Ladder crystal filters

Ladder 0 rystal

Filters N2DCH

MFJ

Ladder Crystal

Filters by John Pivnichny

N2DCII First Edition Printing 1999

1st

ISBN # 1-891237-20-9

MFJ-3509 Copyright (c) 1999 by MFJ ENTERPRISES, INC. Printed in the United States of America All rights reserved. Reproduction or use without expressed wrlttei, permission of

editorial or pictorial content, in any manner, is prohibited. No patent liability is assumed with respect to the use of the Information contained herein.

ML! PUBLISHING, STARKVILLE, MS 39759

Preface In this book I have attempted to bring together for the first time everything that has been developed in the various papers on ladder crystal filters From their early development in France, ladder ciystal filters have had an appeal because crystals ofjust one frequency are required. there are many sources of such crystals including the citizen band radio crystals and microprocessor crystals. The work in France by Poehet, Cohn, and Amstulz was eventually translated into English in the UK and further developed by Hardcastle and Hawker. QST magazine reprinted Hardcastle's paper to bring ladder crystal filters to the attention of the US community. The first article by Hayward in QST in which he pointed out that the passband of a ladder filter can be calculated using a circuit simulator program is what started this author's interest. After having previously built a frequency counter, sensitive if voltmeter, and rotary step attenuator, all of the instruments were on hand to start building and measuring ladder crystal fihtert Other authors have added further developments in their papers, too many to mention here. They are all listed in the reference section which I believe includes a listing of every published paper on the subject to date. Using the information in this book, the ordinary amateur as well as the professional can design and construct very high quality crystal filters for use in shortwave radio, amateur, and commercial equipment.. I would like to express my thanks to Mr Martin Jue of MFJ for agreeing to publish the book and to Mr Richard Stubbs, Jr. of MFJ for his assistance in getting it ready for print

Table of Contents page

Chapter I - Crystal and Capacilor Characteristics Chapter 2- Measurement of Crystal Parameters

7

Chapter 3 - Lower Sideband Filters

21

Chapter 4 - Upper Sideband Filters

41

Chapter 5 - Dual Filters

53

Chapter 6- Tunable Filters

60

Chapter 7- CW Filters

81

ChapterS - Lattice Filters

94

Chapter 9 - Programs for Filter Design

04

Appendix A - Derivation of Holder Capacitance

120

Appendix B - List of Crystal Manufacturers and Dealers

122

Appendix C - Table of Filter Coefficients

128

Refrrences

129

Index

133

Chapter 1 Crystal and Capacitor

Characteristics The basic components used in the construction of crystal ladder filters are the individual crystals themselves and various capacitors. An understanding of what is available to the designer is essential for the successthl construction of narrowband filters such as those used in voice and CW service. Both crystals and capacitors have requirements on Q or component quality which must be observed. In this chapter the various types of crystals and capacitors are presentet The chapter on measurements lists some typical values of popular crystals in use today. The terminating resistors are assumed to be external to the filter circuit and are not covered In any event, carbon composition resistors which are readily available easily provide this function.

Crystal Holder Types Perhaps the most distin8uishing and obvious characteristic of a crystal is its holder. So we will divide the treatment of crystals into categories of holder types.

Pressure type holders Many of the older crystals were housed in pressure type holders such as the well known FT243 type made in tremendous quantities during World War II, These crystals were subsequently released to the surplus market after the war providing many crystals to experimenters at low cost. One

advantage of the pressure holders is that the crystal blank can be easily removed from the holder and its thickness reduced, then re-inserted in the holder producing a crystal whose series resonance is higher than before. Manufacturers and experimenters could therefore grind crystals to any specified frequency and tolerance by selecting one slightly lower in frequency than desired, and then lapping or etching the blank to bring it up to the specified frequency. These holders, because they are rather large, are no longer in general use. However they are still available from the CW Crystals Company. Some of the other World War II surplus crystals are the FF241, OCIO, CR-7, CRIA, and MC7. There is also a holder in the shape of an octal vacuum tube designed to be plugged into an ordinary 8-pin octal socket. However the crystal itself is sometimes mounted in an FT243 holder which is itself then mounted within the octal holder.

Mctal Can Holders There are several holder types constmcted of a fbrmed metal can of about 3/4 inch width by 3/4 inch height by .352 inch thickness, with leads coming out one end. They are practically identical except for the lead diameter and length. The leads are spaced about 1/2 inch (actually .486) apart center to center. These include the HC-6, HC-33, F-700, HC-17. Another series of smaller metal cans are about .5 inch high by .4 inch wide by about .2 inch thick. Leads are spaced 192 inch center to center. These are the UC-IS, HC-25, HC-43, HC-49. Several shortened versions of the HC-49 are also produced. Finally there is and even smaller metal can .342 inch high by 325 inch wide by .125 inch thick with leads spaced .148 inch. The HC-45 is the most popular type in this size. Another popular metal can used primarily for larger, low frequency crystals is the HC-13.

2

Surface Mount Holders A sreat variety of leadless or surface mount holders are becoming available at the present time to complement the

shift of many electronic components from pin-in-hole mounting to direct surface attach soldering. These include the ECX-6. CSM-7, ECX-3A. MC-405, 1-1-13, MA-505, MA-506, U4B, CM-309, CM-200, FC, FR FE, FPX and finally the HC49SI) which is basically a shaft HC-49 can with the leads bent outward to allow surface mount attach.

Capacitors Although the tolerance requirements on absolute capacitance 'snot nearly as critical as for example the series resonance frequency for crystals, capacitor Q is important. Silver mica capacitors provide the best overall characteristics. Low value ceramic capacitors, up to about 100 pF appear to have satisfactory Q especially the NPO types. Those above 100 pF for some unknown reason are markedly inferior to silver micas. An alternative approach which works is to place two or more ceramic capacitors, each of capacitance less than 100 pF in parallel to create higher capacitance values. This method is also used to create capacitors with non-standard capacitance values. One of the best ways to determine the loss (and therefore the Q) of a capacitor is to use it in an oscillator circuit, preferably at a frequency in the vicinity at which it will be operated and see the effect of the loss. One such circuit, adapted from one given by V. Bapat [2 ] is shown below. The oscillation control, Ri is easily calibrated using a high Q capacitor, such as an air-dielectric variable trimmer with fixed resistors in parallel or series to simulate a known loss.

3

TI =97, T2=3, T37 turns L= 2501JH

0 = 105 at 1.2 MHz

adjust to start oscillation

to oscillation detector

Capacitor under test

Figure 1.1 - Circuit for measuring 0 of a capacitor

Recall that for a lossiess capacitor with resistor the Q is given by: Q 4

2ittCR

a

parallel

where f is the frequency of operation e.g. the center frequency of the filter in which the capacitor wiLl be used. For a series circuit of a lossless or very low loss capacitor, in series with a resistive loss:

Q= l/2,rlCR Either connection can be used to simulate a capacitor with a certain specified Q. For the parallel circuit, very higji value resistors, often unobtainable, will be needed. The series connection uses very low value resistors which are sometimes more readily available. For example, a 22 pF capacitor is used in a ] 0 Mhz crystal filter If it is to have a Q of 10,000, then for the parallel circuit:

l0'7x22x I0'-12xR ft

724 Million Ohms

For the series circuit: 10,000

I/ 2x x 1V7 x 22

x

,K

R = 0.72 Ohms

Capacitor Tolerance Because the actual capacitance value is not a critical requirement, niornal 5% or tighter values are usually acceptable for ladder crystal filters. There is no requirement that equal value capacitors in the circuit be matched exactly fix the filter to thnction correctly. Usually silver mica or NPO ceramic capacitors will be a good choice. Furthermore they tend to also have the highest Q values and of course have very good temperature stability.

5

Recommendations Before constructing any ladder crystal filter a Lest batch of crystals should be obtained from the supplier and checked for crystal parameters using the methods of chapter 2. The most important crystal parameter will be the average Q of the crystals. For an acceptable filter, the crystal Q must be several times greater than the filter Q, where filter Q is defined as: Qfllter = center frequency /3 dB bandwidth

Crystal Q A crystal Q of S to 200 times the filter Q will be needed depending on the filter type and number of poles. Carver [4] recommends the factors in the table below: Filter tyDe

Butterworth .1 dB Chebyshev .5dB Chebyshev

32 x filter Q 90 x filter Q 130 x filter Q

In general it is best to use 1% tolerance NPO capacitors for values up to i 00 pF and 1% silver micas for values belween 100 and lOGO pP. Two capacitors can be put in series or parallel to produce values between the standard ones if necessary. Air dielectric trimmer capacitors set to the correct capacitance value before insertion into the circuit are also acceptable. Do not attempt to adjust the value after insertion in the circuit as the effect of adjustment is extremely complicated so that it is basically impossible to know when the corFect value is obtained.

6

Chapter 2 Measurement of Crystal

Parameters For any set of crystals specified by their oscillating frequency and load capacitance, it is necessary to know the motional inductance, motional capacitance, and holder capacitance in orde,- to design them into a ladder filler. The crystal series resistance must also be known in order to determine the crystal Q and decide whether the crystals will be satisfactory for use in the filter. The series resistance will also be the main facLor controlling the filter insertion loss

IF

=

Figure 2.1 - Crystal Parameters These four parameters shown in figure 2.1 should be measured using the techniques described in this chapter. Although network analyzers and calculating software are now available to automate such measurements, the parameters can be measured using relatively simple equipment. As a minimum, a signal generator, frequency counter, sensitive RF voltmeter, and 3dB altenuator will be needed. Even these instruments are relatively simple to 7

construct by the individual who does not have access to a well furnished laboratory. A test jig will also need to be constructed With a circuit such as the one shown in figure 22. A 50 ohm pi-network is recommended by Kinsman [23] for measurements on thodamental crystals above 1 MHz.

66.2

66.2

Figure 2.2 - Test Circuit This circuit has a 12.5 ohm input and output resistance to the crystal. The series resonant frequency can be measured as the frequency of maximum transmission. It can also be measured as the frequency of zero phase shift across the crystal if a vector voltmeter is available. Zelenka [39] points out that the phase shift is varying rapidly at series resonance while the transmission maximum is a broad peak. Therefore the phase shift measurement can be 10-i 00 times more accurate. Nevertheless entirely satisfactory results are given by the transmission maximum measurement. Motional capacitance is measured with this circuit by placing a load capacitor" in series with the crystal and measuring the new (higber) series resonant frequency. A value of 20 or 32 pF is typical. Then the motional capacitance is given by the formula:

(2.1)

8

crystal series resonant frequency crystal plus load capacitor resonant frequency Cl load capacitor Co holder capacitance The holder capacitance can be measured on a standard capacitance bridge provided the test frequency is sufficiently removed from the etysta! series resonani frequency. Series resistance Rs is measured by taking a voltage reading Vo at the output in figure 2.2 at the series resonant frequency. Then replacing the crystal with a short, the new (higher) output voltage Vr is recorded. Then,

where Ix 11

(2.2) Vo

if we assume the generator output voltage does not change during this measurement. Hayward [19] suggested another procedure for crystal parameter measurement which can be used by experimenters with simple instruments. A test set which presents 50 ohms to the input and output of the crystal is used. See figure 2.3. The author of this book uses the circuit of figure 2.4. which works well with his 200 ohm RF voltmeter and unknown output impedance signal generator. In fact the circuit will present 51 ohms +1-1 ohm to the crystal at the input end with a generator of any impedance level. Hayward recommends measuring series resistance by first making note of the output amplitude at the series resonant frequency (peak output). Then the crystal is replaced by a small-value variable resistor which is adjusted for the same output amplitude. The variable resistor is then removed from the test circuit and its value measured on a dc ohmmeter This resistance is taken as the crystal series resistance. The procedure

will provide satisfactory results if a high quality generator is notes however, that the frequency selectivity of used. Carver 9

0

p

50 ohm generator

062 56

01

Figure 2.3- Hayward's 50 Ohm Test Circuit

240

high impedance voltmeter

p

0-

generator

39

270

220 68

Figure 2.4- Author's 50 Ohm Test Circuit

p______ 200 Ohm RF voltmeter

________ _______

the crystal being tested Wifi reject generator harmonics but the variable resistor will not. This difference will require a larger resistance value for the adjustable resistor if oscillator hamionics are present. As a consequence the czystal resistance will be over estimated i.e. the crystal Q will appear to be lower Lhan it actually is. Carver suggests using a simple S pole low pass filter to remove harmonics from the generator signal. The crystal is then re-inserted in the test circuit of figure 2.3 and the two frequencies 1112 where the output amplitude is down 3 dB from the peak are recorded. From the difference between these two readings, AF LI - 12, the motional capacitance is calculated.

L,r19.l

(2.3)

where Lm is in Henrys and e%F is in Hertz. Equation (23) is derived as follows: Consider the circuit below where the crystal holder

capacitance is ignored and the test circuit is represented as a 50 ohm source and 50 ohm load.

50

R

L

V=[ IOO+Rs+sLrn+ IIsCm]l Vout = 501

12

C

vout

Vout/V = 504 100 + Its + sLm + 1/scm] let r'jco then after rationalization, taking the magnitude, and some algebra; =

(100+Rs)2 +(mLm- 1/cocm)'

V

check

at series resonance wLm = 1/oCm, and Vout = V

50

IOD+Rs

correct Now at the 3dB down points

Vout V so

707x

50

I00+Rs

*

707 x 50 100 + Rs

± (100 + Rs)2 -F (wLm - Ihacm)2

squaring both sides

.5

(100 + Rs)'

1

(100 + Rs)' + (wLm - l/wCm)2

This is only true if oLm - lhaCm = 100 + R

ie reactance equals resistance at 3dB down point in a 13

series RLC circuit.

At the two 3dB down points

and w2

w1 Liii - I/a1 Cm = 100 +Rs

o,Lm- l/w1Cm = -(l00+Rs)

2-I

(a,

2

i/w1Cm - I/wCni -2(lOO+1(s)

Now, let Ao a, - a1 then at Ihe series resonant frequency au woLm - lJaoCm 0 -

wo'L -2(]O0+Rs)

02

'note -3dB down is 707946 so squared is .501187 from series resonant circuit theory, the 3dB down points are located such that coo = a2 x a!

'4

AwLm + 2(100+ Rs)=w1 Lrn- m2 Lm- &.,t.m

2AeLm = -2(100 + Rs)

Lm-(l00+Rs)

Lm

100-Rs

(24)

2,tAF

now if Rs

0, (infinite crystal Q) then:

Lm= 15.9151AF Haywards formula of Lm = 19. l/AF therefore makes allowance for a crystal series resistance of approximately 20 ohms. If the series resistance is measured first, then equation (2.4) will give a more accurate calculation of Lm. Once Lm is known, then Cm is calculated from the series resonant frequency

Cm

2irAF

I

ox, Lm

oc((00+Rs)

Cm 2itFo2 (100 + Ps)

again if Rs

(2.5)

0 (infinite crystal Q)

15

Cm = 159155xl0'AF/Fo2

where Fo is in M1lz

L.326x I0'AFfFo again allows

Hayward's

for a 20 ohm series resistance. For any other series resistance, use equation (2.5) to calculate a more accurate value for Cm. Another way to measure holder capacitance while the crystal is inserted in the test fixture is to tune the generator above series resonance to the parallel resonant frequency. Watch the output amplitude for a null at up to 10 or 20 kliz above series resonance, and record the null frequency. From the formula for capacitors in series, the holder capacitance is given by

Ch-= fslCip

*

- fs2

Again note that ifharmonics are present in the generator signal then they will interfere with a true null producing instead a broad null making the frequency reading less accurate.

Table 2.1 below lists some typical values for various crystals. These were either measured by the author or taken from the literature as measured by others where noted.

* this equation is derived in the appendix of the book 16

Table 21 - Typical Crystal Parameters

gMHz) 3.006 3.579 3.579

C(pF) L(H)

030

R.(ohms)

065

23

40

4

.01336 .148 MID .199 .0107 .148

4.434

.0135

.0955

8

.0255

.01552 27

9 9

.00851 .0367

9.83 10

.02438 .01076 .012 .021!

10

.0127

3.579

Ch(pf) Q

6.6

6.2

5.0

5

.012

20

.026

.02

4.9

500K 63K 76K 721K 150K 133K 230K 29K 103K

7

Hayward Hayward Carver

Hayward

20K

3.6 3

Carver Hayward

Sykes

3

33

note

200K

Kinsman Hayward

Simple Measuring Equipment A number of articles have appeared in the experimenter/amateur literature with plans for constructing suitable signal generators and sensitive RF voltmeters. The author frequently uses the equipment shown below in figure 2.5 for a generator. His RF voltmeter as shown in figure 2.6 has proven to be a very useful instnjment and has been reproduced by a number of experimenters. Additional references are also listed.

17

Figure 2.5-

I8

Signal Generator

Construction details for the generator of Figure 2,5 are published in Ham Radio Magazine July I 9S9 pages 62-67

See also Electronics Now, Nov. 1995 pp. 112-113 and 158-159 ThisdBm meter and a step attenuator are available in kit form from Unicorn titled A sensitive RE Voltmeter

Electronics, Valley Plaza Drive, Johnson City. Ny 13790(607) 798-0260, www.unicornelex.com. Mother signal generator reference is [211 page 170. Other RF voltmeter references are [3], [21] pages 147-i 48, and [19].

Figure 2.6 - r.f. Voltmeter

19

Figure 2.7 - dBm Meter

Figure 2.8- Step Attenuator

20

Chapter 3 Lower Sideband Filters The most rudimentary fonn of ladder filter is in Figure 3.1 consisting of a single crystal with just two shunt capacitors and terminators. This simple filter will have a bandpass characteristic as shown in figure 31 Early experiments with such simple filters by ilardcastle [13) showed that the width of the bandpass can be decreased or increased by increasing or decreasing respectively the value of the capacitors. The terminating resistors are also changed to keep the RC product constant

RI xci

R2 x C2

By placing additional identical filter sections in cascade as shown in figure 33, the general thrm thr a lower sideband (LSSB) ladder filter is produced. Note that all crystals have identical characteristics. This is a key characteristic of the ladder filters described in this book. As the number of filter sections is increased, the filter skirts become sharper and the ultimate attenuation outside the passband is increased See figure 34. Because each crystal produces a pole in the equation of the transfer fUnction of the filter it is normal terminology to refer to a filter containing eg. 4 crystals as a 4 pole fitter As we shall see laler, in the general case it is necessary to place a capacitor, Cp, across the crystals. For some designs, the holder capacitance itself will be sufficient, while in general an additional external parallel capacitor will be used. The smallest possible value of parallel capacitance will be the holder capacitance, Ch, and this value sets a limit on how wide a bandpass is possible for any particular cTystal.* Fortunately the 21

1

i

Figure 3.1 - Basic Ladder Filter

22

•0 C C

0 (0

E C

I-

Frequency

Figure 3.2 - Bandpass Characteristic of a Ladder Filter

23

Figure 3.3- Basic Ladder Filters Connected in Cascade to Form a 3-Pole Ladder Filter

111111

-40

-20

—100•

-80

j-60

0 0

0

I

......

Figure 3.4- Effect on Bandpass of Additional Poles

Frequency - each division equals 1 kIt

Gpoles.

poles

I

AT cut crystals available in the high frequency spectnim have characteristics which allow ladder bandpass filters to be designed with up to several kilohertz of bandwidth, This is enough for normal voice or slow speed data types of modulation. For even wider bandwidth filters, Hayward [20] has explored the idea of placing an inductor in parallel with each crystal to resonate with the holder capacitance. See figure 3.5 By cancelling Cp, he is able to produce a 3.5 kHz wide filter for AM radio using color burst crystals at 3.58 MhZ. An additional benefit is that a more symmetric fiker is the result. One drawback is that variation in the values of the indMdual inductors requires that a small trimmer capacitor be placed in parallel with each and an adjustment procedure be used to set the value of each trimmer capacitor We will also see that for filters of 6 poles or greater, it is necessary to add series capacitors in some of the sections in order to keep the resonant frequency of each loop in the filter constant. Values for the series capacitors are easily calculated based on the values of the coupling capacitors. Another approach to maintaining the same loop resonant frequencies involves using the small variation in series resonant of each crystal in a batch of identical frequency frequency, crystals. Because low-cost microprocessor crystals are often specified to have +1- 100 PPM initial tolerance of fs, an individual 10 MHZ crystal can have up to +/- 1000 Hz variation. But the particular crystal v.411 be very stable and maintain its own Sc, wherever it happens to fall within this tolerance. Each crystal in a batch can be measured for Sc and marked or placed in an individual envelope with its fs indicated. When it is time to build a filter, ctystals are selected based on their ft. for each position in the filter as needed to maintain identical loop resonant frequencies even though the coupling capacitors will vary for each loop (except that by symmetry there will be two identical loops for each required frequency in a filter with an even number of crystals). In the case where there in no crystal in the batch close enougb 26

3-l2pF

3-l2pF 3-l2pF

Figure 3.5- Use of Inductors to Cancel Holder Capacitance

3-l2pE

to the required frequency, a slightly lower one can be selected, and an appropriate series capacitance Cs added to shift its Is sIigJiIIy higher. This is the basic procedure outlined by Mackinson [26] in his description of excellent 10. 12, and 14 pole filters for SSB service. Needless to say, considerable effort is required to perform all the measurements, marking, and selection with this procedure. In return, superior filters are produced. The process would probably not be appropriate for high volume production. The general schematics of LSSH filters are shown in figures 3.6- 38. Almost all published designs of ladder filters are a special ease ofthese genera' schematics

Passband shape The attenuation vs frequency curve of an LSSB filter as shown in figure 3.9 consists of three distinct regions. The lower frequency skirt, referred to as the slow cutoff side, extends downward from the lower 3 dO down point through the series resonant frequency point of the crystals to a gradual relatively flat stopband attenuation of[alphaj d13. From this we can see that the center frequency, and in fact the entire passband will be located above the series resonant ftequency of the crystals. At the high frequency end of the passband we find the steep cutoff edge. This skirt extends all the way from the upper 3 dB down point to a null, or attenuation maximum, at the "parallel resonant" frequency ofthe crystals. Parallel resonance in this case is taken to mean the effective parallel resonance ofihe crystal when it is shunted by its own holder capacitance plus any external parallel capacaance and also the effective capacitance of the coupling and series capacitors in the filter circuit. Beyond this null, the transmission increases again and gradually levels out at the same stopband attenuation value [alpha] as the slow cutoff side. This region of the attenuation curve is referred to as the "return hill" portion. The value for [alpha] can be determined by a capacitance voltage divider

C12

T023

1C34

Figure 3.6 - General Schematic of a 4-Pole Ladder Filter

29

0

Csi

Cp

Cp

Tc23

Cs3 CM

Cp

Tc45

Cp

Figure 3.7- General Schematic of a 6-Pole Ladder Filter

C12

4i1i ji1cj

Cp

I: uCs6

Cp

Pt

Csi

'H

Op

Tc23

Cp

Cp

T

C45

Cp

Cp

Figure 3.8- General Sthernatic of an 8-Pale Ladder Filter

TCI2

Cp

Coz

Cp

1Czs

Cp

H-c 058

C

V

C

0 m

Frequency

Figure 3.9- Passbancj Shape of an LSSB Ladder Filter

32

calculation. See chapters on Lattice filters for more details on this calculation. Another way to select taipha] is to refer to tables or examples of typical filters, refer to chapter II, in order to approximately determine how many crystals will be required in a filler in order to produce a given value of attenuation [alpha] outside the passband. Of course the number of crystals also has a significant effect on the shape factor of a filter so there will be interaction between these two parameters for a given number of crystals. This is a case where experience with ladder filter designs can be invaluable in directing one to a particular design which will satis& both an ultimate attenuation [alpha] and shape factor, sQ simultaneously. Without such experience, a lot of trial-anderror will be required. A starting point can be selected using the graph developed by Sykes [36] which is reproduced as figure 3.10. This graph is based on a two pole filter. The x-axis is in multiples of the half bandwidth (BW/2). As such it shows the effect of the location of an attenuation peak located above the passband by 1.5, 2, and 4 times BWI2. You can see as the attenuation peak or null transmission, is shifted further from the center of the passband, the ultimate attenuation [alpha] increases at the expense of the sharpness of the steep sided skirt and the near-in attenuation of the high frequency side of the filter. This attenuation peak is of course a result of the parallel used in the filter, where resonant frequency of the two the crystals act a parallel resonant circuits, or traps so that no signal can pass through the filter at that frequency. The spacing between series and parallel resonance will depend not only on the crystal holder capacitance, but also on the effect of all other capacitors such as the coupling capacitors which act in parallel with the holder capacitance. In general one may also place a single value of fixed capacitor, Cp, directly ri parallel with each of the crystals In Dishals paper which appeared 7 years after Sykes, he defines this x-axis location of the transmission null as the 33

fa

Figure 3.10- Attenuation of 2-Pole Filter

34

r variable lJrov3. which the filter designer is free to select.

However for adder filters, the maximum value of lfrov3 is limited by the holder capacitance itself since the effect of additional parallel capacitance is to move the parallel resonance closer to the series resonant frequency Also the parallel resonance must be at least above the upper cut off frequency (tJrov3> I). Since the series resonant frequency is usually located part way down the lower skirt, this means that the bandwidth nf a ladder filter can never be greater than a fraction of the spacing between the series and parallel resonant frequencies of the crystals themselves. The last curve, D, in figure 3.10 represents the attenuation for the case of no attenuation peak except at zero or infinite frequency. This is the case of an ordinary coupled resonant filter using two LC resonators such as an ordinary IF transformer. The primary and secondary resonators are coupled either by mutual inductance or with a series capacitor. Because there is no finite attenuation peak above the passband, the attenuation in this part of the stopband is considerably inferior to that of curves A, B, and C. However, stopband attenuation of the low frequency side is better. In practice, use of LC resonators is limited by the Q of the elements to frequencies below 100 kHz if one is interested in voice or CW bandwidths. Crystals, on the other hand, because of their much higher Qs allow satisfactory voice and CW filters to be built in the 2 -20 MHZ region. So the advantage of the improved low frequency stopband attenuation of curveD unfortunately can not be put to practical use in the high frequency region. If one cascades multiple units of the two pole filter of figure 3.10, then curves for 6, B, and 10 pole filters can be derived. These are basically the curves presented by Dishal [10]. One such curve is reproduced in figure 3.11, In this case, the frequency axis and bandwidth is kept constant, and several curves are drawn for various values of the shape factor variable l/rov3. Recall that this variable represents the ratio of the 35

0 -o C

0 (U

a,

Frequency

Figure 3.11 - Effect of Shape Factor

36

spacing of the attenuation peak above the series resonant frequency to the bandwidth Such curves can be used to determine the minimum number of poles (crystals) needed to achieve a particular attenuation shape. in the Note that these curves neglect the effect of crystals due to Ks so that they only provide a starting point. Nevertheless they do let you know whether a particular attenuation shape can be achieved at all with say 4 crystals, even with perfect crystals (i.e Its = 0). If the shape is not possible by these curves, then the only choice is the increase the number of crystals in the filter. However, more crystals means more dissipation so that eventually the effect of dissipation will also be a

limitation. So some filter shapes can not be achieved at all with

any practical cryslals, no matter how many are used- Most filters in use today contain 4 to to crystals. Carver [4] refers to a 14 pole design, but doesn't give the insertion loss figure. Mackinson [26] gives more details for his 14 pole filler. In general, dissipation effects show up much sooner as a limiting factor in narrowband (CW) filters.

Determining Filter Component Values The design process for determining the value of the capacitors in a lower sideband filter can be described as follows. Note that programs are available as described in chapter 10 to compute these values, but it is also possible but laborious to calculate the values by hand with a simp'e calculator. -

The number of crystals and their parameters are selected.

2. The 3 dB bandwidth and lfrov3 parameters are chosen.

3. The filter type, i.e. Butterworth, Chebychev. etc. is chosen and the coefficients d1, klh k,,... etc. are looked up in a table.

37

4 Calculate the value of the termination resistance from:

dAW.W-rov32) 2mfo2Cx(I - roy3 (k12 * k,9 )f

S. Calculate the single value for all the parallel capacitors Cp. which go across each crystal in the filter using:

Cp BW3

Note: Cp must be

((iLrovJ)rQc1 ± k2J) (l/rov3)1 - I

Ch

Subtract the value of the holder capacitance Ch to get the actual value of external capacitor needed.

6. Calculate the n-I values for the n-I coupling capacitors

Cijforll ton-I andjl+ I. Cij= kij 8W3

(I

- rov32)

7. Calculate the values for the n-2 series capacitors Csl, Cs3, Cs4 etc using:

38

Cs! = I

=

Cs3

I

—

C12

=

Cs4

C21

I C13

÷

I

-

I

-

C,,

etc.

Many authors note that the purpose of these series capacitors is to tulle each of the loops in the filter to the same frequency. Indeed that is another way of deriving values for Csi which are identical to those given above. There is another way for the amateur filter builder to achieve the same result. Because the series capacitors effectively shift the series resonant frequency of the crystals higher, one can replace a crystal that has a slightly a particular crystal and capacitor higher series resonance frequency. That is provided that the higher frequency clystal is exactly what is required and one is available with that Some authors suggest sorting a batch of crystals by series resonant frequency and carefully selecting a ciystal for each position in the filter. This process is also referred to as "tuning" the crystals for the filter. The practice is perfectly acceptable if one has enough crystals with just the right spread in frequencies. This author however has found that most stock microprocessor crystals if they have a reasonable Q will have very little spread of frequencies and it is better to calculate values far Csi assuming all crystals are 39

identical. Many practical SSB and AM filters have been constructed this way without measuring each crystal beforehand With CW filters, you may want to be more careftil.

40

Chapter 4 Upper Sideband Filters By placing the crystals in the shunt arms of a ladder filter, an upper sideband bandpass is generated This is conceptually a

kind of dual circuit to the filters described in chapter 3 and the results are analogous except that the steep cutoff side of the passband is now the lower frequency skirt. Although originally given equal emphasis by Dishal [10] in his theoretical analysis, the upper sideband arrangement has received little attention and essentially all published reports of practical applications of ladder crystal filters use the lower sideband approach. Two recent exceptions are [27, 31]. And crystals in the shunt arms but Sykes [361 shows an example they are of different series resonant frequencies. Figure 4,1 shows a typical upper sideband fiher passband with several important variables identified. The passband is located entirely above the series resonant frequency ft of the crystals. A transmission null occurs at ft when all crystals shunt the signal to ground. The series resistance of each crystal prevents a direct short however so a low series resistance is desirable here to maximize the shunting effect. The bandwidth between points 3 dB down on the skirts, BW3. is shown. Normally this is a parameter the filter designer wants to choose. There is a maximum limit available which turns out to be a fraction of the difference between the series and parallel resonant frequencies of the crystals used. The difference between the series and parallel resonant frequencies for any crystal is controlled by the ratio of the holder, Ch, to inotional Cx, capacitances. For example in chapter 2 we noted that the minimum ratio for AT cut crystals in the 10 MHZ range is about 200, This may produce a difference in resonances of up to 25 kHz at 10 MHz, which is typical for 41

V C

0 Iv

C 0,

Frequency

Figure 4.1 - IJS8B Filter Passbancl

42

microprocessor crystals available today.

1/2m( LxCx )°'

fp = l/2x( LxCxCh/(Cx+Ch )f'

For any particular set of crystals, as the desired bandwidth of an upper sideband filter is increased, the value of the shunt capacitors decreases as we shall see later in this chapter. The lowest possible value for any of the shunt capacitors Cp is obviously the value of the holder capacitance, Ch. Furthermore, the lowest shunt capacitor will usually be the second one, Cp2 because for most networks, kI 2 + k23 is greater than for example k23 ÷ k34. Dishal shows that the maximum possible bandwidth will be given by:

BW3 = (foCx/Ch)((lJrov3) - (k12 +

— I)

For example, an eight pole Chebyshev filter with 0.1 dB ripple will have k12 + k23 1.272. With a 10 MHZ crystal described above as having a minimum CIVCx ratio of 200, the equation fr,r BW3 above is plotted in figure 4.2 as a function of the variable 1/rov3. The maximum occurs at a bandwidth of 2 kHzor about 50% of the separation between the resonant frequencies fs and

43

0

cci

a)

a

P0

o 0 0 a

ci

o

C

N)

ci ci ci C

C ci

o xi

oc

C

0 o ci

a a

o o o rô

Hertz in Bandwidth Max

0mb,3

H.

- WflW!XevJ

tSP!MPuee

JO

9 ajod

SSsfl

C

Effect of 1/rov3 on passband shape Analogous to the lower sideband filters, the overall shape of the passband will be controlled by choice of the design variable l/rov3. The general trend is that the lower frequency skirt (the sharp cutoff one) will become more gradual as l/rov3 is increased, while the reverse is true of the higher frequency skirt. The attenuation ofthe return bill is also increased for higher values of I/rov3. For most upper sideband filters, then, the design variable l/rov3 should be chosen as large as possible, in the range of to tO. This is limited by the ability to achieve an acceptable bandwidth and a sufficiently steep cutoff on the lower frequency side.

Higher values of l/rov3 will also require higher values for the termination resistors. Since these tend to be fairly high for SSB bandwidth upper sideband filters, this may also be a limitation as it is possible to wind up with terminations of over 10.000 ohms. In some applications impedance step-up transformers or nctworks will be required to use these high impedance filters.

Locafion of the center frequency In many applicatons the precise location of the center of the passband 'snot important Often other frequency determining elements of an application e.g. BFO frequency can be adjusted or set in relation to the filter center frequency. When the center frequency must be fixed by design to a set frequency between the series and parallel resonant frequencies of the crystals chosen, then the upper sideband filter allows for considerably more flexibility in center frequency positioning than the lower sideband approach. Of course one can always specie' the ft of crystals and order them from one of the manufacturers listed in the Appendix. Then the center frequency can be made to come out wherever desired, provided the designer knows where

45

the center frequency will be located relative to the series resonant frequency. But in this book we are assuming for cost reasons the designer is starting with a set of crystals of a given or stock frequency and needs to position Ihe filter's center frequency in relation to this given fic. In wiy ease, the center frequency clan upper sideband frequency filter is given as by the relatively simple formula:

fin

fs +

x (l/rov3)

A graphical representation of this flexibility is shown below in figure 43 for a six pole CW filter using 9 MHZ crystals. Approximately 1.2 kHz of positioning is available (for a constant 500 Hz bandwidth) by appropriately selecting I /rov3

intherangeof5to 10. This positioning of fin is the basis for the tunable filters described in chapter 6. Most applications today are satisfied by fixed fitters, however, so a single design point is appropriate

Design Equations for Upper Sideband Filters The actual element values of the capacitors and termination resistors to use with a particular set of crystals for the selected filter are calculated using the design equations given in this section. These equations were originally developed by Dishal [10]. A]though the equations are complicated, it is entirely feasible to find the element values for one filter using just the equations and a calculator, prefezably one with scientific or floating decimal capability, in one sitting The reader who plans to evaluate many designs is referred to the computer program found in chapter 9 which eliminates the tedium of many repeated calculations. It is first necessary to select Ihe number ofcrystals, ii. to be 46

I

(dB) Attenuation

oin6uj

n

-

ia;uao AouanbaJd

JO

9 010d

MD JSIIIJ

LV

used and determine their characteristics Cx, Lx, Rs, and Ch using the techniques of chapter 2. The filter type - maximally fiat. etc. is selected and the corresponding d and k coefficients found in an appropriate table suth as those in chapter 10. Filter bandvidth at the 3 dli down points. BW3. is selected. Finally the value of the design variabk l/rov3 is selected using as a guide the information given earlier in this chapter. The termination resistors are calculated using:

Rt= BW.3.L(ikQy3?- II

The series capacitors, CiJ. are calculated for i

I

..

n-I,

j=I+I

Cij

11W3[(l/rov3)2- II

There vñll be n-I of these and the values will be symmetric, that is the first and last have the same value, etc. Finally the parallel capacitors which shunt each crystal are calculated by first calculating the smallesi one, Cp2, using:

48

—A

Cp2 =

l/rov3) - (k12 + k23)J/[(lIrov3Y - 1)

Each of the other Cp's for p 1, 3, n is then calculated to make the total capacitance of each node with all the other nodes short circuited to ground be the same as for node 2. That is Capacitance at node I

Capacitance at node 2

CplfCl2 = C12+Cp2+C23 and Capacitance at node 3 = Capacitance at node 2

Cp3 + C23 + C34

C12 + Cp2 + C23

and so forth.

Note again that the values of the parallel capacitors will also be symmetric i.e. Cp] Cpn etc. This symmetry cuts the work of calculating series and shunt capacitors in half, a significant savings when calculating by hand. It is always a good idea to that the frequency response of the filter matches what one expects using a frequency response computer program as described in chapter 9. This calculation can not be done by hand. It is preferably done before actually constmcting the filter so that any errors in the calculations will be detected at this stage. Minor changes of 5% or less in element values for the capacitors and terminating resistors not have a great effect on the frequency response. Large errors, such as a factor of 2 or 10 in value or misplacing a capacitor at the wrong node will cause the frequency response to differ severely from what is expected. Corrections are much easier to make before the filter is constructed rather than to attempt to find out why the 49

measured response of a filter actually built isn't right. After a satisfactoiy response calculation, actual capacitors must be selected to build the filter. Inmost cases, the standard values available will not be close enough to the calculated values, Usually a parallel or series combination of Iwo standard values will do thejob. This can double the number of capacitors needed.

The filter is the built on a small piece of circuit board. In general, physical layout will not be important for the top 40dB or so of the passband. That is the actual filter should match very closely the calculated response in the passband and down 40dB of the skirts. Beyond that, the actual component layout is very critical and will be a dominani factor from 60 - 80dB and thither down the skirts. Carver [4j reports on the cflècts of filter layout and shielding and his paper should be consulted if superior stopband performance is desired. For ordinary use, sensible layouts i.e. keeping input and output separated, use of a nearby ground plane etc. should provide acceptable performance and no further efforts will be needed. Note however that the upper sideband filters generally have higher impedance levels so that stray couplings in the filter will have more effect Ihan with the lower impedances found in lower sideband filters. The measured response of an USSB filter will therefore tend to deviate more from the calculated response than is found with LSSB filters.

Use of the USSB Computer Design Programs Design programs for 6 pole USSB filters are given in Chapter 9. The limiting factor in choice of the variable I/rov3 is the smallest value of calculated parallel capacitance, Cp]. This value most always be more than the holder capacitance of the crystals one intends to use in the filter.

50

Practical Results The only measured results reported to date are those found in a

CW filter of reference [21] and the upper sideband half of the

dual filters of reference [31] Rather severe rounding of the filter frequency response due to the series resistance of the crystals is evident in both responses. The rounding in the measured response is reproduced in the calculated response when series resistance is included in the

crystal models. verifying the source of the effect Use of low Q cTystals will therefore limit ones ability to achieve sharp corners in the passband response, and may be prohibitive for SSB applications. It is not clear at this point whether the effect is more severe in USSR designs than in LSSB ones. Experiments with the dual filters seems to indicate that the effects of series resistance are comparable for either LSSB or USSB filters. See chapter 5.

Insertion Loss There is no simplified circuit diagram comparable to the method of figure 6 of[3 I] one can use to estimate insertion loss in USSR filters. The best way to calculate insertion loss is to model the filter with a frequency response program and note the loss in dB between input and output at the center frequency. This calculated value should agree with measurements on the actual filter. A slightly more precise method is to measure the actual series resistance of each crystal and use these values in an

individual model for each crystal in the overall filter modeL En any event the effect of crystal Q on insertion loss in USSB filters seems to be comparable to that found in LSSB filters. S. Cohn's paper [6] gives some simplified formulas fbi insertion loss in coupled resonator filters which might have some application to crystal fitters. However additional work needs Lo

51

be done to see how well they apply. The interested reader may want to use these as a starting point for such further work. As of now, they do not yet provide a practical approach for crystal filters.

52

Chapter 5 Dual Filters The concept of dual filters applies to single sideband voice service where either the upper or lower voice sidebands adjacent to a (suppressed) ri. carrier frequency are transmitted and received. It is often most convenient to maintain a steady carrier frequency and select whichever sideband is desired by switching in either an upper or lower sideband filter. This is in contrast to the somewhat more prevalent practice of using just one filter and positioning the carrier or receiver bfo to either the upper or lower filter skirt. Lo addition to the ease of sideband selection, one may also want to transmit both sidebands but with a different information content of a slow content on each one. For example, the scan image transmission may be sent on the upper sideband while simultaneously sending a voice signal on the lower sideban& Both signals would use the same carrier frequency for ease of tuning in the receiver. This rather new concept is referred to in the literature as independent sideband, ISSB. Obviously a single filter can not perform this function and two will be required. Due to the non-symmetrical nature of ladder filters, it is desirable to place the carrier on the steep sided skirt in order to provide maximum rejection of the undesired sideband. We saw in chapters 3 and 4 that the lower sideband filter has its sleep side on the high frequency edge and a transmission null at the parallel resonant point of the crystal and capacitor network. The upper sideband filter is just the opposite with its steep side on the low frequency edge and a transmission null at the crystals series resonant point. So at first s]ance it appears impossible to build both an upper and a lower sideband filter each with the carrier on the steep skirted side using a single carrier frequency 53

and a set of crystals all of the same frequency. The filters will overlap. A more catefiul analysis shows that while indeed the filters will overlap, this overlap can be made to occur at very high attenuation levels, it is possibLe to design both filters using a single set of crystals as the attenuation curves of figure 5.1 show.

Design Procedure It is desirable to use the same value fbr the shape parameter 1/rov3 and bandwidth BW3 for both filters so they will be minor images. The bandwidth should be selected first. Then a trial and erTor procedure is used to select 1/rov3. A value of 5 is a good starting point. First compute the lower sideband passband using the selected BW3, 1/rov3, number of crystals, and crystal parameters, and filter type (maximally fiat, etc.). We will assume the cattier is to be positioned 500 Hz above the 3 dB down point on the high frequency skin. Note this carrier frequency as fear. Now the upper sideband filter will have to use the same carrier frequency and have its 3 dB down point on the low frequency skirt 500 Hz above fcar. The center frequency of this filter will therefore have to be one half BW3 above the 3 dB down point. The actual upper sideband attenuation curve is calculated again using the same BW3, lJrov3, number of crystals, crystal parameters, and filter type as used for the lower sideband calculation above. Examine the curve to see whether the calculated 3 dB down point on the lower skirt is more or less than the 500 Hz above fcar. If less, then the center frequency must be raised by selecting a larger value for l/rov3. A reference to the equations in Chapter 4 may help in deciding how much larger for a given increase in the center frequency. However, this is not the whole story, because an increase in l/rov3 will also move the center frequency of the lower sideband filter, although 54

0

C

t

9824

-80

-60

0 -40

C

C

0

-20

0

9828 9630 Frequency in kHz

9832

Figure 5.1 - Attenuation of Dual Filters

9826

9834

not nearly as much. One must therefore re-calculate the lower frequency filter component values and re-compute its attenuation curve with the new value of l/rov3. A new carrier frequency is selected

500 Hz above the new 3 dB down point on the upper skirt of the lower sideband filter. A re-calculation of the upper sideband filter component values and re-computation of its attenuation curve should now result in its 3 dB down point on the lower skirt being closer to 500 Hz above the carrier than befort After several iterations, this process should converge to a suitable solution. Naturally the use of computer programs such as those of chapter 9 is essential for this procedure to be practical. One problem remains. The upper and lower sideband Jilters will in general require very different termination resistors. If they are to be switched into the same circuit, then the terminations must be identical. Small transformers constructed from ferrite cores with the proper turn ratios can be used on one of the filLers to match the other, without affecting the shape of the filter. Another alternative is the use of an L network at each end of one filter to change its termination impedance level.

Example Consider a pair of 6 pole filters to be constnicted using a surplus microprocessor crystal with the following measured characteristics. This crystal is available from Digi-Key Corporation part number X037, Price $ 1.24. (1998). 0.02438 pF 10.76113 mH Its 33 ohm Ch 7 pF Fs = 9,825,945 Hz Cx

56

0I

22

89

10

10

122

10 10

Figure 5.2 - Example LSSB Filter

10

9.56

All

are fl pF All crysiSs &e9S3MHZ

89

10

00

r'

cfl non are in pF

3.76

T15 !_1_• 116 i'

3.9 3.9

'

5.2

Figure 5.3- USSB Filter Complementary to LSSB Filter

Al c'yS.l. we 9.83W*

AlP

119

5,2

Using the iterative procedure described above. two six pole filters are designed with component values shown in figures 5.2 and 5.3. The upper sideband filter has a termination resistance of 283! ohms and the lower sideband filter has a termination of 201 ohms (before step up). Neglecting the series resistance of the are calculated. crystals, the filter attenuation curves of figure

The carrier frequency will be 9828.7 kflz in order to have identical termination resistances, the lower sideband filter's circuit is modified by the addition of L networks at each end The design equations for these L networks can be dejived form Hayward's book [211 page 164 as:

Cend

LI

VRI -Kin 27rfRIfiTh C RI Bin

201 ohms, RI 2831, giving values of Cend 22 pF. LI 9.56 M11 as shown in figureS 2. Note that the inductor value is not critical. It does not resonate with anything in the 9.83 MHZ range. Itis used to step up the impedance without changing the shape of the passband or the insertion loss. Likewise the capacitor value of 22 pF is not particularly critical either. A 5% tolerance ceramic or mica is perfectly satisfactoty. As seen in Chapters 3 and 4, the other capacitors are also not critical, so it is very reasonable to duplicate these duai filters in the home workshop or company lab without use of special instrunientat ion. where

59

Chapter 6 Tunable Filters Piezoelectric cTystals have historically been used in electronic circuits to provide a stable frequency reference. This stability of the series resonance frequency point with only slight variations due to temperature and aging is so well known that designers routinely count on an accuracy of about ±100 Hz and a stability of±l Hz for an ordinary crystal in the 3-16 MHZ frequency range. Even better accuracy and stability is available with cam in crystal selection and manufacture. Crystal filter designers count on this stability and until recently all crystal Jilter products were fixed frequency products with a specific center frequency and bandwidth/attenuation curve. Once constructed, no adjustment of the filter characteristics was possible.

Practical uses for adjustabic filters A great variety ofdigital signaling modes using various types of frequency shift keying schemes are in use today. In general it is best to select a filter bandwidth slightly larger than the maximum separation between the shifted frequencies. The center frequency of the filter should be positioned below (or above) the carrier or BFO by an amount equal to the average of the audio tones in use. Clearly an adjustable bandwidth and center frequency capability is a desirable feature to have in a receiver if it is to accommodate a variety of digital modes. Recent work with digital signal processors is another approach to this problem. However, signal processors today are somewhat limited in the IF frequencies they can handle and ultimate attenuation is limited by the number of poles etc. Separation of a single voice or digital signal in the presence 60

of many nearby interfering signals is another task for an adjustable filter This situation occurs in shortwave broadcasting and even more so in amateur radio bands whose individual stations may select any frequency within a band in which to transmit. A receiver operator may elect to reduce the bandwidth of his IF filter (reducing the audio fidelity of this received signal) in order to reject the audio components of the nearby interfering signals.

Sideband selection through use of an adjustable filter is also possible. If the center frequency is adjustable above and below a

carrier or IWO frequency then either the upper or lower sideband can be seLected. In general, however the shape of the non-symmetrical ladder filter will be even more gradual due to the need to shift the center frequency. For example, see figure 6. I. This eflèot occurs for both (JSSB or LSSB adjustable ladder filters. A better approach for sideband selection is the use of the dual filters of chapter 5. 1-layward [19] suggests that a switched bandwidth adjustment might be possible by switching different value capacitors into the filter circuit. Article [30) gives one example of this capability for a simple 3 pole filter. Note that a fairly large number of switching contacts are required, even for a 3 pole filter. Either fixed value capacitors can be switched in to the circuit or else a multigang mechanically variable capacitor can be used. Both approaches require extensive design calculations, especially if more than two different bandwidth positions, or a continuous adjustment is desired. The Cohn filter circuit of(l8] with its equal value shunt capacitors may be attractive for use with a multigang variable capacitor where all sections have the same capacitance values. See figure 6.3. One can also use voltage variable capacitors for the adjustable capacitors. Apparent'y this is the approach used in the adjustable bandwidth filter of a Ten Tech transceiver reviewed in QST magazine, and subsequently revealed in a US patent 5,051,711 by Lee Jones. See figures 6,4 and 6.5 below. One drawback mentioned by the reviewer which applies to 61

Frequency in kit 7999

7999.5

8000 I

8000.5

8001.5

I

I

C

0

110

Figure 61 -

62

Pole 500 Hz Adjustable Frequency Filter

1881

Jeirid q;pIMpueH

OLPI

T

- t9 ejn6ij

1OLP

IOLZ

'0

a

0'

P 1

IC

Figure 6.3- Cohn Filter with Equal Value Capacitors

IC

both these altempts is that the center frequency ofthe filler moves left (to a lower frequency) as the bandwidth is decreased. This shift occurs with lower sideband designs if the simplified design procedures of Hayward are used. Basically a large value of 1/rov3 is assumed, probably to produce the most symmetrical filter shape i.e. the steepest lower skirt. Another way to switch capacitors in and out of the circuit is through use of PIN diodes. These can be connected in such a way as to "shunt one end of a fixed capacitor to &ound when biased on, or leave the capacitor unconnected when the diode is biased off. Koenig [24] uses this technique for bandwidth adjustment of a crystal filter, however he uses it with a monolithic crystal filter. Such filters use specially built crystals with more than two contacts and are beyond the scope of this book. It may be advantageous to replace mechanical switches with PIN diode switches in a switched bandwidth filter. The diodes can replace an expensive multi-contact mechanical device and probably provide better isolation i.e. less stray coupling than any kind of mechanical device.

Termination resistance All adjustable lilters have the problem of a valying termination resistance as the bandwidth (or center frequency) is changed. An adjustable L-network (the L in this description does not denote an inductor but merely the shape of the schematic) at each end of the filter can be used to compensate for the change in termination resistance provided that the component values in the L network are adjusted simultaneously with the bandwidth or (center frequency) adjustments. A simplified L network consisting ofjust an impedance step up capacitor is used in the switched bandwidth filter [30]. In the general case however an L network consisting of a series inductor and shunt capacitor is needed to transform a larger range of filter impedances to a constani end impedance. If 65

INPUT MATCHING SECTION

L

p

L

4

FILTER

—

I[

500Hz

—

—19

seats 135!) I motlonal 3SmH

r,erl.,

6.1 423M4z

4Op(@I 2V

——

51M

BIA SING

ARE lOOK

ALL RESISTORS

SECTION

OUTPUT

500

..—jsEcrIow

1

Figure 6.4- Ten leo Adjustable Bandwidth Filter

CRYSTALS:

I

L

TYPICAL VARACTOR CAPACITANCE:

VARACTOR VALUES ARE

ijl

DC CONTROL VOLTAGE

6.1423

dB

6.14

6.144

6.142

6146

MHz

Figure 6.4b - Passband ol Ten Tec MiustabIe Filter

61

the adjustable inductor is out of the question, then a fixed inductor in series with an adjustable capacitor can sometimes the necessary range of reactance required of the inductor. This's the approach taken by the author of [29] in his experimental 3 pole filter to maintain a 2000 ohm termination while both the center frequency and bandwidth are varied See figure 6.9 for an example of the frequency adjustment of this filter.

Achievable tuning range and bandwidth adjustment range The factors that limit the type of adder filter which is possible for any particular cryst& unit selected in a fixed filter also limit the tuning range of a Tunable filter. That is, for a lower sideband filter the parallel capacitance across the crystals can not be less than the holder capacitance ofthe crystal unit itself Practical limits on the capacitors and termination resistors may also apply. Capacitances less than I pF or impedances above 10K ohms are undesirable. Another limitation is the variation in capacitance values available to the designer in the variable capacitors he intends to

use. Many voltage variable capacitors cover only a 3:1 range in capacitances. Some newer ones with abrupt or hyper abrupt junctions cover up to 10:1 but with a very nonlinear characteristic. Mechanical variable capacitors are generally limited to a 10:1 range or less. By far the most challenging part of designing a tunable crystal filter is satisfying the requirement to track all capacitor values as the center frequency and bandwidth are independently varied. Symmetry of the filter reduces the number of independent values of capacitance which must be established by two but even so for a 3 pole filter, 4 different capacitance values must be set for each center frequency and bandwidth. This seems like a good job for a microprocessor.

68

Figure 6.5 - Experimental Filter with Independent Center Frequency and Bandwidth Adjustment

200k

b200k

Figure 6.6 - Control for Adjustable Filter

70

In figure 63 for example, a microprocesser with two analog inputs could be used to sd (perhaps in real Lime) the desired center frequency and bandwidth. Four analog outputs are generated to be used to set 4 separate bias levels for the voltage variable capacitors. Note that more than one actual capacitor may be connected to each voltage level i.e. both end capacitors have their bias set by the Cend voltage etc. In real time the microprocessor can read the command inputs and then using internally stored equations or look-up tables, set the corresponding control voltages. Some type of voltage step up or scaling with operational amplifiers will usually be needed to covet the Ito 20 volt range required by typical voltage variable capacitors Current requirements of capacitor bias levels are negligible. The simplified control circuit of figure 6.6 can be used to set voltage levels manually for experimental tests

Practical Tuning Elements Voltage variable capacitor characteristics are best described by the following two examples which are produced by Motorola lnc Other manufacturers make similar units. These diodes are designed for genera] frequency control and tuning application. The MV209 has a capacitanec of 26 to 32 pF at a reverse voltage of 3V when measured al 1 MHZ. Q is a minimum of 200 at SO MI-Il. As the reverse voltage is increased up to 25 volts the capacitance is reduced by a ratio of 5.0 to 65. That is, if the capacitance at 3V was 26 pF, then the capacitance at 25 volts could be 4 to 5.2 pF. Maximum allowable reverse voltage is 3ff The capacitance does not decrease linearly, and a typical curve given by the manufacturers is plotted on semi-log paper. uk at 2YC increasing to I uA at Leakage current The temperature coefficient of capacitance is 300 ppMPC, typicaL For larger capacitance, the MVAMi IS diode is available This diode was designed to tune AM radio receivers, 71

35

30 Li-

£

25

2

4

6

8

10

12

14

Volts

Figure 6.7- Capacitance of MV2O9VariCap

72

lOOk

.01

control voltage

capacitor terminals

100k

.01

Figure 6.8- ISolation Circuit

73

fl

0

-4

dB

-8

&

-12

8006

8008

8007

8009

KiloHertz

Figure ES - Practical Results with 3-Pale Adjustable Filter

74

undoubtedly to replace the well known 365 pF mechanical variable capacitors. Maximum allowabk reverse voltage is IS volts. No maximum ratio is specified A Q of ISO is specified at I MHZ and I volt bias. By far the must challenging problem is using these diodes as electronically adjustable capacitors is their wide tolerance on capacitance and capacitance ratio. Each capacitor must be measured and a capacitance vs voltage curve established, It is just not possible to use a sing'e curve for all devices in crystal filter application. Measurements show that the voltage required to set a particular capacitance value can vary from unit to unit by as much as I volt. See figure 61 for two samples of the MV209. Isolation circuils are required to separate the dC control voltages from the hf signals present in a filter application. Figure 6,8 below shows a practical circuit which can be used in the case where both ends of the capacitor have rf voltage present.

Mechanical Variable Capacitors The supply of mechanical variables here almost disappeared as maxw companies have stopped production of these relatively expensive components. The Oren ElRott Products Company in Ohio may be the only U.S. manufacturer. Several distributors also cans' products mostly manufactured outside the U.S. And finally, Fair Radio Sales in Ohio stil3 has some military surplus units available. Custom variable capacitors ace very expensive but can be made. It is unlikely that any stock item niultigang capacitor will have the proper capacitance vs. shaft rotation characteristics in all gangs to properly track. One possible exception is the Cohn type of ifiter which uses capacitors with all the same value. Even with this, some means of adjusting the tennination resistance is needed. Another disadvantage of mechanical capacitors is that only one adjustment is available so it is not possible to set both 75

bandwidth and center frequency

Programmable Capacitors A solid state non-volatile serially programmable capacitor is now available from Hughes as part # HC202I Eight binary weighted capacitors can be connected in parallel under program control to produce any capacitance value from Ito 256 pF in 1 pF steps. While this device may be appealing at first, ftjrther investigation revealed a very low Q at RF frequencies making it unusable as an adjustable capacitor device in crystal filters Perhaps further development of these devices will provide an ideal solution. Evidently this tolerance is not a problem in frequency tuning whereby the action of a closed loop PLL etc. can correct the capacitance variations.

Design

Equations for a Tunable Crystal Filter

Either the upper or lower sideband configuration can be used to construct a tunable filter. In this section the lower sideband equations which were used for the experimental filter of reference [29] are &ven. Subsequent examination of the upper sideband equation of chapter 4 seem to indicate that a wider tuning range may be possible. Impedance levels are much higher resulting in much smaller capacitor values and exposure to stray capacitances. Further investigation of tunable upper sideband crystal filters is warranted.

Lower Sideband Equations From Chapter 3 the center frequency of the filter fin is given by:

76

fic

flui +

[±uulltQY3)Qc,2+ k23L

(T)

2

Now define variable F fin - fk as the difference between the center frequency of the filter and the series resonant frequency of the crystals F will always be positive,

that is the filter center frequency is above the crystal series resonant frequency Also

let B = BW3 and

I

I/rov3. Then equation (I) becomes;

-F

L-Jik2+ Ic,,)

(2)

2

For simplicity we assume a 3 pole Butterworffi So:

v'51-i

21-11

design, then

(3)

Now solve (3) for las a ilinction ofF and B.

2 Fl - 2v7F

12B I - B

(2 F - 12 B) I

2v7F - B

1= 2

F -12 B

(4)

77

If you specify a center frequency and bandwidth for the filter, then equation (4) gives the value of the design variable I /rov3. For any configuration other than the 3 pole butterworrh, the value (2) must be replaced

the (k12 + k23) values for that

configu rat ion.

Define and calculate Q = flUE

Now it is possible to calculate the required values for the parallel capacitor Cp, and the coupling capacitors Cnn = 1.. using the equations from chapter 3

CpCxQIrJY -Ch

(5)

must be positive, and

(6) —

For higher order filters, there will be a series of capacitors and the initial square root of 2 must be replaced by Ilkij The required termination resistance also from chapter 3

is:

RI=

I

coCxQ where o

78

2ith

j..j2

(l-JYQ'

(7)

Equations(S), (&), and (7) completely define the values for the filter elements for any given choice ofF and B. Note: lithe filter has more than 4 poles, then series capacitors will also be needed as described in chapter 3. Their values are determined from the values of Co. It is necessary to determine the largest termination resistance value RI for any pair of values for F and B. This will generally occur when F and B are at their greatest value. Then, select a final lermination resistance R greater than the largest value ofRi. MI values for RI will then be scaled up to the final fixed value R, so that a smgle terminator can be used for all values ofF and B. This impedance step up is done with elements Cend, L. and Cs as shown in figure 6.5. The value for Cend is given for each value ofF and B (Cend must be adjustable) by

Cend=l

/ R-l

wIt

V

(8)

RI

Now compute the intermediate variable

0=

—

I

-Cend

(9)

w2R2 Cend

and choose a fixed inductance L large so that Cs given below is positive for the entire range of dcsired F and B.

Cs

I

(10)

l/Cn- 1/Ct -&L 79

Cs will generally be smallest for largest F and smallest B. Again. if the filter has order greater than 3, then the correct value to use for Ci. is C21 Note that Cs is also an adjustable value that will depend on the values ofF and B selected. The inductor however, remains fixed. The value for all the filter capacitors are now given by equations (5), (6), (8), and (10).

hawker's frequency shift A small change ii the center &equency of a ladder filter can be made by placing a capacitor in series with each crystal to "shift the series resonance upward Hawker uses this to move the center frequency of his ladder filters described in [17] to

exactly 9000 MHZ. The actual shift for the filter of figure 7.1 is about 1350 Hz. The bandwidth decreases slightly. Whether this technique can be used in general, and over what frequency range and bandwidth remains to be determined. But it appears to be a very useful technique for positioning filters built from stock crystals to exact center frequencies.

80

Chapter 7 CW Filters Desirable Characteristics of CW Filters In general, a filteT designed for CW seMce (on-off keyin8 of carrier) will have a very narrow bandwidth in the range of 200 to 500 Hz. This will depend on the keying speed and prevalence of adjacent interference signals. Ringing must be avoided, so the filter shapes with steep shirts but severe time domain distortion such as the chebyshevs can not be used.

A typical high performance commercial CW filter, the Spectrum International XE - 9NB has the Ibllowing specifications: Center frequency 6 dB bandwidth Ripple Loss Shape Factor Ultimate Attenuation Cost (1992)

9MHZ ±200 Hz 500 Hz

0 to 20%

90 dB $165

It's often desirable to build a CW filter using crystals from the same batch that was used for upper or lower SSB filters. If one is using "srnplus" microprocessor crystals, then only one crystal part number may be available at the desired frequency. Note however, at some frequencies, there is both a series and a parallel resonant crystal available. The parallel one being merely one with a lower series resonant frequency that is specified by its 20 or 32 pF parallel resonant frequency. For those willing to bear the cost of a crystal with a specially ordered frequency, one hopes to avoid the cost of a second 81

crystal frequency order for the CW filter. Usually an acceptable CW filter can be made from the SSR crystals as long as the crystal Q is several times greater than the CW filter Q. Recall that Filter Q is defined as the center frequency of the filter divided by the 3dB bandwidth. As the crystal Q approaches the CW filter Q then the situation is hopeless and no CW filter can be built with ihese crystals. A higher Q crystal will be required. In general then, it can be said that a CW filter will require higher Q crystals than an SSB filter. Carver [4] gives approximate values of desired crystal Q for 6 to S pole filters as follows:

Filter type 3 pole .5 error equiripple filter Q x 15

6 pole

filter Q x 20

Gaussianto6dB

fllterQx45

filterQx35 *

Butterworth

filter Q x 50

filter Q x 32

* This number appears to be in error compared to the others but does not explain how these guidelines were determined. Practical experience with many filters shows that while the higher the better, much lower crystal Q's can still be used although the overall shape of the passband will be more rounded at the top.

Matching Tolerance The narrower bandwidth of CW filters requires that the crystals used have closely matched series resonant frequencies. This can be a problem with surplus microprocessor crystals

which typically have a tolerance of+50 parts per million. At 10 M1-1Z then this would be +500 Hz which is too wide a variation for random use in a 500 lIz wide filter. Fortunately a measurement of fs on a batch of crystals will show most of them fail within +100 Hz of the specified series resonant frequency If you are unsure of the spread of fs of your crystals, then they should be individually measured, and recorded. A supply of 82

small envelopes is uselbi for this purpose so the can be marked on the outside and the crystal placed in the envelope immediately after testing to avoid mix-ups. After a batch is processed in this manner, a selection of closely matched units can be put together. Those not selected can be put away and used later, perhaps for another CW filter at a slightly different center frequency or an SSB filter, without having to re-check their frequencies.

Overall Shape of a CW Filter In reality, the CW ladder filter is just a narrower passband version of either a lower or an upper sideband filter Usually it is desirable to have a symmetric shape for the shirts so a large value for l/rov3 should be used in the design. The narrower bandwidth will cause the CW filler to have a lower impedance than a similar SSB filter. Stray capacitances in the actual filter are therefore not as disturbing. This lower impedance however may require modifications to the interface circuits if they were intended to dtive the higher impedance SSB filters, Impedance can be stepped down and back up with inexpensive HF transformers constructed with powdered iron or ferrite cores. Alternatively the impedance can also be adjusled *4th L networks of series inductors and shunt capacilors at the ends of the filters. See chapters 5 and 6 for more details on this Also note that the best source by far for practical information on inductors is the recently published "Radio Components Handbook" by Guido Silva, ISBN 1-891237-18-7 available through Borders Book Stores and MFJ.

The swjtchable filter One question that immediately comes to mind is whether a single set of crystals can be used to first build an SSB filter.

83

Then can the filter bandwidth be decreased to that of a CW filler by "switching in" additional capacitors? And of course Ihe answer is yes provided you are wiLling to accommodate the resulting drop in impedance as previous'y mentioned. This idea is the basis of the filter circuit shown in figure 6.2, originally described in [30].

Switchable Bandwidth Filter A somewhat disturbing characteristic of the switchable bandwidth filters that the center frequency of the CW filter will

be partway down the (less steep) low frequency skirt of the LSS filter. See figure 6.4b. In a normal short wave receiver, the beat frequency oscillator (IWO) will have lobe moved from its position (s) for SSB use to another frequency about 500 to 1000 Hz above or below the center frequency of the CW filter. Whether the IWO can be shifted this far will depend on the actual circuit used. The designer should remember that the BFO crystal will often come from the same batch used in the jilter construction

Design Procedure To design a CW filter, one can refer to the design procedures in the LSS and USSB sections of this book, but select a butterworth or other desirable time domain slope. The programs in chapter 9 include butterworth 6 and 8 pole variations. It will be immediately apparent that the holder capacitance Cli will be of minimum importance, but that crystal Q is now Ibe limiting factor.

Examples of CW Filters A number of published designs are included here to show some of the range of filters currently used. In figures 7.1 and 7.2 84

Hawker

adds series capacitors to a simple 3 pole design to

shift the center frequency upward. A pair of filters designed for a CW transciever includes a six pole CW filter shown in figure 7.3 and a companion 3 pole post IF filter in figure 7.4. Individual passbands are shown in figure 7.5 and the combined effect in figure 7.6. Note that the post IF lifter removes wideband noise generated in the IF amplifier from the opposite side of the BFO where it would otherwise be detected in a balanced (or unbalanced) detector as audio frequency noise. This noise would otherwise add to the wideband noise on the signal side of the BFO which is not rejected by the post IF filter. It appears therefore that if all the noise on the opposite side of the BFO is rejected, then the total noise detected will be reduced by one half (3 dB noise power reduction). The 3 pole filter shown has greater than 40dB rejection in this range and therefore will reduce the noise amplitude on the opposite side to C I % of its value. Three poles are therefore adequate for this Ibnetion. The discussion above assumes the bandwidth of the audio amplifier following the detector is comparable to the IF filler bandwidth. If it is wider, then much more broadband noise would be detected than would using a post IF filter. The improvement may therefore he more than a 3 UB noise reduction relative to a signal when the post IF filter is used.

Infigures 7.7 and 7.8 a Cohn filter of[lSj is shown using4 MHz crystals.

85

0'

00

68

780

1600

50

1600

50

Figure 7.1 - Hawkers CW filter

50

1

66

780

500

dB

-60

-50

-40

-30

-20

-10

0

kit

9000

Figure 7.2- Passband of Hawkers CWfilter

8998

9002

00 00

3000

180

1220 1501

180

Figure 7.3- A six pole CW filter

1180

180

100

180

3000

120

2000

1201

1120

2000 p

Figure 7.4-Three pole post IF CW filter

89

0

-80 -

-100-

dB

-40

-20

0•

9002

I

6-po'o

3-pole

Figure 75- Passband of S pole and a pole CW filters

Frequency in

I

9000

I

8998

-.

—

—1

-60

dB

-40

Frequency in kiloHertz

9000

9002

Figure 7.6- Combined overall passband of 6 po!e and 3 pole CWfilters

8998

300

4MHZ

4MHz

4MHz

4MHz

I Figure 77- Cohn filter for CW

92

300

'0

-80

-60

-40

-20

0

dB

0

800

1200

1600

Figure 7.8- Passband of Cohn CW filter

4cc

2000 Hz

Chapter 8 Lattice Filters Simple lattice filters using a single crystal and a circuit similar to figure 8.1 were included in shortwave receivers many years ago.

Design equations fix such simple filters were given for example in the 1953 Radiotron Designer's Handbook (251. In fact the information shows how to make the bandwidth adjustable by varying the load resistance. This simple lattice will have a bandpass shown in figure 8.2. Capacitor C is often made from a variable capacitor which is adjustable from the front panel of a shortwave radio. Adjusting the value of C moves the frequency of the null point of figure 8.2. Of course such simple filters with a single crystal have very poor skirt selectivity by todays standards.

Modern Lattice Circuits The fill lattice circuit of figure 8.3 can also be replaced with the half lattice of Figure 8.4 by use of a center tapped transformer. In either case crystals with two different series resonant frequencies YI and Y2 are required. The bandwidth of the filter will be in the range of twice the separation in frequency of the series resonances of the two crystals. In practice the circuits of figures 8.3 and 8.4 are repeated and cascaded in order to increase the number of filter poles and thereby produce filters with sharper skirts published a computer program for calculating the Rohde crystal frequencies, tuned circuit elements and termination resistances of the lattice filters. Additional information on the theory ollattice filters is given in Kinsman, [23] page 77. 94

I

Figure 8.1 - Simple attics filter

0

-10 -20 dB

-30

-50

1

2

3

4

5

6

kiloHertz Figure 8.2 - Bandpass of simple lattice filter

96

Figure 8.3- Full lattice crystal filter

97

I Figure 8.4- Equiva'ent half lattice filter

98

Kinsman and others have shown that every ladder filter can be converted mathematicaLLy to an equivalent lattice But the reverse in not true. Lattices provide a more general span of filters of which ladder filters with all the crystals in either the series or shunt arms are a subset. How therefore do the passband shapes of the lattice and ladder filters compare? Sykes [36] shows that the key parameters are the bandwidth and spacing of the null frequencies to the 3dB down points. Jn a ladder filter with all identical crystals, there will be a null on only one side of the passband. The passband on this side ofthe center frequency in a ladder filter is essentially the same as that produced in a lattice filter using the same crystals for one of the two required frequency crystals. A lattice will also have a null on the other side of the passband which is not present in the ordinary ladder designs. This is the main difference between the two approaches. In order to match the skirts on both sides of the center frequency, a ladder filter would have to use crystals in both the series and shunt anns. Two different crystal frequencies would be required in the ladder as it is in the lattice.

Ultimate Attenuation Because the (half) lattice filters use a halanced transformer, their ultimate attenuation (far from the passband) depends on the balance in the transformers and balance in the holder capacitances of the crystals. This balance is difficult to determine beforehand and difficult to achieve in practice over a wide frequency range. Various unknown stray capacitances and inductances come into play. Ultimate attenuation in the ladder circuits isjust based on the ratio of capacitances i.e. a capacitance voltage divider. For example, the three pole LSSB filter can be depicted as shown in Figure 8.5 below. The crystals are represented by their holder capacitance Ch A parallel capacitor Cp, if used, is also present. Then the 99

CiT Figure 8.5- Circuit for calculating ultimate rejection of a ladder crystal filter

lao

ultimate attenuation can be calculated from this equivalent circuit. Similar capacitor voltage divider networks can be drawn for higher order (more poles) filters. The attenuation calculated will apply except in the neigbborhood of the passband and at odd harmonics of the crystals fundamental frequency.

Crystals for Lattice Filters The two (or 4) crystals used in a lattice circuit must have matched holder capacitances. They should therefore come from the same manufacturer One possibility which does not appear to have been explored to date is the use of low cost Inlicroprocessor crystals where both a series and parallel specified crystal is available for the same frequency. The parallel crystal will have a series resonant point several kilohertz below the marked parallel frequency If the two series resonant frequencies are separated by half the desired bandwidth of the

lattice filter, then these crystals can be

used.

More information on Lattices devoted As mentioned in the introduction, this book is primarily to ladder designs. This chapter on lattices in included only for a bilef comparison between the two types. The reader is referred to Kinsman [23] for a thorough coverage of the lattice design theory. For more practical information on building lattice filters,

refer to references [11,25, 34, 35, 37, 39, 40).

Examples of Lattice Crystal Filters Included here are a number of published passband shapes of commercially available filters assumed to be of the lattice type. filters of The reader can use these for comparison to the ladder

chapters 3 to 7.

l0l

Table W I

Fox Tango YF-90111 .8 filter 8-poic 9MHz AttenuatiQn (dB)

Bandwi4th (Hz) 1750

10 20 30 40

2060 2170 2320 2440 2590

50

60 70 80

2720 2810

90

Table 8.2 Spectrum International XF9B S pole 9MHz

(dB) 6

60 80

102

Bandwidth (Hz) 2400 4320

5280

Table &3 Heat hk it

Partii 404-284-I CW filter used as an accessory in SBIOI transciever. 3.395 MHz Attenuation (dB)

Bandwidth (Hz) 400 2000

6 60

For comparison purposes, the RME 6900 receiver which uses a 50kHz IF frequency (no crystal thter) has the bandwidth shown in Table 8.4. The Collins 75A-4 receiver uses a 455 kHz mechanical filter with the characteristics shown in Fable 8.5.

Table 8.4

RME 6900 receiver

Attenuation (dB) 6

60

Bandwidth (Hz) Narrow Wide 2000 3600 7300 11000

CW 500 3300

Table 8.5

Collins 7SA-4 mechanical filter (CW)

Attenuation (dB) 6 60

Bandwidth (Hz) 500 +25% 2000

03

Chapter 9 Programs One naturally turns to use of a computer in the design of crystal filters in order to handle the mathematical complexities involved. In this chapter I have collected what information is available on programs which may be of use to the reader. No endorsement of any of the products is intended. Of course one can work out the mathematics by hand with the help of a hand calculator. The author has calculated many 6 pole ladder designs by hand. Calculation of the passband response is another matter. Even

for simple 2 or 3 pole designs, calculation of a frequency response plot by hand is just too much. Here a frequency response program is absolutely required.

Ladder Design Programs Dishals equations from chapter 3 and 4 can be coded into relatively simple high level language e.g. DAS1C programs. Reproduced below are four examples for calculating 6 pole LSSB and USSB filters with Butterworth and Chebyshev shapes. By entering a particular crystals parameters Lx, Cx, Rs, and Ch and choosing a desired bandwidth. BW3 and shape factor, tlrov3, the program calculates the necessary termination resistance and coupling capacitors. For LSSB filters, the parallel capacitance is checked to make sure it is less than the holder capacitance Ch. The programs display the termination resistance and capacitances. Optionally a complete circuit description can be saved to a data set for use hy a network analysis program such as Schnider's described below. Readers with this language familiarity can easily modify the statements to design other filter types or add additional poles. 104

Contact the author by mail at 3824 Pembrooke Lane, Vestal, NY 13850 for additional questions or copies. Wes Hayward has written a program for LSSB crystal filter design which is included in the 1994 edition of his book [2 I]. This was used by Makhinson in the design of his 10, 12, and 14 pole SSB filters [261.

Lattice Programs Rhode developed and published [34] a simple program for design of half lattice filters. Another lattice program by Frey LII] uses the WINDOWSTM operating system.

Programs for Calculating the Passband Almost any circuit analysis program can be used to calculate the passband of a crystal filter by using a frequency domain sweep. Crystal filters have one unique characteristic which may cause numerical errors with some programs. The series

capacitance of a crystal is very low compared to other capacitances in the filter and this large spread in values can cause round-off errors when inverting the large circuit matrix. A six pole filter for example typically requires a 24 x 24 matrix to describe the circuit elements and interconnections. Other than this one caution, it is a straightforward matter to enter the circuit element by element into a circuit analysis program. Each crystal is representee by its equivalent circuit of Figure 2.1. Termination resistors of the proper value are added and a voltage generator at the input end. A frequency sweep of the voltage across the output termination resistor is requested and plotted with a dB or log scale. Note that for simple computers without a math coprocessor, this calculation may take several minutes of calculating time. A version of one of the best known circuit analysis programs. SPICETM, is widely available, for flee, from semiconductor 1 05

manufacturers. An output plot of a 6 pole 9MHZ SSB filter is shown below in Figure 9.1 as an example. This calculation took 39 seconds for 100 frequency points using an 80486 computer. Crystal filters with just a few poles can be analyzed using the BASLC program published by Schnider as Verify network frequency response..' EDN. Oct. 5, 1987. pp. 87-89. This program, however, uses a determinant procedure to invert the circuit matiix. Determinant procedures are known to have round-otTproblems which result in "divide by zero" errors. The program is suitable for simple computers with small memory capacity The author has replaced the matrix inversion part of the above

program with a Gaussian elimination routine with lull pivoting as described by Forsythe and Moler in their book Comouter Solution of Linear Al2ebraic Systems, Prentice Hall, 1967 but modified for complex numbers. This eliminated any round off problems, even for circuits with up to 100 nodes. A screen plotting routine with dB scale was also added. This modified program was used to calculate most of the passbands shown throughout this book. Contact the author for more details. The program will run on any 8086, 8088, or higher machine, or any other machine with BASIC language capability.

106

17: Ot 23

Frequency

LOOaIqh

FILE FOR SPICE

9.OOSPt

Figure 9.1 - Pasiband results using SPICE program

OOB(24}

Date/The run: 09/09/93

Basic Statements to design a six pole USSR Filter with a .1dB Cliebyshev shape 10 CLS 20 PRINT

SIX POLE .1DB CHEBYSHEV USSB FILTER DESIGN! 30 PRINT 40 PRINT "INPUT CRYSTAL PARAMETERS ,CH(PP)" CX(PF) .LX(F1) 50 INPUT CX,LX,RXCH 60 70 80

90 FO=t/(2*PI*SQR(LX*CX)) 110 PRINT "FX=",FO," IS THIS CORRECT? 120 INPUT Y$

130 IF LEFT$(Y$,1)"N" THEN 40 140 BX2*PI*FO*CX 150 PRINI' "INPUT BW3(HZ), 1/ROV3" 160 INPUT BW3,R0V31 170 IF (ROV3I20) THEN 150 180 788: K12'

1(23=. 539 :

K34=.

518 :

K45. 539

R56 .716

190 G=BX*D*NFO/BW3)/N(R0V31)42)-1)) 200 R1/G :PRINT "R",R, OHMS' 210

C12.C12*1E+12,

PE"

PRINT "023=",C2341E+12," PF" 230 C34C12*K34/K12 :PRIINT 220

PF"

240 C45C23:PRINT

c45=,c45*IE+12," PF"

250 C56=C12:PRINT

C56*IF+12

PF"

260

CP1=CX*(FO/8W3)*((ROV3I.(0fKl2H/u(ROV3I)A log

j

2)-i)) 265 PRINT 270

PF!!

)A2)-1))

275 PRINT 1lCp2"Cp7*1E412 280 )A2) -1))

285 PRINT •!cP3=!! CP3*1EI-12

!

290 CP4CP3:PR1NT "CP4=",CP4*1E-f12." PF'

300 CP5CP2:PRINT CP5,CP5*IE+12,P PF CP6*1E+12 310 CP6CP1;PRINT CP6 PF" 320 IF CP1