Wireless Communications Design Handbook Space Interference

WIRELESS COMMUNICATIONS DESIGN HANDBOOK Aspects of Noise, !nte~emnce, and Environmental Concerns VOLUME I" SPACE INTERF...

Author: Reinaldo Perez

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WIRELESS COMMUNICATIONS DESIGN HANDBOOK Aspects of Noise, !nte~emnce, and Environmental Concerns

VOLUME I" SPACE INTERFERENCE

WIRELESS COMMUNICATIONS DESIGN HANDBOOK Aspects of Noise, !nte~emnce, and Environmental Concerns

VOLUME I" SPACE INTERFERENCE

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VOLUME !' SPACE INTERFERENCE

REINALDO PEREZ

Spacecraft Design Jet Propulsion Laboratory California Institute of Technology

ACADEMIC PRESS San Diego London Boston New York Sydney Tokyo Toronto

~ i s book is printed on acid-free paper. Copyright © 1998 by Academic Press All rights reserved. No. part of this publication may be reproduced or transmitted in any form or by any means, elec~onic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. ACADEMIC PRESS 525 B Street, Suite 1900, San Diego, CA 92101~4495, USA http://www.apnet.com Academic Press .2.4-28 Oval Road, London ~ I

http://www~hbuk.co.ukJap/

7DX, UK

Library of Congress Catalo~g-in-Publication Data Perez, Reinaldo. "Wireless communications design handbook : aspects of noise, interference, and environmental concerns / Reinaldo Perez. p. cm. Contents: v. 1. Space interference- v. 2. Terrestrial and mobile interference- v.. 3. Interference into circuits. ISBN 0-12-550721-6 (volume I); 0-12-550723~2 (volume 2); 0~12-550722-4 (volume 3) 1~Electromagnetic interference~ 2. Wireless communication systems--Equipment and supplies. I. Title. TK7867.2.P47 1998 98-16901 621.382'24- A, ellipse: 1

B

g

a(i - e2) '

A

a(1 - e 2)

B = A, parabola: 1

B--

a

A=-.

1 a

0 < B < A, hyperbola ( + branch): B -A < B
.v'X/% ........................................................................................................ ~-~.i.~.............................. I

.I.

WTo Input Signal Common Tie l ............................ II 0.1 p.F

Une impedance = R ..................

~-,/x,,,'X,

I

~J-

Figure 3.6 Decoupling network for operational amplifiers.

3.2. Reaction Wheels: Physical Principles

55

R2 Rt

Vo

Figure 3.7 Improper grounding of operational amplifiers.

as a result of the current flow through these lines, known, as ground impedance coupling, In Figure 3.7, both. the signal and power supply are connected to the same single ground point. However, a potential Vg is created when the current through the load also sets a potential on the noninverting input of the operational amplifier, Now the amplifier output voltage with respect to. the system ground is given by

V°

Rf = -R~

Vi

+

Rf + R i RI

Vg.

(.3.1)

The error term from. Equation (3.1) can be significant, since narrow printed circuit board conductors and connector pins can have considerable impedance (resistance and inductance.).

3.2

Reaction Wheels: Physical Principles

Momentum and reaction wheels are. used for the storage of angular momentum. They have several purposes in a satellite AACS: first, to add stability against distorting toNues; second, m absorb cyclic torques; and third, m transfer momentum to the satellite body for the execution of slewing maneuvers, These devices depend on the momentum of a spring wheel, h = Ioz where 1 is the moment of ine~ia about the rotation, axis of the. wheel and ~ is the angular velocity.

56

3. Attitude Control and Navigation

Figure 3.8 shows a diagram of the typical reaction wheel. In general terms, a momentum or reaction wheel consists of a housing that. contains the rotating wheel, bearing assembly, drive motor, and drive/control electronics. The motor in the momentum or reaction wheel produces a net acceleration torque about the wheel (angular velocity which is constantly changing direction produces a torque). The drive/control electronics provides two modes of operation: (I) constant anguI~ momentum by providing a constant speed, and (2) torque control motion. In constant angular speed, the momentum is maintained at a desired value. In the torque control mode, the wheel speed is changed using a close feedback system to respond m external torques, with the objective of mai.nt~Jning a determined direction for a pa~icular axis. ~ e r e are two types of motors: AC two-phase induction motors and DC brushless motors. AC motors do not require brushes or slip rings; therefore, they have higher reliability and a longer life. However, £ne efficiency is low since they have a low torque and need a high operating speed. DC motors, however, can provide high to.rque at low speed. The n o d a l brash comrp:atators are replaced with a type of electronic commutation.. From a reliability point of view, the lubrication system in reaction or momentum wheels must be well controlled: when ~ e seal is exposed m the space environment, it tends to evaporate somewhat, increasing the friction, of the bearing

Thin Cover FlatWeb of

\\~t ..........

Shaft ~ _ / B.earing

Hyw

........

~zz:/L17z:

_.i LZ3,,L,L ............................................... ~~"

~i

~ 2 ~ ..... ;.____i"ziiiiiz 2_iiii 2....

L..~rzzi z : z z . 2 z z

KN _..............N k-W jHoo og

of....Flywheel"~-~¢&~v.;~

x ", .i~.i ....i _~i..:~.'i~:~t~ ~ ' # ~

!i

• %%

Mot

es

/

Thin Cover

!

Bearing

~

"

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

~'~-~"

Figure 3.8 Reaction wheel assembly.

Hermetic

Connector

Powerand Control Circuits for Motor


57

to a point where the drive/control electronics can be damaged. Low-vaporpressure lubricants and even dry lubricants are cu~ently used for bearing lubrication. In essence, momentum and reaction wheels are like gyroscopic actuators m offset disturbing toNues on. communication satellites. For example, in order t.o properly point a recently deployed anmnna (the deployment itself generates a disturbing torque), the momentum or reaction wheel is used m compensate for the disturbing torque. Normally, three reaction wheels are used to control a satellite, with the wheel axes aligned with the body principal axes; a redundant fourth wheel is often used in case of a failure, of one of the main wheels. The momentum or reaction wheels are powered off during launch. As soon the satellite is put into orbit, the wheel is spun. ~ e equivalent generated torque is used to despin the: satellite (most satellites are released with a spin imparted by the launch vehicle). Though thrusters can also be used in attitude control (e~g., despin), they are used only if (1) a momentum or reaction wheel has failed for a particular axis and (2:) the disturbing torques exceed the control of momentum wheels. Therefore, reaction/momentum wheels also play a real role in decreasing the fuel consumption of thrusters.

3.2.1

REACTION WHEEL FUNCTIONAL BLOCK DIAGRAM

There are three main components in the design of a reaction whe~l: the motors/ bearing unit, the wheel, and the drive/control electronics.. In the. motors/bearing unit, the pe~ane.nt magnets of the rotor provided a desired magnetic field. The stator consists of three-phase windings wound on sheets of a metal core. Commutation is accomplished electronically. The associ~ ated electronics is found within the wheel housing; status signals concerning speed and speed direction are also found. Precision bemngs provide long life if lubricated properly. The lubricant will remain within the bearings if migration or outgassing is prevented by seals. For a particular angular momentum desired the wheel mass has to be optimized so as to keep the motor power consumption within specified limits. Generally, wheels that resemble: either a disk or spoked wheel, have been designed. A simplified block diagram of a typical drive/control electronics assembly for a reaction wheel is shown in Figure. 3.9. The drive/control electronics is the interface between the motor/bearing unit and the wheel. The drive/control assembly receives commands from the C&DH subsystem and determines the torques, speed, and speed direction of the wheels. The electronics are normally equipped with up to three channels for satellites equipped with up to three wheels. Most

58


torque commanc!~

from Motor I- -iLH~at! . Comparator~I

|

~

t t

1 !

current TLM

t

Hall Generators

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

]

Tachomelor l L I(_F .............................!

Figure 3.9 Reaction wheel drive electronics~ reaction wheels have the DC-DC converter to supply the needed voltages if the input power is unregulated. Torque commands that originate in the C&DH subsystem are used to generate a pulse-width modulated signal which will drive each of the three phases of the motor windings, A series of FET drivers will do the job of providing the motor driver currents. The block diagram in Figure 3.9 also shows a current sense circuit to be read by the C&DH software as an indication that the driver circuits for the three-phase motor are working properly; current TLM circuits; and tachometer sensing and TLM circuits. Such circuits provide a measure, of how fast the wheel is rotating. Notice from the figure that a series of Hall sensors (at each motor winding) together with Hall generators/ comparators s e r e as the feedback me~hani.sm to the motor drive electronics by providing the proper enable signals.

3.2.2

NOISE PROBLEMS IN REACTION WHEEL ASSEMBLY

~ e most impo~ant noise issue found in reaction wheel electronics is the noise associated with motors, power conve~rs, and switching transistors. The noise provided by such. sources far outweighs the possible sources of interference from


59

other major components such as comparators and digital logic. A detailed study of noise problems in power converters will be addressed in a later section, here we cover mainly interference concerns due. to DC motors and switching devices. From the DC source point of view (the DC source is provided by one of the outputs of a DC-DC converter inside the reaction wheel drive electronics), the DC motor behaves like a variable but unidirectional emf E behind a resistance R. The latter consists of an "external" part (.the cu~ent-limiting starting resistor) and. an "internal" part (contact resistance between fixed and moving parts), plus conductor resistance or armature resistance. A DC motor is shown in Figure 3.10a. An equivalent circuit of the motor is shown in Figure 3.10b. The motor is fed from an armature voltage source supplying a terminal voltage '~. The field coils are separately fed from an excitation on field voltage Vf. The total resistance of the armature winding, including the blush contact resistance, is lumped into the armature resistance R ~. The difference between Vaand the generated emf E is equal to the voltage drop across the armature, resistance, that is,

'~

-

E

=

(,3,2)

RaI..

ta

Va Tm

(a) Power Flow

DC Source

LOAD Power Flow

(b)

Figure 3.10 (a) DC motor representation, (b) circuit representation of motor.


The motor emf E is given by E = Kwh,

(3.3)

where K=

p = n = a = o~= =

pn 2 ~a

number of poles in motor number of conductors in armature windings number of paralleled paths in armature windings angular velocity (rad/sec)of windings uniform magnetic core flux density (Wb).

The motor torque is given by T = K~b!a.

(3.4)

In the. DC motor, as the cu~ent to the rotor windings is connected to and disconnected from the DC source through the commutator segments, arcing at the brashes occurs due to the periodic interruption of the current in the rotor windings (inductors). The arcing has a very high-frequency spectral content. The arcing spectral content tends to create radiated emissions in the 2.~ MHz to 1 GHz frequency range. In order m suppress the arcing, resistors and capacitors are placed across the commutator segments. These can be implemented to the f o ~ of capacitor or resistor tings attached directly to the commutator or resistive rings placed around the commutator. Another source of high-frequency nNse and associated radiated and conducted emissions is that produced by the switching electronics of the driver transistors shown in Figure 3.t l. ~ e s e driver circuits are used. to change the dir~tion of rotation to provide optimum position control of the DC motor, A typical drive circuit is shown in Figure 3.1ia. When transistors T I and T4 are turned on., current flows through the commutator and the rotor windings, causing the rotor to turn in one direction (winding #1). "When these are tuxned off and transistors T2 and T3 are tumext on, the rotor turns due to windings #2. These driver circuits ~ e usually connected to the motor via by pair of wires as shown in Figure 3.1 lb. Because of t h e ~ a l cooling, the motor housing is usually attached to the metallic frame of the product on the heat sink. This causes a large parasitic capacitance Cm between the motor housing and reaction wheel assembly frame. This capacitance


61

:?v.c ................................

T3

[

LB

•

~, ..............."....................................... ... , ~

Lc

Lo

T2

(a)

Common Mode Choke

(b)

[ F i b r e 3.11

kooPArea

"

~ . .

(a) Motor drive transistors, (b) conversion of common-mode: current into differential-mode cu~Tent,

62


provides a path for common-mode currents to pass through the connection wires from the rotor to the motor frame via capacitance between windings and eventually to the reaction wheel frame. The current provided to the motor by the driving transistors has fast rise time spikes due to the constant switching, and so does the current through the commutator. These spikes have very high-frequency spectral content, and can couple to other parts of the reaction wheel drive electronics and then radiate. The radiation potential tends to be a direct function of the loop area occupied by that current; the lm~gerthe loop area, the larger the radiated emissions. In order to block this common-mode current, a common-mode choke may need to be placed in. the driver leads, as illustrated in Figure 3.1 lb. The capacitance Cm is also represented in Figure 3.1 l b. Concerning the switching of transistors, Figure 3.12 shows the typical voltages and current waveforms. The switching time is shown as t, the delay time is ta. The figure shows the waveforms for gate-source voltage Vgs mad drain current ID of the power transistor for switching off. The drain current/~ continues to flow until time ts, called storage time. During this time inte~al, the charge carriers will be removed from the depletion region. After the storage time, the collector current falls to zero. The fall time of the collector current is rather short, usually in the range of I0/xs to t 00 ~ , depending on the rated power of the transistor. The Fourier transform of Figure 3.12a waveforms will show emission levels of noise covering a wide spectrum as shown in Figure 3,12b.

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

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

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

I D

I .................................................

!..

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

,o/,,.... i v

.

.

.

.

.

.

~

i . .......................

,

~

Figure 3.12 (a) Power transistor switching process, (b) s~ctrum of switching process.

3.3. Intrinsic Noise in Operational Amplifiers

3.3

63

Intrinsic Noise in Operational Amplifiers

Since operational amplifiers are composed of active devices (transistors, FETs) and resistors, operational amplifiers experience shot (Schottky), thermal (Johnson), and flicker(l/f) noise in an intrinsic manner. Undesired electrical signal present in the output voltage of an operational amplifier is classified as noise. The internal operational amplifier noise is modeled simply by a noise voltage source V,~. As shown in Figure 3.13, Vn is placed in series with the noninverting input. On data sheets, noise voltage is specified in microvolts (RMS) for different values of source resistance over a given fr~uency range. For example, the 74I operational amplifier has 2 #V of total noise over the frequency range of 10 Hz to 10 kHz for source resistor R i between 100 ohms and 20 kohms. The noise goes up in direct proportion to R i a s R i exceeds 20 kohms. The noise current in the operational amplifier input appears as a bias current. The output noise voltage from this bias current becomes (3.5)

Vnl : inR r.

Of Rf

VO = - Vn ( t + R f / R i )

~V

] .................................. " V V ' ~ , ...................i.._.. . L N

PA

Figure 3.26

P~atform

Basic acceterometer description.

3. Attitude Conlrol and Navigation

Cmds,

/4

°, 1

!

~m~~~l...:.i.....!....Dampi .. ng

::i" .............................

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

................ - .... ~*-;

......... M_O___!r_O___ ...........

"~,.L___J

'

Spring

"

;Friction

OA

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

........

~'

o.'om

............................................................................. l

Gyro Base Platform

Figure 3.27 Schematic diagram of PGtA.

Since the turntable rate is proportional to acceleration., the total turntable swept angle is precisely proportional to the time integral of acceleration. The output of each accelerometer is a current proportional to acceleration. The current is converted to digital pulses by the accelerometer's digitizer electronics. The pulses are then accumulated and read by the processor to determine the satellite's velocity and linear displacement. Figure 3.28 shows a block diagram of the accelerometer digitizer for one of the three identical accelerometer axes, The digitizer functions as a precision cun'ent-to-frequency converter. The operation of this converter is the foundation of the accelerometer.

3.9.5

NOISE ISSUES IN ANALOG.TO.DIGITAL CONVERTERS

At the heart of accelerometers and gyroscopes is the ability to receive and record sensor-acquired data and manipulate such data so. as to provide useful info~ation. In order to.. make that happen, analog-to-digital ( A ~ ) converters, such as those involved in current-to-frequency converters, must function properly and reliably

3.9. The Inertial Measurement Unit

81

with minimum noise interference. We now address the noise problems in A/D conve~ers in some depth. Noise in Aft) converters originates from two different sources: quantization error that is part of the data conversion process; and electrical noise, which includes the noise generated by the converter and noise that is part of the signal., as well as externally generated noise. Therefore, if the analog signal is later retrieved, it will represent not only the original recorded analog, but also the noise.. The total noise signal in the comparator of the A/D converter is the result. of the oDamp input noise, noise in the summing resistors, noise that is part of the original analog signal, and noise that is coupled, either from the power supply or from the external environment. As previously stated, the most basic noise is due to thermal resistance, also known as Johnson noise, given by the expression v,, = ~ ( f ) ,

(13,33)

where k T B R

= = = = V,~ -

1.381 × l0:23 J/K, known as the Boltzmann constant °C + 273.2 effective bandwidth in hertz resistance in ohms 0.129 (#V)

V/B(f)-R

Since the Johnson noise is just one of the listed noise sources, the overall noise from all other known independent noise sources can. be given by Vn(,,.,~a~ } = %/"V :~ I.......................... + V~':n2 .................................................................................... + " " • + V ~n'~ .....

(3.34)

~ e significance of the total noise in a high-resolution conversion depends on the magnitude of the quantum step (I least significant bit, LSB). Integrator

Sync .

............... I TorqueCurrent

! . . . . . . . . . . . . . . . .

i............../:..:.:~..4.%A~ ......._... _ ~

Comparator ~

'~7

Control

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

Commands

Figure 3.28 Accelerometer digitizer electronics.

Putses

82


If the A/D converter is linear, LSB =

FSR 2n ,

(3.35)

where FSR is the full-scale range of the converter and n is the: resolution in bits. The equivalent input noise can be compared to this value in order to determine its digital significance: K = 2n V'~ FSR"

(3.36)

If the noise is Gaussian, the RMS value is that corresponding m the standard deviation or. We can relam, for example, to the case of the probability of a peak greater than 0.5, since K corresponds to a bit value of or. For example, the probability of a peak larger than 0.5 LSB will correspond m the probability of peak greater than 3 or, or 27%.

3.9.6

NOISE C O N ~ R N S IN. HIGH-SPEED SAMPLING OF ANALOG-TO-DIGITAL CONVERTERS

Let us look again in more detail at the internal noise of operational amplifiers; we will extend this to the case of high-speed analog-to-digital converters. ~ e r e are basically three noise sources in an operational amplifier: (1) a voltage noise which shows up differentially across the two inputs (inverting and noninverting), (2) a current noise in the inveaing input, and (3) a current noise in the noninverting input. Note that each of these noise sources is independent of the others. Figure 3.29 illustrates these noise sources. The voltage noise of different operational amplifiers may vary from 1 to

In.

Vn

in+ Figure 3.29

Noise sources at the op-amp input.

3.9. The Inertial Measurentent Illlit

83

20 nV/Hz. BJ'r op-atnps tenti to have lower voltagc noisc than JFET opamps. Voltage noise is normally specified on the data sheet. Currcnl noise usually varies much more widely, from 0 . 1 fA/Hz in JFET op-amps to s e v c ~ i lpicoamps per hertz in RJT. In voltage-fcedback op-amps, the current noise in the inverting and noninverting inpiit is uncorrelated (see Figure 3.29) and approxirnatcly equal in magilitude. In simplc BJT and JFET input stages. the noise cilrrcnl is the shot noise of the bias current, given by

where I, is the bias current in amps and 4 is the charge of an elcctron (1.6 X

10

''I

C).

Noise current is only important when it flows into a large impedance. hence generating a largc noise voltage. This means that the choice of a low-noise op-amp depends on the source impedance of the signal. At high impedances, current noise tends alwrtys to dominate. For example, the OP-27, which has a fairly high current noise (I pA/Hz): can best be used with low-impedance circuits. Figure 3.30 shows that different amplifiers arc best suited at different irnpedancc levels.

All horizontal scales HZ

All vertical scales

nv/\C-ii;:

10

100

1K

10K

Figure 3.30 Different amplifiers vs impedance levels. (Printed with permission from Analog Devices.)

3. Attitude Control and Navigation 3.9.6.1

Noise Figure in Op-Amps

The noise figure of an op-amp is the amount (dB) by which the noise of the amplifier is greater than the noise of an ideal (noise-free) amplifier under the same environmental conditions. It is a useful tool to know the voltage noise spectral density as well ~ the current noise spectral density. In operationa! amplifiers at low frequencies, the noise spectral density rises at 3 riB/octave, as shown in Figure 3.31. The frequency at which the noise starts to rise is known as the 1/f comer frequency and is a figure of merit. A currentfeedback op-amp may have as many as three l/f corner frequencies: one for its voltage noise, one for its inve~ing input-current noise, and one for its noninverting input-current noise. ~ e most efficient low-frequency low noise amplifiers have corner frequencies in the range. 1-10 Hz, whereas JFET op-amps have values in the region up to I ~ Hz. The RMS noise is obtained when. the noise spectral density curve is integrated over the BW of interest. In the. 1/f region, the RMS noise in. the bandwidth BW = fl ~ f2 iS given by

-dS) = K~/ln

(3.38)

f'

where K is the noise spectral density at 1 Hz.

NOISE

nV/qHz

White Noise I

""

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

t ....................................................................

ltf Figure 3.31 Frequency characteristic of op-amp noise.

Log f

3,9, The Inertial Measurement Unit 3.9.7

85

TOTAL NOISE OUTPUT

Consider the circuit in Figure 3,32, which is an op-amp containing three resistors (R s represents the source resistance). There are actually six noise sources: the Johnson noise of the three resistors, the op-amp voltage noise, and the current noise in each input of the op-amp. Each one of these elements provides a contribution to the: total noise of the amplifier output. In the circuit shown in the figure, C1 represents the source capacitance; it can also represent a stray capacitance or the input capacitance of the op-amp. C~ causes a breakpoint in the given noise margin; the capaci~nce C 2 is added to the circuit to obtain stability. C l and C2 cause the noise margin to be a function of frequency, and it ~ a k s at the higher frequencies. The DC noise gain is given by 1 + R2/R ~, whereas the AC noise gain is given by 1. + CJC1. The bandwidth is given by BW = 1/27rR2C2. The noise current of the noninverting input: In+ flows into R~ and gives rise to noise voltage ln+R s, which is DC and AC amplified. The op-amp noise voltage Vns and the junction noise of R s ( ~ ) are also amplified. The junction noise

C2

1!

Ii

..put

,,

v_

I

I:ls

............... r - , . Vn2

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

)

in+

Vns Figure 3.32 Modeling noise sources in a feedback amplifier,

86


of R~ is AC amplified over the bandwidth of l]27rR2C 2. The junction noise of R2 is buffered directly to the output with a bandwidth 1/2 ~rR2C2. Because of the negative feedback, the current noise of the inve~ing I n flows into R2, resulting in an amplifier output voltage of I n....R 2 over the same bandwidth of 1/2IrR2C 2. When we consider these six contributions, we can obse~e that if R s and R 2 are low, the effects of noise current and Johnson noise will be minimized, and the dominant noise will be the op-amp voltage noise. When the resistance is increased, both Johnson noise and the noise voltage produced by the noise cu~ent will rise. However, if the noise cu~ent is low, the Johnson noise will dominate the voltage noise~ Because Johnson noise only increases as the square, root of the resistance, while the noise current increases linearly with resistance, it is clear that as the resistance increases, the voltage due to noise current will become dominant. To calculate the total RMS output noise of the operational amplifier requires multiplying each of the six noise voltages by the appropriate gain and integrating over the frequency range of interest, as shown in Table 3.1.

Modeling Noise Sources in a Feedback AmpEfier

Table 3.1

No~e Source Expressed as a Voltage . . . . . . . . .

.

.

.

.

.

.

.

.

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

::...

,

.............:..:

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

Multiply by This Factor to Reflect to Output =

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

Integration Bandwidth .

.

.

.

.

Johnson Noise in Rs:

Noise Gain as a Function of Frequency

Closed Loop BW (Signal BW from Ground to Output)

Noninverting Input Current Noise Flowing in R~:


Closed Loop BW (Signal B W from Ground to Output)

Input Voltage Noise: "v'~


Closed Loop BW (Signal BW from A to Output)

Johnson Noise in R~~ ~V/'4kTRl

-R2/R ~ (Signal Gain from B to Output)

1/2'rrR2C2 (Signal BW from Input to Output)

Johnson Noise in R2:

1

lt2~R2C 2 (Signal BW from Input to Output)

Inve~ing Input Current Noise Flowing in R2: In-R2

I

1/2~R2C 2 (Signal BW from Input to Output)


87

The noise gain for a typical second-order system is shown in Figure 3.33. Notice that the large noise voltage will. be determined by the high-fiequency paix where the noise gain is C~/C2~ The noise which is due to the inventing input current noise, R l, and R 2 is only integrated over the bandwidth 1/2 rrR 2C2. Figure 3.34 shows the noise model for a typical second-order system. In high-s~ed op-amp applications such as in A ~ converters, a first-order system simplification is suitable; the noise gain plot is usually flat up to the close-loop bandwidth frequency. This means that all noise sources can now be integrated over the closed-loop op-amp bandwidth as shown in Figure 3.34. In high-s~ed current feedback loops, the input noise voltage and the inverting input noise current are the dominant contributors to the output no"~se, ~ as shown: in. Figure 3.35.

3.9.8

PROPER POWER SUPPLY DECOI~SOLING .IN OP-AMPS

If the supply of an op-amp changes, its output should not really change, but in reality it does. The term power supply rej~tion ratio (PSRR) is defined as

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

-----~...

GAIN dB

• "

SIGNAL= \ \ \ . \ INPU

R2~ R 21^'^~

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

I I

f2 Figure 3.33

SIGNAL \\ GAIN

NDWIDTH

[ 1 I

fcL

CL BANDWIDTH

"\,\,

"" Loaf

Noise gain inverting signal gain for second-order system. (Printed with permission from Analog Devices.)

88


1

R~

................................................. )I .........................................................

"t__

I ~

l

"'

t "--.

I ~ ......................."-:e.

I

V ~"-~,~.~......... [. ...........~,~N ....... 11 + ~

[

J

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

Jn.'~'

'..

/

~ "" , C 2 ..N~

I. ....................................................... !........................... ,>~

. . . . .

2 R2~1 v,srf 2 ) + t .+ PL + C'~/2~2 ( ~ ' c s ~ .

) + t.? R~

Where fu = Op Amp Unity Gain Bandwidth Frequency fcl = Closed Loop B a ~ t h

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

NEGLECTED

'.

VoN.

Figure 3.34

.O,S~aA,N

7"1

"

1

=~ , 1+C 2

Noise model for a typical second-order system, neglecting resistor noise. (Printed with permission from Analog Devices.)

Rf Vn

[ [

..................................................................^ - , / X / X .

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

+v

/

•

In-,

Figure 3,35

Noise model in high-speed current feedback scenario,

Vo


89

follows: If a change of A volts in the supply produces the same output change as a differential input change of B volts, then the PSRR on that supply is A/N. It is because the= PSRR of op-amps is frequency dependent that op-amp power supplies must be well decoupled. For op-amps at low frequencies, we can use 1 ~ 5 0 #F capacitors for each supply, provided, that no more than 10 cm separates the capacitor from the op-amps. At high frequencies, each IC must have every supply dezoupled by a low-inductance 0..1.-#F capacitor with short leads. The capacitors must also provide a return path for high-frequency currents in the op-amp load. An example of proper low- and high-fi'equency use of decoupling capacitors is shown in Figure 3.36. 3.9.8.1

Bypassing and Grounding to Avoid EMI Noise

As is well known, there is no real ground in operational amplifiers, but rather a "virtual ground." In digital-to-analog conveners which provide current to an op-amp, the current does not really return to ground, but instead returns to one of the power supplies. In order to reduce the impedance in the high-frequency

C3

S/C PWR Main

Coil-Hi

EED Pyro Bus

F i b r e 5.8 Pyrotechnic relay assembly block diagram.

5.3,1

DIGITAL MODUI_ATION

Pulse code modulation (PCM) is a form of digital-to-analog conversion in which the information contained in the samples of an analog signal can be represented or shown in the form of digital words in a serial bit stream of words, ff we say that each digital word has n binary digits, then M = 2'~ unique words are possible, and each coded word has a certain amplitude level. This process is called quantizing, which means that instead of using an exact sample of the analog waveform value, the sample is substituted by the closest allowed value co~esponding to one of the code words. PCM modulation has the advantage that the circuits involved in generating such modulation are simple. Furthermore, PCM signals are very easy in timedivision multiplexing. Finally, the noise performance of a digital signal is usually superior to that of an analog signal. The main disadvantage of a PCM signal is that it uses a much wider bandwidth than an analog signal.

150 Serial CMDs

5. Command and Data Handling Subsystem Serial TLM

Seriat TLM

Sedal TLM

Digitai TLM

Anatog TLM

On/Off CMDs,

PWR

Processor Internal Voltages

Controls Signals

ADRS/Data Bus CnU

Packet I!F

PDA TLM Packets

ETU Star. Indicators

Eng, Data Timecode Data

Clocks and Sync. Pulses

Figure 5.9 Engineering telemetry unit block diagram.

The PCM output is obtained by first sampling, then quandzing, and finally encoding, as shown in Figure 5.1 I. The sampling operation first generates a pulse amplitude modulation (PAM) signal as shown in Figure 5.12. The analog waveform W(0, which is band-limited by B(z), can be converted to a PAM signal using natural sampling, giving % ( 0 = w(o s(o

(5.1)

where s(t) = ~ , n . ........

\

T

/

is a rectangular wave switching at a frequency j~ = l/T~ -> 2B(z). The spectrum of the naturally sampled PAM signal is given by its Fourier transfo~,

5.3. Fundamentals of Modulation Theory and Coding

151

Data Payload interfaces

CICU

Switch Power Supply Electronics

~

Ser, CM L___

. SCU

Discrete

[

.

.

.

.

[DC/DCConv.

: S/C CMD. CLK, t/F ..C0 ntrol ........

CMDs

teed.Solomon ncoder

TLM Module

RAM, PROM

TLM Ana. PDA on

0j-]..j. O .............. .

Contm!

J

Sw[tchPssi TLM

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

I 1

" ! ..................................

Figure 5.10 Payload dam assembly,

W~( f ) = c .....

~

sin ~ n d w ( f _ , ~ ) , ~ nd

....

(5.2)

where c is the duty cycle given, by c = ffZs. The quantization procedure is illustrated in Figure 5.11 for the M = 8 level case. If the steps are of equal size, the quantizer is said to be u n i f o ~ . Because we are approximating the analog values using a finite number of levels, error is then introduced as pan of the output. The error waveform is shown in Ngure 5.1 I. We can minimize the channel noise by sampling at the Nyquist rate of 2B(z). Finally, the PCM signal is obtained from the quantized PAM signal; a specific code must be developed to represent a particular quantizeA level. For example, the code used in the PCM signal is called Gray code. The bandwidth of serial PCM is such that Bee M > 1/2R = 1/2 nf~,

(5.3)

where n is the number of bits in the PCM word (M = 2n), fs is the sampling rate, and: R is the bit rate.. The bandwidth of the PCM signal must be maintained

152

5. Command. and Data. Handling Subsystem

Vout

8 M=8

-8 -6 -4

'.2468 ""-4

--6 (a) ~ I

• "11"--- (Sampling Time) I

(b)

/ PAM Signal

Quantized PAM Difference between analog signal and quantized PAM signal .

.

.

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.

. PCM Word

(c)

!

.

1

1

1

O011001

10001

I

1

I

t

t 1 10101

1

(d) F~are 5.11 The PCM process.. (a) Quantizer output-input characteristic; (b)analog signal, fiat-top PAM signal, and quanti~d PAM signal.; (c) error signal, and (d) PCM signal.

5.3, Fundamentals of Modulation Theo~ and Coding

153

Imputse Train Sampling

! Ws(t)

~J

t

•

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

...........

___t~ ~ Ts ~ 1

Figure 5.12 PAM signal representation.

significantly greater than that of the co~esponding analog signals that it represents.

5.3.2

NOISE ISSUES IN PULSE CODE MODULATION

R e analog baseband signal which is recovered from a digital-to-~alog conversion can be c o ~ p t e d by noise. There are two main sources for this noise: I. Quantizing noise that is caused by the M-step quantizer at the PCM transmitter. 2. Bit errors which are recovered in the PCM signal. These bit errors can be caused by channel noise and/or bad channel filtering, which can cause intersymbol interference (ISI). The term ISI comes from the fact that pulses corresponding to any particular bit will smear into adjacent bit slots as a result of a bad filtering such that the filtered pulse will be elongated.

154

5. Command and Data Handling Subsystem

The recovered analog peak signal-toonoise ratio is given by

S 3M 2 (N)peak = 1 + 4 i.~d2-'~'2- i) Pe"

(5.4)

The average signal power to the average noise power is (~)

M2

OUt

1 +4(M

-- I) P e

(5.5)

where M is the number of quantized levels used in the PCM system and Pe is the probability of bit error in the recovered PCM signN before it is converted back into an analog signal using the receiver DAC. Correcting bit errors reduces the value of Pc" Often, Pe can become negligible, and in such cases, the peak SkY due only to quanfizing errors (i.e., no bit error from channel noise) can be written as (5.6) peak

and the average S/N due only to quantizing errors becomes

OUt

Reducing the value of Pe is a funcdon of channel capacity. Claude Shannon showed that for the case of a signal plus Gaussian noise, a channel capacity c (bits/see) could be calculated by

where B(z) is the channel bandwidth in he~z and S/N is the signal-to-noise power ratio (in watts). Furthermore, Shannon stated that a finite value of SIN l i ~ t s only the rate of ~ansmission. ~ a t means that the probability of error Pe can approach zero, provided that the info~adon rate is less than the channel capacity. This means also that in order to approximate this scenario, coding must be used. Coding reduces Pe for the following reasons: I. The nature of redundancy: redundant bits are added by the encoder to increase the peculiar form of each transrrdtted digital message


155

2, The nature of noise averaging: The coding can be designed so that. the receiver can average out the noise over long time periods Most coding can be divided into two groups: block encoding and convolutional encoding. Block codes is a mapping of K binary inputs into n output binary symbols. Block codes are memoryless. Among the most common block coding schemes are Hamming and Reed-Solomon. Convolutional encoding has memory'. The convolutional coder accepts k binary symbols and produces n binary symbols where the n output symbols are affected by v + k input signals. Memo~ is present, since v > O. Concerning quantizing noise, there are four kinds: overload noise, random noise, granular noise, arld hunting noise.

Overload noise The level of analog waveforrn at the input of the PCM encoders must be set such that its peak value does not exceed the design peak of the quantized V volts. If the peak input exceeds !< then the recovered analog waveform at the output of the PCM will have some fiat tops near the maximum values. Random noise This noise is the result of random quanfization errors in the PCM system under normal operating conditions. Granular noise

When the analog input level is reduced to a relatively small value with resp~t to the design level, the error values are not equally likely from sample to sample.

Hunting noise This occurs at the output of a PCM system. It can occur when the input analog waveform is almost constant, even when there is no signal during these conditions. 5.3.3 BINARY CODING The PCM signaling of " 1 " and " 0 " can be represented in different serial-bit signal f o ~ a t . The most popular formats are shown in Figure 5.13. There are two kinds of formats: return-to-zero (RZ) and nonretum-to-zero (NP~). For RZ coding the waveform returns to zero for about half of the bit interval, Based on the rules which are used to assign the quantized voltage to represent the binary data, the w a v e f o ~ s can be further classified:

Unipolar signal In positive unipolar logic signals, the logic 1 is represented by a positive voltage and 0 by a zero. This is often called on-a~ff keying. Polar signal The binary l's and O's are represented by positive and negative levels.

156

5. Command and Data Handling Subsystem V(t)

I !

I

v(t) t Polar N ~

0

1

I

t

i

I

I

t

i

!

l.....V...°..i.~........:.

1I

0

I I

i

I

i

1 1

11

t

I

!

!

0

I

! I

I I ............. i

t

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

.Vo....(-! ..................... }i_~..t ....................... 1

t

t

I

!

I

t

I

Unipolar RZ .......................... 1 ........

I ..................

I

i

v(~

r

T~~O_~_..

Bipolar RZ

vo

V(

Manchester NRZ

J

I

I ._I I

t

h ~

i

t

.......I-I ........h......i.......................... i

I

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

1

I

I

I

I

I

!

I

I

t._ ...................t t._............ I..i ................. li................. ~M ......II ...........-q, ............. ........... ................ I._l

I

t

I

t

i __ I

t

I

__ I I

i

I

t

hrh, r h ,

...................... i/j l--/.J

.........U

" ~

t

........ E

Figure 5.13 Binary signaling format.

Bipolar signal Binary l's are represented by alternately positive and negative values. The binm-y 0 is represented by a zero value. Manchester signal Each binary I is represented by a 0 positive halfvalue period pulse followed by a half-value negative period pulse. A b i n ~ 0 is represented by a negative half-value period pulse followed by a positive half-value ~riod pulse. The power spectral densities of these signals are as follows.


157

For a polar NR~ signal, the power spectral density is given by

(

Ppolar ( f )

= r \

rr f r

(5.9)

/ '

where r is the pulse width. For a unipolar NRZ signal, the power spectral density is given by 9

i

Pun+polar(f) = 2 - r \

+fr

]

+ I

(5.10)

2 ~f)+

The main. disadvantage of unipolar N ~ is the waste of power because of the presence of a DC level, and the ~ectrum does not aoproach zero near DC. For a unipotar RZ signal, the power sp~tral density for unity power is given by 2¸

P+~(+f ) - 4

~rf v / 2

I + -T

This equation shows that the first null bandwid~ is twice that for unipo!ar or polar signaling, since the pulse width is half the width.. There is also a discrete term at f = l/r; therefore, this periodic component is used for recove~ of the clock signal. For a bipolar RZ signal, the power spectral density for a unity power signal is given, by

Pbipoiar (f)

- + [

rfr/2

'-+>+i J (2-

2 cos ~rfr).

(5.12)

Finally, for the Manchester NRZ signal, the power spectral density for a unity power signal is given by

Pma,~cheswr(f)

= r[

~fr/2

sin2

"

(5.I3)

As previously stated, intersymboI interference arises when pulses are not properly filtered as they pass through a communications system. The pulse will "spread" in time, and the pulse for each symbol will be smeared into adjacent time slots as shown in Figure 5.14.

158


lntersymbo, I Interference 1

0

1

0

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

i ...........................

I

I

i

i

t

Sampling Points

F i b r e 5.14 Example of ISI on received pulses in a binary system.

5.3.4

DELTA PULSE CODE MODULATION

When consecutive sampled values of an analog input are found to be v e ~ close to the same value, there is considerable redundancy, which is not an efficient use of the bandwidth and dynamic range of PCM. One way to minimize redundant transmission and also to diminish the bandwidth of PCM signals is to transmit PCM signals corresponding to the difference in. adjacent sample value. The scheme is usually known as differential pulse code modulation (DPCM). Delta modulation (DM) is a special case of DPCM in which there are two quandzing levels. The delta modulation scheme is presented in Figure 5.15. Notice that the delta modulation system does not need an analog-to-digiml conveaer or a digital-toanalog converter. Therefore, it is much less expensive, which is its main attraction. In Figure 5..I5 a comparator is used as a subtractor and a two-level quanfizer so that the output is either + V or - V (binary). In essence the delta modulation signal is a polar signal, and a representation of the input and output w a v e f o ~ s is shown in Figure 5.t6. From the figure it can be observed that the accumulator output cannot always track the analog input signal. This quantizing noise may be classified into either slope, overload noise or granular noise. The former occurs when the step size d is too small for the accumulator output to follow fast changes in. the input signal. Granular noise


Analog Input ....................................... W(t) -l .........................................i

159

PAM ~ ~ + " ' ~ "

L

]

fs

1

/

z(t)

~ ~'AC~muato ...~-................ Figure 5.15 Delta modulation system

Analog inputand Accumulator OutputWaveform GranularNoise

Slope Noise

Vc~ Y ( t ) t

-Vc i Delta Modulation Waveform Figure 5.16 Delta modulation waveforms.

160


occurs for any step size, but it is proportional to the step sized, so it is important to minimize d. An optimum value for d depends on the nature of the input signal and on the sampling frequency used. Note that if d is increased, the granular noise will. also increase, but the slope overload noise will. decrease. It can be shown that Lhe average signal-m-noise ratio out of a DM system with a sine-wave fast signal is given by S

-

3

.s

(5.I4)

ou, - 87r f ~ B '

where £ is the DM sampling frequency, fa is the frequency of the sinusoidal input, and B(z) is the bandwidth of the receiving system. Fughermore, the step size d required to prevent slope overload noise for the same sinusoidal input is given by d > 27rLA

(5.15)

where A is the magnitude of the sinusoidal input. £3.5

B A N D W I D T H COMMKNICATION FOR DIGITAL SIGNALS

A bandpass waveform has a spectral magnitude that is nonzero for a frequency region concentrated around a cartier frequency f., where fc > > 0. Elsewhere the spectral magnitude is negligible. Digital modulation, is the process by which a digital baseband signal that contains the source of information is imparted with a bandpass signal of carrier frequency ft. The bandpass signal is said to be modulated, while the baseband signal is called the modulating signal. Therefore, the power sp~tral density of a digital bandpass signal is given by !

P ( f ) = ~[em ( f - fc) + Pm ( - f -

£)],

(5.16)

where f~ is the carrier frequency and Pm (f) is the power spectral density of the mapping of the baseband signal re(t) onto the complex plane. The mapping function outlines the type of modulation. Bandpass digital modulation can be divided into two main groups, binary and multilevel types. The most common binary bandpass signaling methods (described schematically in Figure 5.17) are as follows" 1. Amplitude-shift keying (ASK) consists of switching a sinusoidaI carrier on and off with the synchronization of a unipolar binary signal

5,3, Fundamentals of Modulation Theory and Coding t

i 0

,

!

I

1

1 1

I 0

11

1

Unipolar M o d u l a t i o n ............................... lr . . . . . . 1

t 0!1

161

1

1

I

IO

I 1

t

. . . . . . . . .

t

I

I

I

I

i

1

t

t

1

I

1

I

t

t

t

t

t

I

I

1

I

t

1

Polar Modulation

I

ASK

,

....

t

?~V' 'AA ' ',5A' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

l

'A ^'

I

i

'A A'

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

t

t

AAI~ p\IAA I

BPSK

I

I FSK ~-===~---~-=,

..:.

I

I

' I

I

i

I

I

I

I

i

t

t

I

I

1

1

1

!

I

I

Figure 5,17 Bandpass digitally modulated signals.

2. Binary phase-shift keying (BPSK) consists of shifting the phase of a sinusoidaI can-ier 0 ° or 180° in synchronization with a unipolar binary signal 3. Frequency-shift keying (FSK) consists of shifting t.he frequency of a sinusoidal carrier from a frequency representing the sending of a binary 1 to a frequency representing the sending of a binary 0; it is similar to FM carrier modulation with a binary digital signal N o . a l l y , the bandwidth of the digital signal must be limited to obtain s~ctral conservation when the information is transmitted. This can be accomplished, for

162


example, by using a premodulation filter to limit the bandwidth without causing intersymboi interference.

5.3.5.1

ASK Modulation

The ASK signal can be represented mathematically by S(t) = Am(t)cos 27rL t,

(5.17)

where m(t) is a unipolar baseband data signal as shown in Figure 5.17. The complex envelope is given by E(t) = Am(t). The power special density of this complex envelope is proportional to that of the unipol&r signal and is given by

Pro(f)=-2"

fi(f)+

\

7rfr /

'

(:5.18)

where re(t) has a peak value of V 2 so that S(t) has an average normalized power of A/2. The power spec~m density of the ASK signal is then obtained by substituting Equation (5.18) into Equation (5.16). The result for positive frequencies is shown in Figure 5.18.

I I

....f C 2 ~

-~-..................F . . . . . . . . . . . . . . . . . f o

8 (Sin[n(f-fc)k / {n(f-fc~c}) 2

................................................. ] ..................................... f c + 2 / ~

2/T Fi~

5,18 ASK bandpass digital signal spectrum.

5,3. Fundamentals of Modulation Theory and Coding

163

5.3.5.2 Binary Phase-Shift Keying The binary shift keying signal is represented by S(t ) = A cos[2n'fc + Dpm(t)],

(5.19)

where m(t)is a polar baseband data signal and Dp is the phase sensitivity of the phase modulator. The level of the pilot career is set by the value of the peak deviation 80 = Dp. For digital angle modulated signals, the modulation index k is defined by k = 2 80/zr. ~ e complex envelope for BPSK is E(t) = jAm(t).

The power spectral density for the complex envelope is given by

{Mn ~-fT"i

(5.20)

Pro(f) = A.2r,k ~fT ]'

where m(t) has a value of + 1., which means that S(O has a normalized average power of A2/2. The power spectrum density of the BPSK signal is evaluated by substituting Equation (5.20) into Equation (5.16), resulting in the spectrum of Figure 5.19.

1

~ ~ - 4

fc" 2/~

A2/4 /~!'~_

F...................................... fc ....

L~

......................... ~ f

4 (Sin[=(f-fc)]~/ {=(f-fck}. )2

-I

fc +2/~

Fibre 5.19 BPSK bandpass digital signal, spectrum.

164


5.3.5.3

Frequency-Shift K~4ng

The frequency-shift keying signal is mostly generated by feeding the data signal into a frequency modulation as shown in Figure 5.20. A FSK signal is then represented by S(t) = A cos 2 ~ f r + Df

m(~d

,

(5.21)

where m(t) is the baseband digital signal. If the data input is b i n ~ , as with a polar baseband signal, then the resulting FSK signal is called a b i n ~ FSK signal. The approximate transmission bandwidth B t for the FSK is given by Carson's rule, Bt = 2(fl + 1)B,

where fl = AF/B, B is the bandwidth of the digital modulation waveform, and i F is the peak-m-peak frequency deviation, or AF = Dfl2zr form = + 1. The power spectrum density is given by A27 2 ) 2, . P(f) = - ' ~ k ~ ( f [.1 + LI~ (/)] + k (/)[1 + Le2 (/)]

(5.22)

+ 2Lt.2 (.f)k~ (f)k 2 (f), ...................

: : . : . . . : ..: .. _ = .

,,,,

,,

Electronic

Oscillator Freq.=f1

Switch

!

............... 1

lib,-.

.......... osc,,,a,or

FSK Output

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

Binary Data input re(t) ......

•. . . . . . = : . . . .

=. . . . . . . . . . . . . . . .

,,,,= .................................

::::::::.:

,,==

:

: = : . = : = . . = . = . . . : . : . . . : . . : . . : : . . . . . . : ....

Discontinuous-Phase FSK Figu~ 5.20 Generating an FSK signal.


165

where kn(f) :

sin(~ 1 " ( f - A F ( 2 n - 3))) T ( f - A F ( 2 n - 3))

Lnm(f) = c o s [ 2 ~ f T - 2 ~ A F T ( n + m - 3)1 - cos(27r AFT)cos[2~ A F T ( n + m - 3 ) ] 1 + cos2(2 ~ AFT) - 2~os(2 ~ AFf)cos(2 ~rf~') AF is the peak~to-peak frequency deviation, T is the binary pulse width, and the digital modulation index is given by k : 2AFt. (It is assumed that k ¢ 0,1,2.,... ; otherwise, if k = 1,2,3 . . . . . . etc., we get delta functions.) 5.3.5.4

Multisymbol Signaling

The bandwidth that is required to transmit a baseband digital sequence can be reduced by multilevel signaling: the combination of successive binary pulses to form a longer pulse requiting a smaller bandwidth for transmission. If a set of M = 2 '~ symbols is used, with n the number of successive binary digits combined to form the appropriate symbol to be transmitted, 2n bits ls!Hz can then be transmitted using the Nyquist rate. The binary rate is given, by R (bits/se~). Consider the case where n = 2, M = 22 = 4. The resultant set of four bina~ pairs ~,01,t0,11 is used to trigger a high-frequency sine wave of four possible phases, one for each binary pair. Any of the four signals can be represented by Si(t) = A cos (2 ¢rLt + 0~),

i=

. 1,2,3,4,

-T T 2 < - t < - 2"

(:5.23) ~

The possible choices of four phase angles are. Oi = O, ± 7"r!2, 7r

In any case the phases are separated by zr/2. The preceding equation can be represented by Si(t) = Ai cos 27r~,t + Bi sin 2w~t,

~'T

T

T -< t ~

-S' econdary Electrons

Figure 8,16

~S~condary Electrons

...................~.... . . . . . . . . ,-

The charging of GEO spacecraft is determined by the balance of the substo~ electrons and the secondary electrons. The charging of large spacecraft in the auroral region is dete~ined by the balance of the net auroral flux and the space-charge-limited ion flux.

Mach 8 (orbital velocity in low-eaCh orbit) in the severe aurora environment. The dominant currents are the space-charge-limited ram ions and the incident electrons. Figure 8.16 illustrates the difference between these two regimes. Char& ing of large objects in low-altitude, polar orbit is determined by the balance of the net aurora flux and the space-charge-limited ion flux. These spacecraft leave a substantial ions-depleted wake, The lower ion density in the wake region means fewer ions are available to neutralize the built-up negative charge. The comparison (shown in Table 8.8) between the potentials calculated ignoring space charge with those calculated including it show more than an order of magnitude difference. The space-charge-limited result agrees with observation.

Table 8.8 =-:

=-:.

,_,

:u::

.....

-=-=-=-=...

Equilibrium Potentials Calculated by Space Charge ,, =,,,,,,,,,,,,,,,,,,,

:=:

:

............... ,,.

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

:::::::::::::::::::::::::

=:::::::

:

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

Orbit.limited Sphere radius Mach velocity

::,_....

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

-9 V -5 V ...............

:;:;:::: ...............

: :

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

1m

Kapton Silver ..,,

: ................

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

---=-=-=-:

.: .:.

:. :. :......,=c.:::::::::::::::::::::::::::::::::::::::::::

==

Space.Charge-Limited

::,,,.:

i0 m

0.~1

8

0.~1

8

-550 V -250 V

-230 V -99 V

-5400 V -3100 V

-29~ V -16~ V

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

.

.

.

.

.

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.

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.

.

.

.

.

.

.....

-

..........

.:::::

_.,o

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

.:::::

...................................... -

-

-

-

8.8. Differential Charging

8.8

275

Differential Chargng i

The electrons associated with surface charging penetrate tess than a micron into the spacecraft skin. Because of this, surface coatings play a large role in determining spac~raft potentials. While the time to achieve net current balance is very short, on the. order of a millisecond, the time for each surface to achieve its own equilibrium potential is thousands of times longer. The. development of differences between the potentials of different surfaces is referred to as differential charging. Figure 8.17 shows mechanisms for the development of differential potentials. Different materials have different equilibrium surface potentials because the secondary and backscatter yield coefficients are different. This effect can lead to potential differences between neighboring surfaces. The ground, potential of the spacecraft depends on the average prope~ies of the spacecraft surfaces. Each surface charges differently from spacecraft ground. The difference between the surface, potential of a dielectric and the potential of the underlying conductor is another source of differential pomntials.

Figure 8.17 Differential potentials due to difference in secondary emission properties.

276

8. Space Environment and Interl~rence

The rate of absolute charging is determined by the capacitance of the spacecraft to infinity, while the rate of differential charging is determined by the capacitance of the dielectric layer. The rate of change of the potential on a sphere is given by d_~ = dt

!

1

4 ~o R

=

JR

= e0 '

(8.6)

where I is the current to the sphere, J is the current density to the sphere surface, and R is the sphere radius. For a 1-m sphere and a net current of 1 # A m -2, the sphere begins to charge at a rate of 1~ kV sec -~. As the potential on the sphere increases, the net current decreases, as can be seen in Figure 8.I3. Therefore, the charging rate decreases with time. The rate of change of the difference in potential across a dielectric layer is given by d~.: = J d dt

(8..7)

eo '

where d is the thickness of the layer. A 100~#m layer (4 rail) with the same incident current density charges at a rate of ! 0 V sec .....5 Therefore, differential. charging takes place 1.04 times more slowly than absolute charging. Figure 8.18 shows the equilibrium potential contours calculated by the com~ puter code NASCAP of the N A S C A P / G E O codes for a silver quasi-sphere of radius 3.5 m with a 5-rail-thick kapton coating over half of the surfaces exposed to the severe substorm environment of Table 8.3. The surfaces with the kapton coating are those facing the bottom, the left, and the rear. Figure 8,19 shows the time history of charging of this sphere, In 1 sec the entire sphere charges to - 18 kV. After 1500 sec (25 rain), a differential potential of I kV has developed. By 1~,000 sec (28 h), the equilibrium potentials of -22.51 kV on the kapton and - 1 0 . 9 kV on the silver are reached. A thinner kapton coating would charge more. slowly, Photoelectron current densities are about. 2 - 4 ×. 10s A m °, typically an order of magnitude greater than incident electron currents, even before secondaries are taken into account. As a result, in sunlight, high absolute potentials are rarely observed on spacecraft. However, in an intense substorm, spacecraft shadowed from the sun slowly charge to thousands of volts negative, while the sunlit surfaces remain a few vol~ positive. This. process can lead to differential charging as illustrated in Figure 8.20. High. differential potentials can develop between shaded and unshaded dielectric, and high differential potentials can develop between shaded dielectric and spacecraft ground. The sun-shade interface, and


277

t7 16 15 14 13 12

11 •~ x

v

m

m

C

d~ -15

~0 -2:5

I

III •.

_'..

Kapton

~

Silver

Figure 8,1.9 Time histo~ of the potential of quasi-sphere shown in Figure 8.18.

Sunlight

S S S "-~',,,...

Photoemission

+

+

+

+

+

-

L

phot~mission in shaded regions

No

Figure 8,20

Differential charging between shaded and unshaded surface in sunlight.


279

the differential potentials, shifts location through the year. A sun angle that does not cause a problem in one season can in. another. Sunlight differential charging can lead to. high spacecraft ground potentials when the low-energy photoelectrons cannot escape from the spacecraft because of potential barriers [25, 26]. Typically, the saddle point is driven by the balance of photo and secondary electrons and has a height, of a few volts. All the surface then charges negative at a rate co~esponding with differential charging, typically a few hundred volts per minute. Figure 8.21 shows the time histou of the ground potential and the surface potential on the sunlit and d a n sides. The sunlit side st~ts out a few volts positive. The dark side charges negatively. After a half second, the dark side is at - 8 V and the sunlit side at 3 V. A potential barrier of 1 V has developed. The potential bamer grows until the photoelectrons cannot escape. Once the photoelectrons cannot escape, the entire space charges. Sunlight charging is a multidimensional effect calculable only by models that include the three-dimensional geometry of real spacecraft. As illustrated in Figure 8.22, during aurora, low-altitude, polar-orbiting spacecraft can develop differential potentials between their ram and wake sides. The ram side of the spacecraft has a much higher ion current than the wake side,

Time (sec) 0.01 ,

1

t00

104

t06

-5 -t0 -15 -20 -25

i

I

~

Sunlit

"-

Ground

I I

Fig~Jre 8.21 Time history of surface potentials and spacecraft ground on the sunlit kapton quasi-sphere.. Charging of spacecraft ground occurs on the differential charging time scales due to the formation of a barrier: The final ground potential of -18 kV is reached after I ~ 0 sec (17 rain).

280

8. Space Environment and Interference

Ram Ions ............_=_=_=_=~ _=_== .........................................= _ = . _ = _

............/~..

................................................................ ~._

Beam

J=~ 11~

Auroral Beam

Figure 8.22 During aurora on low-altitude, polar-orbiting spacecraft, differential potential can develop ~tween the ram and wake sides of a spacecraft.

which must pull in the ions around the spacecraft. The ions reaching the wake side of the spacecraft are attracted from the sheath edge. In this calculation a low-potential region develops on the wake side of the sphere because of the focusing of ions due to the high symmetry. The ground potential is - 6 5 0 "~ the surfaces in the ram are at - 1 V, the surfaces in the center of the wake side are at - 1 : ~ V, and the peak potential on the w ~ e side is - 8 4 0 "v'~The same quasisphere with a Mach velocity of 0 has an equilibrium potential of - 1 . 9 kV.

8.9 Arcing The primary mechanism by which charging disturbs spacecraft is through discharges. The rapid discharging of surface, or arcing, can disrupt operations, disturb measurements, and damage instruments or spacecraft surfaces. The mechanism for triggering discharges is an active field of investigation. Measurements made in the laboratory produce results that cannot be extrapolated to on-orbit spacecraft. Part of the problem is the impossibility of adequately simulating the space environment, the spacecraft, and their resultant interaction. Some e x ~ p l e s of this inadequacy are the breakdown thresholds, area scaling, and satellite response. It is observed that in space, discharges occur on spacecraft when the calculated and measured potentials and electric fields are lower flaan those needed

8.9. Arcing

281

to generate discharges in. typical electron-beam laboratory experiments. Measure~ ments made on uniform, small dielectric samples find that the discharge current scales directly with the square root of the sample area, and the fraction of charge blown off by the discharge is essentially constant for each dielectric type [27]. Large sample measurements that include lapped and butted seams of materials present in real spacecraft, thermal-control surfaces differ from the uniform, small-. sample results [28]. Even though the present understanding of discharges is not. complete, there are some well-established data, plausible analytical treatments, and useful criteria that can be employed in. predicting the location and frequency of discharge. Flashover discharges occur when a layer of neutral gas atoms that has been generated by electron-stimulated desorption breaks down under the local electricfield, stresses caused, by differential, potentials of spacecraft dielectric [29]. This type of discharge frequently occurs at the edge of a dielectric next to another surface, at cracks in dielectric exposing conductors underneath, or at exposed conductor-cover cell interfaces in solar a~ays. The typical field strengths required for flashover is 2 × 10('V m ......t [29], which is an order of magnitude below that for dielectric breakdown, Breakdown of dielectric also provides discharge paths for spacecraft, dielectric. Dielectric breakdown results from the bulk failure of the dielectric material. Two of the theories of dielectric breakdown are (1) that the energy stress produced by the charged surface potentials exceeds the binding energy of the molecules that make up the material, causing rupture of the bonds and loss of the material; and (2) that field-enhanced electron emission provides electrons that generate cascades and heating until material vaporizes. Dielectric failure most often occurs at imperfections or dielectric weak points.. Dielectric failure at an imperfection usually appears as a pinhole through the dielectric and is referred to as punchthrough. Localized material breakdowns are also observed in trapped charge. layers of dielectric about 1 ~m below the dielectric surface. These bulk material failures appear as channels or tunnels just below the dielectric surface and are accompanied by surface damage where the channels penetrate the surface. The typical field strength of dielectric is 2 × 107V m I. B lowoff is a large-scale discharge phenomenon occurring at the surface of the dielectric and sometimes extending over the entire vacuum-dielectric interface. Several. models have been proposed for the primary mechanism that initiates blowoff discharges. One of the most promising is a surface discharge model [30]. The essential idea of the Stettner-DeWald model is that the intense: electric field on the boundary of the charged and discharged region of dielectric surfaces accelerates ions into the surface. Ions with the necessary velocity and angle to

282

8. Space Environment and Interi~rence

the surface cause kinetic emission of electrons, resulting in discharge of the surface. The incident ions also cause sputtering of surface atoms and ions. Newly created ions are also accelerated into the surface, producing further discharge and movement of the charge/discharge b o u n d ~ ~rther into the dielectric's charged region. The initial ions for the Stettner-DeWald model may come from the ions in the ambient plasma or ions desorbed by the incident electrons. A variation of the Stettner-DeWald discharge model, termed the localized plasma sheath model, has been proposed by Kxauss [31] to overcome some of the shortcomings of the ion surface-discharge model. The ion surface-discharge model and variants are promising in that they explain most of the observed features of laxge-scale dielectric discharges and are supported by surface-discharge measurements. Unfortunately, a determination of their validity and usefulness for determining where and how often blowoff discharges occur require further theoretical and experimental work.

8.10

Determination of Path for Discharge Energy

The ~ansient pulse produced by the discharge couples directly or capacifively to the spacecraft structure and to spacecraft cables. Various methods are available to analyze the coupling of the discharge transient to the spacecraft elements. Some of these different coupling analysis methods are briefly discussed next. &lO.1

LUMPED-ELEMENT METHOD

Lumped-element modeling (LEM) is the most cormnon analysis method used for discharge coupling. LEM models replace spacecraft structur~ elements with their equivalent inductance, capacitance, and resistance. They have v ~ e d from simple one-dimensional models, where a few circuit elements are used, to models of the entire spacecraft structure [32], to very complex three-dimensional models where each structural element is modeled by its equivalent RLC circuit [33]. The discharged source is then used to drive the lumpeA-element electrical model at the point in the model associated with the cells identified as locations where discharges are likely to occur.. A circuit analysis code such as SPICE is used to analyze the lumped-element circuit model and to calculate the current flowing on each structural element due to the discharge source. A LEM model is also generated for cables that are attached to or run new the spacecraft structure. The structure cu.~ents calculated by SPICE for the spacecraft LEM are then used to drive the cable LEMs. SPICE runs are made for the cable electrical models using

8.10. Determination of Path for Discharge Energy

283

the structure drive sources to determine coupling of the structure, cu~ents to the cable conductors. The conductor cmTents and the resulting voltage appearing at interface circuits attached to the cable conductor are compared to the interface circuit thresholds to determine if the interfaces will be upset or damaged by the discharge sources. &lO.2

NUMERICAL ELECTROMAGNETIC METHOD

The numerical electromagnetic method uses codes such as the Numerical Electro° magnetic Code [34] m analyze discharge coupling. For NEC the spacecraft structures and cables are modeled as a combination of "rods" and flat polygonal "plates." The NEC spacecraft model is then. driven by direct sources representing the discharge at the model locations identified with the cells that are likely to discharge. NEC is a frequency-domain code, and thus the time-domain discharge sources must be c o n v e g ~ to the frequency domain when. input to NEC. The NEC program solves both an electric field integral equation (EF1E) and a magnetic field integral equation (MFIE) and accounts for mutual coupling between spacecroft model elements. Individual NEC calculations are performed at a single frequency point and thus must be repeated at a number of specific frequencies that cover the range of interest for the frequency portion of the discharge sources. The NEC code output is transfo~ed to the time domain to yield the current flowing on. the cables of interest. The cable currents are then used to determine the cable conductor currents via the transfer characteristics of the cffNes being analyzed or with a iumped~element electrical model. Once the conductors' currents are found, the voltages and. currents appearing at sensitive interface components are dete~ined using usual network analysis techniques. 8,10.3

PARTICLE-PUSHING METHODS

~ e . particle-pushing methods use system-generated electromagnetic pulse (SGEMP) codes such as the two-dimensional Arbitrary Body of Revolution Code (ABORC) [35] or its three~dimensional equivalent MEEC to calculate spacecraft discharge response. These codes solve Maxwell equations by direct finite differencing for asymmetric geometries. Spatial cun'ent densities are obtained from finite particles of charge that are followed through the spatial mesh of zones. In addition to the Maxwell. equation routine, ABRC has a Poisson equation solver from which electrostatic field may be obtained for each time step. Woods and Wennas [36] describe the details of using ABORC to perfo!~ discharge, analysis of spacecraft. Discharge response calculations begin with the static: fields arising

284

8. Space Environment and interference

from the initial charge on the dielectric. The ABORC discharge model assumes uniform spatial emission, a triangular time history, and zero initial electron kinetic energy. Flashover currents are included to the extent that the potential across the dielectric varies with time due to both blowoff and flashover effects. Reasonable agreement has been found between discharge results calculated with ABORC and actual measurements made on spacecraft models in the laboratory.

8.10.4

EMC ~ D I A . T I V E COUPLING METHOD

The EMC radiative coupling method employs EMC analysis codes such as Intrasystem Electromagnetic Compatibility Analysis Program (~MCAP) and Specification and Electromagnetic Compatibility Program (SEMCAP) to analyze discharge coupling for spacecraft. IEMCAP and SEMCAP contain communications, and EMC analysis math model.s to efficiently evaluate the spectra, and transfer modes of electromagnetic energy between generators and receptors within a system, in analyzing a system with these codes, all. system emitters are. characterized by emission spectra and all receptors are characterized by susceptibility spectra. All ports and coupling mechanisms are assumed to have linear characteristics. E~ssions fi'om the various emitter ports are assumed to be statistically independent so that signals from several emitters, impinging at a receptor poR, combine on an. RMS or ~ w e r basis. The function of these codes is to dete~ine, by analysis, whether the signals from one or more emitters entering a receptor port cause interference with that receptor: Electromagnetic interference (EMI) is accessed by computation of an EMI margin for each receptor port. The EMI margin is just the ratio of power received at each receptor port to that receptor's susceptibility. Coupling models built into these codes include antenna coupling, wire-to-wire coupling, case-touche coupling, coupling through filters, and fieldto-wire coupling.

&lO.5

RECOMMENDED COUPLING ANALYSIS APPROACH

The present standard practice used for spacecraft discharge response is the LEM method. The analysis procedure is as follows: i. Obtain the stractural details of the spacecraft m analyze. 2. Obtain the physical details of spacecraft cabling that is routed on or near stmcturai elements and connects to sensitive interface circuits that are susceptible to interface or damage.

8.10. Determination of Path for Discharge Energy

285

3. Construct a physical model of the spacecraft using the following library of structural components: rectangular plates, disk plates, hollow cylinders, bars, and cones. 4. C o n s ~ c t an electrical model of the spacecraft replacing the structural components with their equivalent electrical RLC models. The equiva, tent circuits for plates, hollow cylinders, and disks are shown in Figure 8.23. The structural elements fall into one of two major categories, the exterior structural elements that are capacitively coupled to space and the interior elements that capacitively couple to each other. These free space, capacitances and mutual capacitances are included in the electrical model for each model structure. Capacitances and inductances of stracture

Lser Rser ~

[

I

J

'

~

HOLLOW CYLINDER

PLATE. ......... - "

................ ~..................................... ~ .................... -

Lser Rser

DISC

Figure 8.23 Equivalent circuits for plate, cylinder, and disk.

286


elements may be found in Granger and Ferrante [37]. The eleztrical model nodes should co~espond to structural features with dimensions of 0.3 m or less. 5. Construct LEM electrical coupling models of the spacecraft cabling and insert these cable coupling models at the appropriate locations in the spacecraft electrical model. Simple LEM models can only be used for cables that are less than M10 long, where A is the smallest wavelength used in the analysis. For longer cables, distributed LEMs must be used, where the simple LEM is divided into several sections to account for distributed effects, 6. Insert the discharge sources at the appropriate points in the spacecraft electrical model. The sources drive the spacecraft electrical model through their source impedance, which is capacitive or resistive de-. pending on their spacecraft injection mechanism, Use a circuit analysis code such as SPICE to solve the spacecraft electrical, model for the voltages and currents that appear at the cable conductor loads representing input impedances of the sensitive interface circuits.

8.11 Circuit Upset Circuit upset is a nonpermanent alteration of a circuit or component operational state that is self-correcting or reversible by automatic or manual means. Some examples of upset are provided in Figure 8.24. The conditions under which upset occurs when a circuit is, stressed by a discharge transient are as follows: 1. The dischm'ge transient's amplitude must be a significant fraction of or greater than the circuit's operating signal levels. 2. The discharge tra.n :~ent s time scale must be within the circuit's response time. •

S"

~

.

3. When the discharge transient's time scale is shorter than the clr rats response time, the discharge transient's amplitude required to cause upset exceeds the circuit's operating signal levels by increasing amounts as the time scale differences become larger. ~

C

~

'

4. For digital logic circuits, when stressing discharge transients have time wi.dths that are within, the logic circuit's response time, logic upsets occur when the discharge transient's amplitude is greater than the logic c!r mts noise margins.

8.11. Circuit Upset Discharge

I d Input

I~1':~A'ransient ~

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

j

:

K

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

FlipFlop

Q

•. ........

~

|

Q

287

/ o-output | 'Low

11!

__.

_Jl=.

1

~ - Flip-Flop Response Delay Time "

ii

.: II .....! ..........................I..i

..................~ ,

. . . . . . . . . . ._~ .......

"High"

(a) Flip-Flop Upset Power S .

upply Input

Power Supply

......

.................... ~ ................

Discharge ~.Transient

i b, [ .... ~./~. ~¢ v l ,iv r~ _ . ....................... r ........... ,._ 1

::

I I

4t-] i-~ Gate Response Delay Time C-Output i I"High" ..................................... II

(b) NAND Gale Upset f Adnput

c

B

C-Output

f

Discharge

Transient

Amplifier Response Delay Time

[ ~ i l I1 I..~; ~ • • " '~1 I Ill 4 1 IIi ii I t, :I" ......~ " : J

",J \J

/-'~q

2 ;2 == 1

U V \~

•

(c) Amplifier. Upset

Figure 8.N

Examples of upset from discharge transient pulses.

The upset thresholds for representative logic families are given, in Table 8.9. The upset levels (e.g., noise margin) for commonly used logic families vary from a few hundred milli-electron volts to a few volts. Typical upset energy level thresholds range from l to 50 nJ.

288

Logic Family

Power Supply (V)

Typical Gate Quiescent Power Dissipation (mw)

Typical Upset Threshold and Characteristics of Some Logic Families Typical Propagation Dekzy (nsec)

Typical Signal Line DC Noise Immunity (V)

HTL SCL CMOS CMOS CMOS

5 5 15 5.2 5 10 15

5 15 30 25 0.000025 0.00010 0.00023

30 10 85 2 45 16 12

Logic Voltage Swing

(v)

Typical Energy Noise Immunity on Signal Line (joules x I @ )

High

Low

DTL TTL

Z)pical Signal Line Impedance (ohms)

Min

Z)p

Min

Typ

Low

High

0.7 0.4 5.0 NA 1.5 3.0 4.4

1.2 1.2 7.5 0.2 2.2 4.2 6.5

0.7 0.4 4.0 NA 1.5 3.0 4.5

3.8 2.2 7.0 0.17 3.4 6.0 9.0

50 30 140 7 600 300 250

1.7K 140 16K 7 12K 600 450

Low 4.5 3.5 1.3 0.8 5.0 10.0 15

3

High

3

15 25

48 NA 3 10 22

NA 15 5 13

-


Table 8.9

8.12. ComponentDamage

289

8.12 Component Damage Component damage is a permanent change in one or more electrical characteristics of a circuit component. Circuit components are vulnerable to thermal damage and electrical breakdown when stressed by dielectric discharge transients. The damage energy threshold for various circuit components for a I ~ - n s e c rectangu1~ transient pulse is shown in Figure 8.25. R e damage threshold level ranges from I0 nJ for microwave diodes to several hundred nanojoules for various logic families.=

Component Transformers

Switching

Diodes

Zeners

owo,

Microwave Diodes LED

Transistor

Signal •

.

r

Linear IC ITL s/c

._rtr

jFET

MOS CMOS/SOS Capacitor

Voltage Dependent Failure

~ ~

Thin Film Resistor

Open o---~v,---o [ 20*/o Resistance ° - - A v " ° Charge

Carbon Resistor Relay

o - - J ' --o Weld Contact 10-10

10~

I

10-2

1

102

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

106

Energy (J)

Figure 8.25 Permanent damage energy threshold of components for lf~-nsec pulse.

290


For semiconductors, the most common discharge transient damage mechanism is l~alized thermal runaway triggered by electrothermal overstresses. ~ i s condition produces a resolidified melt channel across the junction once the transient is removed, where the melt channel appears electrically as a low-resistance shunt across ~ e junction. Junction damage is most likely to occur when the discharge transient reverse biases the junction and drives it into second breakdown. Forwardstressed junctions also fail, but typically have damage tbxe.sholds that are 3 to 10 times higher than reverse stressed junctions. For integated circuits, metallization burnout and gate oxide breakdown (for MOS devices) are also prominent failure mechanisms. Semiconductor failure thresholds for discharge transients can be predicted from ~ o w n or measured data using models developed for discrete semiconductors and integrated circuits. Tinese models, which are based on thermal considerations and experimental, results, yield an expression for the failure threshold level, (8.8)

Pp = k~t ~/2

where Pp is the. power in. watts required in t seconds to produce device failure, and k t and k2 are device-dependent damage constants. As illustrated by Figure 826 for discrete devices, k2 is unity for discharge pulse widths less than 100

PF

tp -1

t.p-1/2

tp0 |

~

i t i I t

ta

te

Log tp

Figure 8.26 Pulse power failure dependence on pulse width for discrete semiconductors.

8,12. Component• Damage

291

nsec, 0.5 for pulse widths between 100 nsec and 3 ~ msec, and zero for longer pulse widths. The value of k~ is determined by test when. possible. Measured values of k~ for some common discrete semiconductors are shown in Table 8.10. When test data is unavailable, the value of k~ can be obtained from data sheet information and the analytical expressions given. The failure models for diodes and transistors are shown in Figure 8.27. The diode and transistor junctions am modeled by a resistor that represents the junction's bulk resistance and a voltage source, that represents the reverse bre~down voltage for the junction. Typical. values of junction bulk. resistance and reverse breakdown voltage for diodes and transistors are listed in Table. 8.11. For integrated circuits, k~ and k2 are determined experimentally when possible. For the c ~ e where test data is not available, typical values of these coefficients for diffe~:ent types of inmgrated circuits have been determined by tests and are given in Table 8,12. Tight integrated circuit manufacturing tolerances and standard circuit, designs have allowed integrated circuits to be grouped by their technology into generic failure classes and their terminals categorized into one of the following types: input terminal, output terminal, and power mrminal. The IC terminal failure model consists of a resistor representing the terminal's bulk resistance and voltage source representing the t e ~ i n a l ' s reverse breakdown voltage.

Table 8.10

Damage Constants and Junction Breakdown Voltages for Some Typical Discrete Semiconductors

Device

Type

1N750A 1N756 1N914 1N3600 IN4148 IN4~3 2N918 2N2222 2N2857 2N2907A 2N3019 2N3440

~ner Zener Diode Diode Diode Diode Transistor Transistor Transistor Transistor Transistor Transistor

"kl = k, k 2 = 1./2~

~

( W s t/z)

2.84 20.4 0.096 0,18 0,011 2.2 0.0086 0,11 0,0085 0. I 0A4 1.1

B V ~ ° (V)

B Vcn o (V)

V,D (V)

4,7 8.2 75 75 75 200 3 5 2.5 5 7 7

30 60 30 60 140 3~

292

8. Space E n v i r o ~ e n t and Interference

Transistor Damage Model

PF = kt, t~k2

+

IF =

C

4RBPF 2RB

V F = RRIF + VBD

IC Terminal Damage Model Power

E

input

Output

C :.::::

Diode Damage Model

=-:0

VF--~ li

Anode

RB VBD

Cathode

Reference

Figure 8.27 Transient pulse failure models for ~ansistors, diodes, and integrated circuits.

Table 8.11 Typic~ Junction Bulk Resis~nce for Discrete Semiconductors .

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Device Category

Reverse Bias (ohms)

Forward Bias Whms)

Zener diodes Signal diodes Rectifier diodes Low-frequency transistor (e-b) High-power transistor (e-b)

1.0 25.0 150~0 10.0 2.0

0. I 0.25 0.05 1.0 02

8.12. Component Damage Table 8.12

Damage Constants and Failure Parameters for Va~o~ Logic Families

Category

Farefily Terminal TTL RTL

DTL

ECL

MOS

Linear

293

Input Output Input Output Power Input Output Power Input Output Power Input Output Power Input Output

l~wer

Upper

K1

Kz

"v'Bo (V)

R B (ohms)

95% K t

95% K z

0.00216 0.00359 0.554 0.0594 0.0875 0.0137 0.~40 0.0393 0.I52 0.0348 0A56 0.0546 0.001.4 0.105 0.0743 0.0139

0.689 0.722 0.384 0508 0.555 0.580 0.70.6 0.576 0.441 0.558 0.493 0.483 0.819 0.543 0.509 0.714

7 1.3 6 5 5 7 1 1 20 0.7 0.7 30 0.6 3 7 7

16 2A 40 18.9 20.8 25.2 15.8 30.6 I5.7 7.8 8.9 9.2 i 1.6 10.4 13.2 5.5

0.00052 0.00098 0.12 0.0096 0.026 0.0046 0.012 0.009 0.~5 0.0031 0.22 0.0063 0.~2 0.038 0.0054 0.0045

0.00896 0.013 2.6 0.39 0.70 0.041 0.0136 0.17 0.51 0.397 0.935 0.47 0.0046 0.29 1.01 0.043

From the failure models for discrete semiconductors and integrated circuits, we find that the failure voltage VF and failure current I F at the device t e ~ n a l s are expressed as V ~ = V B + iFR B

I F, = (VB - ~ , ~ _

(8.9) 4RBPp)/2RB,

where VB is the t e ~ n a l ' s breakdown voltage, R B is the terminaI's bulk resistance, and Pp is the terminal's failure power, given previously. The conditions for failure to occur when. a circuit is stressed by a discharge transient are as follows: 1. The discharge transient current produced at the terminals of the transistor, diode, or integrated circuit must be equal to or exceed IF/D, where IF is obtained from Equation (8.9). D is a derating factor to account for statistical variations in device failure thresholds. D is 3 for Pp values obtained using measured damage constants, and 10 for Pp values obtained using damage constants from generic data tables or those obtained from analytical expressions.

294


2. The discharge transient voltage produced at the t e ~ i n a l s of a transistor, diode, or integrated circuit must be equal to or exceed VvO, where VFD = V B + 1FR~/D.

References 1.

Abraham L. Pressman, "Switching Power Supply Design," McGraw-Hill, New York.

2.

Y.S. Lee and Y. C. Cheng, "Computer Aided Analysis of Electronic DC-DC Converters," tEEE Trans. Aerospace Electronics Systems 24(12) 124-132, March 1988.

3..

E. T: Moore and T. G. Wilson, "Basic consideration for DC to DC conversion network.," IEEE Trans. Magnetics 2(3), September 1993.

4.

Lazar Rozennblat, "Understanding the transient response of switching mode supply, .... Electronic Design, November 1997.

5.

N.E. Lindebland, U.So Patent 2, 300,052 filed May 4, 1940 issued October 27, I942.

6.

D. Rubin, "The Linville method of high frequency transistor amplifiers design," Naval Weapons Center, Research Department, NWCCL TP 845, Corona Laboratories, Corona, CA., March 1969.

7.

S.W. Lee and Yr.Rahmat-Samii, "Simple formulas for desiring an offset multibeam parabolic reflector," IEEE Transactions in. Antennas Propagation, AP-29(3), p. 472 (May 1981).

8.

L Ruze, "Antenna tolerance theory--a, review," Proc. IEEE, 54, pp. 663-640 (April 1996).

9.

M.i. Kontovitch, "Average boundary conditions at the surface of the grating with square mesh," Radio Engineering (1962). M.I. Astrakhan, "Reflecting and screerfing properties of plane wire grids," Radio Engineering, 23 (1968).

10. 11.

E Dumont and E Combes, "Study of reflection by metallic mesh," Int. Syrup. Santiago de Compostella, Spain, August 23-26, 1983.

1.2.

E Dumont, "Modelisation radioelectrique des antennes a reflecteur deployable," Thes. Doc. Eng. ENSAE, Totouse, France (1984).

t3.

S.W. Lee and Y, Rahmat-Samii, "'Vector diffraction analysis of relector antennas with mesh surfaces," IEEE Transactions in Antennas and Propagation, 33, pp. 76-90 (January i985).

14a. V.A. Davis and L.. W. Duncan, "Spacecraft Surface Charging Handbook," P L ~ 92-2232, Maxwell Laboratories for Philips Laboratory, Air Force Material Command, Nov. 1992. 14b. C. K. Purvis, K. Ga,~et, A. Whittlesey, and N. J. Stevens, "Design guidelines for assessing and controlling spacecraft charging effects," NASA TP2361 (1984),

References

295

I5. D. A. Hardy et al., "Average and worst case specifications of precipitating auroral ei~tron environment," Spacecraft Environmental Interactions Technology 1983, NASA CP~2359, AFGL-TR-85-00!8, ADA 202020, edited by C~ K. Purvis and C. E Pikes, pp. 13I-I53 (1985). 16. C. S. Lin and R. A. Hoffman, '°Characteristics of the Inverted V Event," Journal of Geoplz~4cal Research. ~ , p. 15 ! 4 (1979). 17. C. S. Lin and R. A. Hoffman, "Nucmations if lnve~ed V Fluxes," Journal of Geoph3~ics Research, ~ , p. 6471 (1979). 18. E. G. Multen and M. S. Gussenhoven, ~'High-Leve! Spacecraft Charging Environments Near Geosynchronous Orbit,"AFGL-TR-82-0063, ADA 118791 (1982). 19. M. S. Gussenhoven et al, '~High, level spacecraft charging in the low-altitude polar auroral environments," Journal of Geophysical Research. 90, pp. 11009-.11023 (t985). 20. E. G. Fontheim et at., "S~tistical study of precipitating electron~" Journal of. Geophysical Research, 87(A5), pp~ 3469-3480 (1982)~ 21. H. C. Koons et al., "Severe spacecraft charging event on SCATHA in September t982," Journal of Spacecraft and Rockets, 25, pp. 239-243 (1988). 22. H. C. Koons and D. J. Gorney, "Relationship between electrostatic discharges on spacecratt P78~2 and the electron environment," Journal of Slmcecraft and Rockets, 28(6), pp. 683-688 (199t). 23. H, B. Garret et at., "Environment-induced anomalies on the TDRS and the role of spacecraft charging," AIAA paper 90-0178, 1990. 24. I. Katz et at., "The importance of accurate seconda~ electron yields in modeling spacecraft charging," Journal q[ Geophysical Research, 91, pp. t 3739..--13744 (1986). 25. U. Fahleson, "Plasma vehicle interactions in space--some aspects in present knowledge and future development," Photon and Partic& Interactions with Surfaces in Space. edited by R. J. L. Grard, D. Reidel Publishing Co., Dordrecht, Holland, pp. 563-569, 1960. 26. M. J. Mandetl, NASCAP Programmer's Reference Manual, S-Cubed Division, La Jotla, CA SSS-R-84-6638, 1984. 27. K. G. Balmain, "Thickness scaling for arc dischalges on electron beam charged dielectrics," IEEE Trans. on Nuclear Sciences, NS-32(6), pp. 4073-4078 (1985). 28. J. Wilkenfeld et ai., "Development of Electrical Test Procedures for Qualification of Spacecraft against EID," Vol. t, IRT 8195-018, IRT Corp. 1981. 29. E.W. Grey, "Vacuum surfaces Jlashover: a high pressure phenomenon," Journal ~ Applied Pkysics, 58(I ), p. 32 (1985). 30. R. Stetmer and A. B. Dewald, "A surface discharge model tbr spacecraft dielectrics," IEEE Trans. on Nuclear Science, NS-32(6), pp. 4079--4086 (!985).

296

8. Space Environment and. Interference

31. A. R. Krauss, "Localized plasma sheath model on dielectric discharge of spacecraft polymers," IEEE Trans. on Nuclear Science, NS-35(6)(1988). 32. C. Bowman et al., "Space-charge level current injection testing to investigate discharge coupling models," IEEE Trans. on Nuclear Science, ~(6), p. 2033 (1989). 33. L E Granger and J. G. Ferrante, "Electrostatic discharge coupling in spacecraft electronics," ESA Journal, 11(14), pp. 19-30 (1987). 34. G. J. Burke and A. J. Poggio, Numerical Electromagnetic Code (NEC), Part 1 and Part 22: Program description, Lawrence Livermore National Lab. UCID-18834, 1981. 35. A. J. Woods et al, "Model of coupling of discharges into spac~raft structures," Spacecraft Charging Technology-- 1980, NASA CP-2182, AFGL-~-81 ~0270, ADA 114426, ~ited by N. J. Stevens, pp. 745-754 (1981). 36. A. J. Woods and E. E Wenaas, "Spacecraft discharge electromagnetic interference coupling models," Journal of Spacecraft and Rockets, 22(3), pp. 265--281 (1985). 37. J. E Granger and J. G. Ferrante, "Electrostatic discharge coupling in spacecraft electronics," ESA Journal, II(14), pp. 19-30 (1987).

Index Note: Page numbers in. italics refer to the figure or table on that page.

Absolute charging, 261 Acceleration of launch vehicle, 8 Accelemmeters, 78-80 Amplitudeoshift keying (ASK). 160 modulation, 162 Anomalies, 45, 47 Antenna factor. 229-.230 Antennas elements, 233-234 steering, 23 theory, 222-229 types, 234 Antenna systems, 233-.242 Apogee, Arcing, 280-282 Ariane launch family, i0-11 Articulation control for satellites, 2 Ascending node.. 45 Assembly of launch vehicles, 14~t 5 At!as-Centaur, 14~ 15. Attitude and articu!ation control subsystem (AACS),. 31, 48 earth sensors, 49 interference problems. 31 ~ 7 Attitude control, 2, 48~96 thrusters, 57 Auroral environment, 255-2.58

Bandwidth communication for digital signals, 160-17/ Batteries, 134~13.9 charging, 137-I 39 NiH z, I36-137

Beam4brming networks, 239-24I Besbcase analysis, 180-181 Binary coding, I55-I57 Binary-phase shift keying (BPSK), 161, I63 Bipolar signal, 156 Blowoff discharges, 281-282 Boost converter, Itl Buck converter, 1 ~ 1 0 7 Bypass capacitors., 8%92 in DC-DC converters, 131

Cable shields, 95, 96 Cadence WCA tool, 172 Cassegrain antennas, 236 Celestial star assembly (CSA), 49 Charged coupled device (CCD) in star camera, 65 Charging auroral environment, 255-258 auroral vs. geosynchronous, 263 currents, 268-274 effect of electron energy, 25%260 effects of, 261-263 environments, 266-268, 269 in geosynchronous environment, 252-255, 26 I multibody interactions, 261 satellite surface, 260~264 Charging potential calculatiom 257 Circuit failure, 293-294 Circuit upset, 28~288 Circular orbits, 40 Clock waveforms, 6%70 Code-division multiple access (CDMA), 21-22, 212~ 217-221 Globalstar system, 2I Odyssey system, 27 297

298

Index

Coding, 148, 155-171 Command and data handling, 3-4. t 4 I~ 148 requirements, 142~143 subsystem (C&DH), 49 Command interlace control unit (C1CU). 1 ~ Commercial launch vehicles, 12-I 5 Common-mode current, 72-73 Common-mode rejection, 9 t-92 Component damage, 28%294 Conducted interference in SMPS, I 13-I i4 Converters coupled to transformers, 10% 109 in SMPS, I26 types, I05~ 1 Coriolis acceleration, 32 Countries with samllites, 13 Coupled cavity TWTA, 205 Coupling analysis, 284-286 betw~n antennas, 23~232 between samllites, ! 7 Crosstalk between satellites, I7 Cuk converter, 107, 1!3 Current collection from a plasma. 2 ~ 2 6 6 common- and differential-mode, 72-73 limiting inrush, 112-113 in SMPS, 122, 125 substorm vs. aurora, 272-274 Current noise, 83

Damage to circuits, 289-294 to components, 28%294 m integrated circuits, 291 Data handling for satellites, 3 4 DC-DC converters, 126-.127 ground and power layouts, 132 optimized design, 135 Decoupling, 179 Decoupling of suNractors, 93 Delta pulse code modulation (DPCM), 158-1 Descending node, 45 Design control of spacecraft charging, 263 laser ine~iat measuremer~t unit, 7%78 reaction wheels, 57"58 reflector antennas, 244 satellite communication systems, 5~8

solar arrays, 102-103 sun sensors, 51-52 Device capacitive loading, 175 Device electrical characteristics, t 82-I 84 Device loading factors, 18 !-182 Dielectric breakdown, 281 Differential charging, 261,275.-280 effect, 261-262 shade~unshaded surface, 27~279 Difl?rentiaPmode current, 72-73 Differential potential of sides of spacecraft, 27%280 Digital modulation, 6-7, !4%153 Digital signaling methods, 160-t 71 comparison, 170 Diode damage, 292 function, l t 5-116 switched OFF operation, 120 switched ON operation, 1t9 Discharge energy path, 282-286 Discharging, 280~.282 Distortions in TW~FAs, 208~2t I Dual-reflector antennas, 236

Earth stations. 7 Eastern Test Range, 10, 12 ~lipse number for LEO,. 134, 135 Electrical connections, 5 Electric field calculation, 22%230 Electron current calculation, 270 Elliptical motion, 35-36 Elliptical orbits, 40-4 I EMC Radiative couNing method, 284 EMI noise, 120-I 21 avoiding, 8%92 from diodes, I t 5-116 filter in SMPS, 126-127 Energy storage, 134-139 Engineering telemetry unit (ETU), 148 Equilibrium potential contours, 276

Feed systems, 23%242 Field programmable gate array (FPGA), 77 Field regions of antennas, 222 Flight processor computer~ I43-144

Index. Floating potential, 264 Flyback converter, It6 Fontheim distributions, 25%258 Forward converter, 107-109 with parasitic elements, 124 Fraunhofer region, 222 Frequency-division multiple access (FDMA), 2t2, 2t3 Frequency reuse, 24%.250 Frequency~shift keying (FSK), 1,61, I64-!65 Fresnel region, 222

Gain., 209 Gate.ways, 7 Geosynchmnous environment, 252-255 Geosynchmnous orbit (GEO), 15, 17-18 Geosynchmnous plasma, 253-255 Gimbal drive electronics (GDE), I46-147 Globalst~ system, 18, 2 t-22 Granular noise, 155 Gray code, 151 Gregorian antennas, 236 Grounding to avoid EMI noise, 89-92 op-amps, 92,-96 SMPS convermrs in PCBs, 125-133 sun sensors, 54-55 to suppress transient effects in SMPS, !2%131 Guard shields, 95 Guidance subsystem. See Attitude and articulation control subsystem Gyroscopes, 74-77 in laser inertial measurement units, 77

Harness, 5 Helix TWTA, 205-206 Horizon sensors, 49 Hunting noise, I55 Hyperbolic motion, 36 Hyperbolic orbits, 4!

Impedance of an antenna, 225-226 Impulse calculation, 8 Inertial measurement unit (tMU), 49, 74-96 laser, 77-78

299

Input noise of power converiers, 110 Input/output board WCA, 184-190 Input ripple noise of power converters, 111 Integrated circuit damage, 292 Interference coupling ~tween antennas, 230-232 Interference paths in SMPS, 122, I25 Intermodulation distortion, 2 I(3-21 t lntersaiellite links for Teledesic system, 26 !ntraboard and connector capacitance, 176 Ion current calculation, 270 Iridium satellite system, 20-2I

Johnson noise, 81, 86

Kep!erian orbits, 38*-4I Kepler's laws, 39 Klystron, 205

Langmuir probe, 264 Laser inertial measurement unit, 77-78 Launch sites, 1O, 12 Launch vehicles, 8-11 assembly, 14-15 commercial, 12.~,,[5 man ufacturers, 13- ! 4 for personal wireless communication, 12-15 Lens antennas, 235 Line delay correction, 178 Line of apsides, 4 4 4 5 Lines of n~es, 45 L~kheed-Martin wrap-rib antenna, 245-249 Ia3w~earth orbits (LEO), 18-20 Lumped element method (LEM), 282, 284-.286

M Magnetosphere, 251-252 Manchester signal, 156 Manufacturers of launch vehicles, t 3-i 4 Masmr crystal oscillator (MXO), 146 Mechanical gyroscope~ 74~75 Mechanical systems in satellites, 4 Mentor WCA too!, I72

300

Index

Mobile satellite communications, 15~30 Mobile satellite multichannel requirements, 249-250 Modulation, 6 Modulation theory, t48-17 ! Motors emf calculation, 60 in reaction wheels, 56 torque calculation, 60 Multibeam antenna system, 241~242 Multilevel. signaling, 165~I71 Multiple access, 212-.2:2I comparison of types, 219 Multiple access system, 7 Multiplexing, 6

N NiH 2 battery, 136-.137 Noise in analog~to-digital converters, 8 ~ 8 2 electromagnetic coupling, 7(t-72 frequency characteristics in oDamps, 84 in high speed sampling of A/D converters, 82-84 intrinsic in op-amps. 63-64 PCB Layout, 130-13 t in power electronics, !09-I 40 from power transistors, 120-122 in pulse code modulation, 153-t55 quantizing, t 55 in reaction wheel assembly, 58~62 from silicon-controlled rectifiers, l 16-120 sources, 69-70 in st~ camera, 66-69 in sun sensor circuits, 52-55 in switching-mode ~ w e r supplies., 10% 133 in telecommunications subsystems, 193-201 temperatum~ 199 tomi input, 85-87 Noise figure, I99,-200 Numerical electromagnetic method, 283

Odyssey system, 18 Offset-fed parabolic antenna design curves, 238 design formulas, 240 Op-amps grounding, 92-96

intrinsic noise. 63-64 noise figure, 84 power supply decoupling, 8%92 total noise outpuL 85~87 Operating environment device derating, 180 Orbitdimited current collection, 264-266 Orbits circular, 40 configuratiol~ vs. satellite coverage, 43 defining, 45 determination, 33~38 elliptical 40-4 I hype.rbolic, 41 Keplerian, 38M ! I.~ation and power system design, 10l parabolic. 4 I types and attitude control, 48 Orthogonal access techniques, 212 Oscillation in sun sensors, 53~.-64 Overload noise. 155

Packet switching technology, 24 Parabolic motion, 37-38 Parabolic orbits, 4t Parasitic currents, 73 Parasitic extraction tools, t3!-I33 Particle-pushing method, 283.-284 Path: of discharge energy, 282-286 Payload data. assembly (PDA), 148 Payloads, 4-5 PCB. See Printed circuit board Pendulous gym inwgrating accelerometer (PGIA), 7%80 Perifoca!, 44 Perigee, 44 Periheli(m, Phase array antennas, 234-235 Physics of rocket motion, 8-9 PN junction, 98 Polar signals~ 155 Potential, rate of change. 276 Power average radiamd by an anwnn.a, 223 calculations for antennas, 22~227, 228 calculations for solar cell, 99 control electronics, 137M39 gain of an antenna, 224 output vs. input, 2t 1 received ~ w e r calculation, t 96-- ! 98 Power converters, 105.-~109

Index Power gain of antennas, 222 Power source for satellites, t-2 Power spectral density binary' code signals, t56~157 binap¢ phase-shift keying, t63 digital bandpass signak I60 frequency~shift keying, 164-165 quadrature amplitude modulation, ~67, 168 Power subsystems, 97-I08 Power supply decoupling in op-amps, 8%92 rejection ratio (PSRR), 87, 89 Printed circuit board layout and ndse reduction, 130-I 3 I layout using parasitic extraction tools, 1.31-133 Propagation delay, 173-~174 correction factor, 176-t 78 end-of-life correction, t,78 open collector calculation., 177-I 78 Propulsion control in satellites, 4 Public switching telephone network (PSTN), 5 Pulse amplitude modulation (PAM), 150M 51 Push-pull converter, 109, ll 7 Pyrotechnic relay assembly, 147

QPSK modulation, 20 Quadraphase shift keying (QPSK), 165~t66 Quadrature amplitude modulation (QAM), I67~i7I

Radial-rib antenna, 245 Radiation damage m solar cells, 103~104 Radiation pattern of antennas, 222 Random noise., 155 Reaction wheel assembly, 49 Reaction wheels, 55-62 design.,. 5Z~58 functions, 55 Received power calculations, 196-t 98 Refere..nce bursts, 2 ! 6 ReNector antennas, 235-238 Ring laser gyroscope, 75~.77 RMS, 63 output noise, 86 Rockets, See Launch vehicles Routing priority lbr Odyssey system, 28

301

Sagnac effect, 75-76 Samllite charging effects, 260-264 communications, 5--8 covemge~ 41-44 defining orbital ~sition, 45, 47 development, 15 as floating pr..o~s, 264~266 mobile communications, 15-30 navigation, 31 space between, 17 subsystems, 1-5 Satellite systems Globalstar, 18, 21-22 Iridium, 20-2 I Odyssey, t 8, 2%30 store and dump, 18 Tetedesic, 22-27 SCATHA satellite, 254, 261 Semiconductor damage, 2.90 constants, 291 Sensors horizons 64 star, ~ 6 6 sun, 50-54 Set-up and hold sr~cificaaons, 178-I 79 Shields in op-amps, 92-96 Signal, 5=8, base band, 14 l carrier, 14 l formats for binary coding, 155 gain, 209 modulation, 6 processing, 5-8 processing by command system, 141- ! 48 Signal control unit (SCU), 145-i46 SignaMo-noise ratio delta modulation system, !~Ki pulse code modulation, I54 Silicon-controlled rectifiers, ! 16-I 20 Single-reflector antenna, 236 Solar arrays, t01-103 So~ar cells, 98~i radiation damage m, 103-!04 in space systems, 10~102 Solar energy, 97 Solar flares, 1 Solid state power amplifiers (SSPA), 202 Sources of interference in SMPS, i 14~-122

302

Index

Sources of l~oise in A/D converters, 81 model, 85-87 in opoamps, 82 pulse code modulation, 153 in TWTA, 207-208 Space-charge limited current collection, 264-266 Spacecraft. See Satellites Spacing for satellites, I7 SPICE-like WCA tools, 173 Spin-stabilized satelliws, 48~49 Spread-spectrum effect, 217 Star camera, ~ 6 6 optical system, 65-66 Steering an.mnna, 23 Stettner-DeWald modeI, 281 Storage cell selection, I35 Strip-aperture model unfurlable antenna, 247 Structure of satellites, 1 Sunlight/eclipse ratio, t01 Sun sensors, 49 design, 51-52 grounding, 54-55 physical Ninciples, 50~55 types, 50 Surface charging,. 262-263 Su.r~ace coating and differential charging, 275-280 Switching Iridium satellite system, 21 transistors, 62 Switching-mode power supply (SMPS), 105-109 current, 125 design, i26 interference paths, 122, ! 25 transient effects in, 12%130

Traffic burst archflecture, 216 ~?affic management~ See Switching Transistor damage, 292 Transistor switching process, 62 Transition times, 18 l ~lS:ansponder noise representations, 202-221 Traveling wave tube amplifiers (TWTAs), 202, 205-208 Two-body central force motion, 31-33 Types of launch vehicles, 10-t t of signals, 5

Unfu.rlable antennas, 245-249 e×ample~ 245-~249 Unipolar signal, 155 Uplink/downlink equations, 200-201. UplinkJdownlink models, 194- t 96 Uplink pwcessor WCA, 190-I 93

V~: variation, I75 "Velocity of rocket ascent, 8 Vis-viva equation, 39-40 Voltage and carrent waveforms boost converter, 11.2 buck-boost converter, 110 buck convener, I08 flyback converter, 117 forward converter, t15 push-pull converter, i18 transistor, t22 "Voltage noise of op-amps, 83 W

Tel~esic satellite system, 22-~27 Temperature balance in satellites, 4 Thermal control for satellites, 4 The~at runaway, 290 Thrusters, 57 Time-division multiple access (TDMA), 20, 212, 214~216 architecture,. 215-216 Titan launch family, t0-1 I Tools l~r worst-case analysis, 172-173 Torque calculation mechanical gyroscopes, 75 motors, 60

WCA. See Worst-case analysis Western Test Range, t 0, 12 Wire-grid mesh unfurlable antenna, 246-247 Worst~case analysis digital circuits, 173M79 examples, 17%193 guidelines, 17 l-172 power electronics, t 3%140 tools, !72-173 Worst case charging events, 254, 257

Wireless Communications Design Handbook Space Interference

Wireless Communications Design Handbook: Interference into circuits

Wireless Communications Design Handbook Terres- Trial Mobile Interference

Wireless Communications Design Handbook - Terrestrial and Mobile Interference

Space-Time Block Coding for Wireless Communications

Space Time Coding for Broadband Wireless Communications

Space-Time Block Coding for Wireless Communications

Space-time block coding for wireless communications