuitry. At present Hall-effect sensors in GaAs are being used for this application.

Figure 3-43. Construction of a pressuremeasuring can based on a mechanical diaphragm moving a permanent magnet over the face of a Hall-effect sensor. The output waveform is also shown.

/

P e r m a n e n t magnet H a l l sensor

3.7 Conclusions Although the Hall effect and the magnetoresistive effect have been known for over 100 years, it has only been since the discovery of III/V semiconductors in 1953 that they have been of any commercial significance. Galvanomagnetic devices in InSb and InAs were produced, and after the discovery of the InSb/NiSb eutectic in 1961 whereby NiSb short-circuit needles can be grown in a InSb base crystal, a breakthrough into semiconductor magnetoresistors was achieved. Through the rapid development of integration techniques since 1968, silicon has also presented itself as an interesting material for Hall-effect IC sensors, and since 1980 GaAs has been added to the palette of useful materials. A wide range of applications for these devices has been built up on this basis and they have, as yet, not been fully exploited. With newer semiconductor/technologies available, cost effective sensors can be produced which meet the stringent requirements of high operating temperature, high sensitivity with small and stable offsets, and high reliability. In addition, they can also be integrated with intelligent signal conditioning. Magnetoresistors of InSb/NiSb eutetic, which have already proved themselves to be very reliable, are being developed further by new production techniques in which ferrite substrates are used to rationalize the process steps. In addition, the electrical and mechanical contact to the sensor is achieved through a copper/Kapton “Micropack” package which allows very high operating temperatures. A new high demand application for example, is in the automotive industry where it is employed as a wheel speed sensor in anti-lock braking systems with an operating temperature up to 180°C. The flexibility of the Micropack-packaged component is further demonstrated in that simply by changing the photomask sets the layout of the sensor can be adapted in intercenter

92

3 Magnetogalvanic Sensors

spacing, in basic resistance, and in geometry to match a number of applications, hence double differential systems for the detection of the sense of rotation in incremental linear and angular encoders can also be produced. A further advantage of the Micropack package is the extremely flat package outline which allows operation in very small air gaps allowing high resolution and high output-signal amplitude to be achieved. Future Hall-effect sensors for measurement and position sensing will, in addition to having small offsets and stable, linear output signals, offer the user an output signal suitable conditioned by integrated electronics. Such “smart sensors” will either offer a temperature compensated analogue signal or a digitized signal with stable switching levels. The greatest opportunities in this area lie with silicon. Hall-effect generators, magnetic transistors and magnetic diodes then, can all be combined together with electronics; Hall-effect arrays would also be possible as would multi-dimensional sensor systems, however, the maximum operating temperature sets the boundaries for silicon. GaAs is the ideal material for high temperature applications (as the intrinsic conductivity starts at over 400°C).Elementary sensors are being produced at present by ion implantation in semi-isolating substrates [loll or through epitaxial growth. Future developments will provide higher output signals, and sensors are already available in which a ferrite concentrator is built into the housing which acts to increase the field level at the active area. At present there is world-wide activity in development laboratories aiming to produce a monolithically integrated GaAs Hall-effect IC with analogue and digital outputs [102, 1031. The major application areas for such “smart sensors” in GaAs lie in the automotive industry due to their potentially high operating temperature range. Hall-effect sensors in InSb are produced by evaporation or by grinding from bulk on ferrite substrates, and in addition, a magnetic concentrator can be mounted onto the active area. As well as trying to optimize evaporation technology, other technologies are being investigated to facilitate the production of thin InSb films. The priority requirements being placed on the new generation of Hall-effect chips then, must be: high sensitivity, small offset, high operating temperature, good long term stability, good thermal stability, high reliability and also the ability to be integrated. Microelectronics and modern semiconductor technology already play a strong role in helping to attain the required electrical performance of sensors, but an increasingly important role is being taken by the packaging. This must be capable of withstanding harsh environments and a resistance to high temperatures, mechanical robustness and resistance to chemicals etc.; and yet the physical outline must also be considered with requirements for a flat package for use in small air gaps, the overall size to be minimal but still be user friendly and yet still afford a reliable assembly method, eg, SMD (surface mount device).

3.8 References [l] Hall, E. H., “On a new action of the magnet on electric current”, Am. . l Math. 2 (1879) 287-292. [2] Thomson, W., “On the effects of magnetisation on the electric conductivity of metals”, Philos. Trans. R. Soc. London A146 (1856) 736-751.

3.8 References

93

[31 Putley, E. H., The Hall Effect and Semiconductor Physics, New York: Dover Publishers, 1960. [41 Beer, A. C., Galvanomagnetic effects in semiconductors, Solid State Phys. Suppl. 4 (1963). [51 Pearson, G. L., “A magnetic Field strength meter employing the Hall effect in germanium”, Rev. Sci. Instrum. 19 (1948) 263-265. [6] Welker, H., “Uber neue Halbleiter-Verbindungen”, Z. Naturforsch. A7 (1952) 744-749. [7] Kuhrt, F., Lippmann, H. J., Hallgeneratoren; Berlin: Springer Verlag, 1968. 181 Weiss, H., Physik und Anwendung galvanomagnetischer Bauelemente, Braunschweig, FRG: F. Vieweg & Sohn, 1969; or: Weiss, H., Structure and Applications of Galvanomagnetic Devices, Oxford: Pergamon Press, 1969. [91 Wieder, H. H., Hall Generators and Magnetoresistors, London: Pion, 1971. 1101 Middelhoek, S., “The sensor lag: a threat to the electronics industry”, in: Solid State Devices 1982, Goetsberger, A., Zerbst, M. (eds.); Weinheim: Physik Verlag, 1983, pp. 73-95. [Ill Middelhoek, S., Hoogerwerf, A. C., “Smart sensors: when and where”, Sens. Actuators 8 (1985) 39-48. [12] Baltes, H. P., PopoviC, R. S., “Integrated semiconductor magnetic field sensors”, Proc. IEEE 74 (1986) 1107-1132. [13] Gallagher, R. C., Corak, W. S., “A metaloxide-semiconductor (MOS) Hall element”, Solid-state Electron. 9 (1966) 571-580. [14] Bosch, G . , “A Hall device in an integrated circuit”, Solid-State Electron. ll (1968) 712-714. [15] Maupin, J. T., Geske, M. L., “The Hall effect in silicon circuits”, in: The Hall Effect and its Applications, Chien, C. L., Westgate, C. R. (eds.); New York: Plenum Press 1980, pp. 421-445. [I61 Randhawa, G. S., “Monolithic integrated Hall devices in silicon circuits”, Microelectron. X 12 (1981) 24-29. [17] Suhl, H., Shockley, W., “Concentrating holes and electrons by magnetic fields”, Phys. Rev. 75 (1949) 1617-1618. [18] Kordic, S., “Integrated silicon magnetic-field sensors”, Sens. Actuators 10 (1986) 347-378. [19] Kireev, P. S., Semiconductor Physics; Moscow, USSR: Visshaia Shkola, 1969, Chap. 4 (in Russian); or: Kirejew, P. S., Physik der Halbleiter, Berlin, DDR: Akademie-Verlag, 1974, Chap. 4. [20] Madelung, O., Introduction to Solid State Theory, Berlin: Springer Verlag, 1978, Chap. 4. [21] Seeger, K., Semiconductor Physics, Berlin: Springer Verlag, 1982, Chaps. 4, 7, and 8. [22] Beer, A. C., “The Hall effect and related phenomena”, Solid-State Electron. 9 (1966) 339-351. [23] Beer, A. C., “Hall effect and beauty and challenges of science”, in: The Hall Effect and its Applications, Chien, C. L., Westgate, C. R. (eds.); New York: Plenum Press, 1980, pp. 229-338. [24] Long, D., Tufte, 0. N., “The Hall effect in heavily doped semiconductors”, in: The Hall Effect and its Applications, Chien, C. L., Westgate, C. R. (eds.); New York: Plenum Press, 1980, pp. 339-354. [25] Allgaier, R. S., “Some general input-output rules governing Hall coefficient behavior”, in: The Hall Effect and its Applications, Chien, C. L., Westgate, C. R. (eds.); New York: Plenum Press, 1980, pp. 375-391. [26] Sze, S. M., Physics of Semiconductor Devices, New York: Wiley, 1981, Chaps. 1 and 2. [27] PopoviC, R. S., HBlg, B., “Nonlinearity in Hall devices and its compensation”, Solid-state Electron. 31 (1988) 1681-1688. [28] Norton, P., Braggins, T., Levinstein, H., “Impurity and lattice scattering parameters as determined from Hall and mobility analysis in n-type silicon”, Phys. Rev. BS (1973) 5632-5653. [29] “Semiconductors” in: Lundolt-Bdrnstein, Numerical Data and Functional Relationship in Science and Technology Vol. 111/17a, Berlin: Springer Verlag, 1982, pp. 380-381, and ref. therein. [30] “Semiconductors” in: Landoft-Bdmstein, Numerical Data and Functional Relationship in Science and Technology Vol. 111/17a, Berlin: Springer Verlag, 1982, pp. 532-535. [31] HSilg, B., “Piezo-Hall coefficients of n-type silicon”, X Appl. Phys. 64 (1988) 276-282. [32] Corbino, 0. M., “Elektromagnetische Effekte, die von der Verzerrung herriihren, welche ein Feld an der Bahn der Ionen in Metallen hervorbringt”, Phys. Z. 12 (1911) 561.

94

3 Magnetogalvanic Sensors

[33] Putley, E.H., The Hall Effect and Semiconductor Physics, New York: Dover Publishers, 1960,p. 49. [34]Wick, R. F., “Solution of the field problem of the germanium gyrator”, J. Appl. Phys. 25 (1954) 741-756. [35]PopoviC, R. S., “The vertical Hall-effect device”, IEEE Electron. Device Lett. EDG5 (1984) 357-358. [36]Hoesler, J., Lippmann, H. J., “Hallgeneratoren mit kleinem Linearisierungsfehler”, Solid-state Electron. ll (1968) 173-182. [37]Lippmann, H. J., Kuhrt, F., “Der GeometrieeinfluB auf den Hall-Effekt bei rechteckigen Halbleiterplatten”, Z. Naturforsch. U a (1958)474-483. [38]Haeusler, J., “Die Geometriefunktion vierelektrodiger Hallgeneratoren”, Arch. Elektrotechn. (Berlin) 52, (1968) 11 - 19. [39]Versnel, W., “Analysis of a circular Hall plate with equal finite contacts”, Solid-state Electron. 24 (1981)63-68. [40]Versnel, W., “Analysis of symmetrical Hall plates with finite contacts”, J. Appl. Phys. 52 (1981) 4659-4666. [41] Versnel, W., “The geometrical correction factor for a rectangular Hall plate”, J. Appl. Phys. 53 (1982)4980-4986. [42]Mey, G. de, “Potential calculations in Hall plates”, in: Advances in Electronics and Electron Physics Vol. 61, P. W. Hawkes (ed.); New York: Academic Press, 1983, pp. 1-61, and ref. therein. [43]Thanailakis, A., Cohen, E., ,,Epitaxial gallium aresenide as Hall element”, Solid-state Electron. U (1969)997-1000. [44]Sugiyama, Y., Taguchi, T., Tacano, M., “Two-dimensional electron gas magnetic field sensor”, Transducers 87 - The 4th. International Conj on Solid-state Sensors and Actuators; Tokyo, Japan, 1987: Digest of Technical Papers, pp. 547-550. [45]Kanayama, T., Oasa, M., Hiroshima, H., Komuro, M., “A quarter-micron Hall sensor fabricated with maskless ion implantation”, Transducers 87 (see ref. 44), pp. 532-535. [46]Maenaka, K., Ohgusu, T., Ishida, M., Nakamura, T., “Novel vertical Hall cells in standard bipolar technology”, Electron. Lett. 23 (1987) 1104-1105. [47]Roumenin, C. S., “Parallel-field triple Hall device”, Dokl. Bolg. Akad. Nauk 39 (1986)65-68. [48]PopoviC, R. S., “Nonlinearity in integrated Hall devices and its compensation”, Transducers87 (see ref. 44), pp. 539-542. [49]Hara, T. T., Mihara, M., Toyoda, N., Zama, M., “Highly linear GaAs Hall devices fabricated by ion implantation”, IEEE Trans. Electron Devices ED-29 (1982)78-82. [50]Kleinpenning, T. G. M., “Design of an ac micro-gauss sensor”, Sens. Actuators 4 (1983)3-9. [51] PopoviC, R. S., “A CMOS Hall effect integrated circuit”, in: 12th Yugoslav ConJ on Microelectronics, MIEL 84; Nis, Yugoslavia, 1984, Vol. 1, 299-307. [52]Kordic, S., Offset reduction and three-dimensionalfield sensing with magnetotransistors, Delft, NL: Delft University of Technology, 1987 (PhD Dissertation). [53]Daniil, P., Cohen, E., “Low field Hall effect magnetometry”, J. Appl. Phys. 53 (1982)8257-8259. [54]“Improved Hall devices find new uses, orthogonal coupling yields sensitive products with reduced voltage offsets and low drift”. Electronics Week, Apr. 29, (1985)59-61. [55]Kordic, S.,Zieren, V., Middelhoek, S . , “A novel method for reducing the offset of magnetic field sensors”, Actuators 4 (1983)55-61. [56]Cristoloveanu, S., “L‘effet magnetodiode et son application aux capteurs magnCtists de haute sensibilite”, Onde Electr. 59 (1979)68-74. 1571 Stafeev, V. I., Karakushan, E. I., Magnetodiodes (in Russian); Moscow, USSR: Science Press, 1975. [58]Lutes, 0.S.,Nussbaum, P. S., Aadland, 0. S., “Sensitivity limits in SOS magnetodiodes”, IEEE Trans. Electron Devices ED-27 (1980)2156-2157. [59]PopoviC, R. S.,Baltes, H. P., Rudolf, F., “An integrated silicon magnetic field sensor using the magnetodiode principle”, IEEE Trans. Electron Devices Ed-31 (1984)286-291.

3.8 References

95

[60] Chovet, A., Cristooveanu, S., Mohaghegh, A,, Dandache, A., “Noise limitations of magnetodiodes”, Sens. Actuators 4 (1983) 147-153. [61] Buehler, M. G., Pensak, L., “Minority carrier Hall mobility”, Solid-state Electron. 7 (1964) 431 -438. [62] Davies, L. W., Wells, M. S., “Magnetotransistor incorporated in a bipolar IC”, in: Proc. ZCMCST Sidney, Australia, 1970, pp. 34-43. [63] PopoviC, R. S., Widmer, R., “Magnetotransistor in CMOS technology”, IEEE Trans. Electron Devices ED-33 (1986) 1334-1340. [64] Ristic, L., Smy, T.,Baltes, H. P., Filanovsky, I., “Suppressed sidewall injection magnetotransistor in CMOS technology”, Transducer 87 (see ref. 44), 543-546. [65] Flynn, J. B., “Silicon depletion layer magnetometer“, 1 Appl. Phys. 41 (1970) 2750-2751. [66] Zieren, V., Duyndam, B. P. M., “Magnetic-field-sensitive multicollector n-p-n transistors”, IEEE Trans. Electron Devices Ed-19 (1982) 83-90. [67] PopoviC R. S., Baltes, H. P., “A CMOS magnetic field sensor”, ZEEE 1 Solid-state Circuits SC-18 (1983) 426-428. [68] PopoviC R. S., Baltes, H. P., “Dual-collector magnetotransistor optimized with respect to injection modulation”, Sens. Actuators 4 (1983) 155- 163. [69] PopoviC, R. S., Widmer, R., “Sensitivity and noise of a lateral bipolar magnetotransistor in CMOS technology”, in: Tech. Dig. Int. Electron Devices Meet., Dec. 1984, pp. 568-571. [70] Gilbert, B., “New planar distributed devices based on a domain principle”, in: IEEE ISSCC Tech. Dig., 1971, p. 166. [71] Persky, G., Bartelink, D. J., “Controlled current filaments in PNIPN structures with application to magnetic-field detection”, Bell Syst. Tech. J. 53 (1974) 467-502. [72] PopoviC, R. S., Baltes, H. P., “A new carrier-domain magnetometer”, Sens. Actuators 4 (1983) 229-236. [73] Goicolea, J. I., Muller, R. S., Smith, J. E., “Highly sensitive silicon carrier domain magnetometer”, Sens. Actuators 5 (1984) 147-167. [74] Gilbert, B., “Novel magnetic-field sensors using carrier-domain rotation: proposed device design”, Electron. Lett. 12 (1976) 608-610. [75] Manley, M. H., Bloodworth, G. G., “Novel magnetic-field sensors using carrier-domain rotation: Operation and practical performance”, Electron. Lett. 12 (1976) 610-611. [76] Weiss, H., Wilhelm, M., “Indiumantimonid mit gerichtet eingebauten elektrisch gut leitenden Einschliissen: System InSb/NiSb”, Z. Phys. 176 (1963) 399-408. [77] Heidenreich, W., Lachmann, D., “Magnetik in der MeRtechnik”, VDI/VDO GMA Bericht l3 (1987) 102- 106. [78] Datenbuch Magne~eldhalbleite~ Siemens, 1982. [79] Borke, U. von, Cuno, H. H., Feldplatten und Hallgeneratoren, Siemens AG Verlag, 1985. [80] Weiss, H., “Feldplatten - magnetisch steuerbare Widerstande”, Elektronische Zeitschriff 17 (1965) 289-293. [81] Hennig, G., Die Feldplatte, Eigenschaften und Anwendung”, Elektronik (Munich) (1965) 225-229. [82] Heywang, W., Sensorik, Halbleiter-Elektronik 17; Heidelberg: Springer Verlag, 1984, pp. 76- 111. [83] Lippmann, H. J., Kuhrt, F., ,,Der GeometrieeinfluR auf den Hall-Effekt bei rechteckigen Halbleiterplatten“, 2. Naturforsch. 13a (1958) 462-474. [84] Wein, H., Welker, H., “Zur transversalen magnetischen Widerstandsanderung von InSb”, 2.Phys. l38 (1954) 322-329. [85] Borcke, U. von, “Feldplatten-Differentialfiihler FP 210”, Siemens Bauteile-Information 10 (1972) 129- 132. [86] Cuno, H., H., “Einfache Berechnung von Feldplattendaten in Abhangigkeit vom Magnetfeld und Temperatur”, Siemens Bauteile-Report 14 (1976) 89-93. [87] Borcke, U. von, “Feldplattenfiihler FP 212 L loo”, Bauelemente der Elektronik 9 (1977) 100-106.

96

3 Magnetogalvanic Sensors

[88] Kuhrt, F., Maaz, K., “Messung hoher Gleichstrdme mit Hallgeneratoren”, Elektrotechn. Z. 77 (1956) 487-490. [89] Heidenreich, W., Kuny, W., “Magnetfeldempfindliche Halbleiter-Positionssensoren; Anwendung, Auswahl und Beispiele, praktische Anwendungsschaltungen”, Elektronik Industrie (1985) 46-52 and 112-118. [go] Teichmann, W., Flossmann, W., “Hallgeneratoren und Feldplatten”, Elektronik (Munich), (1983) 102- 112. [91] Kuhrt, F., “New Hall generator applications”, Solid-State Electron. 9 (1966) 567-570. [92] Cohen, E., “Recent development of Hall-effect devices and applications”, Bulletin of the Electrotechnical Lab. 37, No. 10, (1973) 942-967. [93] Zabler, E.,Hintz, F., “Neue, alternative Lasungen fiir Drehzahlsensoren in Kraftfahrzeugen auf magnetoresistiver Basis”, VDI-Ber. 509 (1984) 263-268. [94] Gutter, F., “Kontaktloses Schalten mit den magnetisch gesteuerten Schaltern SAS 201 und SAS 211 in integrierter Halbleitertechnik”, Siemens Bauteile-Report I2 (1974) 39-41. [95] Lachmann, U., “SAS 231, an integrated Hall effect circuit with analog output”, Siemens Components Report XIV (1979) 225-227. [96] Databook: ICs for Industrial Applications, Siemens (1987). [97] Lachmann, U., “Funktion und Anwendung der Hall-Magnet-Gabelschranke HKZ 101”, Siemens Components 20 (1982) 73-75. [98] Krdger, G . , “Kontaktlose Gleichstrommotoren”, ATM, No. 387, (1968) 79-82. [99] Hanitsch, R., “Electronic control of small DC-machines having a permanent magnetic rotor”, JO Magn. Magn. Muter. 9 (1978) 182-187. [lo01 Huber, W., Neu, H., “Drucksensor nach dem Hall-Prinzip als Lastgeber fur elektronische Zilndanlagen”, Motortechn. Z. 47 (1986) 58-59. [loll Pettenpaul, W., Huber, J., Weidlich, H., Flossmann, W., Borcke, U. von, “GaAs Hall devices produced by local ion implantation”, Solid-State Electron. 24, No. 8, (1981) 781-786. I1021 Pettenpaul, W., Flossmann, W., Heidenreich, W., Huber, J., Borcke, U. von, Weidlich, H., “Implanted GaAs Hall devices family for analog and digital applications”, Siemens Forsch. Entwicklungsber. 11, No. 1, (1982) 22-27. [lo31 Lepkowski, T. R., Shade, G . , Kwok, S. P., Feng, M., Dickens, L. E., Laude, D. L., Schoendube, B., “A GaAs integrated Hall sensorlamplifier”, IEEE Electron Device Lett. EDL-7, No. 4, (1986) 222-224. [lo41 Personal communication with Dr. Marik, Vacuumschmelze GmbH Hanau. [lo51 Wetzel, K., Kuczynski, L., “Leistungsmessung mit Hallgeneratoren an Verbrauchern mit pulsweitenmodulierter Spannung”, Elektronik Information 3 (1986) 132-136. [lo61 Hirschmann, G., “Beriihrungslose Positionsmessung mit Hallsensoren”, Elektronik Information 3 (1986) 66-68. [lo71 ADmus, F., Boll, R., “Messungen an weichmagnetischen Werkstoffen mit dem Hall-Generator”, Elektrotechnische Zeitschrift 77, No. 8, (1956) 234-236.

4

Magnetoelastic Sensors GERHARD HINZ. Vacuumschmelze GmbH. Hanau. FRG HEINZ VOIGT. Daimler Benz AEG.Forschungsinstitut. Frankfurt. FRG

Contents 4.1 4.1.1 4.1.2 4.2 4.2.1 4.2.2 4.3 4.4 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6 4.5 4.5.1 4.5.2 4.6 4.6.1 4.6.2 4.6.3 4.6.4 4.6.5 4.7

Magnetostriction. Magnetoelastic Interaction . Principles . . . . . . . . . . . . . . . . . Theoretical Considerations . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic and Mechanical Properties of Applicable Magnetic Materials . Alloy Requirements . . . . . . . . . . . . . . . . . . . . . . . . Comparison of Crystalline and Amorphous Alloys for Sensors

. . . . .

. . . . . . . . . . . . . . . . Torque Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . Elementary Considerations . . . . . . . . . . . . . . . . . . . . . Basic Magnetoelastic Sensor Systems

Cross-Qpe and Four-Branch-Type Sensors . . . . . . . . . . . . . . Coaxial-Type Sensors . . . . . . . . . . . . . . . . . . . . . . . Realization of Magnetoelastic Components . . . . . . . . . . . . . . Alternative Torquemeter Systems . . . . . . . . . . . . . . . . . . The Influence and Compensation of Effects Superimposed on the Torque Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . Special Magnetoelastic Sensors . . . . . . . . . . . . . . . . . . . AE Effect and Ultrasonic Wave-Propagation Devices . . . . . . . . . Wiedemann Effect Devices . . . . . . . . . . . . . . . . . . . . . Shock-Stress Sensors . . . . . . . . . . . . . . . . . . . . . . .

98 98 98

102 102 104 105 106 106 108 116 120 123 126

Sensors for Forces and Displacements . . . . . . . . . Magnetoelastic Sensors for Compressive and Tensile Forces Position and Displacement Sensors . . . . . . . . . .

130 130 136

Sensors Combining Magnetostrictive Effect and Other Physical Effects Other Magnetoelastic Sensors . . . . . . . . . . . . . . . . .

141 141 143 144 145 146

References

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

. .

147

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

98

4 Magnetoelastic Sensors

4.1 Magnetostriction, Magnetoelastic Interaction 4.1.1 Principles Magnetic materials show a strong interaction between their magnetic and mechanical properties, shape and geometry. Already in the middle of the last century Joule [l] observed that the length of a ferromagnetic specimen changes as a result of magnetization. This phenomenon is known as longitudinal or shape magnetostriction (the so-called volume magnetostriction is not discussed here). About 40 years later Villari [2] described the reverse of this effect, ie, the change in the magnetic properties due to the application of mechanical stress on iron which is also connected with a change in shape. This magnetoelastic effect is the basis for magnetoelastic sensors, excluding special cases. The shape magnetostriction, I , is strongly dependent on the material. It is primarily determined by the composition of the alloy. In crystalline alloys, the direction of the individual crystalline axes varies. For cubic crystals it is customary to refer to the magnetostriction values as I , , , A1,,, I , , , analogous to the denomination of the crystalline axes [3, 41. The longitudinal magnetostriction, I , is dependent on the excitation (field strength or flux density) and attains a saturation value, I , , which is given as a material constant for a particular material; I , can be positive, negative, or close to zero. Amorphous alloys do not have crystals or crystalline axes and, as a consequence, the magnetostriction in these alloys is equal in all directions (isotropic). A quantitive description of magnetostriction and its theoretical derivation from the basic material constants is difficult. However, we wish to point out that the magnetostriction of crystalline alloys is related to the stress dependence of the crystalline anisotropy and to local stresses in amorphous metals [5, 61. A simple dynamic dipole rotation model has been developed for a single domain of a magnetostrictive amorphous metal [7]. From this model, the equation of motion for the coupled magnetization and strain modes was derived. The influence of compressive, tensile and bending stress on the magnetization process and anisotropy energy of amorphous Fe,,Ni,,(P, B)20ribbons has been studied [8] observing also domain structure using the Bitter technique. In this chapter, the magnetostriction and the magnetoelastic interaction are considered mainly from the point of view of phenomena. Depending on the sign of magnetostriction the magnetoelastic effect on the characteristic curve of a soft magnetic alloy varies with the application of compressive or tensile stress. As an example of the effect of tensile stress on materials with positive or negative magnetostriction, the hysteresis loops of crystalline 68% NiFe and pure nickel and of an Co-based amorphous alloy are presented in Figure 4-1. If pressure is applied exactly the opposite behavior is observed.

4.1.2 Theoretical Considerations In the case of magnetoelastic interactions, the conversion of the elastic energy W, into magnetic energy W, is of importance for the efficiency of the sensor [9, 101. Therefore, all

99

4.1 Magnetostriction, Magnetoelastic Interaction

1.2

1.2

T

T

0.8

0.8

1

0.4

6

i

i

0.4

8 0

0

-0.4

-0.4

-0.8

-0.8

a)

-1.2

1

I

-8

0

-4

h)

-1.2

4

Alcm

8

H-

-8

1 0

-4

4

Alcm

8

H-

1.2

T 0.8

t

0.4

B

0

-0.4

-0.8

C)

-1 - 2

-8

-4

0

H-

4

Alcm

a

Figure 4-1. Hysteresis loops under tensile stress 0. (a) Crystalline 68% NiFe, I , = + 25 . (b) crystalline pure Ni, I , = - 35 . (c) amorphous Co-based alloy, I , = - 3 3 . 10-6.

the various types of energy Wi which are significant in a magnetic material should be explained: W,

=

magnetic field energy, which is proportional to the product of field strength and polarization

100

4 Magnetoelastic Sensors

W, = elastic stress energy, which is linked to the magnetostriction I W, = crystalline energy (in crystalline materials), which is heavily dependent on the material; W, does not exist in amorphous materials W, = uniaxial anisotropy energy, which arises, eg, during magnetic field annealing in crystalline and amorphous materials W, = shape anisotropy energy (dependent on the demagnetization factor, N ) .

Let us consider the ratio of stored mechanical energy, W,, to the total stored energy, W i , which determines the magnetomechanical coupling factor K33:

wc7 -K3, = -

c wi

w, w, + w,+ w, + w, +

WN

(4-1)

In order to achieve a large magnetomechanical coupling factor K 3 3 , which should approach to unity, the energy terms W,, W,, W,, and WNmust be small, ie, a soft magnetic material is required with W, and W,, + 0. Moreover, W, should be as small as possible, which is achieved by the selection of the specimen shape. In this case Equation (4-1) is simplified to:

When these conditions are fulfilled, a simple relationship is obtained for an alloy with negative magnetostriction between the mechanical stress 0 applied to a strip and the relative permeability ,ur. Using

and

Equation (4-2) can be transformed after minimizing the total energy into the following relationship [lo]: 0=-.1 PI

Jf 31, * P o

where

J,

=

saturation polarization

,uo = magnetic constant

v, = angle between magnetization and specimen axis

or

(4-5)

4.1 Magnetostriction, Magnetoelastic Interaction

101

where

E = Young’s modulus E = strain. Figure 4-2 shows the magnetization curve of a material in which the above mentioned conditions are completely fulfilled. In this ideal case the permeability, p,, decreases inversely proportional to the tensile stress, 0, and the strain, E . J A

Figure 4-2. Calculated magnetization curves under stress, see Equation (4-6).

I

u=O

material with

As an experimental verification of the calculation with Equation (4-6) Figure 4-3 shows the modification of the magnetization curve of an amorphous alloy strip (composition Co,,Si,,B,,) under tensile load [ll].

r 1.0

-

102

4 Magnetoelastic Sensors

A very high longitudinal magnetomechanical coupling factor K3, of up to 0.95 was reported for amorphous Fe,,(B, Si, C)19 [12], which agrees with a A E effect of 10%. The general relationship is

4.2 Magnetic and Mechanical Properties of Applicable Magnetic Materials As a rule, the magnetic properties of magnetic alloys are of prime importance whereas the mechanical behavior plays a subsidiary role. The exceptions concern applications where hardness, tensile strength and wear resistance are important. Magnetically soft alloys are usually also mechanically soft, soft iron being a typical example. In contrast magnetically hard alloys are mechanically hard, eg, AlNiCo. Magnetoelastic sensors require alloys which combine magnetic softness with mechanical hardness or strength. When considering the known crystalline alloys, for instance the soft magnetic nickel-iron alloys, it soon becomes clear that this combination is possible to only a very limited extent. The tensile strength of nickel-iron alloys is low, and consequently the range of elastic load range is small. On the other hand, a closer look at constructional steels reveals only very moderate magnetic properties in combination with acceptable mechanical properties. Therefore, with classical alloys a compromise always has to be made [lo]. A novel combination of magnetic and mechanical properties is provided by amorphous alloys, which fulfil the above-mentioned specifications in an almost ideal manner, in particular, they are magnetically soft and mechanically hard [13- 161.

4.2.1 Alloy Requirements The requirements on materials for magnetoelastic sensors can be outlined as follows: a) Magnetical. - easily magnetizable, ie, low coercivity H, - high saturation polarization J, - adequate and defined magnetostriction A,. It is important that the ratio dA/dH and dUdB be large, ie, the magnetostriction should vary strongly as a function of the field strength or the induction. b) Mechanical. - high Vickers hardness, HV - high yield strength, R , .

103

4.2 Magnetic and Mechanical Properties of Applicable Magnetic Materials

Table 4-1 gives a survey of the crystalline and amorphous soft magnetic alloys which are suitable for magnetoelastic sensors. The alloys are graded according to the level of magnetostriction [15-171. Table 4-1. Materials for magnetoelastic sensors. Type

A,

Alloy

*

Crystalline

50 Co, 50 Fe 50 Ni, 50Fe 97 Fe, 3 Si 77 Ni, 15 Fe, Mo + Cu 77 Ni, 15 Fe, Mo + Cu +Ti + Nb Spring steel 1.8159 Shaft steel CK 45 Ni

+ 70 + 25 +9 +1

- 0.5 -1 - 35

Hc A/cm

1.4 0.05 0.1 0.01

I .5

-

0.04 0.03 0.003 0.025

Crystalline

+ 2000

50

')

2,

3,

(Tb Dy) Fe,

2,

+8 0.2 -3.5 -8

2.35 1.55 2.0 0.8 0.5 2.1 -2.1 0.6

+ 30

E kN/mm2

200 110 180 100

400 140 350 150

230 140 150 200

220 550

500 1500 450 120

200

T

0.025 15 10 1.5

Amorphous I ) Fe,, B,, Si, Fe,, Ni,, (Mo, Si, B)22 (Co, Fe, Mo)73 (B, Si)27 c075 Sil, B,, Co,, Nil, B,, Si,

R, N/mm2

HV

J,

75

210

0.8 0.55 0.7 0.85 1 .o

460

7003)

30

Examples for trade names of amorphous metals are: METGLAS (Allied Signal Inc.) and VITROVAC (Vacuumschmelze GmbH). New type of rare earth alloy with giant magnetostriction for special sensors and actuators [23]. Compressive strength.

Table 4-1 starts with the crystalline material 50% cobalt-iron, which not only exhibits the highest saturation polarization but also the highest saturation magnetostriction, with I , = +70 however, the magnetic softness is only average. The most commonly used soft magnetic material is silicon-iron with 3 % Si, which also has relatively favorable mechanical properties. Nickel-iron alloys which fall into the category of very soft magnetic materials possess I , with 50% Ni and f 1 values, depending on the Ni content of between +25 for alloys with ca. 77% Ni. However, these alloys are mechanically relatively soft. A pronounced increase in hardness and yield strength of 77% NiFe without a noticeable decrease in the magnetic softness (coercivity and permeability) is attained with precipitation hardening additions such as Ti and Nb. Steels, eg, spring steels or constructional steels, have low magnetostriction values and favorable mechanical properties, but with regard to magnetic softness they are on the boundary between soft magnetic and magnetically semi-hard materials [18]. Pure nickel has a high negative magnetostriction, but as a bulk material it is mechanically very soft. In comparison, sputtered Ni layers are harder. In the family of amorphous alloys which have a n isotropic magnetostriction - a result of their non-crystalline structure - the iron-rich alloys have excellent I , values with good

104

4 Magnetoelastic Sensors

magnetic softness and a high yield strength. In the group of amorphous nickel-iron alloys, depending on the composition, the magnetostriction is average (ca. + 5 10 -6 to +10 . Co-rich alloys with ca. 60 at% Co exhibit lower I , values, in the range k 1 . 10 - 6 . In certain Co-rich alloys the magnetostriction may assume negligibly low values ( I , < 0.1 . 10 -6). A further increase in the Co content leads to negative I , values. All amorphous alloys have hardness values and yield strengths which exceed those of crystalline alloys by several orders of magnitude. It follows that these materials appear to be particularly suitable for magnetoelastic sensors when there are no constructional arguments against their use. However, it should be pointed out that amorphous alloys can only be produced as thin strip (ca. 0.05 mm) and not as solid material or with greater thicknesses. To complete the picture, it should be mentioned that the soft magnetic oxides (ferrites) also exhibit magnetostriction which, in this instance, is also heavily dependent on composition as for for metals and alloys [19, 201. For MnZn ferrites I , is in the range -0.5 to +0.5 NiZn ferrites I , is in the range -1.5 to -10 But there are special ferrites with higher magnetostriction. Giant magnetostrictive alloys are based on rare earth metals such as Tb and Dy [23, 241. They form a new group of materials for special applications.

-

-

4.2.2 Comparison of Crystalline and Amorphous Alloys for Sensors The differences between crystalline and amorphous metals, in particular the mechanical properties, will be discussed in more detail later. The stress-strain curves show extreme dif-

soft magnetic, amorphous ICo based alloy)

/--

spring material, non- magnetic

(Cu Be 2 )

b

7 7 '10 NiFe, hardenable) ........(... .,.................* ***...*.*.*.*

soft magnetic, crystalline --__-__--------------( 7 7 O / 0 NiFe)

-0

I

2 strain .c-

41a

3

Figure 4-4. Stress-strain curves of several materials.

105

4.3 Basic Magnetoelastic Sensor Systems

ferences (Figure 4-4). While amorphous alloys have an almost ideally straight characteristic curve which is even superior to that of (non-magnetic) spring alloys, very slight stress gives rise to plastic flow in crystalline alloys. The tensile strength and yield strength are almost identical in amorphous alloys, and there is no plastic flow. For amorphous alloys elastic strains of up to and over 1% are feasible, for crystalline metals 0.1% is hardly possible. If the coercivity is taken as a measure of magnetic softness versus mechanical hardness, we obtain Figure 4-5. A factor in the range of 5 to 10 separates amorphous and crystalline alloys exhibiting the same coercivity [21, 221.

1oou

-

Fe- alloys Co-a 11oys

amorphous materials 800

1

600

HV

400

200

age-hardenable Fe-77 % N i

-

crystalline materials

-

high purity iron

Fe-77 % ~i

I

Em

Fe-Co

177777771 I

4.3 Basic Magnetoelastic Sensor Systems If we consider the principles of the construction and design of magnetoelastic sensors, three basic systems can be described based on the Villari effect: a. systems with a predefined magnetic flux path where the inductance or permeability is changed by mechanical loading in one direction (“one-dimensional”) b. systems with a flux configuration which changes in two directions but in one plane due to loading (“two-dimensional”) c. systems where the flux configuration is spatially and vectorially changed by the applied load. Figure 4-6 shows sensors of these three types [lo]. For some general information see also [25]. A review on basic principles of amorphous sensor constitutions is represented in [26].

106

4 Magnetoelastic Sensors

IF sensor type

3

1

process variable flux configuration

impresslor tension

bending

I

I

1 - dimensional

5

4

tors ion

compression

1

2- or 3-dimensional

I

Figure 4-6. Principles of magnetoelastic sensors. F Force, T torque.

Simple magnetoelastic force sensors (1) and (2) belong to type (a). They consist either of a single strip or of a pot-core like design. They operate as chokes or coils, their inductance changes being used to indicate the load. Examples of type (b) are circular rings (3) or laminated core packages for load cells (4). In both designs the load can be compressive or tensile stress. The ring (3) is deformed to an ellipse. The core package of an isotropic magnetic material becomes magnetically anisotropic under stress because the core is deformed to a different longitudinal and transversal degree to the load axis. A change in the inductance of the ring or the voltage in the secondary winding of the core indicates the load. Type (c) as a three-dimensional system is realized in torque transducers of shafts (5). The torque changes the permeability of the shaft surface or of a surface layer. The permeability in this instance must be considered as a tensor quantity. Its change can be detected either by cross-type chokes or by cylindrical coils around the shaft.

4.4 Torque Sensors 4.4.1

Elementary Considerations

Measurements of the torque on shafts with the aid of the magnetostrictive effect utilize the dependence, as described in Section 4.1, of the magnetic properties of the shaft material itself or of an additional magnetic coating on the shaft surface on the mechanical stresses arising in the shaft. Therefore we are dealing with indirect measurement of the torque because the effect of the torque on the mechanical stresses arising on the surface of the shaft must be known.

4.4

Torque Sensors

107

In the pure torsion of a cylindrical solid or hollow shaft two principal orthogonal directions of stress arise, ie, compressive and tensile stress. These run in screw-like lines around the shafts, and each forming an angle of f 45 O with the shaft axis [27] (Figure 4-7). The calculation of the principal stresses t at the surface due to a moment of torque T [28] is based on Hooke's law and is expressed as

where t

=

y

= = = = =

G a,

I r

shear stress shear strain shear modulus angle of torsion length radius of shaft

/

,

/

Figure 4-7.

Explanation for calculation of torque on a shaft.

F

In the general case of a hollow shaft with inner and outer diameter d, and do respectively the (radius dependent) torque and shear stress are obtained by the integration of T ( r ) . r . dA (with T = torque, proportional to A = area):

I 'i

'i

Gap - -.-

I

7~

2

(r: - r4)

(4-9)

Gap t d and with -= - and r = - we obtain: I r 2

5 =

32 * T 7~ (d: - d?)

.r.

(4-10)

108

4 Magnetoelastic Sensors

The maximum stress om on the surface of the shaft is (4-11) The relevant maximum strain

E,

defined by (4-12)

(4-13)

where v = Poisson ratio E = Young’s modulus. The complex path of stress and strain on the shaft surface (see Figure 4-8) results, in practice, in equally complicated coil arrangements which can pick up the magnetoelastic interactions. For constructional reasons, it is almost impossible to mount detector coils so that they are capable of directly picking up the changes in amplitude of the permeability in the particularly sensitive principal directions of stress according to Equation (4-6). As described in detail in the following Sections 4.4.2 and 4.4.3 for symmetrical reasons coil arrangements are 45 O to the main directions of selected which permit both the field input and detection in stress. This can be performed successfully with “crossed” yoke coils (Section 4.4.2) or with cylindrical coils (Section 4.4.3) mounted coaxially to the shaft.

*

(T R,/L, the second term causes a frequency independent noise density as shown in Figure 6-28 at (w/w,) = 1. Thus, to make this type of a sensor as quiet as the one with the high impedance amplifier it is a case of matching the induction coil and the amplifier. For the third kind of induction coil sensor, with a transformer coupled negative feedback to the induction coil on a high permeability core, one additional noise source, compared to those shown in Figure 6-28, contributes to the total noise. It is calculated in [38] and the result is shown in principle comparable to that shown in Figure 6-28. Since the frequency response of the sensor output voltage or of the sensitivity does not show a resonance step-up, the damping resistor R,,can be either very large or completely omitted, and the noise equivalent = 1. magnetic field then becomes very low at frequencies (w/w,)

6.5

Applications

There are many different applications of induction coils with air and high permeability cores, and an accordingly large variety of specific designs, described in the literature. Not always the term induction coil sensor is used according to the definition given in the introduction. Sometimes, for example, magnetic field probes are called induction coil sensors when the field to be measured causes a change in the self-inductance of the coil. Among the well-known applications are the control of traffic lights by waiting cars, the magnetic doors in airport buildings, and nondestructive testing of conducting workpieces. These sensors are excluded here by definition. An extension of these sensors, however, leads to forms with two coils, where small changes of the mutual coupling inductance between them is measured. Their functioning principle, in turn, is comparable to the operation of an induction coil sensor (receiving coil) measuring an artificial magnetic field (generated by the transmitting coil). Both types of active measuring devices are widely used in geological prospecting. In the following, a short survey of applications of sensors with stationary induction coils is given, together with some comments on the most typical requirements and properties. In-

6.5 Applications

241

teresting and important applications of sensors with moving coils can be found in the literature cited in review articles [39-411. Several kinds of such sensors have also been applied in geophysics [42, 431, where those with rotating coils are the most significant types. They are suited for measuring very accurately the direction of the earth’s magnetic field and can be advantageously used to determine small inhomogeneities and field gradients. A modern standard application is the precise testing of the quality of multipole magnetic fields in nuclear physics. Since induction coil sensors are preferably used in scientific research, the definition of the measuring task and the necessary development of related sensors with specific properties were often established at the same time (or even in a reversed order) and a broad variety of industrially fabricated sensors is not available in the market. By far the most numerous applications of induction coil sensors can be found in the field of geophysics. With the measurement of waveforms of magnetic field fluctuations and/or of the spectral density functions of magnetic noise, and by recording their variations in time and space, naturally ocurring physical phenomena can be identified. The measuring ranges, if not regarded as unlimited, may be characterized by the amplitude limits and T and the frequencies and lo5 Hz. Since the early beginning of geomagnetic observations micropulsations have been investigated. These are often near harmonic oscillations of the earth’s magnetic field, lasting for many periods and with spectral energy concentrations at certain frequencies between and about 1 Hz. For measurements on ground air-cored coils and two- or three-axis coil systems up to many meters in diameter have been used. Highly sensitive low-frequency induction coil sensors with long high permeability cores are more easily to transport and, therefore, utilized at many geomagnetic observatories. Besides the AC magnetic fields of the comparatively strong micropulsations a background continuum of magnetic noise of many natural sources induces currents in the conducting earth’s surface with the associated secondary magnetic and electric fields. From measurements of related H and E field components the magnetotelluric exploration method determines the electrical conductivity distribution in the subsurface. Preferably, induction coil sensors with high permeability cores are used here. In the last years the audio-frequency magnetotelluric exploration at higher frequencies became more and more important and is now the domain of induction coil sensor applications. Some details of sensors used for the above purposes are given in Table 6-1. Magnetotelluric measurements, using the above mentioned active devices, are also performed on ground, in boreholes, and on the ocean floor. The magnetic fields are sensed during or after their artificial excitement. This does not change the requirements to the sensors drastically. But their response is exactly defined in time and/or frequency, which leads to a considerably higher sensitivity of the measurements. The need for the development of low-noise and highly sensitive sensors with volumes and weights of typically less than 1 dm and 1 kg, respectively, came from their accomodation on many spacecrafts [l]. With these sensors the temporal and/or spatial fine structure of the earth’s outer magnetic field or of the interplanetary magnetic field has been investigated followed by the identification of a large variety of electromagnetic waves in the earth’s magnetosphere and in the solar wind plasma. Some details of such recently used sensors are listed in Table 6-2. Induction coil sensors have also been used for biomagnetic measurements. The magnetic fields of the human heart and brain have been discovered with their aid. The necessary

I

2

. 105 5.6 . 10' 3 .1 0 ~

5 . IOS/AWG36

I

Mumetal

annealed Permalloy

material

150

x 3.5 $

180 x 2.5

length x diameter

Cnre

Metronix 878

-

ferrite

ferrite frame (2 components)

2372/AWG 14

too00

laminated Mumental

45 OOO/AWG 3 1

90 x 2.2 $

36 x 36 x 3.8/1.8

60 x 1.6 $

120 x2.3 $

183 x 2.5 $

I

0.7 mV/(nT.Hz)

Coil sensitivity

I 8.6 pV/(nT.Hz)

23 pV/(nT. Hz)

2.6 mV/(nT. Hz)

transformer output; f, = 1.3 kHz

current amplification

;lf

1

[491

[481

mation source

I I Hz.. .20 kHz

0.2 Hz.. . = l0kHz

0.0006.. .10 Hz

0.001.. . 2 Hz

0.001.. .I0 Hz

feedback

1 quant. step

Remarks

t

0.001...10Hz

Frequency range

A great number of similar applications of induction coil sensors are reported in the more recent literature, but normally the technical details of sensors are missing.

1

Metronix 879

1 1

2~

S

v

U

1

laminated Mumetal

1 ~ ~ laminated ~ 2 2 Moly-permalloy

fi --t

3

3

L'Aquila, Italy

-

3

ponents

I Number of1

Siple, Antarctica

Manufacturer/Type

AudioUniversity of Magnetotellurics California

Magnetotellurics

I

Or

1 Observation

Induction coil sensors with high permeability cores used for micropulsation, magnetotelluric, and audio-magnetotelluric measurements.

Micropulsations

Application

Table 6-1.

I

2

GALILEO Jupiter Atmospheric Probe (Lightning and Radio Emission Detector)

ULYSSES (Radio and Plasma Wave Experiment)

275

3o0x5@

2000/140 pm

1500/60 pm

5 $

...100 kHz

10.. SO0 Hz

D,I

1...50 kHz

10 Hz.. .3.5 kHz

70 Hz.. .2.8 kHz

10kHz.. .2MHz

260 x I I

266

laminated high-p material

~~

20 Hz.. .60 kHz

0,I.. ,400 kHz

1 Hz.. . I kHz

260x l l @

frame 800 x 1250

400

0.18 pV/(nT- Hz)

threshold 5 pT

13 pV/(nT-Hz)

Hz

. .So0

394 x 4.8 $

~~

6 pV/(nT. Hz)

3.5 pV/(nT. Hz)

5 Hz.. .2.2 kHz

Coil sensitivity

...10 kHz

S

Frequency range

410

350(320) x 6

length x diameter [mml

50OOO/70 pm

ferrite

ferrite

Sakigake/MST 5 (Plasma Wave Probe)

GALILEO Jupiter Orbiter (Plasma Wave Investigation)

ferrite

(Plasma Wave Instrument) 105

laminated Mumetal

Core

AMITE

I /aluminiumtube

(Plasma Wave Instrument)

nickle-iron

8OOOO/AWG47 laminated high-p material air-core

Mumetal

bundle of 0.2 $ Mumetal wires

material

loo00

60000/50 pm

Coil (turns/wire)

5oOO/AWG40

I

I

3

Number of measuring :omponents

Dynamic Explorer A

~

ISEE 3 (as above)

ISEE 1 (2) (Plasma Wave Investigation)

HELIOS A and B (AC Magnetometer)

Spacecraft (Experiment)

Table 6-2. Examples of induction coil sensors on spacecraft.

flux feedback

flux feedback

matching transformer

Remarks

Information source

250

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

utilizable sensitivity is still higher than in geophysical applications, but the measuring ranges are less extended in amplitude and frequency and range approximately from 10 - I 4 to 10 T and from 0.1 to 500 Hz, respectively. Here, the superconducting SQUIDS are successful competitors (see Chapter 10). For measurements at such low levels in amplitude, a trade-off between spatial resolution (limited by sensor size) and sensitivity can become a problem and the application of very expensive magnetic shielding is often necessary. Some important applications demonstrate the utility of low-frequency magnetic fields for information transmission, where the applied transmitting loops and receiving antennas are built similar to induction coils. Many railway traffic safety systems depend on the simple and reliable functioning of these devices. Some of them indicate only the passing of a train, others additionally enable a speed measurement and offer a bidirectional communication between train and stations. Moreover, a traffic guidance system for motor-cars on freeways is under investigation, using similar transmission devices. Further examples are the pick-up coils in hearing aids, which directly receive the audio-frequency field generated by loops in the floors of conferencerooms, concert halls, classrooms, churches, etc. The signal-to-noise ratio during operation replaces the amplitude measuring range in these applications. Induction coil sensors are often called magnetic antennas, since they receive the magnetic component of electromagnetic waves. There is no difference in principle as long as they are designed for use at low frequencies. In the increasingly important field of “Electromagnetic Compatibility” the magnetic antennas used for measuring the “radiated” emissions of electronic modules or equipment are actually induction coil sensors picking-up induced magnetic fields. Jaw-type probes, eg, induction coils on slotted ferrite ring cores, d o the same when measuring the “conducted” emissions o n the associated cables. True applications of magnetic antennas include: the long solenoidal induction coils on a high permeability core proposed for reception on submerged submarines, and the low-frequency loop or ferrite antennas for direction finders in navigation systems of for field-intensity meters. The induction coils used as magnetic field sensors or magnetic antennas in the various and very diversified applications described above, have been specially designed for suitable measuring ranges and, if necessary, according to the results of optimization theories. Here the design and realization of the sensors was independent of certain basic technological developments, if one disregards the manufacturing of improved soft magnetic high permeability materials and low noise integrated amplifiers. In relation to induction coil sensors, therefore, a general trend of future development parallel to technological progress on certain areas cannot be seen clearly. But, without doubt, occasionally sensors with a further increased sensitivity and an improved signal-to-noise ratio will be required. A noise reduction by only one order of magnitude without extending volume and weight already seems to be unattainable, but could possibly, at least partly, be realized using 1. further improved soft magnetic materials with a high material permeability, even under premagnetization and in a wide temperature range, 2. materials having a small Barkhausen noise, which so far has often been considered as negligibly small and unneccessary to be investigated, 3. high permeability cores of special geometrical shapes, eg, allowing miniaturized coils with a small thermal noise, and 4. electronic amplifiers having a low input noise voltage as well as a low noise current and, at the same time, a small input capacitance. Recently developed amplifiers have an input noise voltage density of less than 1 nV/I/Hz (if bipolar transistors are used) and a noise cur-

-’

6.6 References

251

rent density of less than 1 f A / m (in case of field effect transistors at the input). A matching of the sensor coils to these extreme values normally causes difficulties. 5 . The use o f correlation techniques in order to extract a signal from the embedding noise is customary. The application of two identical smaller sensors instead of a single bulky one, and a cross-correlation of their output signals, has been proposed for magnetic field measurements on spacecraft [44]. In connection with that, the question can be posed and more generally be investigated, what improvement in both signal-to-noise ratio and bandwidth could be gained, if one bulky sensor would be replaced by an array of smaller sensors with the same total weight. The multiple sensors, of course, must be decoupled from each other and, would thus require much more space.

6.6 References (11 Ness, N. F., “Magnetometers for Space Research”, Space Sci. Rev. 11 (1970) 459-554. 121 Sonett, C. P., “The distant geomagnetic field; 2: modulation of a spinning coil emf by magnetic signals”, J Geophys. Res. 68 (1963) 1229-1232. [3] Brown, F. W., Sweer, J. H., “The flux ball: A test coil for point measurements of inhomogeneous magnetic fields”, Rev. Sci. Instr. 16 (1945) 276-279. [4] Lindsay, J. E., “Wide-band E/H field sensing probes: A discussion of probe interactions and coupling problems. A model for the analysis of the loop antenna”, Report E-19 of the PhysikalischTechnische Bundesanstalt, Braunschweig, Fed. Rep. Germany, 1981. [5] Blackett, P. M. S., “A negative experiment relating to magnetism and the earth’s rotation”, Phil. Trans. Royal Society of London. Series A-Mathem. and Phys. Sciences (App. 3) 245 (1952) 309-370. [6] Campbell, W. H., “Induction loop antennas for geomagnetic field variation measurements”, ESSA Techn. Rep. ERL 123-ESL 6, Envinronmental Science Service Administration Earth Sciences Labs., Boulder, COL., USA, 1969. [7] Macintyre, S. A., “A portable low noise low frequency three-axes search coil magnetometer”, IEEE Trans. on Magnetics MAG-16 (1980) 761-763. [8] Terman, F. E., Radio Engineers’ Handbook, New York: Mc Graw-Hill, 1943, p. 52ff. [9] Welsby, V. G., The Theory and Design of Inductance Coils, London: MacDonald, 1960, p. 42ff. [lo] Terman, F. E., Radio Engineers’ Handbook, New York: Mc Graw-Hill, 1943, p. 77. [Ill Welsby, V. G., The Theory and Design of Inductance Coils, London: MacDonald, 1960, p. 148. [12] Hak, J., Eisenlose Drosselspulen, Leipzig: K. F. Koehler, 1937, p.145. (131 Terman, F. E., Radio Engineers’ Handbook, New York: Mc Graw-Hill, 1943, p. 101. [14] Selzer, E., “Determination experimentale du champ d’un cylindre d’alliage permeable, suppose place dans un champ magnktique uniforme, parall6lement a son axe de revolution”, Ann. Geophys. 12 (1956) 144-146. [15] Ueda, H., Watanabe, T., “Linearity of ferromagnetic core solenoids used as magnetic sensors”, J Geomagn. Geoelectr. 32 (1980) 285-295. [la] Russell, R. D., Watanabe, T., “A Proposal for a Bridge Method for the Calibration of Geomagnetic Sensors”, J. Geomag. Geoelectr. 32 (1980) 155-170. [I71 Zambresky, L. F., et al., “A New Method to Calibrate Induction Magnetometers”, J Geomag. Geoelectr. 32 (1980) 47-56. [18] Hayashi, K., et al., “Absolute Sensitivity of a High-p Metal Core Solenoid as a Magnetic Sensor”, J Geomag. Geoelectr. 30 (1978) 619-630.

252

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

[19] Warmuth, K., “Uber den ballistischen Entmagnetisierungsfaktor zylindrischer Stabe”,. Arch. $ Elektrotechnik 41 (1954) 242-257. [20] Bozorth, R. M., Chapin, D. M., “Demagnetization Factors of Rods”, J. Appl. Phys. 13 (1942) 320-326. [21] Wiese, H., et al., “Geomagnetische Instrumente und M e h e t h o d e n ” , in: Geomagnetismus und Aeronomie, Vol. 2, Fanselau, G. (ed.); Berlin: VEB Deutscher Verlag d. Wissenschaften, 1960, p. 358. [22] Whitham, K., “Measurement of the Geomagnetic Elements”, in: Methods and Techniques in Geophysics, Vol. 1, Runcorn, S. K. (ed.); London: Interscience Publishers, 1966, p. 134. [23] Richter, W., “Induktionsmagnetometer fur biomagnetische Felder”, Experimentelle Technik d. Phpik 27 (1979) 235-243. [24] Hill, L. K., Bostick, F. X., Micropulsation sensors with laminated mumetal cores, Report No. 126, Electr, Engineering Res. Lab., The University of Texas, Austin, TX, USA, 1962. [25] Meinke, H., Gundlach, F, W., Taschenbuch der Hochfreguenztechnik Heidelberg: Springer-Verlag, 1968, pp. 17-32. [26] Cerulli-Irelli, P., Progretto e ottimizzazione di un magnetometro ad induzione, Rep. LPS 71-2, Lab. di Ricerca e Technologica per lo Studio del Plasma nello Spazio, CNDR Roma, Italy, 1971. [27] Lukoschus, D. G., “Optimization theory for induction-coil magnetometers at higher frequencies”, IEEE Trans. Geoscience Electronics GE-17 (1979) 56-63. [28] Onishi, N., Kato, Y.,“Characteristics of the Induction Magnetometer with a High Permeability Cylindrical Metal Core”, in: Proc. Fac. Engineering Tokai University, Tokai, Japan, 1976, No. 1, pp. 171-176. [29] Saito, T., et al., “Development of new time-derivative magnetometers to be installed on spacecraft”, Bull. Inst. Space Aeronaut. Science Llniv. Tokyo, B 16 (1980) 1419-1430. [30] Ueda, H., Watanabe, T., “Comments on the Anti-Resonance Method to Measure the Circuit Constant of a Coil Used as a Sensor of an Induction Magnetometer”, Sci. Rep. Tohoku University, Series 5, Geophysics, 22 (1975) 129-135. [31] Porstendorfer, G., “Magnetotellurische Untersuchungen unter Verwendung hochpermeabler Spulen”, Freiberger Forschungshefte C174 (1965) 91 - 108. [32] Thellier, E., “EnquCte sur les appareils enregistreurs des variations rapides du champ magnktique terrestre” Ann. Intern. Geophys. Year 4 (1957/58) 255-280. [33] Wiese, H., et al., “Geomagnetische Instrumente und M e h e t h o d e n ” , in: Geomagnetismus und Aeronomie, Vol. 2, Fanselau, G. (ed.); Berlin: VEB Deutscher Verlag d. Wissenschaften, 1960, p. 352ff. [341 Whitham, K., “Measurement of the Geomagnetic Elements”, in: Methods and Techniques in Geophysics, Vol. 1, Runcorn, S. K. (ed.); London: Interscience Publishers, 1966, p. 130. [35] Lokken, J. E., “Instrumentation for receiving electromagnetic noise below 3000 cp/s”, in: Natural Electromagnetic Phenomena below 30 kch, Bleil, D. F. (ed.); New York: Plenum Press, 1964, p. 404ff. [36] Schmidt, H., Auster, V., “Neuere M e h e t h o d e n der Geomagnetik”, in: Handbuch der Physik, Vol. 4913, Flugge (ed.); Heidelberg: Springer, 1971, p. 342ff. [37] Clerc, G., Gilbert, D., “La contre-reaction de flux appliquee aux bobines a noyau magnktique utilisee pour l’enregistrement des varations rapides du champ magnetique“, Ann. Gdophys. 20 (1964) 499-502. [381 Micheel, H. J., “Induktionsspulen mit induktiver Gegenkopplung als hochauflosende Magnetfeldsonden”, ntz archiv 9 (1987) 97-102. [39] Gordon, D. I., “Methods for Measuring the Magnetic Field”, IEEE Trans. Magnetics MAG4 (1972) 48-51. [401 Trenkler, G., “Verfahren zur elektrischen Messung magnetischer Felder (Teil 1)”, messen + prufen (1972) 535-538, 797.

6.6 References

253

[41] Germain, C., “Bibliographical Review of the Methods of Measuring Magnetic Fields”, Nuclear Znstr. and Methods 21 (1963) 17-46. [42] Wiese, H., et al., “Geomagnetische Instrumente und Mehethoden”, in: Geomagnetismus und Aeronomie Vol. 2, G. Fanselau (ed.); Berlin: VEB Deutscher Verlag der Wissenschaften, 1960, pp. 308-361. [43] Whitham, K., “Measurement of the Geomagnetic Elements”, in: Methods and Techniques in Geophysics, S. K. Runcorn (ed.); London: Interscience Publishers Inc., 1960, pp. 127-135. [44] Anav, A., et a]., “A Correlation Method for Measurement of Variable Magnetic Fields”, ZEEE Trans. Geoscience Electronics GE-14 (1976) 106- 114. [45] Taylor, W. W. L. et al., “Initial Results from the Search Coil Magnetometer at Siple, Antarctica”, J. Geophys. Res. 80 (1975) 4762-4769. [46] Cantarano, S., et al., “A Facility for Measuring Geomagnetic Micropulsation at CAquila, Italy”, ZI Nuovo Cimento 6C (1983) 40-48. [47] Benderitter, Y., le Donche, L., “Contribution a L’Etude des Capteurs Magnttique a Induction pour la prospection Magneto-Tellurique”, Rev. Physique Appliqut!e 5 (1970) 183- 185. [48] Vozoff, K., “The Magnetotelluric Method in the Exploration of Sedimentary Basins” Geophysics 37 (1972) 98-141. [49] Catalog of Geophysical Instruments and Services, 1987, Metronix and Geometra, Braunschweig, FRG. [50] Labson, V. F., “Geophysical Exploration with Audio-Frequency Natural Magnetic Fields” Geophysics 50 (1985) 656-664. [51] Dehmel, G., et al., “Das Induktionsspulen-Magnetometer-Experiment(E4)”, Raumfahrtforschung l9 (1975) 241-44. [52] Gurnett, D. A., et al., “The ISEE-1 and ISEE-2 Plasma Wave Investigation”, ZEEE Trans. Geoscience Electronics GE-16(1978) 225-230. [53] Scarf, F. L., et al., “The ISEE-C Plasma Wave Investigation”, ZEEE Trans. Geoscience Electronics GE16 (1978) 191-195. [54] Shawhan, S. D., et al., “The Plasma Wave and Quasi-Static Electric Field Instrument (PWI) for Dynamics Explorer-A”, Space Science Instrumentation 5 (1981) 535-550. [55] HBusler, B., et al., “The Plasma Wave Instrument on Board the AMPTE IRM Satellite”, ZEEE Trans. Geoscience and Remote Sensing GE-23 (1985) 267-273. [56] Hirao, K., “The SuiseiBakigake (Planet-A/MS-T5) Missions”, ESA SP-1066 (1986). [57] Yeates, C. M., et al., GALZLEO: Exploration of Jupiters System NASA SP-479, 1985, NASA, Washington, DC, USA. [58] Stone, R. G., et al., The ZSPM Unnifed Radio and Plasma Wave Experiment, ESA SP-1050, 1983, ESA.

7

Inductive and Eddy Current Sensors WALTER DECKER.PETER KOSTKA. VDO Adolf Schindling AG Schwalbach. FRG

Contents 7.1 7.2 7.2.1

. . . . . . . . . . . . . . . . . . . . . . . . . . Sensors Excited by Permanent Magnets . . . . . . . . . . . . . . .

Introduction

257 257

7.2.1.1 7.2.1.2 7.2.1.3 7.2.2 7.2.2.1 7.2.2.2 7.2.3 7.2.3.1 7.2.3.2 7.2.3.3

Variable Reluctance Sensors with Fixed Permanent Magnets (Magnetic Pickups) . . . . . . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . . Variable Reluctance Sensors with Moving Permanent Magnets . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Tachometer Generators with Permanent Magnets . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . .

257 257 260 261 264 264 266 266 266 267 268

7.3 7.3.1 7.3.1.1 7.3.1.2 7.3.1.3 7.3.2 7.3.2.1 7.3.2.2 7.3.2.3 7.3.3 7.3.3.1 7.3.3.2 7.3.3.3

AC-Excited Sensors for Linear Movement . . . . . . . . . . . . . . Linear Variable Differential Transformers . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . . Variable Inductance Sensors/Variable Leakage Path (VLP) Sensors . . . Physical Principle and Construction . . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . . Variable Gap Sensors/Differential Cross-Anchor Sensors . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . .

269 269 269 275 277 278 278 280 282 283 283 287 287

7.4 7.4.1 7.4.1.1 7.4.1.2 7.4.2 7.4.2.1

AC-Excited Sensors for Rotary Movements . . . . Synchros . . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . Applications and Properties . . . . . . . . . . . Resolvers . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . .

287 287 287 288 293 293

. . . . . . . . . .

......... . . . . . . . . . . ......... . . . . . . . . . . . . . . . . . . .

256

7 Inductive and Eddy Current Sensors

7.4.2.2 7.4.3 7.4.3.1 7.4.3.2 7.4.3.3

Applications and Properties . . . . . . . . . . . . . . . . . . Inductosyns . . . . . . . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . .

7.5 7.5.1 7.5.1.1 7.5.1.2 7.5.2 7.5.2.1 7.5.2.2 7.6 7.6.1 7.6.2 7.6.3 7.7 7.8 7.9 7.10

.. .. . . . . . . . Eddy Current Sensors . . . . . . . . . . . . . . . . . . . . . . Eddy Current Tachometer . . . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Proximity Sensors . . . . . . . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Inductive Flowmeters . . . . . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . . Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noise of Inductive Sensors . . . . . . . . . . . . . . . . . . . . . Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

.

. .

294 295 295 296 297 297 299 299 300 300 300 304 304 304 306 306 307 308 309 31 1

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

7.2 Sensors Excited by Permanent Magnets

257

7.1 Introduction This chapter describes different types of sensors based on Faraday’s law of induction : inductive sensors, which use the effect of voltage induction, and eddy current sensors, based on the induction of currents due to alternating magnetic fields. These sensors have become very important in industrial measurement for measuring, among other things, displacement, proximity and rotation, force, accelerations, weight and pressure, and torque. Hence there are different principles available and the designer of the sensors can choose the optimum type to meet special demands and to achieve the best performance. This chapter can give only brief descriptions for some main principles since the range of sensor principles and applications is very extensive. The effects used to generate a voltage within the sensors are a varying magnetic flux within a magnetic circuit due to variations of an air gap or changes of the direction of the magnetic polarization, variation of the coupling between coils, or changes of inductance of coils due to the displacement of a soft magnetic core within the coils or relative motions of coils. Eddy current effects are utilized by the displacement of electrically conducting material within the oscillating magnetic field of a multipole permanent magnet or a coil.

7.2 Sensors Excited by Permanent Magnets 7.2.1 Variable Reluctance Sensors with Fixed Permanent Magnets (Magnetic Pickups) 7.2.1.1 Physical Principle a n d Construction

Variable reluctance sensors with permanent magnetic excitation are sensors that do not need any external energy or supply. They are based on the principle of electromagnetic induction, as follows. A permanent magnet produces a magnetic flux within a magnetic circuit of various shape. Owing to changes of the length of an air gap within the circuit, the reluctance of the circuit and hence the magnetic flux will change. This change in flux induces a voltage U in a pickup coil according to Faraday’s law : U(t) = - N *d@/dt

(7-1)

where

N @J

t

= number of coil windings = magnetic flux through the = time.

coil

The output voltage thus depends on the change in flux with respect to time, ie, the quicker the flux changes, the larger is the voltage.

258

7 Inductive and Eddy Current Sensors

The construction of variable reluctance sensors depends on the application. In its simplest form, it consists of a permanent magnet in coil. Here we shall describe a typical, commonly used form. The sensor consists of a cylindrical or rectangular permanent magnet with axial magnetization, attached with an iron pole, which is surrounded by a pickup coil (Figure 7-1).

Figure 7-1. Construction of an inductive sensor (courtesy VDO Adolf Schindling AG). 1) contact socket, 2) terminal package, 3) permanent magnet, 4) cap, 5 ) soft magnetic core, 6) coil, 7) plate, 8)Wade connector.

The pole is positioned in front of a rotating impulse gear, a ferrous milled steel disk or an approaching iron component. The impulse gear or steel disk is carried by the shaft whose speed is to be measured or the moving iron component joined to the body whose displacement is to be measured. Hence the air gap between the gear or iron component and the pole changes when they are approaching or receding from the sensor. In several cases a ferromagnetic yoke is used to close the magnetic circuit in order to increase the flux concentration within the circuit which will result in a higher output voltage [l, 21 (see Figure 7-2). The changes in magnetic flux for a sensor as shown in Figure 1-2 can be seen in Figure 7-3 which shows two computed shapes of the magnetic field for two positions of the gear wheel: with a tooth placed opposite the sensor core at minimum air gap (continuous lines) and the tooth displaced to it with maximum air gap (dashed lines). The shape of the sensor is determined by many parameters. The dimension of the impulse gear and the sensor core diameter must be well tuned. In general, the core has to be slightly smaller than or at most as wide as the teeth width and the distance between the teeth must be larger than the core diameter. Other parameters are the maximum available space for the

7.2 Sensors Excited by Permanent Magnets

259

yoke

Figure 7-2. Sensor with yoke.

impulse gear

coil

magnet

Figure 7-3. Changes in the magnetic flux with varying air gap. Continuous lines: minimum air gap; dashed lines: maximum air gap.

sensor, the maximum coil resistance, and the minimum output voltage at a given minimum speed of the parts to be measured. Hence, for different applications we have many different variations and dimensions of the sensors. Some different forms of sensors are shown in Figures 7-4 (C-shaped sensor) and 7-5 (radially magnetized permanent magnet). Instead of the permanent magnet, some systems use a DC excited coil [3]. The choice of materials for and the shape of such sensors will mainly depend on the constructor’s experience in magnetism, since the mathematical treatment of the magnetic circuit is inaccurate in most cases. As many parameters are unknown or can be predicted only with difficulty, such as the operating points of both the magnet and the yoke on the hysteresis loop, the influence of small air gaps following mechanical mounting and the magnetic and mechanical tolerances of the impulse gear, calculations of the circuit with the reluctance model, for example, will lead to only rough approximations.

260

7 Inductive and Eddy Current Sensors

cores

gear

magnet

coils

Figure 7-4. C-shaped sensor.

coil

magnet yoke

gear

/

core

I

I

Figure 7-5. Sensor with radially magnetized permanent magnet.

In order to achieve improved magnetic pickups, the use of numerical field calculations with finite-element or finite-difference methods with the aid of a computer is necessary [4]. An example for such a computation is given in Figure 7-3, where the exact course of the magnetic flux of a sensor is shown.

7.2.1.2 Applications and Properties The main application of these sensors is the detection of rotary motion and proximity. Most applications involve the measurement of the rotary speed of shafts or wheels. Owing to some advantages which will be described below, they are used, for example, in a large number of automotive control systems to measure

- the rotational speed of position of crankshafts, gearings, etc., and - the rotational speed of car’s wheels to generate a speed signal or for break control (ABS)

P, 31. Another application of this type of sensor is the measurement of proximity or velocities. In this case, the inductive sensor is often used as a switch to recognize the approaching of a ferromagnetic part which will change the flux within the coil like the tooth of a wheel. Since the output voltage of the sensor depends on the varying magnetic flux, only movements above a certain minimum speed can be detected. An example of a variable magnetic reluctance speed

7.2 Sensors Excited by Permanent Magnets

261

sensor which measures cam-shaft rotational frequency was given by Armstrong and Wilkinson [ 5 ] . Furthermore, this type of sensor is used for material testing based on a leakage flux principle [6]. In general, inductive sensors using permanent magnets have major advantages over other types of sensors. They are very robust and have a nearly infinite lifetime because they do not contain mechanically movable parts. Since they can be constructed with fully hermetically sealed housings, they may be used within aggressive media and under rough conditions. The limits of operation depend on the properties of the materials used, such as the plastic sealing material, or the corrosion resistance of metallic capsules and electrical connections. They can be used within an environment of 100% humidity. They are almost insensitive to shock, where levels of up to 30000 g have been reached. The pressure resistance is good and may reach values of 140 x lo6 N/mZ. For these sensors no external supply will be necessary. They can be used over a large temperature range, which will be limited by the mechanical properties of the materials used, the temperature dependence, and the Curie point of the magnets. Typical operating temperatures of these sensors are from -50°C up to more than 200°C. If special materials are used, they also can be used at cryogenic temperatures. Values of output voltage vary from 0.2 up to 80 V. A high resolution (depending on the size of the teeth or parts to be measured) can be obtained. For example, the rotating shaft speed can be measured with an accuracy of less than 0.1% and magnetic transduction of gears can be determined with an accuracy of hundredths of a mechanical degree. The frequency range varies from 1 Hz up to the MHz range. It is limited by eddy current effects, which reduce the effective magnetic cross section and increase the impedance of the pickup coil. Further, the iron core acts like a shortened secondary winding of a transformer. As a result of these effects the output voltage of the sensor is not linear at high frequencies, as expected from Equation (7-1). Some disadvantages of this type of sensors should be mentioned. The dimensions of the sensor must be adjusted to the size of the parts to be measured, eg, the teeth of the gear. Hence, a specifically dimensioned sensor can only be used for a small range of applications. Different applications require different constructions. Slow rotations and small displacements are difficult to measure, since the induced voltage becomes smaller the more slowly the flux changes. To avoid this influence, Forkel [7] proposed a modified sensor with a measuring range from 1 Hz up to 10 kHz with constant output amplitude. However, it requires an external supply and is based on the principle of a flux-gate magnetometer. Another problem is the control of the air gap under production conditions. Small changes to the gap may result in large changes in the amplitude of the output signal [8]. In order to change the reluctance of the magnetic circuit a force is necessary. Although it is very small, it cannot be neglected in some applications, eg, in sensors which measure streaming fluids or gases with an impeller.

7.2.1.3 Signal Conditioning The output signal of DC-excited sensors with permanent magnets consists of one or more voltage peaks, induced within the coil. If there is only one soft magnetic object (eg, a single

262

7 Inductive and Eddy Current Sensors

tooth of an impulse gear) approaching the sensor we have an analog output signal as shown in Figure 7-6. The amplitude of the signal depends on the speed of the approach. U

-U position Figure 7-6. Output voltage U of a DC-excited sensor with permanent magnets, when a single iron object passes by.

If the speed of the gear wheel is to be measured, the signal will be an alternating voltage and depends on the type of wheel used. For example, spur gears generate sinusoidal signals, whereas star wheels will give some sharper pulses, owing to the distribution of the iron in the wheels. With a given sensor and actuator shape, the output signal generally depends on two factors:

- The speed of the approach or removal of the gear wheel or iron part will influence the amplitude of the signal. An example of the output voltage versus speed is given in Figure 7-7 for a typical sensor used in automotive applications. Hence there is a lower limit for the speed to be measured, which is given by the lowest signal-to-noise ratio which can be decoded. - Further, the signal amplitude is to first order inversely proportional to the air gap between sensor core and moving iron objects. This relationship is shown in Figure 7-8 for different speeds. These two parameters mainly have to be taken into account for signal conditioning. Using a gear wheel there are two possible means of evaluation: measurement of the output amplitude or measurement of the frequency which is always proportional to the rotary speed.

Output voltage measurement This sort of evaluation is acceptable only f w simple rotary speed control systems because there are influences that can disturb an exact result. First there is the length of the air gap

7.2 Sensors Excited by Permanent Magnets

38

->

I

-

25

-

20

-

a,

263

a=0.5rnrn

m

4-

P

4-

1s:

P

4-

0

10

-

5

-

/

I

i

0

508

1000

1500

frequency [Hzl

Figure 7-7. Output voltage U versus frequency f. a : distance between impulse gear and sensor.

air gap [mm I

Figure 7-8. Output voltage U versus length of the air gap for different rotary speeds.

which is important. If the air gap is small, the sensor’s output voltage can vary owing to mechanical tolerances of the system such as eccentricities of gear wheels and shafts. If greater distances are realized, this influence becomes less important owing to the smaller slope of the voltage versus air gap characteristic (see Figure 7-8).

264

7 Inductive and Eddy Current Sensors

The temperature coefficients of the magnets have to be taken into account when the sensors are used at different temperatures, since they are related directly to the output voltage. Using hard ferrite magnets, for example, the temperature coefficient of the remanence (and with it the magnetic flux) is of the order of -0.2%/K.

Frequency measurement If more exact measurements are required, the frequency of the sensor signal is considered. In most cases, the output voltage is transformed by a Schmitt trigger into rectangular pulses (see Figure 7-9). Hence the signals can be evaluated in digital form.

~

-

To measure small signals, the design of both, the sensor and the electronic unit are important. The noise level of the sensor and the trigger level of the electronics define the minimum speed that can be measured. When the input impedance of the circuit and the ohmic resistance of the sensor match well, optimum power transfer can be realized which is insensitive to disturbances.

7.2.2 Variable Reluctance Sensors with Moving Permanent Magnets 7.2.2.1 Physical Principle and Construction This kind of inductive sensors consists of an iron (in most applications) C-shaped core which is surrounded by a pickup coil. The magnetic flux through the sensor is produced by a rotating or linearly moving multi-pole magnet positioned in front of the sensor. A rotating ring magnet is used to detect rotary movements and a linearly moving magnet is used to

Figure 7-10. Construction of a variable reluctance sensor with moving permanent magnet. 1) magnetic field, 2) magnet, 3) coil, 4) C-shaped soft magnetic core, 5 ) signal terminals.

7.2 Sensors Excited by Permanent Magnets

265

Figure 74. Variable reluctance sensor (courtesy VDO Adolf Schindling AG).

measure displacements. The distance between the ends of the core, which means the length of the sensor, is determined by the distance of the magnetic poles. The construction of such a sensor is shown in Figure 7-10, and Figure 7-11 gives a view of a complete sensor. Owing to the alternating polarity of the magnet, the magnetic flux through the core changes its direction and an AC output voltage is induced according to Equation (7-1). The amplitude and frequency of the induced voltage depend on the speed with which the magnetic poles pass the sensor. The sinusoidal output signal is given in Figure 7-12 for various speeds of motion.

Figure 7-12,Output voltage U of the sensor for different speeds u ( v , < u2),

266

7 Inductive and Eddy Current Sensors

7.2.2.2 Applications and Properties As described above, this type of sensor is used to measure rotary speed or linear displacement. The sensor shown in Figure 7-11, for example, is used in automotive applications as speed pickup to detect the rotary speed of a speedometer magnet. The sensor is attached to the speedometer in such a manner that the magnetic field of the speedometer magnet will give a maximum induction within the sensor coil. As can be seen in Figure 7-12, the output voltage of the sensor is small for low rotary speeds, so the magnet should have a larger number of poles which ensures that a sufficiently high output voltage is reached at the lowest rotary speed. Typical values for automotive applications are, for example, 8 or 12 poles at a minimum rotary speed of about 350 rpm. The induced voltage will then be greater than 300 mV [9].

7.2.3 Tachometer Generators with Permanent Magnets 7.2.3.1 Physical Principle and Construction Tachometer generators are electrical devices based on the AC dynamo principle. They are able to transform rotary motions into electrical signals, such as voltage or an frequency signals, proportional to the rotary speed. There are two types of tachometer in use: DC and AC generators. Both are based on the same physical principle: a multi-pole permanent magnet is mounted tightly on a shaft, the speed of which is to be measured. This rotor is moving inside several stator coil windings as in a synchronous machine (Figure 7-13).

permanent

b L,,

L,,

L,i

stator windings

Figure 7-0. Principle of a construction of tachogenerator.

According to Faraday's law, a voltage will be induced within the coils, which depends on the number of coil windings N , the exciting magnetic flux GE and the rotational speed n [lo]:

7.2 Sensors Excited by Permanent Magnets

267

The frequency f of the voltage induced is proportional to the rotational speed n and the number of magnetic poles p :

f

-n.p.

(7-3)

The signals described above are typical of an AC tachometer. To obtain a DC output, the voltage induced within the stator windings is rectified with a commutator and brushes. This construction is more complicated and has several disadvantages, such as wearing out of brushes and the commutator and influences of dirt, air pressure, and humidity. Also, a DC amplifier is needed for signal conditioning. Owing to these problems, DC tachometers today are used only in applications where it is necessary to prevent errors due to phase shifting. To obtain a DC output signal, today some external electronic units are available, which offer the cheaper and less sensitive means of rectifying the AC tachometer signal [ll].

7.2.3.2 Applications and Properties A typical application of tachometer generators is to count numbers of revolutions. They are built in different forms, depending on the application, and offer some good properties [12-141. With DC tachometers typical speeds of 750-2000 rpm can be measured. The linearity within this range can be limited to less than 1% depending on the respective load resistance (see Section 7.2.3.3). The amplitude of the voltage lies between a few volts and hundreds of volts [lo]. Commercially available DC tachometers have a peak-to-peak ripple of less than 1% [15]. Using AC tachogenerators, the frequency of the output signal can be used for the determination of rotational speed, Typical ranges of speed are 150-3000 rpm. With special devices measurements up to 50000 rpm are possible. Hence the output frequency depends on the number of poles of the permanent magnet. The number of poles has to be adjusted to the rotary speed : small speeds require a large number of poles, high speeds need smaller numbers of poles. Advantages of these sensors are:

- they are very robust; - they do not need external supply advantage; and - they offer a high output voltage. Some of the disadvantages are:

- the linearity depends on the effective load resistance (see Figure 7-14); - the temperature dependence of the stator windings (copper) is of the order of 0.4%/K; - a high armature reaction; and - harmonic oscillations of more than 10% of the output signal.

268

7 Inductive and Eddy Current Sensors

7.2.3.3 Signal Conditioning Tachogenerators can only measure speeds at a certain minimum level. TYpically they are used for the measurement of speeds in the range of a few hundred revolutions per minute. At such speeds, the output voltage has an amplitude of several volts which allows the direct measurement of the signal without the use of additional electronics.

Figure 7-14. Output voltage U versus rotary speed n for different load resistances R.

The linearity of the output signal depends on the specific load resistance. Figure 7-14 shows different output signals with respect to different load resistances. As can be seen, linearity for higher rotary speeds can only be obtained with a good adaptation of the tachometer to the load resistance. The linearity within the typical measuring range can be limited to less than 1% [lo]. Since the output voltage and the changing angular velocity are proportional, tachogenerators offer additional applications for arithmetic operations such as integration or differentiation. A description of such networks was given by LazAroiu and Slaiher [16]. Weschta [17] described an additional electrical circuit for the determination of the angular position of the rotor.

7.3 AC-Excited Sensors for Linear Movement

269

7.3 AC-Excited Sensors for Linear Movement 7.3.1

Linear Variable Differential Transformers

7.3.1.1 Physical Principle and Construction The linear variable differential transformer (LVDT) is based on the principle of a differential transformer with variable coupling between primary and secondary coils. It was pioneered in the 1940s by Schaevitz [18]. Since that time, many different sensor forms and applications have been developed and various new functional ranges have been found. The form of this type of sensor depends largely on the application. Therefore, the following descriptions can only give a general overview of the principles of these sensors and of some of their applications. The LVIYT consists basically of one primary and two secondary coils located on either side of the primary coil. The three windings are situated on a cylindrical bobbin, in which a movable soft magnetic core is located (Figure 7-15). The armature is mounted on a non-

secondary winding 1

I

I

primary winding

secondary winding 2

I

I \ I \

bobbin

core

Figure 7-15. Principle of construction of an LVDT.

magnetic plunger, which is sometimes spring loaded, and placed against the device to be measured. Figure 7-16 shows an example of such a device with very small dimensions. The secondary windings are connected in series circuit (differential coils), so the resulting output signal corresponds to the differential voltage of the two coils. Figure 7-17 shows the electrical circuit of this sensor. The primary coil is excited by an alternating current. The magnetic coupling between the primary and secondary windings and the magnetic flux then will be determined by the position of the core in relation to the coils. The core is displaced by the parts to be measured via the nonmagnetic rod.

270

7 Inductive and Eddy Current Sensors

Figure 7-16. Photograph of a small size LVDT (courtesy Althen Mess- und Datentechnik GmbH). output voltage 0

secondary winding 1

secondary winding 2

core

I

primary winding Figure 7-17. Electrical circuit of an LVDT.

From Faraday’s law, the voltage U induced in one secondary coil can be calculated from

U

=

- N * d@/dt = - M dI/dt ,

where N = number of coil windings @ = magnetic flux M = mutual inductance between the primary and secondary coil I = primary current.

(7-4)

7.3 AC-Excited Sensors for Linear Movement

271

The following holds for differential transformer :

M , and M2 are functions of the position x of the soft magnetic core. Hence M = M2 - M I = M ( x )

or

U 7 M ( x ) .TtI/dt U

M(x) = dI/dt *

(7-7) (7-8)

The amplitude of the secondary voltage is thus proportional to the position of the core and the phase displacement of the primary and secondary signal indicates the position of the core relative to the zero position. As already stated, the output voltage of the sensor corresponds to the differential voltage of the two coils. With the core in the zero position in the center of the two secondary coils, the secondary voltages have the same amplitude and are 180" out of phase. Therefore, the difference will be zero. If the core is now displaced, the magnetic flux within the secondaries changes as shown in Figure 7-18. The voltage induced in one secondary coil will increase, whereas the voltage induced in the other will decrease. The resulting signal gives the dependence of the sensor output voltage on the core position according to Equation (7-7). The output signal of a sensor with a normal uniform winding is shown in Figure 7-15 is linear only for small displacements of the core near the zero position. If the core approaches one end of the coil system, the output voltage decreases owing to the reduction in the magnetic field in this direction. Hence larger displacements produce a nonlinear output voltage as shown in Figure 7-19. In its basic form, the LVDT can be used in many applications for the measurement of short strokes. To measure larger displacements, the relationship between the measured displacement with a linear output signal and the length of the sensor will become disadvantageous. To obtain better relationships between stroke and sensor length, some modified forms of coil windings were used, which were first described by Lipshutz [19]. However, this type of coil winding has the disadvantage that their production is difficult. Some commonly used examples of modified coils are summarized below.

Balanced linear-tapered secondaries Figure 7-20 shows the principle of the construction of a sensor with balanced linear-tapered secondary windings. It can be seen that the arrangement of the coils differs considerably from the basic construction shown in Figure 7-15. The primary winding uniformly covers the whole length of the sensor, whereas the secondaries are wound on the primary tapered from both ends to the middle. This form of sensor coil requires perfect symmetry of the two secondaries to obtain a good balance. Nevertheless, the magnetic field will decrease at the ends of the coils and the stroke will not reach the full length of the sensor.

212

7 Inductive and Eddy Current Sensors

a)

Figure 7-18. Computed magnetic field of the LVDT. a) core in zero position, b) core displaced.

7.3 AC-Excited Sensors for Linear Movement

273

U

Figure 749. Output voltage U versus core displacement 1.

secondary winding 1

- V

bobbin

primary winding

* a : limits of a linear range. secondary winding 2

I

core

Figure 7-20. Balanced linear-tapered secondary windings.

Overwound linear-tapered secondaries A second type of sensor has overwound linear-tapered secondary coils as shown in Figure 7-21. In this case the secondaries are wound tapered over the whole length of the sensor, which will give a good relationship between sensor length and stroke, but it may be show an unbalanced behaviour.

Balanced overwound linear-tapered secondaries Using the balanced overwound linear-tapered form of windings shown in Figure 7-22, the above-described imbalance can be avoided. For this modification the primary winding is split into an inner and outer coil with tapered secondary windings in-between.

214

7 Inductive and Eddy Current Sensors

secondary winding 1

primary winding

bobbin

secondary winding 2

core

Figure 7-21. Overwound linear-tapered secondary windings.

secondary winding 1

primary winding

secondary winding 2

1 1 1 1 1 1 1 1 1

bobbin

core

Figure 7-22. Balanced overwound linear-tapered secondary windings.

Balanced profiled secondaries A sensor with balanced profiled secondary coils (Figure 7-23) is a variation of the first type described above, in which the section profile of the secondaries is adjusted so as to maintain a greater linear range of measurement.

Complementary tapered windings This is another variant with which the linear range can be extended. Here the bobbin is divided into a number of chambers which carry a defined number of windings of the three coils. A schematic view of such a sensor construction is given in Figure 7-24. Another proposal for increasing the linearity range was given by Wouterse [20]. He suggested using a highly permeable metallic tube surrounding the sensor as a magnetic keeper. This construction leads to a transversal-shaped magnetic field within the sensor instead of the more axial form shown in Figure 7-18.

7.3 AC-Excited Sensors for Linear Movement secondary winding 1

bobbin

275

secondary winding 2

primary winding

core

Figure 7-23. Balanced profiled secondary windings. core I

prlmary wlndlng secondary wlndlng 1 secondary wlndlng 2

Figure 7-24. Complementary tapered windings.

A general statement as to which shape of sensor windings is the best cannot be made; the choice depends on the specifications required and the application. Some of the important features for the sensor construction are sensor size, linearity, absolute reproducibility, resolution, hysteresis, temperature dependence, output voltage required, and stroke to be measured.

7.3.1.2

Applications and Properties

Although the sensor principle of the LVDT has been known since the beginning of this century, for decades these sensors were only rarely used. However, within the last 20 years, many new application in automation, process control and measurements have been developed. LVDTs are well known as optimum position and displacement sensors in thousands of applications in research and industry as a result of their excellent characteristics and properties which will now be described.

216

7 Inductive and Eddy Current Sensors

LVDTs have a nearly infinite mechanical life because owing to the absence of contact and friction between core and coil systems there will be no mechanical or electrical wear. In practice, carefully constructed LVDTs can reach an MTBF (Meantime Between Failure) of several million operating hours. The frictionless operation, combined with the induction principle on which the sensor's operation is based, gives a truly infinite resolution. Only the external electronic unit used limits the resolution, not the sensor itself. The minimum measuring range of today's LVDT displacement sensors is from a few micrometers up to a maximum of 1 m, depending on the construction of the sensor. The linearity in general extends from k 0.025% up to k 0.5% of the nominal displacement. It depends mainly on the previously described shape of the secondary windings (Section 7.3.1.1). The designer of an LVDT should check carefully the linearity required to prevent additional costs due the complicated structures of the coil windings. Another accurate feature of this sensor is the null repeatability. In practice, deviations of the order of less than 0.05% are observed. Since the zero position of the sensor is extremely stable and repeatable, the LVDT can be used as a precision zero-position transducer itself as a part of closed-loop control system or servo system [21]. The temperature dependence of LVDTs is determined by several factors which depend on the mechanical behaviour of the materials used such as creep, rupture or softening. A second limitation is given by electrical properties of the materials such as dielectric strength, changes in conductivity of the conductors, reluctance and resistivity of insulating materials and permeability, and reluctance and Curie temperature of the magnetic materials used. Another influence is given by the use of LVDTs within an environment of rapidly changing temperatures. In this case the inertial thermal reaction of the sensor has to be taken into consideration. According to the construction and the materials used, temperature ranges from -50" up to 600°C can be obtained [22, 231. The temperature coefficients of typical LVDTs are given to O.Ol%/K. The sensors show very little response to transverse motions of the core, and the cross-axis rejection is negligible. This property allows measurements in situations where the core is not moving in a perfectly straight line. Since the movable core and the electric parts of the transformer are perfectly separated from each other, the sensor can be hermetically sealed, so that it can be used in aggressive media and under rugged conditions. The resistance to rough environments depends on the materials used as mentioned above. According to this, some extreme properties of the sensors may be achieved, so they can be used

- in corrosive liquids or vapors ; - at cryogenic temperatures (liquid oxygen, nitrogen or helium down to 4 K) ; - in flammable vapors and particles with temperatures up to 600°C; - in nuclear radiation areas with high radiation levels ;

- at high pressure levels of up to 2 . lo7 N/m2; and - at water pressure of 75 m water column.

Some disadvantages of LVDT-type sensors are : - they need an external supply and electronic units for signal generation and processing;

- electrical and magnetical protection against external fields is necessary ; and - when operating at high temperatures, the sensors need some temperature stabilization.

7.3 AC-Excited Sensors f o r Linear Movement

277

LVDTs can be used for the direct measurement of position and displacement, but in many applications these sensors are used as secondary transducers. In this case the quantity to be measured is transformed into a linear movement of the sensor core. There are many different constructions and methods of transforming the quantities to be measured into core motions which cannot be described in this chapter. Therefore, here we shall give an overview of some commonly used applications of such devices. LVDTs are used as secondary transducers - for the measurement of force, weight and pressure (load-cells and weight cells) [24];

- as level meters; - as plummet flow meters [25] ; - as strain-gage heads ; and

- as gage heads [21] and in other measuring applications. The differential transformer principle is also used for the measurement of angles of rotation. In this case it is called a rotary variable differential transformer (RVDT). The stator windings of RVDTs consist of one primary and two secondary coils wound on a bobbin as in the case of LVDTs. The core, in this case acting as a rotor, has a cardiodic or other special shape which can change the coupling between the stator coils [21, 261. RVDTs can detect angular motions within the range of 180°, and linear operation is possible within the range of f40" with an accuracy of less than 0.5%. With an angle of displacement of about f5", the accuracy will reach a level of less than 0.15%FSR (Full Scale Reading). The flexibility of the LVDT construction and the advantages of this type of sensor have made them virtually indispensable in various modern industries such as the aircraft and spacecraft, nuclear power and automotive industries, mechanical engineering, mining, and materials testing.

7.3.1.3 Signal Conditioning Two main principles are used for signal conditioning of the LVDT ; that is either a carrier amplifier/synchronous demodulator system or a passive demodulator/DC amplifier system. Irrespective of the system used, the sensor needs AC excitation, which is realized by a carrier generator. This generator consists mainly of two or three parts, the oscillator, followed by a power amplifier, and an optional feedback amplitude control. The carrier oscillator produces a sinusoidal signal with a small distortion factor. Sometimes a rectangular signal is used, but it produces an unreliable zero voltage so that the sensor cannot be used as a null-position transducer. An overview of carrier amplifiers is given in [27]. The carrier frequencies used vary from less than 50 Hz up to 1 MHz, but the optimum performance is reached within the range 0.5-10 kHz. When measuring dynamic processes, the following rule of thumb can be applied : the frequency to be measured should not be greater than 10% of the carrier frequency. The supply voltage of LVDTs typically are within the range 1 - 10 V (rms), depending on the size of the sensor and its internal resistance. In special applications voltages up to 50 V (rms) are used.

278

7 Inductive and Eddy Current Sensors

The oscillator feeds a power amplifier which provides a buffered output voltage at low impedance. The gain of the amplifier is adjusted for the LVDT. To obtain a stable primary exciting voltage the carrier signal is fed back to the oscillator via an amplitude control circuit. The secondary voltage of the LVDT can be evaluated in several ways. Using a carrier amplifier/synchronous demodulator system (Figure 7-25), the output signal is amplified by a carrier amplifier and then rectified by a synchronous demodulator with full-wave rectification, which very often is followed by a low-pass filter.

power supply

carrler - gen.

auto,

- amp,

- LVDT - carrler - demodulator

amp.

control

3

phase

Figure 7-25. Block diagram of a carrier amplifier system.

The demodulator is triggered synchronously to the primary supply via a phase shifter from the carrier oscillator. This circuit now produces a signal with an amplitude proportional to the sensor core position. The passive demodulator/DC amplifier system uses a passive demodulator, such as a diode discriminator, followed by a low-pass filter and a DC amplifier (Figure 7-26). Together with a DC-to-AC converter within the primary circuit, the LVDT can be used as a complete DC sensor. power supply

passlve

- carrler - LVDT - demod- gen, ulator

DC amp.

3

Figure 7-26. Block diagram of a DC amplifier system.

This type of DC sensor became important in recent decades with the development of semiconductor and integrated circuit technology which allow the integration of the electronics in the sensor housing. Today integrated interface circuits are available, that include the whole DC electronics described above [28, 291. Owing to the miniaturization of the electronics, it is possible to integrate the electrical circuits within the sensors [30].

7.3.2 Variable Inductance Sensors/Variable Leakage Path (VLP) Sensors 7.3.2.1 Principle and Construction This type of sensor is based on the change in the inductance of one or two coils, produced by a diplacement of a core within the coils. In its simplest form the sensor consists of a coil, wound on a cylindrical hollow bobbin, inside which a soft magnetic core is positioned. The

279

7.3 AC-Excited Sensors f o r Linear Movement

core is connected via a nonmagnetic shaft to the object that is to be measured. When the core is displaced, the inductance of the coil changes, which can be signal processed in an electrical bridge circuit. Hence this construction with one sensor coil has the disadvantage of having a nonlinear characteristic; the VLP sensor type with two coils, which will be discussed in detail, has some more benefits. Two coils of the same shape are wound on a cylindrical hollow bobbin, inside which a cylindrical armature is located as described above. Figure 7-27 shows the principle of construction of this sensor. sensor coils

core

Figure 7-27. Principle of construction of the VLP sensor.

In several constructions, a soft magnetic yoke is used that surrounds the coils axially and gives a more closed magnetic circuit. This increases the linearity range of the sensor. The coils of the sensor are connected as a bridge or half-bridge circuit together with variable complex resistances and the amplifier used (see Section 7.3.2.3). Like the sensor based on the transformer principle (LVDT, RVDT), the variable inductance sensors need an external AC supply, which drives the bridge circuit as shown in Figure 7-28. I I

Figure 7-28. Principle of a bridge circuit.

i

I

OR

The inductance of a cylindrical coil is given by (see, eg, [31]) (7-9) where vacuum permeability relative permeability of the core material N = number of turns A = cross-section area of the magnetic flux I = average length of the magnetic flux path.

p,, = pr =

280

7 Inductive and Eddy Current Sensors

With the core in the zero position, both coils have the same inductance: L = L, bridge voltage UAis then zero, since

UA = UB * (iw L,/(iwL,

+ iwL,)

- t/2)

=

L,

. The

(7-11)

and with L , = L,, UA = 0, where o = excitation frequency and U , = excitation voltage. An axial movement of the armature will now increase the inductance of one coil and decrease the other one. This detunes the bridge circuit and a voltage UAcan be seen: UA = UB * (L

U, = UB * ((L

+ AL/((L + AL) + (L - AL))

+ AL)/2L

- 112)

UA = 1 / 2 . UB AL/L

- 1/2)

(7-12) (7-13) (7-14)

where AL = change in inductance. Let us assume that the amount of inductance, dL,with the displacement of the core dl, that is, dL/dl, is known, then the following holds for small changes in 1: AL = dL/dl* A1

(7-15)

Inserting this term into Equation (7-14), we obtain UA/UB = 1/(2L) dL/dl' AI.

(7-16)

This result shows the dependence of the ratio of the bridge voltage to the input voltage, UA/UB,on the core displacement, Al. The change in the coil inductance as a function of the core position is generally difficult to calculate because of the unknown leakage flux distribution. Moreover, it depends on the material used for the core and the overall size and the geometry of the sensor. The relative permeability, p r , of the core material influences the inductance directly and should be chosen to give a good performance of the sensor. The size of the sensor is normally given by the fitting dimensions of the environment, and the geometry depends on the travel and linearity requirements of the sensor.

7.3.2.2 Applications and Properties The range of applications and properties of variable inductance sensors is nearly the same as for variable differential transformers (LVDTs, see Section 7.2.1.2), so only some of the main properties of this type sensor will be discussed here briefly. The sensors offer a simple construction and, owing to the absence of friction between core and coils, a nearly infinite mechanical life. Depending to the materials used for the construction of the sensors, they can operate under severe conditions and within aggressive media.

7.3 AC-Excited Sensors for Linear Movement

281

The linear displacements that can be measured with variable inductance sensors vary between ca. lo-’ and 1 m, depending on the sensor geometry. The linearity range (measuring range) can cover up to 80% of the sensor length with an error in linearity of less than 3% [32]. Smaller displacements will produce smaller errors. The resolution is truly infinite and is limited only by the noise voltage and the electronics. When used for dynamic displacement measurements, the sensors can be applied within a frequency range from 0 Hz up to several kHz, depending on the excitation frequency. They are limited by the inertia of the armature. The maximum frequency to be measured should be smaller than 20-25% of the carrier frequency. Variable inductance sensors such as LVDTs, are able to work with temperatures near absolute zero and up to approximately 150°C. Some special constructions permit their operation at ambient temperatures of up to 600°C [33]. Higher temperatures may be reached with the sensor construction described by Grinrod [23], involving a DC-supplied coil instead of the soft magnetic core. The sensors are insensitive to high nuclear radiation levels and can withstand accelerations up to 1000 g. Some of the disadvantages of variable inductance sensors are: they need external AC supply and electronics for signal generation and processing; there is a temperature-dependent zero drift of sensitivity with temperature coefficients of the order of 0.05-0.2%/K ; the compensation of temperature effects is possible only within certain limits; a shielding against outer electrical and magnetic fields is necessary. The applications of this type of sensor are numerous. In addition to their operation as position or displacement transducers the sensors are used as gage heads, eg, in mechanical Tension Compression

U

G =Housing Z = Tension link W = Displacement transducer type W 1 K = Core U = Overload stop ET = Sensitivity trimmer

Figure 7-29. Principle of a construction of a force transducer (courtesy Hottinger Baldwin Messtechnik GmbH).

282

7 Inductive and Eddy Current Sensors

engineering and for material testing [6]. Another range of applications involves the measurement of the forces such as load, weight, and pressure [34]. An example of a load cell or force transducer is given in Figure 7-29. It can be seen that the force to be measured is transmitted via the tension link Z which is fixed by a diaphragm spring to the core K. The deflection of the springs has to be strictly proportional to the effective force in order to obtain a linear dependence between force and sensor output signal. For the measurement of pressure, the pressure deflects a diaphragm which is coupled with the core by a tension link and produces a linear motion. Today's pressure sensors typically operate with pressures up to 2 x lo7 N/m2 [35]. Vibrations and accelerations can be measured if the core is connected to a seismic mass which is spring actuated (Figure 7-30). The frequency range of such sensors depends on the mass-spring system used and the damping [361. Further applications include the measurement of fluid levels. For this purpose, a float is fixed to the armature of the sensor. Using a circular construction of the coils and the core, the measurement of angles can be reduced to a displacement measurement with this sensor. With such devices the determination of angles within a range of 300" is possible.

setsntc nass sprmg.

houslno colt 1 core

Figure 7-30. Vibration/acceleration sensor.

7.3.2.3 Signal Conditioning As described in Section 7.3.2.1, the variable inductance transducers operate as a part of a bridge circuit. The AC supply and the signal conditioning are typically realized by a carrier amplifier system, consisting of a carrier generator, a resistor half-bridge, an AC amplifier, and a demodulator (Figure 7-31). The carrier oscillator (generator) G produces a highly stable AC voltage U, which supplies the precision resistor/inductor network. The carrier frequencies used are in the range 50 Hz-500 kHz; a typical value is 5 kHz. With the help of the zero balance N, the bridge voltage U, is balanced to zero if the sensor core is in the zero position. If the bridge is now detuned by displacing the core, a voltage U, will appear. The ratio U,/U, at the input of the amplifier represents the standard output of the variable inductance sensor. This signal is now amplified by the amplifier A and then demodulated by the synchronous demodulator D to produce a DC output signal.

7.3 AC-Excited Sensors for Linear Movement

--

I I -

7

I

I

I

283

I

I

I

I

I

D I

I A

I

t

.-.I I . I

I

J

P = Power supply unit, G = Generator, N = Zero balanCe,UB = Transducer output signal,

U&

= Transducer measuring signal, A = Amplifier, D =

Demodulator

Figure 7-31. Schematic electrical diagram of a force transducer connected with an amplifier (courtesy Hottinger Baldwin Messtechnik GmbH).

7.3.3 Variable G a p Sensors/Differential Cross-Anchor Sensors 7.3.3.1 Principle and Construction The physical principle of variable gap sensors is based on the variation of an air gap within a magnetic circuit. These sensors may be realized by winding a coil on a C-shaped ferromagnetic core. If a ferrous part approaches the ends of the C-shaped core, the ratio between air gap and length of the core is reduced (Figure 7-32). The inductance L is given by (7-17) where vacuum permeability number of coil windings cross section of the core length of the magnetic path iron permeability lL = length of the air gap pL = 1 = permeability of the air gap. po = N = A = IF, = pFe=

The maximum inductance is given at l, = 0 for (7-18)

284

7 Inductive and Eddy Current Sensors coil

1

armature

I

core

Figure 7-32. Construction of a variable gap sensor.

There is a hyperbolic dependence of the normalized inductance L/L,,,

to the ratio

LL ' luFe , see Figure 7-33. * PL

LFe

1

0 Figure 7-33. Characteristic of a variable gap sensor.

The sensitivity is constant only for small displacements of the armature. To achieve a better performance with respect to linearity and temperature dependence, the sensors are constructed as differential variable gap transducers. Two variable gap sensors are connected in series within a bridge circuit, as shown in Figure 7-34. The ferromagnetic armature is positioned in the air gap between the two sensor elements and can move in the direction of the magnetic flux lines. Here the inductance of one coil increases, whereas the inductance of the other when - - .decreases, -

7.3 AC-Excited Sensors for Linear Movement

285

c-,

Figure 7-34. Construction of a differential cross-anchor sensor.

the armature is moved. A short analysis of this circuit was given, for example, by Rohrbach [lo]. If the air gap of the sensor is varied, the ratio U,/U, changes accordingly. If the air gap is changed only slightly, the ratio is nearly proportional to dl. The materials used for the construction of the coil systems and the armature are described in Section 7.7. Some consideration should be given to the core material. A high sensitivity depends on a high relative permeability of the core material. Therefore soft magnetic materials as described in Section 7.7 are used. In cores of solid material eddy currents may become an important factor and may reduce the sensitivity and linearity of the sensor. To reduce eddy currents, the core has to be built of laminated material.

Figure 7-35. Output voltage LI versus core position x.

* a : limits of the linear range.

286

7 Inductive and Eddy Current Sensors

8 I

U

6

a Figure 7-36. Applications of differential cross-anchor sensors.

I

f

7.4 AC-Excited Sensors for Rotary Movements

287

7.3.3.2 Applications and Properties Variable gap sensors show some advantages in the measurement of small displacements. They are highly sensitive and have a high resolution of less than 1 nm [37]. The maximum nonlinearity typically is given as 0.5% [38]. They are used for non-contact applications and offer reaction-free operation. The construction for these sensors can be very robust and they can be used within the same environments as variable inductance sensors (Section 7.3.2.2). Nevertheless, these sensors show larger errors in accuracy than sensors with plungers. Some disadvantages for example, are a small range of linearity (see Figure 7-35), the temperature dependence of the sensitivity, and zero drift which causes difficulties with static measurements. Further the measuring forces cannot be neglected. Variable gap sensors are therefore mainly used in applications where it is not possible to use sensors with plungers. These sensors are typically used as strain gages [lo] and to measure torque [39], pressure, force, load, weight, vibrations, and accelerations [27, 401. Some of these applications and principles are shown schematically in Figure 7-36.

7.3.3.3 Signal Conditioning Variable gap sensors are used as parts of an electrical bridge circuit like variable inductance sensors. Hence for the electrical circuit and operation the conditions are the same as for the latter sensors (see Section 7.3.2.3).

7.4 AC-Excited Sensors for Rotary Movements

7.4.1 Synchros 7.4.1.1 Physical Principle and Construction Synchros are AC-excited electromechanical devices that are used to measure rotary motions from a distant point. They are based on the physical principle that the magnetic coupling between coils changes. In its basic construction, a synchro consists of a stator, which contains three windings displaced by 120". Inside the stator an armature with armature windings rotates. This rotor is supplied with an AC voltage with the help of collector rings. Figure 7-37 shows the principle of construction of the synchro. The sensor transforms the rotational angle a = f ( t ) which is to be measured into phase angles of AC voltages p = f ( t ) . At a given position of a rotor, voltages Uxo,Uyo,and Uzo are induced within the stator windings. They are either in-phase or out-of-phase with the

288

7 Inductive and Eddy Current Sensors

0

S t s2, s 3 stator windings

Figure 7-37. Principle of construction of a synchro.

excitation voltage U , , depending on the rotor position. These voltages change with the angle of rotation a according to

U,,

=

K

U , cos a

(7-19)

-

U,, = K . U , cos (a - 120")

(7-20)

U,. cos ( a - 240")

(7-21)

U,, = K

where K is a constant, depending on the synchro construction (eg, ratio of rotorhtator windings). The voltage U , in general is of the form U , = U,, sin ot. For typical applications, the stator windings are joined in star connection. This gives the following output voltages:

-

u,, = u,, -

~ ' .7sin(a -

Uyo = U , K

v

1200)

(7-22)

sin(a - 240")

(7-23)

=

U,, - U,,

=

U, . K

.

U, =

uz0- U,,

=

U, K

. ~7. sin a

U,,

(7-24)

The shape of these voltages is shown in Figure 7-38. They are similar to the voltages of the three-phase network, that is, they are out-of-phase by 120". A detailed analysis of this type of sensor is given in [16].

7.4.1.2 Applications and Properties The measurement of the above voltages by these sensors is used to determine the angular position of the rotor only, but can be used to determine the errors of the synchro. In typical applications, two synchros are connected to transmit the rotor position, one acting as a transmitter and the other as a receiver.

7.4 AC-Excited Sensors for Rotary Movements

289

Figure 7-38. Output voltage of a synchro.

Tho types of synchro circuits, which will be described here, are in use: torque-type synchros and control-type synchros. a. Torque-type synchros These sensors represent a simple device for driving pointers and dials directly without any amplification. The rotors of torque synchros are both connected to the excitation voltage U,, and their similar stator windings are connected as shown in Figure 7-39. transmitter

receiver

stator 1

stator 2

rotor 1

Figure 7-39. Principle of construction of a torque-type synchro.

rotor 2

290

7 Inductive and Eddy Current Sensors

If both rotors are displaced to the same extent, ie, atransmitter

a, = a,

- areceiver

,

then the terminal voltages of transmitter and receiver are the same and no compensation currents flow. If the transmitter rotor is turned around, ie, a,

>

a,,

compensating currents occur. Depending on the rotor position, they produce a torque on the rotor of the receiver synchro, which tries to adjust this receiver to the same angular position as the exciting one. The torque vanishes only if the position of the receiver rotor equals that of the transmitter. With such torque-type synchros, the angular position of the transmitter rotor can be transmitted directly to the receiver rotor and produce a suitable indication of the rotor position. The active torque is approximately sinusoidal of the form (see Figure 7-40) M

- K . sin(a, - a,) .

(7-25)

Hence we have a maximum torque if the angle between the rotors is nearly 90". If the position of the two rotors is similar (a, = q),we have a nearly linear dependence. Some typical properties of such devices are now given. The transmitted torque is typically of the order of 5 10 - 4 - 1 10 - 2 Nm/ 4 Detection errors of torque-type synchros are bet-

M

angular diff.

Figure 7-40. Torque versus angular difference.

7.4 AC-Excited Sensors for Rotary Movements

291

*

ween k0.5' and 1.50. The maximum rotational speed is typically given as 300 rpm. The diameter of synchros is given as 20-90 mm for a length of 40-150 mm [lo]. b. Control-type synchros If the required torques are high o r the transmission errors have to be kept small, controltype synchros are used. The principle of such devices is shown in Figure 7-41. transmitter stator 1

rotor 1

receiver .stator 2

rotor 2

0

0

Figure 7-41. Principle of

The construction of control-type synchros is similar to that one of the torque-type transmitter, with the rotor connected to the excitation voltage U , . The rotor is mechanically turned to the angle that is to be measured. The receiver synchro uses a drum-wound rotor, which should not produce torques, but should induce a voltage depending o n the angle difference of the rotors: U,

- U,

cos(a, - a , ) .

(7-26)

This voltage is supplied to an amplifier which drives, for example, an induction o r a Ferraris motor. The motor turns the receiver rotor until the rotor voltage U,= 0. Then

a,

=

a,

+ 90"

holds for both rotor positions. The control-type synchro now gives a direct representation of the two rotor positions. Figure 7-42 shows the output voltage versus angular difference. In some applications a gear is inserted between the motor and receiver rotor to reduce the setting error of the rotor. The accuracy reached with these synchros is of the order of k 5' to k 15'. Another typical application of synchros is in surveyors' chains. To measure sums or differences of angles, three or more synchros are connected in series. An example of such a device, which is the so-called differential synchro, is shown in Figure 7-43.

292

7 Inductive and Eddy Current Sensors

Figure 7-42. Output voltage versus angular difference.

transmitter

“1

differential

receiver

I

Figure 7-43. Principle of construction of a differential synchro.

A torque-type synchro is used as a transmitter synchro. Its stator is connected to the stator of a synchro differential and produces a field within the stator that has the same direction as the transmitter rotor field. The rotor of the differential synchro is built like a three-phase rotor which results in additional rotation of the rotor within the receiver synchro: a, = a,

+ ad

Some examples of synchro combinations are given in [24]. In practice, synchros show some errors, which are of mechanical, electromagnetical or external origin. Mechanical errors are produced, for example, by friction of brushes and bearings, an imbalance of the rotors, nonuniform air gaps, and the presence of rotor teeth. Electromagnetic errors mainly occur because of the magnetic anisotropy of the electrical sheets,

7.4 AC-Excited Sensors for Rotary Movements

293

different resistances of the windings, or turn-to-turn short circuits. Some of the external influences are changes in the voltage, frequency of the drive voltage, and temperature effects. The above reasons for errors in synchros lead to a decrease in the accuracy of transmission of the angle. Therefore, for high-performance synchro systems there are demands placed upon the construction and the materials used.

7.4.2 Resolvers 7.4.2.1 Physical Principle and Construction Resolvers are a variant of synchros (rotating transformer). These induction-type devices transform a device's angular rotor position into a signal, that varies with the sine and cosine of the rotor position. A typical resolver consists of a rotor which has two windings displaced by 90" from each other. The stator is built with a single winding or two windings displaced by 90" from each other. The resolver offers the possibility of driving the rotor or the stator coils. Here we shall describe the principle of a resolver with only one winding.

Resolver with one stator winding The stator winding is excited by a voltage:

U,

=

U,, . sin ot

.

(7-27)

Within the rotor windings there are then two voltages of the form

U,, and

=

U, . K

. sin a

(7-28)

- . cos a

(7-29)

U,, = U , K

where K = constant, depending on the resolver construction, and a = actual angle of the rotor position (Figure 7-44). This construction gives directly the vector coordinates U,, and U,, of the rotor angle a. stator

rotor

Figure 7-44. Principle of construction of a resolver with one stator winding.

Resolver with two stator windings Using two stator coils, both the rotor and stator can be used as the primary, depending on the application. We shall describe the case of driving the rotor. The supply of the rotor wind-

294

7 Inductive and Eddy Current Sensors

ings can be realized by a commutator and brushes. Another principle is to use an internal rotating transformer within the resolver, as shown in Figure 7-45. As shown in Figure 7-46, the rotor is excited by two sinusoidal voltages, U,, and U,,. The following output voltages occur at the stator windings :

-

U,,

=

K . U , , sin a

+K.

U,,* cos a

(7-30)

U,,

=

K . U , , sin a

+K.

U , , . cos a .

(7-31)

rotor windings

rotating transformer

housing

rotor supply voltages

/ stator windings

I

++

stator output voltages

Figure 7-45. Schematic principle of a brushless resolver. rotor

stator

7

4 1

uzl

Figure 7-46. Principle of construction of a resolver with two stator windings.

7.4.2.2 Applications and Properties The output voltages of a resolver depend on sine and cosine terms of the angle a of the rotor position. This gives a basis for some special applications of resolvers. They are used, for example, for analog arithmetic operations with trigonometric functions. A second application

7.4 AC-Excited Sensors for Rotary Movements

295

is the determination of the vector coordinates of angles, in general the coordinates of the angle of the rotor. Further, they can be used for coordinate transformations such as conversion from rectangular to polar coordinates [24]. Resolvers are combined with resolver-to-digital (RID) converters, which transform the output signal relationships into digital form. These converters can be produced in hybrid technology with a resolution of typically 12 or 14 bits; with special devices up to 23 bits may be reached [41, 421. They offer accurate measurement and signal processing. Some values obtained with these sensors are:

- an accuracy of less than 1% ; - a resolution of a few angular minutes; and

- frequency ranges from 100 Hz up to 10 kHz. Resolvers are very robust and reliable and can be used in many applications. A typical application is the measurement of angles and rotations within closed-loop servo systems of machine tools and robots.

7.4.3 Inductosyns 7.4.3.1 Physical Principle and Construction Based on the principle of inductive coupling between two windings, inductosyns are a sort of multi-pole resolver (see Section 7.4.2). Depending on the construction, they can be built for measurement of rotation or linear movements. An inductosyn consists of two magnetically coupled parts, which are realized by two planar windings on an insulating material. The first winding, called scale, is fixed to a solid body, such as machine-tool bed, and operates as a stator. The scale of an inductosyn for rotary movements consists of a circular fret-type winding (Figure 7-47 a). Typically the winding is designed as a printed circuit track, bonded to a disk. The other part, the slider, operates as the rotor of the transducer. It is positioned opposite to the scale and turns around with the device, the rotation of which is to be measured. It consists of two identically printed separate windings of fret-type waveform, exactly like that of the scale (Figure 7-47b). One track of the

a) scale Figure 7-47. Schematic diagram of a rotary inductosyn.

b) slider

296

7 Inductive and Eddy Current Sensors

slider is shifted one quarter of a cycle against the other track. The scale and slider are separated by a small air gap. For the discussion of the operating principle, we shall consider the linear inductosyn, which can be derived from the rotating one by reeling off the stator and rotor winding circles. Figure 7-48 shows a schematic drawing of such linear windings.

scale

slider

Figure 7-48. Schematic diagram of a linear inductosyn.

T+T/4

If the scale now is excited by a sinusoidal AC voltage U , , this voltage induces a secondary voltage in each of the two slider windings. The voltages obtained depend on the position of the slider windings relative to the scale. If two tracks are positioned opposite to each other, the induced voltage will reach a maximum value; it becomes zero if the displacement x is one quarter of the track periode p and reaches its minimum when the tracks are displaced by half of the cycle. Hence the output voltage of the slider windings depends on sine and cosine terms of the slider position: U , , = U , . sin (2 u 2 2 =

u,

*

cos (2

71

*

7t

*

x/p)

(7-32)

x/p) .

(7-33)

With this, the position of the slider can be determined for each position within the track cycle. The slider signals arise from an average of several spatial cycles; small errors in the track spacing have little effect and the inductosyn offers a high resolution.

7.4.3.2 Applications and Properties Inductosyns show some advantages in the direct measurement of angular and linear movements. They offer a high resolution and sensitivity, contactless sensing and no wear. Operation in industry with dusty and dirty environments and within vacuum or non-conducting fluids is possible [43]. The temperature stability is good if the materials used for scale and slider have the same temperature coefficient. Some typical values for inductosyns are given in Table 7-1.

7.5 Eddy Current Sensors

297

Table 7-1. Properties of inductosyns. Accuracy

Rotary inductosyn

Linear inductosyn

Absolute error Reproducibility Sensitivity

f 5" < 1" < 0.25"

Ho. Unfortunately, these conditions are insufficient: The restrictions on external fields must be tightened in order to create a stable characteristic. It has been shown by experiment that the magnetization may divide into several domains [27]. This situation is caused by the high field energy of a single domain and by unavoidable imperfections in the layer which favour the creation of domain walls. The effects are twofold: For energetic reasons, adjacent domains may have different signs of M,, so destroying the sensor signal. Secondly, domain walls can move and domains may even switch under external fields, thus the signal is impaired by “Barkhausen” noise. The theory surrounding these effects [28, 291 is commonly known as the ripple theory [3]. The magnetization is said to have a ripple, that is a more or less periodic variation of its direction: The local direction varies around the mean value a, calculated above. The angles a,, or a,,, which include 90% or 50% of M around a, respectively, are determined experimentally. Thus by simple conclusion, the mean value of a, must be lower than 90” - ago,in order that the rotation remains below 90” even locally. The ripples are ascribed to local variations of Hk and of the e.a. Theoretical treatments [28, 291 have successfully introduced internal stray fields which may “block” the magnetization. These stray fields are calculated taking into account exchange coupling which causes magnetization dispersion, and different orientation of crystallites. Blocking by stray fields hinders free rotation of M which is then registered by hysteresis in the characteristic. The field relations are explained best by the blocking curve shown in Figure 9-4: the dashed curve (a) is the left wing of the astroid and the single domain theory “allows” all H-vectors to the right of (a). The ripple theory restricts the permissible area to the right of the blocking curve, eg, (b). M will be blocked if the tip of H touches the blocking curve and cannot be rotated back until H i s to the far right of the blocking curve. It can be seen that blocking can occur for certain values of Hy even with positive H,.

Ah,

Figure 9-4. Restrictions for field vectors given by the blocking curve. The dashed curve (a) is the Stoner-Wohlfarth astroid, the solid curves (b) and (c) are two different blocking curves. Only field vectors to the right have a reversible field-magnetization-behavior. Magnetization becomes blocked if the vector tip touches the blocking h ;x curve. The fields given are normalized to Hk:eg, h, = H x / H k ;demagnetization has not been taken into consideration (taken from [28]).

I

00

-9

-1.0

-0.6 ha&)-1

-0.2 0 0.2 0.4 ha(k1-l

350

9 Magnetoresistive Sensors

In using a magnetoresistive sensor then, the operator must guarantee that H is always to the right of the blocking curve (or at the left of its mirror image if M, < 0), otherwise the characteristic may become unstable. It is sufficient, but not always necessary, to have H, higher than a certain minimum. Data must be determined by experiment or checked from the data sheet. An example of sensor characteristics, showing the effect of a stabilizing field, is given in Figure 9-11. The actual position of the blocking curve depends on film quality: a good one would be that described by curve (b) in Figure 9-4, not too far from the astroid, whereas the curve described by (c) belongs to a film unsuitable for sensing applications. Film quality is essentially determined by deposition parameters (especially crystallite diameter, oxygen content, and surface smoothness). Most of these parameters can be summarized in the structure constant S [29] (not to be confused with the sensitivity).

9.3 The Magnetoresistive Sensor The basic element of all sensors is a film (thickness: t ) f a magneto :sistive alloy etched into a rectangular shape (length: 1, width: w) as shown in Figure 9-5a. Electrodes are attached at both ends in this example causing the current Z flowing parallel to the easy axis. Usually the geometry is chosen to make I > w & r.

- I-

C)

I

x

e.a.

Figure 9-5. Geometries of magnetoresistive sensors. White rectangles (length: I, width: w, thickness: t ) are the magnetoresistive layers, hatched parts are electrodes of much better conductivity. a) is the simplest geometry: the current I flows parallel to the e. a., resulting in the square characteristic. b) and c) show linearized sensors due to inclined elements or to barber poles; the current is rotated out of the e.a.

351

9.3 The Magnetoresistive Sensor

The material is characterized by the anisotropy field Hk and the geometry must be described by the demagnetizing field H d . The long, flat rectangle is a good enough approximation of an ellipsoid to allow calculation of the demagnetizing factor: N = t/w

(9-23)

with sufficient accuracy. N may be chosen within a wide range simply by varying width and thickness, as long as N 6 1. Demagnetizing fields perpendicular to the layer plane (N, = 1 -N,-N, = 1) are very large, to the extent that normal field strengths will not elevate M out of the layer plane, a fact that was made use of earlier. As the ellipsoid shape is only an approximation, there are deviations from the assumed homogeneous demagnetizing field. M is rotated less in the upper and lower edges than in the middle of the stripe; the sensor signal is given by a mean value of q. This heterogeneous rotation is the reason for differences between the calculated and measured sensor characteristic at higher fields (see Figure 9-13). The sensor resistance R can be calculated using Equations (9-3) and (9-15). Furthermore, with 0 = q, (ty = 0), having H, = 0 and abbreviating R , + A R = Rb, then:

R ( H ) = Rb - A R (H,/HO)’.

(9-24)

In the same manner, it is possible to calculate the signal of the planar Hall effect starting with Equations (9-5) and (9-15):

U,

=

A p * Z * (l/t)

*

H,/Ho

*

1/1- (H,/H0)’

.

(9-25)

H, must be replaced in both equations by H, + H,/cos p if H, # 0. Both curves are drawn in Figure 9-6: the (dashed) parabola of the magnetoresistive effect and the solid curve with a linear center, representing Equation (9-25), which describes both the barber-pole sensor as well as the planar Hall effect.

Figure 9-6. Calculated characteristics of the simple magnetoresistive sensor in Figure 9-5 a (dashed) and the barber-pole sensor (solid) in Figure 9-5c. The solid curve also represents the characteristic of the planar Hall effect, only the ordinate caption needs to be altered.

I

-1

I

-0,s

I

I

I

0

0.5

1

L

352

9 Magnetoresistive Sensors

Equation (9-24) establishes a square relationship between magnetic field and resistance, whereas (9-25) contrastingly describes a symmetrical S-shaped curve with a linear center part; the linearity error may be made small when only small fields are involved since there is a point of inflection at Hy = 0. It is necessary to remark upon the two possible states of magnetization that can exist, discussed for H, = 0. The calculation of the magnetoresistive signal (9-24) was straightforward - both solutions, pl c 90" and pz = 180" - p,, give the same resistance (depending on the sine and the squared cosine). The signal of the simple magnetoresistor does not depend on the state of magnetization. This does not hold for the planar Hall effect - the calculation of Uyrequires sine and cosine, but the sign of the cosine is different in both solutions. The planar Hall effect transducer thus alters the sign of its signal if the magnetization switches from one state into the other. Correct operation requires that only one of the states is maintained. It has been discussed above that domain splitting and wall movement may occur unless precautions (certain fields with H, > 0) are taken to ensure the desired state of magnetization. The simple magnetoresistor does not require these precautionary measures to secure a correct characteristic - but it will suffer from magnetic noise if these fields are not applied. It is important now to consider what possibilities for linearization of the parabolic fieldresistance relationship exist, and it will then further be discussed whether it is possible to obtain linearized relationships, with positive and negative slopes, for the field dependence of R. A procedure that can yield both signs is advantageous as it allows cancellation of the constant (but temperature dependent) part by combining four, or at least two, elements with different slopes in a Wheatstone bridge. If necessary, a distinction will be made between the single resistor, called a sensor element, and the sensor circuit or sensor bridge consisting of four or two elements.

9.3.1

Linearization

It can be said generally that the square characteristic is caused by the parallelism of magnetization M and current Z without external fields. Linearization can be achieved by either rotating M or by rotating I in this rest state. The simplest way is to rotate M by addition of a constant bias field HB in the y-direction [ll]. Replacing Hy in (9-24) by Hy + HB yields: R ( H ) = Rb

- 2 * A R * Hy * H B / H i - AR (H:

+ H;)/Hi,

(9-26)

which is linear for Hy 4 H,. Unfortunately, this method demands a stable bias field as each variation of H , appears as a variation in the signal H y ; moreover, different slopes require different signs of H s imposing additional difficulties. Methods for introducing additional fields will be discussed later. A bias-linearized sensor will still work well in both magnetization states, although magnetic noise may be present. An alternative way to achieve linearization is by rotation of the current Z through an angle v/ against the e.a. Figure 9-5b gives one of the two solutions known.

9.3 The Magnetoresistive Sensor

353

The rectangular resistive element is inclined at an angle v/ to the e. a. with the current still flowing along the stripe axis [8, 91. The figure shows both of the two possible inclinations. The rest magnetization M, is partly rotated from the easy axis to the stripe axis (see Equation (9-22)) as drawn. It is necessary to force one of the magnetization states by a stabilizing field having the easy direction and this field will, of course, further influence M,. The signal can be calculated by setting 0 = a, - v/ and using Equations (9-3), (9-15), and (9-22). The result is more complex than other cases unless the angle a,, - v/ between M, and I is chosen to be 45 ". This will simply create a term sin (a, - a,,) cos (a, - a,,) as seen in the discussion of the planar Hall effect. The slope of the R-H-dependence can be adjusted by the sign of the inclination - see the two examples in Figure 9-5 b. A Wheatstone bridge can then be realized without any problems. The designer must pay for this advantage however, as the linearized sensor must always be driven in the same state of magnetization stabilized by a field with H, > 0. The inclination angle v/ is chosen by most designers to be +45" [8,91, but steeper inclinations have been reported, too [30]. Different slopes of characteristics can be attained not only by different inclination, but also by the application of positive and negative stabilizing fields to elements with equal current directions [31, 321. This more complicated technique reduces the sensor's sensitivity to asymmetries caused by misalignment, lithographic errors, and to strain gauge effects (which are even present in nonmagnetostrictive materials) since the current flows in the same direction anywhere in the sensor. The second means for rotation of current is the application of slanted stripes of good conductivity as shown in Figure 9-5c [12]. This arrangement is usually termed barber poles because it looks like the well-known sign for barber shops. The barber poles represent a short circuit - the current flowing in the gaps between them will therefore take the shortest path, i. e. perpendicular to the barber poles. If the current inclination is v/, the barber poles will be inclined v/ +90" (this will be modified when edge effects are considered later on); normally I// = +45" will be chosen. The field-resistance relationship can be calculated; with v/ = *45" it yields:

*

R (H) = R, f AR

*

(Hy/H,)

1/1

- (H,/Ho)~

.

(9-27)

This is represented by the solid characteristic in Figure 9-6 which shows good linearity for Hy < 0.5 H, (error 5 5 % ) . Calculation is much simpler than for the inclined element because the ferromagnetic rectangle exhibits the same magnetic behavior as the rectangle in Figure 9-5 a, discussed in detail above. The barber-pole sensor will, like most of the linearized sensors, only function properly in one magnetization state. Switching of M results in the adaption of the other sign of the slope. There is one disadvantage to the barber-pole sensor: its resistivity per unit area is smaller since firstly, its area is partly short-circuited and secondly, the current path is broader, although it is shorter in the gaps between. A Wheatstone bridge can be built of elements with positively and negatively inclined barber poles, and it should be noted that the method utilizing positive and negative stabilizing fields is also applicable.

354

9 Magnetoresistive Sensors

9.3.2 Sensitivity and Measuring Range The quantity actually measured by the magnetoresistive sensor is the magnetic field strength H - in contrast to normal Hall sensors which respond to the flux density B. In a vacuum (and to a good approximation in all non-ferromagnetic materials as well), H a n d B are related by B = po . H with the magnetic field constant p0 = 4 n 10 V s/A m. The sensitive axis is, with few exceptions, the hard axis or y-direction. Sensitivity in the easy or x-direction is lower, sensitivity to fields H, perpendicular to the film plane is negligible due to the large demagnetizing field. The sensitivity So can be defined as the variation of the output voltage Uswith the field variation related to the operating voltage Uo,thus:

-’

So = (AUs/AHy) * l / U , ,

(9-28)

to be measured in (mV/V)/(kA/m). Some authors define a different sensitivity S, = So . Urn,,, where U,,, is the highest permissible operating voltage. So is of significance in linear sensors only, ie, if So is not dependent on the field. For the purposes of example here, the sensitivity for barber-pole sensors will be derived; they are linear and their magnetic behavior is easily calculated. The sensitivity of sensors with inclined elements does not differ markedly, but they may have a lower linearity range. It will be assumed further that the sensor is a full-bridge circuit; half bridges have only half the sensitivity. The calculation begins with Equation (9-27) which gives the field-resistance relationship of a single barber-pole element. The full bridge is a combination of four elements, each adjacent one having a different sign. This full bridge sensor has the signal:

Us= Uo * Ap/p * (H,/(HO

+ H,))

*

fl

- (Hy/(Ho + H,))’

(9-29)

and for Hy 4 Ho + H, the sensitivity becomes

Equation (9-30) shows the importance of the characteristic field H,: the sensitivity So is reciprocal to Ho for H, = 0. A field H, > 0 will decrease So, and So is proportional to the magnetoresistive effect Ap/p. A second quantity describing the sensor is the measuring range H, - which can be defined as that field range within which the linearity error will not exceed a certain limit. Taking barber-pole sensors (or planar Hall-effect devices) and a limit of 5% it holds that: HG

0.5 (Ho

+ H,)

(9-31)

Other sensor types, eg, those with inclined elements may have narrower linearity ranges depending on the bias field, H,, and the angle of inclination. Combining Equations (9-30) and (9-31) results in the term:

9.3 The Magnetoresistive Sensor

So HG = 0.5 Ap/p

.

355 (9-32)

With the magnetoresistive effect Ap/p given as constant, the sensitivity can thus only be increased by decreasing the linearity range o r vice versa. The linearity range HG and the sensitivity So are primarily fixed by the designer of the sensor in their choice of thickness t and width w of sensor stripe. Taking t / w = 1/1000 . . . 1/10 and M, = 800 kA/m, this gives Hd = 0.8 . . . 80 kA/m; and with Hk = 0.25 kA/m (Permalloy) it follows that HG = 0.5 . . . 20 kA/m is given essentially by the demagnetizing field. The user may only increase HGby applying a field H, - and normally the designer demands and takes into account a certain H, in order to stabilize the characteristic. A high sensitivity can be achieved with a low characteristic field. One way is to induce the e.a. perpendicular to the long stripe axis (usually the hard direction) and ensure that Ho = IHd - Hkl , according to Equation (9-21). Ho may be made very small if Hd = Hk, but then the relative error in Ho becomes much higher than that in H k , which itself depends considerably on process conditions. A better way is to use a system which depends only on Hkby ensuring Hd Q H k , which can be achieved by making I = w, using the given formulas. However, sensors such as this would have a very low resistance and so be unsuited for most applications. A high-resistance sensor with low demagnetization can be realized by putting a number of stripes parallel with respect to their geometry (but connected electrically in series), ensuring the width of the gaps between them is of the order of their thickness [30]. The signal voltage Usof the sensor can be increased by increasing the operating voltage U, until its maximum value U,,, is reached. The limits of Urn,, are given by the power dissipation maximum Po (or a tolerable temperature rise AT which is related to the thermal resistance R,,and power dissipation maximum Po by Po Rth = AT) or by the tolerable current density j,,, . The lowest detectable field Hmi,is given by the lowest detectable signal voltage which itself must be higher than the noise level. There are a number of sources of noise, and these are thermal noise (the same formula as for normal resistors applies), magnetic o r Barkhausen noise [27], and offset drift, eg, due to thermal gradients or thermal mismatch of the bridge circuit. Thermal noise will be small, whilst Barkhausen noise will be suppressed by a stabilizing field (see Section 9.2.4). Drift effects are minimized by operating the sensor at constant temperature and low power; these are, of course, low frequency signals. The electronic amplifiers necessary with low signals will usually generate more noise than the magnetoresistive sensors themselves. The frequency range of magnetoresistive sensors extends from DC-fields to at least 65 MHz [8].Theoretically, the upper limit should be about 1 GHz, although experimental verification failed due to inductively coupled signals.

356

9 Magnetoresistive Sensors

9.4 Sensor Fabrication 9.4.1 Magnetoresistive Materials From the point of view of the developer in this field the most important properties for a magnetoresistive material are: a large magnetoresistive effect A p / p to ensure a high ratio of signal to operating voltage, a large specific resistance p to realize a certain resistance in a small area, low variation of p and Ap with temperature, low anisotropy field Hk, low ripple or coercivity H,, zero magnetostriction, otherwise mechanical stress will impair sensor data, long term stability of all properties. Most established materials are (crystalline) binary and ternary alloys of Ni, Fe, and Co

- the most preferred one being Permalloy (NiFe 81/19) [2-4,6-14, 16-19,27, 33-39]. Amorphous films, however, have provoked a degree of interest in the last few years [19, 381. Comparisons of measurements done by different authors should be treated with caution; properties like p, Ap/p, Hk,and H, depend not only on thickness, but also on deposition and processing conditions, which are not always reported. The anisotropy field Hkis plotted in Figure 9-7. The lowest values are found with binary NiFe alloys having high nickel content. Amongst these is the Permalloy, already mentioned, with zero magnetostriction. It is seen that even small additions of Co will increase Hkconsiderably; they may at the same time otherwise improve the layer. Hkdepends to a great extent on processing conditions. Data on the magnetoresistive effect A p / p - the most important figure of merit - are reproduced in Figure 9-8. Here the NiCo alloys are favourable showing a peak value of

Ni

Figure 9-7. Anisotropy field Hkas a function of film composition for the Ni-Fe-Co system, deposited at 250°C. Compositions with zero magnetostriction are indicated by the dashed line. The field strength is given in Oersted (1 Oe P 1000/4x A h ) (taken from [33]).

9.4 Sensor Fabrication

351

L.0

r.\

NiCo A NiFe

3.0

I

i I

-"as 2.0

I

a

Q

1.0

Figure 9-8. The magnetoresistive effect A p / p of binary NiFe and NiCo alloys as a function of Ni content. Evaporated films of 30 nm thickness, deposited at 2 0 0 T (taken from [34]).

50

"0

100

% Ni IN FILMS

Ap/p = 3.7% with the composition NiCo 70/30. Unfortunately, this alloy suffers from magnetostriction. NiFe alloys show a much lower Ap/p, but the maximum is found at 85% Ni, a composition in the region of Permalloy. Data on the less common CoFe alloys are given in 1391. If the search is restricted to alloys free of magnetostriction the best alloys are NiFe 81/19 and NiCo 50/50, both with Ap/p = 2.2%. There have been attempts to find alloys which show a higher magnetoresistive effect. In particular, many efforts have been made to improve the NiCo 70130 alloy through addition of a third element [36, 381, but these have so far proved unsuccessful. The magnetoresistive effect of amorphous films is one to two orders of magnitude lower than that of crystalline ones [19, 381. An improvement in this figure could be expected however, because the search was only started a few years ago.

38-

\

\

Figure 9-9. Specific resistivity p of Permalloy as a function of layer thickness t. The dashed curve shows data after cathode sputtering the solid one after annealing in vacuum at 450°C , 2 h (adapted from [51]).

I

40

120

200

I

I

-

280 t / n m

358

9 Magnetoresistive Sensors

The specific resistance p of these alloys is comparable to that of other alloys; generally, it is found that p is increased by Co addition. p shows a marked thickness dependence, an example of which is seen in Figure 9-9 for Permalloy. It increases with decreasing thickness for t < 100 nm. In addition, p depends on deposition or annealing conditions [4, 37, 39-41]. Deposition at T t: 250°C is said to yield the lowest resistivity - but annealing effects will be less pronounced. Since, as a rule of thumb, Ap is not dependent on thickness or processing, all variations in p will introduce inverse variations into Ap/p. The temperature coefficient (TCR) of p, 8 p / a T . l / p , is akin to that of normal metals and to 4 is in the order of 3 . K-I. A positive correlation between Ap/p and the TCR is reported [38], but replacing Fe in the Ni-Fe-Co system by Ge or Zr reduces the TCR much more than it does Ap/p. The dependence of the TCR on thickness and processing is similar to that seen for Ap/p. The variations of Ap with temperature are smaller than those of p ; values between -0.5 and -1.5 K-I are found, the lower figures applying to NiCo alloys. The upper temperature limit - in theory the Curie temperature (= 550°C for permalloy) - is determined in practice by restrictions imposed by the technology used. Magnetoresistive data may - according to the author’s experiments - be extrapolated linearly at least up to 250°C. The magnetic quality of materials is specified best by the coercivity H, which is easily measured (see Figure 9-3) or by the ratio H,/Hk; both should be low. Data for H , in the NiFe-Co system are found in Figure 9-10 [42]. Again, the lowest values are found near the Permalloy composition; the datum of 80 A/m varies, of course, with process conditions. Whilst NiCo alloys have higher H,-values, the ratio H,/Hk may be lower than for Permalloy [18, 35, 361, so producing less magnetic noise. The lowest H , data reported are measured with amorphous layers [19], probably due to absence of grain boundaries - a fact which compensates for the low magnetoresistive effect. H , decreases with increasing temperature; low temperatures are therefore the most critical. The anisotropy Hk may be reduced by annealing but, as has been learnt from experience, this is not true of the coercivity H , [37, 431. The effect of a reduction in Hk would be to shift the blocking curve to lower field strengths. The coercivity has been decreased successfully by using a multilayer structure: several NiFe layers were separated by thin (nm range) nonferromagnetic layers (SO, SO,, Si, Au, Ti) [44]. The improved quality must be paid for, however, by a reduced Ap/p = 1.6 . . . 1.8%. It has been found that H , increases with a decrease in the width of the sensor stripe [26, 361 - the magnitude, however, cannot be explained by demagnetization only. The long-term stability of magnetoresistive layers is excellent [45], even at temperatures above 200°C - results which are much better than with the equivalent semiconductors. (An exception to this are the amorphous layers which may recrystallize at T > 150°C.) These layers, however, need to be covered with good passivation layers, since the nonnoble NiFeCo alloys suffer from corrosion. Corrosion of the alloy is enhanced by it being in contact with more noble metals, like gold conductors or barber poles. Addition of several percent of Cr or Rh reduces susceptibility to corrosion [46, 471, but at the same time this diminishes the magnetoresistive effect. In summary, the most important data are assembled in Table 9-1. Tho compositions stand out as the most promising for application in magnetoresistive sensors. There is, on the one hand, the well proven permalloy, which has zero magnetostriction and low anisotropy, but only moderate magnetoresistive signal. It is a good candidate for sensors intended for the

9.4 Sensor Fabrication

359

Fe

Figure 9-10. (Wall) coercive field H, as a function of composition for the Ni-Fe-Co system; coercive field strength is given in Oe (taken from [42]).

Table 9-1. Comparison of some important magnetoresistive thin-film materials. Parameters shown are specific resistivity p, magnetoresistive effect Ap/p, anisotropy field Hk, coercivity H , , magnetostriction coefficient A, and saturation magnetization M,. Values apply to films of about 100 nm thickness at room temperature. Some of the data, especially H , and Hk, may vary considerably as a result of process variations. Material NiFe NiFe NiCo NiCo NiFeCo CoFeB ') ')

81:19 86:14 50:50

70:30 60 : 10 : 30 72 :8 : 20

amorphous

22 15 24 26 20 86

2.2 3.0 2.2 3.7 2.5 0.07

250 200 2500 2500 2000 2000

80 100 1000 1500 250 15

=O - 12 -0 -20 -5

=O

1.1 0.95 1.25 1 .o 1.3 1.3

360

9 Magnetoresistive Sensors

detection of low fields and for operation in a wide temperature range. There are, on the other hand, the alloys containing about 30% cobalt which show a much better Ap/p but worse magnetostriction behavior; Hk is high, but H,/Hk may be lower than for NiFe, and these cobalt-containing alloys show a lower temperature dependence for Ap. Their best field of application seems to be in bubble memories and reading heads.

9.4.2 Fabrication Techniques 9.4.2.1 Magnetoresistive Layers Magnetoresistive layers are deposited by vacuum evaporation or cathode sputtering (electroplating has decreased in popularity) [3, 251. Deposition conditions have to be controlled carefully as the layers are very sensitive to contamination or composition variation. Oxygen partial pressure has to be low ( < 10 - 4 Pa) [48], since magnetic properties of NiFe films will be degraded with only a 2% oxygen content [49]. Most papers recommend - though this is in contrast to the author's experience - substrate temperatures between 200 and 300°C [18, 29, 34, 351. There are doubts whether this temperature effect is really due to crystallite growth or is, in fact, caused by incorporation of residual gas atoms at grain boundaries [SO]. The deposition - at least if done at low temperatures - should be followed by an annealing process (see below). The easy direction may be induced by deposition in a homogeneous magnetic field of at least 1 kA/m. The requisitions for homogeneity (deviation < 1 " in industrial production) poses problems, particularly in the vicinity of a ferromagnetic target. Substrates used must have extremely smooth surfaces; different glasses (quartz or hard glass), or oxidized silicon are a good choice, whilst ceramic substrates are not so good. Single crystal substrates may produce unwanted anisotropy. Different thermal expansions of substrate and layer are tolerable, at least with zero magnetostriction layers. Vacuum evaporation as a technique has been used very successfully for quite a few years now [34-36, 39, 41, 45, 48, SO]. The (temperature dependent) deviation of composition between source and layer has to be kept in mind; an advantage of evaporation is the simplicity of composition variation. Medium deposition rates (about 5 m/min) are approved. Cathode sputtering is quite well established too, be it normal RF sputtering [19, 20, 49, 51, 521 or magnetron sputtering [37]. Worse results have been achieved with ion-beam sputtering

WI. Targets must be pure, especially free of oxygen, and should be vacuum melted. Bias sputtering reduces oxygen contamination but will also influence the composition [52], and bad experience with bias may be caused by the latter effect. The real deposition process has to be preceded by a careful preclean of the target. Cathode sputtering gives good reproducibility and well adhering layers and is thus favored in industrial production. It has been reported that permalloy films may be improved (better Ap/p and lower H , ) by H;-ion implantation [54]. Annealing of magnetoresistive films is recommended, especially for films deposited at low temperatures [19, 20, 35, 37, 41, 42, 45, 54-56]. Annealing has to be done under low oxygen pressure in vacuum or hydrogen [56]. It reduces p (and thus increases Ap/p) and H k , but may have no or even negative influence on H, [29, 421. Annealing should last several hours

9.4 Sensor Fabrication

361

at T 300°C; this temperature is relevant since crystal growth may impair magnetic properties at T > 350°C. Annealing should occur in a homogeneous field of several kA/m, since this field will rearrange crystal orientation to induce the easy direction - if this has not already been achieved during deposition. Lowest H,-values have been attained by rotating the easy direction into the former hard direction or by annealing in a field rotating with a frequency of one to several Hz [19, 56, 571. ;5:

9.4.2.2 Contact and Passivation Layers Magnetoresistive sensors consist not only of the ferromagnetic layer already discussed in detail but also - like other components made in thin-film technology - of layers for contact and passivation purposes. These will be dealt with only briefly here as they are produced by well-known technologies. Experience has shown that magnetoresistive alloys adhere very well, so special adhesion layers would be superfluous. Contact layers are necessary not only for external connections, but also for realizing the barber poles which rotate the current paths. The most well established materials for this purpose are gold and aluminium, and both may be contacted by bond wires. Au has the lower resistivity and better stability, but NiFeCo layers are less noble and so may corrode under humidity when in contact with the gold. This problem can be solved by using Al, but only at lower temperatures. A1 is less stable, only permits lower current density, and develops intermetallic compounds when in contact with Au (bond wires!) at T > 150°C; this last effect is known as “purple plague”. Contact layers can, in addition, diffuse into the NiFeCo alloys. Although magnetic degradation has not been observed [45], considerable interdiffusion or even formation of intermetallic compounds must be considered as a potential problem with respect to long-term stability [ 5 8 ] . Thus, barrier (and sometimes adhesion) layers of Mo, Ta or WTi are recommended as countermeasures. The demand for long-term stability can only be completely fulfilled with proper passivation layers. The necessary prerequisites are an impermeability to oxygen or water and deposition by low temperature processes. Best approved are SiO, and Si,N, layers laid down by plasmachemical processes or sputtering, a standard technique employed in the semiconductor industry. These layers were unsatisfactory, however, for sensors with the barber-pole structure [51]: it was found that covering of the steep slopes was incomplete. As an alternative, organic passivation layers of polyimide were found to give good results. The careful structuring of magnetoresistive, contact, and passivation layers is achieved with well established techniques [51] that need not be mentioned here. It is worth noting, however, that pemalloy can be wet chemically etched with an etch consisting of H,SO,, H,O,, HF and H,O [51]. Restrictions o n dimensional tolerances for magnetoresistive sensors are much more severe than for other microelectronic devices since the sensitivity and resistance depend o n the width of the stripe. But more critical, perhaps, is the fact that most sensors are bridge circuits containing resistors whose structures are perpendicular to each other (inclined stripes or barber poles). The author noted the experience that lengths perpendicular to one another may differ

362

9 Magnetoresistive Sensors

by an amount in the order of 0.1 to 0.2 pm due to errors in the photolithographic processes. Although this is only a fraction of a wavelength, it amounts to several percent of, eg, a barber-pole gap of 4 pm and appears as a bridge unbalance of the same magnitude. Nowadays, high-precision electron-beam masks and well adjusted exposure equipment help to minimize these deviations.

9.4.2.3 Measurement Techniques Production processes are monitored closely by measurements during processing in a similar manner to the completed sensors. Only techniques specific to magnetoresistive sensors will be dealt with here, however. All magnetic fields are weak enough to be generated by air coils like Helmholtz coils or cylindrical coils; their field is homogeneous, easily calculated and (contrary to coils with ferromagnetic cores) absolutely proportional to the current. It may be necessary to shield (or compensate for) the earth’s field and other stray fields. The parameters which are measured during processing (the layer data) are H k , H,, Ap/p, p, and the position of the easy axis. Hkand H, are determined by creating an M-H- (or BH-)diagram (magnetization curve), a circular shape (silicon wafer) is appropriate. Figure 9-3 gives the curves to be expected though other examples are drawn in [25]. The positions of the easy and hard axis are found by rotating the sample. The characteristic field Hois obtained in the same way with the structurized layer, whilst p and Ap/p may be measured using the well established four-point probe; the four probes should be arranged in a square or rectangular manner - formulae can be found in [59]. It is possible to buy specialized commercial apparatus which has been especially adapted for thin-film evaluation. Sensitivity and linearity range can be taken from the characteristic of a complete sensor (ie, the output signal Usis taken as a function of the external field H,, with a bias or stabilizing field as parameter). The direction of the external field, however, must be aligned precisely with the sensor’s sensitive axis (hard axis or y-direction), especially when no stabilizing field is being applied. If the alignment is not precise, small components H, are induced which will switch the magnetization and thus, indirectly the characteristic also, resulting in what is known as the “butterfly-curve”. An example of characteristics showing the influence of a stabilizing field in the x-direction is given in Figure 9-11. The minimum stabilizing field H, necessary (hysteresis should be lower than even that shown in Figure 9-11c) is an indication of layer quality - this H, depends on the maximum applied field H,,. A better form of quality estimation is a plot of Usagainst H, with a constant (but preferably not vanishing) H,,. Since this is a horizontal line in the Stoner-Wohlfarth astroid Since switching (Figures 9-2 and 9-4), the magnetization switches and changes the sign of Us. should occur without transition when crossing the astroid, smaller switching fields and broad transitions are thus an indication of lower quality. max to The magnetoresistive effect Ap/p should be the ratio of maximum signal swing Us, operating voltage Uo.This is true only in the first approximation due to the effects of incomplete current rotation and inhomogeneous demagnetization (see Section 9.4.3.1). The former effect can be corrected for by also measuring the square terms (Figure 9-13), but the

9.4 Sensor Fabrication

/

363

1

Figure 9 4 . Influence of stabilizing field H, on the sensor output signal Us; for clearness shown on a bad sample with high H,; t t: 60 nm, w = 40 pm, H, = 1.5 kA/m. a) H, = 0, M is blocked and will not be deblocked totally, and there is severe hysteresis; even the offset differs from b) and c). b) H, = 0.19 kA/m, hysteresis max. 12%, the s-shaped curve is recognized. c) H , = 0.38 kA/m, hysteresis reduced to 2%, maximum signal higher than in b) and occurring at higher H,,.

latter cannot. The magnetoresistive effect measured with complete sensors is smaller than that measured with the circular shaped layer.

9.4.3 Sensor Layout 9.4.3.1 General Considerations The layout is determined primarily by the type of sensor required (biased, slanted stripes or barber poles), sensitivity So, and resistance R . The simple stripe arrangement like that drawn in Figure 9-5 is used only when the field to be detected is restricted to small volumes (eg, magnetic disks). Industrial general-purpose sensors are designed to have greater resistance in the order of 1 kQ or higher, in order to ensure a high signal voltage in spite of low power dissipation and so be comparable with other sensors, like pressure sensors. Several technological restrictions must be needed, however. Firstly, the thickness t has a lower limit; otherwise the magnetoresistive effect becomes too low and the resistivity shows too much scatter. This limit is between 30 and 40 nm, although layers of only 20 nm have been reported. Secondly, the current density j has an upper limit j,,, may be high compared to usual conductors if the magnetoresistive alloy has been passivated (j,,, = 10" A/m2 for

364

9 Magnetoresistive Sensors

Permalloy [45]). Nevertheless, the current I may itself be limited as t is sometimes very low. (Further restrictions with barper-pole sensors are discussed below.) In addition, power dissipation must be small in order not to exceed certain temperature limits and to ensure low temperature gradients. Even a layer of t = 30 nm and p = 30 l o - * SZ m has a sheet resistance of R, = 10 sZ/O. Thus, a resistance of 1 kSZ requires a length-width ratio of I/w = 100, usually only ever realized in a meander structure. The design starts with material selection which will determine Ap/p, p, and Hk : thickness effects should always be borne in mind. Sensitivity So or linearity range HG (the two are interrelated, see Equation (9-32)) must be given in order to determine & and the thickness to width ratio t / w = p (Equations (9-13), (9-22), and (9-23), respectively); the demagnetization may be reduced by ensuring small gaps between the stripes, thereby introducing mutual magnetic coupling. Additional quantities to be fixed are resistance R,, power Po,or operating voltage U,. Design of a sensor linearized by a bias field is the most simple task; a similar treatment may also be used for sensors with inclined stripes, however, barber-pole sensors require a different approach. Assuming normal resistor geometry, R = p . I/(t w), one gets:

-

-

(9-33) Both, t and w must be increased if t happens to be below its lower limit (30 to 40 nm). The designer should also bear in mind that current density j achieves its highest value at the point of current reversal in the meander. Length I and area A are easily calculated when R,, p, t, and w are known. Normally, the designer tries to minimize A by utilizing the permissible values of t or j . The area decreases with increasing linearity range HG , so high-sensitivity sensors need larger areas. This simple, straight forward procedure can, however, be improved; the general idea is to reduce demagnetizing effects, to increase HG and optimize the bias field [16, 18, 30, 32, 601. Lower area or higher sensitivity are obtained by reducing demagnetization with tight coupling between the stripes; separation between stripes must be of the order of their thickness. The effects of mutual coupling and of heterogeneous (ie, nonhomogeneous) demagnetization have been analyzed quantitatively with great success [32, 601. Further optimization can be achieved through the choice of the best inclination angle p of the elements (normally taken to be 45"). The difference between p and (p, (angle of rest magnetization M,, ie, without unknown fields but with bias) should amount to 45". (po depends on anisotropy Hk and demagnetization H d , but also on the bias field and even on p itself. There are no simple formulas or recipes available to help determine the right solution - optimization must be performed using computer simulation. A lot of relevant information for this can be found in [60]. The description of barber-pole sensors is different from the others as barber-pole sensors have a simpler magnetic behavior. All stripes are in the e. a., and the distances between them must be increased (barber poles extend the stripes and must have a clearance) so that no coupling effects are present. Understanding the electrical behavior of barber-pole sensors on the other hand is more difficult, although simple calculations will lead to an optimum design [51, 611; a more detailed computer simulation, however, will be found in [62].

9.4 Sensor Fabrication

365

The geometry of the barber poles is shown in Figure 9-12. Disregarding edge effects, it is seen that each gap has length a and width w fl, and that the fraction s/(s + a) is shortened by the barber poles. The resistance therefore is:

R,

=

1/2

. a/(s + a) . p . l/(w - t) .f .

(9-34)

/b-P\

T

Figure 9-12. Geometry of the barber-pole structure; current paths are drawn. Rotation of current is f45' in the middle, but much less at the edges; the rotation averaged over the gap is thus 45" -5. The current paths in the barber poles are longer and denser than in the gaps.

W

The correction factor f accounts for edge effects and the resistivity of the barber poles; experience shows that f = 1.2. The resistance in this type of sensor is 2 to 4 times smaller than that in any other sensor having the same area. The important parameters to be considered are voltage drop U, and current density j , (all barber-pole parameters will be denoted by the index B). U, and j , are calculated in relation to U and j in the magnetoresistive layer, since the expressions can be split up into material parameters and factors dependent on geometry only:

j,/j = t/t,

q

.

(9-36)

The geometric factors 0 and q depend only on the ratio a/s of barber-pole gap to barberpole width, and both are drawn in Figure 9-13. A good design would have U,/U d 1, and usually U B / U = 0.1. If 1 < a/s < 2 with 0 < 5 and taking good conductors (Ag, Cu, Au, Al) with p B / p 0.1, the barber-pole thickness t, must be at least five times the thickness of the magnetoresistive layer t, so that the quotient of the current densities j,/j will be in the region of 0.3 to 0.5. However, the lower j , may restrict the maximum current since j,,, of good conductors ( j < lo9 A/m2 for Al) may be much lower than that of, for example, Permalloy. Furthermore, barber poles impose a number of geometrical restrictions: J

- t,

- 1

2 5.t

< a/s < 2

- w 2 2.a - s 2 2 . tB

(as discussed), (as discussed), (otherwise edge effects will influence sensitivity), (otherwise the current will not flow in the whole layer).

Combining these four inequalities gives t/w < 1/20 . s/a from which it is possible to deduce that HG < 25 kA/m * a/s. The linearity range HG of barber-pole sensors is more

9 Magnetoresistive Sensors

366 L

14 -

12 10 -

8-

64 2 -

0,l

0,2

0,5

1

2

5

10

a/S

Figure 9-13. Variation of current density ratio q and voltage drop ratio Q in the barber poles with geometry a/s.

constricted than that of other sensors, though H G can, of course, be increased by applying a field in the easy direction (H, > 0). To the designer, the choice of barber-pole width is a compromise. The barber-pole width s should be small to create small stripe widths w and thus ensure that high HG values are feasible (small area!), whilst large barber-pole widths ensure that only small errors are incurred due to width variations caused by the lithographic processes, as mentioned above. A good compromise, in the author's experience, is to have s = 4 pm. The current flowing in the barber poles generates a magnetic field in the magnetoresistor which can be used as a stabilizing field [63]. The x-component of this field is:

H, = U(2 * w) * a/(a

+ s) ,

(9-37)

where I is the current. Normally this field should have the same direction in all stripes; this prohibits some of the possible combinations of current direction and barber-pole inclinations [15] and instigates the need for normal conductors for current reversal in meanders. It has been shown that the linearization created by barber poles is not perfect [61]. The reasons for this are edge effects (the current flows parallel to the stripe axis, see Figure 9-12) and the voltage drop U, (a part of the current remains in the magnetoresistor). The mean current is thus inclined at an angle less than 45" to the x-axis, say 45" - 5. This effect can be described (in place of Equation (9-27)) by the term: R(H) = R ,

*a

H , / H , . 1/1 - (H,/Ho)2

- p a(H,/Ho)2,

(9-38)

where a and p may be interpreted as A R . c o s 2 5 and A R s i n 2 5 respectively. The total resistance variation can be defined as A R = (a2+ p2)'". These equations are also valid for sensors with inclined elements.

9.4 Sensor Fabrication

367

When elements with different slopes are combined in a bridge, the bridge signal Usonly contains the linear part, whilst the square part influences the total resistance; in other words, the bridge resistance is field dependent. Both terms can be measured separately as shown in Figure 9-14. Small square terms have a negligible effect on the linear signal; any nonlinearities can be completely removed by driving the bridge with constant current. The relative square part P/(a2 + p2)”2may be approximated by a simple formula [61]: /?/(a2+ P2)1’2= U B / U + a/l/Z- . w. The first term represents the voltage drop ( ~ 0 . 1 ) and the second the geometry of the gap between two barber poles (see Figure 9-12); it is simply the ratio of the areas of the triangles at the edges (area: a2/2 each) and the total stripe area

(w

a.

l/Z-).

I I

1%

Figure 9-14. Measured linear and quadratic terms of a barber-pole sensor with HG = 2 kA/m. The maximum voltage swings of the linear part (a) and the square part @?) are indicated. The deviations from the theoretical curves (the bell shaped curve, for example, should be the parabola of Figure 9-6) are due to the heterogeneous (ie, nonhomogeneous) demagnetizing field present at higher field strengths.

kAlm

9.4.3.2 Examples These explanations can now be ameliorated by demonstrating the layout of a number of genuine sensors. The full-bridge circuit in Figure 9-15 is the first modern example of a magnetoresistive sensor known to the author. Linearization is achieved using inclined elements, with the long resistor folded into a meander; the arrowlike outline indicates its (horizontal) sensitive axis. The layer is constructed from NiFeCo 73 : 16: 11 alloy, thickness 100 to 200 nm, and the easy axis is vertical, but in the paper plane. Figure 9-16 is a schematic layout of the first commercial general-purpose sensor: the Sony DM 101A, described in [9]. Linearization is achieved using perpendicular current paths, which is similar to the inclined elements arrangement. The half bridge is made from NiCo 76 :24

368

9 Magnetoresistive Sensors

Figure 9-15. Full-bridge sensor linearized by inclined elements; white areas represent the NiFeCo alloy. Each of the four horizontal fish-bone structures is one of meandered resistors. The resistors are connected; outside contacts have to be made at the crosses. The sensitive axis is horizontal. Dimensions are not reported, but are supposed to be in the mm-range; the resistance is estimated to be 300 i2 (taken from [S]).

Figure 9-16. Scheme of the layout of an industrial halfbridge sensor with perpendicular elements. (The real sensor has two meanders of 23 stripes each, width = 27 pm, length = 1.1 mm, gap = 20 pm.) Chip size = 3.0 x 2.5 mm2, total resistance 1.5 ki2 (taken from Sony data sheet DM 101 A).

Figure 9-17. Commercial barber-pole sensor with median sensitivity (KMZ 10 B). The left photo shows the complete device with four resistors in the four quadrants and bond pads beneath; between the pads are two "digital" resistor networks for laser trimming. The right photo is an enlarged view of the center, where bright aluminium conductors are discerned from the grey Permalloy stripes. The resistors differ in the inclination of the barber poles. Chip size is 1.6 mm x 1.6 mm, resistance 1.7 kQ, w = 10 pm, t = 44 pm, a = s = 4 pm.

369

9.4 Sensor Fabrication

alloy of 100 nm thickness. It is designed to measure fields above 5 kA/m, the signal being dependent on the direction of the field only (as seen in Equation (9-16)). Field intensity can be measured by adding a known bias field. A commercial barber-pole sensor, designed by the author, is shown in Figure 9-17. The four resistors of the full bridge are located in the four quadrants. The magnetoresistive layer is constructed from Permalloy, at a thickness of 44 nm, and conductors are made from aluminium. Each resistor consists of 13 Permalloy stripes, between which are the A1 conductors carrying the reverse current. The unavoidable offset can be cancelled out by laser cutting the shorting bars of trimming resistors located between the bond pads. This sensor was not designed to have the lowest area, and a more sophisticated example is shown in [20].

9.4.3.3 Layout of Special-Purpose Sensors Special sensors have been designed, which by virtue of a special layout will measure only fields which show spatial variation; these fields may be generated, for example, by permanent magnets with multipole magnetization or by soft iron gear wheels plus a single-pole magnet. The first of these layouts, shown in Figure 9-18, utilizes the fact that the resistors of a bridge are (usually) located apart, separated by Ax and Ay [17, 641. The field is described by a linear approximation over the sensor’s dimensions, which is permissible for low and medium spatial variance: H ( x , y ) = H , + aH/& . Ax + aH/ay Ay. A straight forward calculation shows that a sensor can not only be sensitized to H , (as for the usual sensors), but also to aH/& or aH/ay, resulting in sensors which respond to the gradient of the field only. These sensors are suited for large gradients, the output being given by aH/ay . Ay; the field at each resistor should not exceed H,. The gradient sensor may be (and has been) realized using the general arrangement shown in Figure 9-17 (but not with the layout in Figure 9-15) which was originally made for a linear sensor. Gradient sensors are produced by changing the inclination of the barber poles as indicated in Figure 9-18. They can, of course, also be constructed from elements linearized by inclined current paths.

Figure 9 - 1 Spatial arrangement and electrical connection of magnetoresistors to build full-bridge circuits. The resistors are denoted by the squares, the sign in the square gives the sign of the characteristic. The sensitive axis is the y-axis - the output of each element is a linear function of the field at its center. The normal arrangement is shown in Figure 9-18a with signal proportional to the field at the center of the whole bridge. The arrangements in Figure 9-18b and 9-18c cancel constant fields and respond to field differences at the resistor center only, ie, the gradients.

S - Hy

a)

aHY S- aY

bl

S-- aHY ax C)

310

9 Magnetoresistive Sensors

The magnetoresistor can also be made sensitive to fields which show only a periodic spatial variation [19, 651. Figure 9-19 gives an example layout. The magnetic field has the wavelength I , say H (s) = H , . sin (s . 2 x / I ) , where s is a spatial coordinate. The resistors shown are simple stripes with no linearization; their square characteristic produces a signal with spatial period I / 2 . Stripes located at even and odd multiples of I / 4 respectively, produce a signal with 180” phase shift and are connected in a bridge. The sensor layout must match the field period; it is a system well suited for sensing fields of short wavelengths, where other sensors have failed.

Figure 9-19. Measurement of periodic fields. This fullbridge sensor has resistors with square characteristics, R , , , R , , , . ., R4,. They are located at even or odd multiples of 114, producing thus a signal during mutual displacement of sensor and field; the period is 1/2 (taken from [65]).

.

9.4.4 Generation of Auxiliary Fields It has been emphasized that a bias or a stabilizing field should be applied during sensor operation. The magnitude of this auxiliary field is in the order of 1 kA/m, and the direction can as well be the easy direction (stabilizing field) as the hard direction (bias field). There are three modes of field generation that are generally known: by a current conducting coil, by a permanent magnet, or by exchange coupling with an antiferromagnetic film. The simplest way, applicable in the first two cases, involves the use of an external coil or magnet. This will not be discussed here, since the details of its use are subject to the preferences of the user. Rather, this section concentrates on “integrated” solutions, i. e., the means of field generation - namely the deposited and structured layers - are prepared during sensor processing and are inseparable from the sensors themselves. Most arrangements described are used in magnetoresistive recording heads, the sensors working in an environment without high fields. Industrial general-purpose sensors, however,

9.4 Sensor Fabrication

371

have to be stable after (not during) incidental magnetic pulses of at least 10 kA/m, imposing severe demands on the coercivity, for example, of hard magnetic layers. All additional layers must preserve the smoothness of the magnetoresistive layer, which prohibits making multiturn coils around the magnetoresistor. Fields can be generated by singleturn conductors, but the current will flow along the long stripe axis due to the geometry. The field thus points in the y-direction and, whilst being suited for linearization by bias fields, it is not suited for stabilization which requires an x-field. Several biasing schemes are discussed in [13, 66-68] and are depicted in Figure 9-20. The arrangement shown in Figure 9-20a consists of a nonmagnetic conductor and the magnetoresistor; the two may be separated by an insulating layer, the advantage being there is no partial shorting of the magnetoresistor signal. However, the disadvantage is the thickness and that a more complicated process is required. The current I can be approximated to: I z t . M, which is rather high (30 to 100 mA). The sandwich shown in Figure 9-20b is more complicated, but has two magnetoresistors with opposite bias, thus enabling a bridge circuit. The bias current can be described by I = t . M, d / w (where d is the total thickness of the sandwich) which is much lower than the former example. The sensing current itself can also be used for creating a bias field, as shown in Figure 9-2Oc. The ferromagnetic shunt can additionally act as a second magnetoresistor allowing for a similar arrangement as that in Figure 9-20b, but without the separate conductor. The layers should be isolated electrically. Figure 9-20. Bias field generation. The outline gives cross sections along the hard axis and shows conductor C, magnetoresistor MR and ferromagnetic shunt Sh. Current direction and field lines are indicated. a) Single magnetoresistor and conductor, b) dual magnetoresistor with separate conductor, c) magnetoresistor with ferromagnetic shunt.

MR

Sh

a)

In barber-pole sensors, a field with an x-component is generated automatically, as already discussed in Section 9.4.3.1 and Equation (9-37), its magnitude being in the region of 0.05 to 0.5 kA/m during normal operation. This value is too small for stabilization in general-purpose applications but suffices, for example, when measuring the earth’s field. In addition, this field can be used for forcing the correct magnetization state by applying a short (- 1 ps) high (10 times normal) current pulse. It is also possible to generate auxiliary fields using permanent-magnetic films [68, 70-731. Generally, permanent magnets will produce a field with local inhomogeneities [70] - an effect which may be overcome by increasing the distance between the layers via a spacer layer (which has an additional role as an insulator). The field H , generated by a layer of thickness t,, length I, and remanent flux density B, (demagnetization is negligible for I 2 tp) is given by:

H,

=

t,

*

BJ(1. fig) .

(9-39)

372

9 Magnetoresistive Sensors

t, may be small for biasing purposes, t, = 0.5 . t (B, = 0.8 T as in ferromagnets), but it becomes rather large for generating stabilizing fields; t, amounts to several vm for I = 0.3 to 1 mm. This is inconvenient for thin-film technology, but t, can be reduced by splitting the layer with a number of small gaps in the field direction and increasing the demagnetizing field. Most hard magnetic layers have their preferred direction perpendicular to the plane and are thus not suited to this application unless they have been deposited by oblique incidence. In-plane fields may be generated by CoCr [72], Copt [73], SmCo, and similar materials [74, 751. These layers are sputter-deposited at high substrate temperatures and in a high field, yielding a coercivity which can be higher than 100 kA/m. In addition to these ferromagnetic films, other ferrimagnetic films such as Fe,O, and Fe,O, have been used successfully [70, 711, although the thickness t, of these layers needs to be about three times those described above. This type of layer may be sputter-deposited from an Fe target, either by reactive deposition with 0, addition or by subsequent oxidation of the Fe film. An alternative method of deposition is by screen-printing 'of an SmCo, or ferrite powder, preferably onto the rear of the substrate [51]. An example of the characteristic of such a sensor is shown in Figure 9-21. The Curie temperature Tc of all these layers is much higher than the usual operating temperatures of the sensors, so irreversible demagnetization due to temperature effects can be disregarded. The generated field Hp has a negative temperature coefficient (that of Br); in certain circumstances this may even be advantageous since not only does it compensate for the negative TC of the sensitivity So, but also the required stabilizing field is lower at higher temperatures.

Figure 9-21. Characteristic of a barber-pole sensor (see Figure 9-17 for layout) stabilized by hard magnetic ferrite powder, screenprinted to the rear of the substrate. The sensor was overcharged twice to demonstrate stability without further stabilizing means.

9.4 Sensor Fabrication

373

Sensors that possess a hard magnetic layer should be magnetized only once, since remagnetizing will alter the offset of a full bridge when the field direction is altered by this process. The third method used to stabilize the magnetoresistive layer is exchange coupling with an antiferromagnetic film [76, 771. This induces a unidirectional anisotropy in contrast to the uniaxial situation described so far. Best results are reported with an FeMn film, possibly deposited on a Cu film to stabilize the antiferromagnetic y-phase [77]. The direction of anisotropy can be induced by deposition in a field or by subsequent annealing in a field above the Nee1 temperature. One advantage of this method of stabilization over permanent-magnetic layers is that the system is restored even after periods of high magnetic noise, but it can tolerate only small fields in the x-direction (opposing the “unidirection”). To date, exchange coupling like this can only be used at low temperatures, the upper limit being 100 to 150°C [77]. It seems to be a good alternative solution for reading heads, but is less suited for the industrial sensors.

9.4.5 Data on Magnetoresistive Sensors Having dealt with the theoretical description, some data on actual magnetoresistive sensors are given below. The information is representative for the different types of sensors, although preference has been given to sensors which are commercially available. The first example is the Sony family, the design of which is shown in Figure 9-16 and described in [9]. These sensors are made from NiCo 76:24 alloy which has both a high magnetoresistive effect, but also a high H k . There is obviously no easy direction induced into the layer, this would be superfluous since the sensor is built to measure high fields. The direction u, of magnetization is thus parallel to the field direction (see Equation (9-16)), the angledependent part of the signal being described by a term cos (2 . q). The external field H has to be higher than a field HI ( H I 4 kA/m) to avoid blocking and thus hysteresis, but a maximum signal is attained only for H 2 H , ( H , = 8 kA/m), where magnetization is saturated. The magnitude of an external field H may be measured by applying a fixed bias field HB whose magnitude should be at least H I , but better H,. Some data has been collected in Table 9-2. Although the sensitivity is not very high, the signal swing can be rather large. The company also offers sensors with fixed bias magnets (not

Table 9-2. Some examples of Sony magnetoresistive sensors. The first two are half bridges, the DM-208 is a full bridge. The sensitivity has been calculated (assuming a bias field H , = H , ) so they are comparable to other sensors. The maximum signal swing is also quoted as this is relevant to proposed applications. Type

DM-106B

DM-110

DM-208

Dimension

Resistance R , Sensitivity So at HB = H , Signal swing Max. oper. voltage

2.3 1.8 8 16 10

280

0.65 3.5 8 38 13

kC2 (mV/V)/(kA/m) kA/m mV/V V

1.7

8 15 50

374

9 Magnetoresistive Sensors

integrated). Another special sensor (DM-211) is of the type described in Figure 9-19, intended for gear-wheel measurements, etc. All these sensors have a low temperature coefficient of ~p = -0.5 10-3 K - 1 . A second example of commercial magnetoresistive sensors are the Philips barber-pole sensors of the type shown in Figure 9-17. Having a Permalloy layer and aluminium barber poles, the sensitivity can be varied using different thicknesses and widths. The most important data are given in Table 9-3 - not only information relevant for application, but design data also, and this sensor line shows that the sensitivity may be adjusted by varying the geometry, but not the material. Their characteristic is the s-shaped curve drawn in Figure 9-6, which is measured in Figure 9-21 (only the center part - 2 kA/m Q Hy Q 2 kA/m may be used). These sensors require - except at very low fields - a stabilizing field, whose magnitude (max 3 kA/m) depends o n the amount of magnetic noise present. Table 9-3. Data on Philips barber-pole sensors. All three are full bridges with equal chip sizes of 1.6 mm x 1.6 mm; see Figure 9-17 for layout of KMZ 10B. The sensors should be operated with a stabilizing field whose magnitude depends on the sensor type and on the amplitude of magnetic noise present. Type KMZ 10 Layer thickness Stripe width Number of stripes Barber-pole width Barber-pole gap Characteristic field Measuring range Sensitivity at stabil. field TC of So (U = const.) TC of S, ( I = const.) Bridge resistance TC of Ro Max. oper. voltage

A

t W

n S

a

33 30 14 4 10

HO

1.2

HG

f0.5 14 0.5 -0.4 -0.15 1.3 + 0.25 9

SO Hx

RO

UO

B

44 10 13 4 4 3.8 f2.0 4.0

3 -0.4 -0.1 1.7 + 0.35 12

C

130 6 30 4 4 17.6 f7.5 1.5 3 -0.5

-0.15 1.4 + 0.35 10

Dimension nm Pm

Pm Pm kA/m kA/m (mV/V)/(kA/m) kA/m "70 . K - I To ' K - I kC2 % .K-' V

All these sensors are mounted in plastic housings similar to plastic transistors (especially the Philips sensors), but flattened to allow tight contact with the magnets and iron parts modifying the field lines. Another commercial magnetoresistive sensor available is the MRE-104 made by Nippondenso; although only a small amount of information is supplied, the sensor appears to be very similar to the Sony DM-106B described above. The contribution from Honeywell should also be noted, who have completed their line of magnetic sensors with a magnetoresistive sensor based on Permalloy, called SS2. This sensor is integrated with an electronic switch and switches between 1.2 and 0.9 kA/m irrespective of field polarity, although unfortunately no further information is available. For comparison, data from noncommercial sensors with optimized sensitivity [16, 30, 321 will also be given. These sensors are linearized by inclined elements, similar in layout to the

375

9.4 Sensor Fabrication

arrangement in Figure 9-15. Sensitivity has been optimized by reducing demagnetizing effects and adapting inclination angle and bias field. These sensors are made for low-field measurements, such as the determination of earth's field and its variations. The signal swing, when a field 8 A/m is applied, varies between 400 and 950 pV/V (optimum bias) which may be converted to a value of So = 30 ... 60 (mV/V)/(kA/m) [30]. The best of these full bridges have resistances of 50 kSZ or even more; smaller resistances tend to increase the noise level. The authors have also given the detection limits, which are determined by the sensor and amplifier noise levels [16]. The equivalent magnetic noise level is, in the best case, reported A/(m . to be 3.7 The operating range of different arrangements of magnetoresistive sensors has been drawn in Figure 9-22 on a logarithmic scale of the field strength H (and for comparison on a scale of the flux density B, too). The normal operation covers the range from some 10 A/m to some 10 kA/m, but this measuring range may be extended up to eleven decades by variations of the measuring arrangement and/or improved signal evaluation.

*

-

m).

a: b:

I

I

I

I

I

I

I

I

I

I

I

I _____ -_-

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

-.

L.

d:

H I

'

1

'

1

'

l

'

i

'

lo2

loo

I

'

I

lo6 Alm

loL

B I

'

I

'

I

10-l2 10-lo

'

I

'

I

'

I

lo-'

'

I

10'

T

Figure 9-22. Operating range of magnetoresistive sensors. a) Normal operation as described throughout this chapter. b) Measurement of field direction only (see Equation 9-16) or sensitivity reduced by a high x-field (see Equation 9-30). c) Drift reduced by switched magnetization as discussed in Section 9.5 and [82, 831. d) Noise and drift minimized by switched magnetization and bandwidth reduction [16].

9.4.6

Comparison with Other Magnetic Sensors

Magnetoresistive sensors are adapted to medium field strengths from a few amperedmeter to several 10 kA/m. They are further characterized by having an analog output with a frequency-independent signal, and they are produced by a mass-fabrication technique resulting in low prices. When compared to other sensor types, the best match is found with (normal) Hall sensors. These have mostly similar properties except that they need to be operated at higher fields

376

9 Magnetoresistive Sensors

(from 1 kA/m to 1000 kA/m); they also suffer from larger temperature effects unless GaAs is used, since they are made from semiconductors. Both types of sensors can be integrated with on-chip signal conditioning electronics. The sensitivity of Hall elements is about 0.2 to 0.3 (mV/V)/(kA/m) (converted data) and consequently lower than that of the magnetoresistives (see Chapter 3). Field plates, which are sometimes called magnetoresistive sensors as well, use the same physical effect as Hall sensors (the Lorentz force in semiconductors), but they are made to vary their resistance. They have a square resistance-field relation, so the resistance can increase more than 10 times, but they also need high fields of about 1 T ( P 800 kA/m). Linearization, if needed, has to be achieved using a bias field. Field plates are made from InSb (high electron mobility!) which limits the upper temperature at which they can function accurately to 100 to 120°C. The sensitive axis of Hall sensors and of field plates is perpendicular to the plane of the element, enabling arrangements with smaller airgaps. When considering the best sensor type for the important application of incremental position sensing, two more competitors appear in induction coils and pulse wires; however, whilst the first of these can withstand rather high temperatures, it is unsuitable at low frequencies, and neither type can be produced by batch processing because of the coils used. They do, however, have the advantage of being active sensors which do not need a power source. In addition to this group of sensors, used mainly in mass applications, there is a second group intended for the measurement of low fields or low gradients. All these, like flux gates or even squids, are more expensive as they need more electronic equipment. There is only a minimal chance that a sensor of one group could replace one of the other, and this holds true even for the magnetoresistive sensor which is the most sensitive of the first group.

9.5

Applications

Applications will be discussed only briefly here, since they are the topic of Chapter 11. Nevertheless, there are certain points specific to magnetoresistive sensors which need to be mentioned. It should be remembered, however, that producers of magnetoresistive sensors do offer information about applications for their products. Magnetoresistive reading heads had been proposed as early as 1971 [7, 11 - 131, but they have been used only in special applications for control purposes. Solid-state devices, especially magnetoresistive ones, are superior compared to inductive heads and may replace them in high density recording [78]. The most important application for general-purpose sensors, however, is contactless position sensing. This is done with the aid of a permanent magnet in utilizing its position-dependent field or by evaluating the field distortions created by soft-iron moving parts [lo, 19, 20, 65, 79, 801. The arrangement is similar to that used by other magnetic sensors, especially Hall sensors, but magnetoresistive sensors can and should be driven with lower fields; indeed, ferrite magnets will suffice in many cases (although they have a higher temperature effect). The arrangement for incremental position measurement (eg, by counting the teeth of a gear wheel) shown in Figure 9-23, differs from that used successfully by other sensors: The field

377

9.5 Applications

Figure 9-23. Position sensing via field distortion caused, for example, by a soft-iron gear wheel. The drawing shows the sensor (with its sensitive axis) fixed to the magnet (marked with its poles); only one gear cog (hatched) is indicated. a) Symmetric position: no field component in the sensitive axis; b) asymmetric position: considerable field distortion produces a component in the sensitive direction; c) arrangement perpendicular to a) and b): the sensor is mounted off-center to use the magnet’s stray field for stabilization.

@$jlB N S

a)

bl

C)

distortions (which have a higher relative variation than the main field) are sufficient to use the full linearity range of the sensitive magnetoresistive sensor. This method works quite well as long as the cog dimensions are larger than the sensor chip. Smaller cogs, giving better resolution, are measured using the special sensors discussed in Section 9.4.3.3; the mounting is that depicted in Figure 9-23. Other applications cover measurement of currents or electric power [lo, 18, 79-81]. The use of magnetoresistive sensors as magnetometers, ie, for inspecting the magnetic field of the earth (also a compass), has been described by several authors [8, 16, 18, 30, 321. A special operating mode can be used when it is only these small fields that are to be measured: The magnetization is switched between the two stable states, thus switching between two characteristics of different slope but equal offset. A phase-sensitive detector or even a lock-in amplifier eliminates offset and offset drift of sensor and amplifier and decreases the noise level. Magnetization switching can be effected with a square wave bias (with amplitudes > H , to guarantee stable states, see Figure 9-2) [82] or with short pulses only [83]. The measurement can be done without any stabilizing field in the latter case, although this method will only work for small fields (300(d)

0 (e) 10(O

+

Inductive

10

- 213

1000

> 300

1 1000(h)

- 273 50(h)

SQUID

+ (B)

+++

Notes : (a) Typical linear dimension (b) Relative indication only (') Upper limit in brackets for GaAs (d) Upper limit set by insulation of windings (e) Sensor power only: signal processing not included (0 Only for rotating coil type (g) Sensor requires milliwatts. Refrigerator power not included (h) Only with or including dewar

Good linearity. Sensitive to radiation. InSb most sensitive. GaAs best for high temp. Si less sensitive but good for integration More sensitive than Hall effect, but less linear High linearity, possible direct digital measurement with pulseposition-type Absolute. Self generating in alternating fields. Inherently linear. Very radiation tolerant. Operation under rugged conditions, long duration of life Only considered where the need to measure very weak fields justifies cost

457

11.4 Magnetic Field Measurement

11.4.2 Applications of Magnetic Field Measurement Numerous examples of applications are mentioned in the text of earlier chapters. The major areas of primary application are:

-

Biomagnetism Geomagnetism Identification Laboratory field measurement - Nondestructive testing - Planetary and space research - Submarine communication and detection The sensors in common use in these areas are shown in Table 11-8. Note that it has been necessary to include resonance field sensors in order to give a realistic comparison between available types. We now discuss in more detail applications within selected areas. Table 11-8. Sensors used in various application areas of magnetic field measurements. Application area

Hall effect

Flux-Gate

Induction coil

Inductive

++

+ ++ ++

+ +++ +

+

+++

+

++

++

Nondestructive testing

++

++

++

Planetary and space research

+++

+++

+++

++

Biomagnetism Geomagnetism Identification Laboratory field measurement

Submarine communication and navel warfare and detection I)

+

Magnetoresistive

+ +++

SQUID Resonance ')

+++ +

+++ ++

+

+ ++

+

++

Only for the sake of completeness

11.4.2.1 Biomagnetism

Biomagnetism is the study of the magnetic effects produced in or near living matter by (a) ion currents, (b) magnetic contaminants, or (c) paramagnetic or diamagnetic material in an applied magnetic field. The main attraction of biomagnetism as a diagnostic technique is its noninvasiveness; except for the third type, it is totally noninvasive. The goal of biomagnetic measurements is to diagnose, or help to diagnose, malfunction in organs, or other

458

11 Applications

pathological conditions giving rise to magnetic effects outside the body. Ideally the equipment for this purpose should be cheap enough for widespread use. The main characteristics of biomagnetic activity are the strength, frequency spectrum, and spatial distribution, of the resulting external field. The first two characteristics are shown in Figure 11-2 [7] for several sources.

1

,

I

I

I

I

(

Maqnetized lunq cmlarninanls

Abdominol currents v

Cardioqram

I

I-

Owlopram piomgnelic nwmal tissue in 0.1 mT field

--

Fetal cardioaom Encaphologram ( 8 ) Enceqhologrorn ( a I

,-.-

Hts Purkinle HipOocamprs Scnsarimotor cater

.

.._...._

Evaked ccdical activily

10 lo-'

I

10'

10'

FREQUENCY ( Hz 1

lo3

Figure ll-2. vpical amplitude and frequency ranges of biomagnetic effects [7].

It is clear from Figure 11-2 that biomagnetic fields are very weak. Reference to Figure 11-1 shows that, for most of the sources, only induction coils and SQUIDS are sufficiently sensitive. If the sole purpose of a measurement is to detect activity, induction coils offer a cheaper alternative to SQUIDS. However, the high sensitivity of induction coils at the low frequencies typical of biomagnetic effects is only achieved with large coils (Chapter 6 ) . This makes the spatial resolution very poor, and so most measurements of biomagnetic fields reported until now have been obtained with SQUID magnetometers. A further complication is that in normal environments the ambient magnetic noise greatly exceeds all but the strongest biomagnetic fields. Elaborately screened low-noise chambers have been constructed [8], in which the weakest signals can be observed directly (see also Chapter 1, Section 1.8). For routine applications these are often far too large and costly; it is therefore necessary to use gradiometric coil configurations (see Chapter 10, especially Figure 10-20). Until recently, only single sets of coils were used, and in order to obtain spatial information the coils had to be scanned around the subject. This was time-consuming, and often the signal did not remain stable for long enough. Now it is possible to obtain spatial information in a much shorter time, by using multiple-coil arrangements ; typical of the current art is the seven-channel system described by Knuutila et al. [9]. Examples of the results obtained using the system are shown in Figure 11-3.

459

11.4 Magnetic Field Measurement

n v)

01

0

1

I

I

1

20

LO

60

80

Frequency ( H z )

Figure 11-3. Examples of magnetic brain signals made using a multichannel SQUID magnetometer. a) Spectral density of brain noise over left occipital lobe; b) Auditory evoked response to sound in ear, recorded over auditory cortex; c) Isocontour field map recorded over auditory cortex [9].

1

460

I 1 Applications

11.4.2.2 Geomagnetism and Space Research Geomagnetic measurements are among the oldest in science. For instance, measurements of the magnetic declination in London are available from 1570 to the present [lo]. Nowadays, measurements of the magnetic field at or near the earth’s surface can be used for a wide range of scientific and technical purposes. At the fundamental level, they can give information on the composition of the earth’s mantle, and about the dynamic processes in the earth’s core. At the more applied level, geomagnetic measurements are invaluable in mineral exploration and the location of buried objects. The magnitude of the earth’s field is typically about 50 pT at the surface; this sets the range of interest towards the lower end of the scale in Figure 11-1. Taken in conjunction with the need for rugged operation, often unattended for long periods, this indicates that the most suitable sensor types are fluxgates and induction coils. With these, once again, the resonance magnetometers are commonly used. Longterm measurements of the geomagnetic field are normally carried out at fixed observatories, which are located in most parts of the world [ll]. Standard equipment at such stations includes either fluxgates or induction coils to measure the vector components of the field, and a proton precession magnetometer to measure the total field. (Note that all the sensors considered in this book are vector types, which measure a particular component of the field.) Some information on induction coils and their applications to geomagnetic measurements are given in Chapter 6. Here we give an account of some of the other geomagnetic measurements that have been carried out. Many of the interesting features of the geomagnetic field occur on a long timescale (at low Hz and frequencies). Figure 11-4 shows a power spectrum of the field between about 10 - 2 Hz. It will be seen that there are a number of small peaks in the spectrum, corresponding to various terrestrial and cosmic phenomena. The 11-year peak corresponds to the solar cycle, the 27-day peaks to the solar rotation period, and the 1-day peaks to the earth’s rotation. Examples of raw data from fluxgate magnetometers are shown in Figure 11-5. Such data are of the utmost importance to geophysicists involved in modelling the behavior of the earth and sun [ll]. In recent years, geomagnetic measurements have been extended into the atmosphere and space, by magnetometers carried in aircraft, rockets, satellites and spacecraft. Magnetometry on the earliest spacecraft was dominated by helium resonance instruments, modified to permit

Log,,frequency / Hz

Figure 11-4. Power spectrum of the geomagnetic field at low frequencies, showing features of geophysical interest (after [ll]).

461

11.4 Magnetic Field Measurement

---I

t-

z

100 nT

43700 nT 0

6

3

-50

9

12

2‘1

15

i4

t :

-700t

0

100

200

300

Days

Figure ll-5. Typical time records of the earth’s field a) 24-hour record of vertical component at Hartland, U.K., 12th February 1989; b) Daily mean of the vertical component at Chambon-la-Forst, France, in 1986 [Ill.

vector measurements to be made. These reached their final form in the Pioneer 10 and 11 missions to Jupiter and Saturn [12]. Typical data for the combined sensor and signal processing , 3.4 kg, volume were as follows: Ranges + 4 nT to +140 pT, noise power 10 ~ T / H z ” ~mass 6000 cm3, power 4.4 W. The wide range required for these missions, set by the strong magnetic field around Jupiter should be noted. A detailed account of these measurements is given in [13]. At about the time of these flights, fluxgate magnetometers where achieving performance adequate for the purpose, and were extensively deployed in subsequent missions. In 1977 the International Magnetospheric Study was launched, to study the dynamic plasma and field environment of the earth. Instrumentation included two indentical triaxial fluxgates o n separate, closely orbiting spacecraft [14]. The highly elliptical orbit exposed the magnetometers to a wide range of fields, requiring a correspondingly wide range for the sensors. The instruments used had ranges of f 2 5 6 nT and f 8 1 9 2 nT, accurate to 0.025%, or 1 in 213. The noise level was about 3 pT/Hz”* at 1 Hz. The total mass was 2.4 kg, volume 4500 cm3, power 3.9 W. In 1984 the Active Magnetospheric Particle Tracer Explorers project, a collaborative venture between the USA, the FRG, and the UK, used three satellites equipped with triaxial fluxgates to map the field 550 km above the earth’s surface, as part of a study of ion transport through the magnetosphere. The instruments aboard the U. S. spacecraft [15] were similar to those used in Voyager, Viking and GIOTTO missions, with ranges from k 16 nT to + 65 536 nT and 13-bit

462

I 1 Applications

resolution, requiring only 1 W of power. The European version [16] was similar to that used in the HELIOS mission. It had ranges of *4 pT and +60 pT, with 16-bit resolution. The . results from this instrument are shown in noise level was less than 25 ~ T / H Z ’ ’ ~Typical Figure 11-6.

c

t 100

&

-

&

50 0 100 50

G O

- 50

- 150

c

f.100 Q

50

n

w

30 32 34 36 38 40 42 44 4 6 48 50 52 14 1984 SEE 4 DAY=248

54 56 58

0

2

4

6

8

10 12

min

15 h

Figure ll-6. Typical record from the IRM fluxgate magnetometers, showing multiple crossings of magnetic boundary layers during a magnetic storm [16].B, BX, BY, BZ: flux density and its components.

11.4.2.3 Identification By identification we mean applications such as card reading, coin validation and security systems. Taken together, these probably account for the most widespread application of magnetic sensors. The basic principle of magnetically encoded cards is shown in Figure 11-7. Alternately magnetized regions indicate a “0” or a “1” in a binary sequence. In practice, the regions are usually between 0.1 and 0.5 mm apart, which limits the distance over which the stray field extends to a similar range. The magnitude of the stray field amounts to 0.1-1 mT. The sensor requirement is thus for sensitivity in the range 10 -4- 10 -3 T, spatial resolution of 0.1 mm, combined with extreme cheapness and reliability. Figure 11-1 and Table 11-7 suggest that either Hall effect or magnetoresistive sensors might be suitable ; in practice, magnetoresistive sensors are preferred for their higher output for the necessarily small size. Coin validation, like card reading, is an extremely common operation worldwide. Various systems are in operation, among which the system based on magnetoresistive sensing, illustrated in Figure 11-8, is a competitive choice [18]. The principle is that the alternating field between the two coils is disturbed by the coin as it passes through. The phase of the magnetic field close to the coin with respect to the far field varies in a characteristic fashion for a particular type of coin, as shown in Figure 11-9. This phase signature is sent to a microprocessor to identify the type.

-

11.4 Magnetic Field Measurement

--VISA

463

MAGNETIC -.#STRIPE

-CARD

L

/i

Figure 11-7.Schematic diagram of magnetically encoded card and card reading sensor [17].

COIL D R I V E

co"'t

r *

MAQNETO RESISTOR

I

MICROPROCESSOR

ACCEPT

Figure 11-8. Schematic diagram of a coin validation system [18].

I

-.

464

11 Applications

40 OA

W Ill

w

35

g

30

LL L3

x

- COMMON POUND SLUG - POUND

COIN

8 25 z

g 20 W

15 O

w vl

10

2 a

5 0

I

-5 -15 -lo

i 0

0

5

5

10

10

15

15

20 25 30 35 POSITION OF COIN l m m )

20 25 30 35 POSITION OF COIN l m m )

40

40

45

45

50

50

Figure 11-9. Signatures of various coins measured with a magnetoresistive validation system [18].

Security systems for checking the movement of items are in widespread use in shops, offices and other public buildings. Perhaps the most familiar are those in use in shops to detect when an attempt is made to remove goods without paying. The item is “tagged” with a magnetic element, which responds to an interrogating signal at the exit. A similar system is used in libraries, to detect the unauthorised removal of books. A discussion of the use of Wiegand and pulse-wires for this purpose is given in Chapter 8, Section 8.6.2.

11.5 Solid Mechanical Transducers

465

11.5 Solid Mechanical Transducers 11.5.1

Basic Material Requirements

For transducers involving the conversion of mechanical information to magnetic or electric signals, the prime consideration must be the magnetic properties of the material. However, many mechanical transducers have to work in environments which are mechanically, thermally or chemically hostile. It is these extra constraints which must either be overcome by engineering design, or by careful choice of magnetic material. Designs can be produced which involve no direct contact between transducer and the input mechanism (eg, in a rotary encoder), but for many force or torque transducers there is a direct mechanical linkage. The following sections review the material-related issues in applications of magnetic sensors (see also Chapter 1, Section 1.5). With crystalline magnetic materials the general rule is that magnetic and mechanical softness go together, as do mechanical and magnetic hardness. This is a direct consequence of the link between macroscopic metallurgical properties of the material and the magnetic properties ~91. For transduction of force (linear and rotational) or displacement, where there may be mechanical contact with the magnetic material, the transduction element must be rugged. This would, in general, involve high hardness, a high tensile strength, and a high shear modulus. In choosing crystalline materials there must always be a trade-off between the magnetic and mechanical requirements. Soft materials such as the NiFe alloys can be mechanically hardened by alloying with Ti or Nb, without serious degradation of certain magnetic properties. However, this causes the material brittleness to increase. Magnetically hard materials, such as TbDyFe alloys, are mechanically hard and also mechanically brittle, which can lead to severe handling problems. As pointed out in the specialist chapters (eg, Chapter 4), the advent of metallic glasses over the last twenty years has overcome much of the incompatibility between mechanical and magnetic properties. Good magnetic softness is combined with high hardness and high yield strength. Metallic glasses also offer other advantages. Many form a passive layer giving a measurement of corrosion resistance. Their wear resistance is very high (laminations of metallic glases are being used in tape recorder heads for metallic tapes), and their coefficient of sliding friction is very low, typically ~ 0 . 2 - 0 . 3 [20]. Also, the wide compositional ranges available (non-commercially as yet) allow fine tuning of both magnetic and mechanical properties (see, for example, [21]). To obtain the maximum material response in any given transducer arrangement, the relative orientation and coupling between input mechanism (force, displacement etc.) and magnetic properties must be optimized. Optimization of the response of the magnetic properties is primarily achieved by control of the magnetic anisotropy. In crystalline materials the magnetocrystalline anisotropy dominates. This is related to, and often has the same symmetry as, the crystal structure. The NiFe materials are capable of supporting an induced uniaxial anisotropy produced by field annealing. Anisotropy can also be introduced via strainmagnetostriction coupling in any material with a non-zero saturation magnetostriction. In metallic glasses there is no macroscopic magnetocrystalline anisotropy as a consequence of the topological disorder, and the easy direction can be controlled by thermo-mechanical treatment (see, for example, [21]). The anisotropies introduced are stable up to continuous service

466

I1 Applications

temperatures of = 120°C. A drawback with metallic glasses is that for many compositions the ductility is severely degraded by the heat treatments necessary to optimize the magnetic response. This problem can sometimes be circumvented by heat treatment after the device has been configured. Magnetic elements in transducers come in a wide range of forms : toroids, wires, rods, films on substrates. Some transducer elements are free-standing, others form part of a more complex structure. Careful matching of thermal expansion coefficients may often be needed in order to avoid unnecessary straining of material. Constraints imposed by bonding between magnetic material and other elements of the system must also be considered. Mechanical strain can couple with the magnetic properties to degrade the overall device response. Crystalline magnetic materials are available in all bulk forms, and compositions have been optimized for transducer applications. Commercially available metallic glasses come in the form of thin sheet (20-40 pm thick by up to 25 cm wide), or wire (initial diameter 125 pm). The commercial compositions have not been optimized for transducer applications, but special alloys are available. Both crystalline and noncrystalline materials can be deposited by sputtering or evaporation.

11.5.2 Displacement Transducers Garratt [22] has reviewed the whole field of displacement transducers, and Table 11-9 shows his classification scheme. Figure 11-10 illustrates the possible ranges of linear displacement which may be sensed using the sensor categories listed in Table 11-2. The boundaries defined should be taken as order of magnitude figures only. It is clear that there is considerable overlap between the sensor categories, and other factors than available range must be taken into account in choosing a given technology. Magnetoresistive Inductive (LVDTI Inductive variable

1 Magnetoelastic 1

gap

I P

-9

I

-0

-1

Hall Effect

1

I

-6

-5 -4 -3 -2 Log,,, displacement (m)

-1

0

I

1

Figure ll-10. An indication of the useful ranges for various linear displacement transducer technologies.

Hall effect and magnetoresistive sensors for displacement rely on the same basic principle (see Chapter 3). The stray field from a permanent magnet is measured by the sensor. In a basic system of a single sensor element and magnet, the detected signal is a nonlinear function of distance from the permanent magnet. Linearization of the output signal requires further signal processing and/or multi-element sensors. The need for post-detection processing has brought about the development of “smart” sensors. Here the Hall element or magnetoresistor is integrated with the processing and drive circuitry onto a single “chip”. The only require-

Strain :

Indirect Position :

Temporal metrology :

Surface metrology:

Direct Dimensional metrology :

Force, velocity Acceleration Displacement, velocity Acceleration, force

Length, height, width Diameter Thickness (thin films) Position Angle Level Texture Roundness Straightness Flatness Contours and surface deformations Thermal expansion Vibrations Creep Tilt

lo4

5 x lo5

1 x 106 1 x lo5

1 x lo5

5 x 10’ 5 x 10’ 1 x 105 5 x 106 2 x lo4 1 x lo3 4 x lo4 2 x lo4 2 x 104 1 x lo4 2 x lo4 1 x 106

Maximum rangeto-resolution ratio

Table 11-9. Classification scheme for displacement transducers (after [22]).

5 mstrain

50

1 1 0.1

20 1

1

50 2 to 50 0.1 50 2 0.5 0.2 0.5 2

Range (mm)

0.5 pstrain

10 - 1

1 to 10-1 10 - 1 10 - 3 10 -2 10 - 1 5 x 10-1 5 x 10-~ 2.5 x 10 - 1 10 --I 1 10 - 3 10 -2 10 - 3 10 - 3

Resolution (vm)

102 to 106

102 to 106

10 10 10