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 DIGITAL COMPUTER LABORATORY 
 UNIVERSITY OF ILLINOIS 
 URBANA, ILLINOIS 
 
 Report No, l^k 
 
 EMITTER FOLLOWER STABILITY 
 
 by 
 
 T. Moto-Oka, T, A„ Murrell, and H. Guckel 
 
 March 5^ 1963 
 
 thi^Atn^^ ""r "^PP°^^^^ i^ P^^^ ^y the Office of Naval Research and 
 1t(11-1^4i5!^''^^ Commission under Contract Nos. Nonr-l834 (15) and 
 
1 ( l^r 
 
 Synposis 
 
 Stability problems in the non-restoring logic part of the new computer 
 resulted in a re-examination of the emitter follower problem. Parts I and II 
 describe the theoretical problem based on the work of R, Beaufoy and 
 T, T, Sparkes. This again is a small signal theory and results are similar 
 to earlier work. The important addition is the sufficient condition for 
 stability. Comparison of theory and experiment yield good results. 
 
 Part III presents measurements on "typical layouts" made to determine 
 the magnitude of the negative real part of the input impedance which actually 
 occurs. Part IV gives details of the compensator design. 
 
 LW 
 
 1 
 
 Measurements were carried out with the Boonton RX Meter. Evaluation 
 of preceeding data lead to the design of an RL compensator. Tests performed 
 with the filter indicate its functionality and non-interference as far as signals 
 are concerned. 
 
 I- Equivalent Circuit 
 
 The elements of the equivalent circuit are discussed in detail in the 
 paper by Beaufoy and Sparkes, but a few words of explanation here may be in 
 
 R. Beaufoy, T. T. Sparkes, "The Junction Transistors as a Charge- Controlled 
 Device, ATEJ, vol. I3, pp. 31O-327 (October, I957). 
 
 ■1- 
 
order. The more familiar elements are r^^, the ohmic part of the base 
 resistance; C^, the combined transition region capacitance (voltage dependent) 
 and diffusion region capacitance (current dependent) of the emitter-base diode; 
 and C^, the transition region capacitance of the collector-base diode. Typical 
 values for the GF-45011 and S-I66 transistors are : 
 
 ^bb " ^5 ^° ^50 ohms 
 Cg = 5 pf or so (the effect is found to be negligible) 
 Cp = 2 pf 
 
 The element shown as r^ represents the voltage-current relationship 
 across the emitter-base diode. For small signals, this becomes equivalent to 
 Shockley's r^, and has been shown to be 
 
 kT 
 r_ = 
 
 ' ^^E 
 
 For typical circuits r^ is some 3 to 5 ohms. 
 
 ^ is the base control charge, consisting of hole flow from emitter 
 to base and electron flow from the base lead,, both stored on S^, the base store. 
 V^B ^^^ V^C ^^^ "^^^^^^ generators . T and T^ are related to a and co 
 
 The value of a, the low frequency current amplification factor, is 
 chosen as an average over the relatively large current swing of the signals 
 encountered in emitter-follower oscillations, and is typically O.96 to O.99. 
 Some care is necessary in interpreting co^, the forward (normal direction) cutoff 
 frequency. As Pritchard has pointed out,^ this is the cutoff frequency 
 associated with the factor a, the current generator of the standard tee equiv- 
 alent circuit, rather than the measured cutoff frequency associated with alpha. 
 The difference becomes more important for transistors in which drift due to an 
 electric field in the base is appreciable. This includes all mesa transistors 
 as well as those known specifically as "drift transistors." 
 
 2 
 
 I R^F ^f ^"^^^^^ "Electric Network Representation of Transistors-A Survey " 
 I.R.E. Trans., vol. CT-3, p. 5, March. iqs6. survey. 
 
 \, p. 5, March, I956. 
 -2- 
 
To arrive at a reasonable value for c^, one can set Z (in the emitter 
 load) and L (the collector load) to zero and solve for p, the short-circuit 
 current gain for common emitter. 
 
 After some manipulation, the result can be expressed as: 
 
 1 + P = 
 
 1 + ja^r n 
 e E 
 
 1 - a + J(^JC~rc^ 
 
 where 
 
 a = 
 
 1/T^ 
 
 a 
 
 N 
 
 1 ^ ja3ii:22) 
 
 CO 
 
 N 
 
 If we assume that 03^ = (2n) (800 mc ) and evaluate |p| for f = 100 mc 
 the result is 1^1 = 5.6. This is only a little above the minimum specifications 
 
 Of the GF-45011 and S-166, and corresponds to an alpha cutoff frequency of 
 about 500 mc. Assuming the usual distribut: 
 reasonably typical value. 
 
 ;ion curve for production, this is a 
 
 II. The Theory 
 
 The problem is essentially that of finding the input impedance of the 
 following circuit: 
 
 Figure 2 
 
Evaluation of the indicated loop currents yields : 
 
 B 
 
 sa 
 
 L 
 
 
 
 -z 
 
 
 
 1 
 
 
 
 
 
 
 
 
 (r,^ 
 
 z) 
 
 -z 
 
 -z 
 
 -1 
 
 (r + Z + sL) (-sL - 4") 
 
 sC^ 
 
 'J 
 
 i; 
 
 L°J 
 
 By making use of the relationship: 
 
 (1) 
 
 A 
 
 1 
 
 1 1 
 
 
 = J. 
 
 'I'm 
 
 T^ T 
 
 E 
 
 B C 
 
 
 T„ = 
 
 1.22 
 
 C ao). 
 
 N 
 
 y 
 
 (2) 
 
 and 
 
 Z. = r'^ + Z! 
 
 m bb m 
 
 (3) 
 
 in A. 
 
 32 
 
 ^33 " ^5 
 
 (h) 
 
 the input impedance may be expressed 
 
 as 
 
 -k- 
 
Z! = Z 
 m 
 
 1 + sr T 
 e E 
 
 s^i- c 
 
 1 
 
 2, 
 
 (s + — )(1 + s LH ) 
 E ^ 
 
 + sC Z 
 
 1 + sr C 
 e E 
 
 ^ 1 + s^LH 
 
 (5) 
 
 Addition of r^^ to equation (5) will yield the desired impedance. It was found 
 that for the operation conditions of interest, both L and r may be neglected. 
 
 Z! 
 
 m 
 
 = Z 
 
 s + 
 
 r =L=0 
 e 
 
 s + 
 
 1_ 
 ^E 
 
 (5a) 
 
 if 
 
 Equation (5a) becomes 
 
 2 = G + sC 
 
 Z! 
 
 m 
 
 1 
 
 S + rr, 
 
 r =L=0 , , T, 
 
 e sn + (g + sC) - 
 
 s + 
 
 1 
 
 (5b) 
 
 If this is evaluated for s = jco and the real part if 
 results . 
 
 part if examined, equation (6) 
 
 R(Z! 
 
 ' (i-»^(C^.C)).c.2(G,_C,^) 
 
 T ^T 
 E B 
 
 m 
 
 T T 
 E B 
 
 'G ..2,„ _^^2 2 ^' 
 
 r -L-0 'T, 
 e 
 
 E B 
 
 (6) 
 
 -5- 
 
The denominator is positive for < c < +.. a negative real part is therefore 
 due to the behavior of the numerator. The root of this equation for a: > is 
 given by 
 
 CO = 
 
 
 
 2 1 
 
 (^ d - q; ) iP 
 
 ^°22 ^nV - 1°22gJ 
 
 (7) 
 
 Hence, for 03^ < ox . the input impedance of (5b) will have a negative real 
 part if 
 
 %%^G 1 
 
 1.22 C RC (8) 
 
 Equation (8) is then the necessary condition for instability. It is of cours 
 not sufficient. It indicates that for a given transistor large values of R 
 and C will be more likely to result in instability, whereas for a given load 
 high values of a^ and 03^ may lead to difficulties . It is interesting to note 
 that equation (8) results if the positive real condition is applied to 
 equation (6) as cd -> oo. 
 
 The sufficiency condition for stability may be obtained in several 
 ways. A direct approach would include the determination of the maximum with 
 respect to o) of equation (6) and a subsequent evaluation of the equation at 
 
 The criterion for stability is then of course given by: 
 
 e 
 
 this value of o) 
 
 max 
 
 R(Z. I 
 m 
 
 + r.', > (9) 
 
 "bb 
 
 r =L=0 a>:co 
 e max 
 
 However, due to the degree of the equations involved only numerical examples 
 may be treated. In order to avoid this difficulty use is made of the theorem 
 that both zeros and poles of the driving point impedance are restricted to the 
 left-half s plane. Furthermore, since an expression of the form 
 
 3 
 
 Bode: Network Analysis and Feedback Amplifier Design 
 
 -6- 
 
Z. = -R(a)) - jx(a)) is not unstable per se the wiring inductance L in the 
 m ' w 
 
 base circuit is now added. The test is then to be performed on 
 
 Gn 
 
 LJC^ . C)s- + [rJC^ + C) . rLjs'= + (1 + r^r . L^ ^]s + (f- + -^) 
 
 B 
 
 'T T 
 E B 
 
 m 
 
 r =L=0 
 e 
 
 (c^ + c)s^ + rs + I 
 
 B 
 
 where 
 
 (10) 
 
 r- (G + ^ + f) 
 
 E B 
 
 The poles of this equation are always in the left-half plane. For a third 
 degree equation with positive coefficients 
 
 F(s ) = as + bs + cs + d 
 
 (11) 
 
 The Hurwitz test leads to the condition: 
 
 £ . a 
 
 d b 
 
 (12) 
 
 which, when applied to equation (T.0) yields 
 
 C 
 
 T ^ T 
 E B 
 
 V^c^^^)^^ 
 
 (13) 
 
 2 
 
 b b 
 
 PL - 
 w 1 
 
 ,c^ + c + r 
 
 > 
 
 W 
 
 -E^ 
 
 L (1 + L ^) 
 w^ ^ ^E 
 
 The wiring inductance L will change from circuit to circuit. It may be 
 
 w 
 
 assumed that any value of L occurs. In order to find the minimum permissible 
 
 w 
 
 -7- 
 
value of r' as determined by this parameter^ that value of L must he found 
 
 "bb 
 
 w 
 
 which maximizes r' . This value is found by differentiating equation (13) 
 
 and letting -v^ = 0. 
 
 w 
 
 \c 2G 
 
 c^. c 
 
 '/ 
 
 1 - r. r 
 
 b 
 
 ''b^^c -^ =' / 1 
 
 2G 
 
 TT, 
 
 1 + r^r\2 
 
 (Ik) 
 
 Substitution into equation (13) yields the sufficient condition for stability: 
 
 ^b r - ^G TJ? C + C 
 
 (15) 
 
 L = L 
 w wc 
 
 Equation (6) was evaluated for a series of parameter values. The 
 strong effect of a^ and C is to be noted. Since, if r' = 0, any base-to-ground 
 capacity (C^) is in parallel with C ;, the damping effect of this parameter was 
 considered. The beneficial effect is shown in Figure 8. 
 
 In order to achieve some type of compensation network the effect of 
 r^ and L^^ the collector inductance, was studied. There is nearly no problem 
 associated with the collector inductance. However, if L becomes large fast 
 pulses will yield voltage drops, which in turn cause C (collector depletion 
 layer capacity) to be modulated. But this effect is beneficial, since C would 
 tend to increase, resulting in a decrease of the negative real part magnitude. 
 But a side effect occurs, also. If several collectors are tied together 
 through a common power supply wire and marginal stability exists, instability 
 of one may cause instability of all. 
 
 The effects of r^ are shown in Figure 10, Since r is always current 
 modulated it is possible to have stability for some injection levels, namely 
 the low ones, and instability for higher ones. The possibility of relaxation 
 oscillations exists and has been verified experimentally. 
 
 Figures 11 and 12 represent worst-case wiring conditions. The 
 capacitive loading curve shows the worst load for a GF~i+5011 to be about 120 ji^uf . 
 
 -8- 
 
smqo = a souBq-STsay 
 -9- 
 
o 
 o 
 o 
 
 o 
 
 o 
 
 O 
 
 o 
 
 o 
 
 o 
 
 o 
 
 o 
 
 o 
 
 PO 
 
 CM 
 
 H 
 
 o 
 
 o 
 
 o 
 
 o 
 
 o 
 
 o 
 
 o 
 
 H 
 1 
 
 CM 
 
 1 
 
 ■10- 
 
-Tl- 
 
 o o 
 
 o o 
 
 ' UNIVERSITY OF i 
 ILLINOIS LIBRARY 
 
-12- 
 
siuqo ^ a aou-BC^sisaa 
 
 ■13" 
 
siuqo UT aouBpadurr anduj; jo Q-j-bj i^aa 
 ...14- 
 
-15- 
 
suiqo = y; aDU'B':^ sissy 
 -16- 
 
5 6 7 « 
 
 C 
 
 Figure 11 
 
 Effect of loading capacity on 
 negative real part of input 
 impedance (Equation 15} 
 
 •IT" 
 
III. Experimental Results 
 
 Previous results depict the theoretical problem and rather idealized 
 situations. The wiring which occurs in practice permits nearly any value of 
 \} and, in particular,, mostly those values which are too large for the critical 
 case discussed earlier. These arguments led to the measurement of transistors 
 "in their environment," that is to say, in situations which hopefully simulate 
 worst cases in the new computer. 
 
 The experimental data fall into two groups : 
 
 a) obtained from high-frequency jig connection 
 
 b) actual metal chassis connections 
 
 The basic difference is, of course, the length of the interconnecting wires. 
 However, an effect which is at least as strong if not stronger, is due to the 
 capacity from base to ground. Data taken from the high-frequency jig may be 
 ten times larger than in the actual case. 
 
 In order to measure the non-linearity due to changing injection levels 
 the data shown in Figure 13 were taken. The effect of cascading had to be 
 studied to test the feasibility of a single compensator in a chain of emitter 
 followers (Figure 8). It is reasonably safe to assume that the data represents 
 an average situation. 
 
 IV. Compensator Design 
 
 The requirements of the damper are as follows: 
 
 1. Its direct current resistance should be zero in order 
 that additional direct current requirements may not 
 be needed. 
 
 2. Its pulse response must be so that no ringing results 
 with fast rise times and rise times are not affected. 
 No additional delay should be generated, 
 
 3. It must provide an impedance such that R(Z) > (|r(Z )|) 
 
 in ' ' ° 
 
 Point (l) is, of course, satisfied by any network which is shunted 
 by an inductance. Simplicity and space requirement suggest an RL circuit as 
 shown in Figure 17 . 
 
 -19- 
 
FIG. 14 
 
 -21- 
 
- T ?^ T ^ 
 
 ^ ^^ \ 
 
 . ^^ N 
 
 a: vl'l. LiLJi 
 
 - ■-> () A* -r- 
 
 ■sir^ ^r io — n t 
 
 31 'T rT' —Itr — \- TI 
 
 K— !tl-0:-v- '_i_ i rn 
 
 ILL _l ^ (D 
 
 O ,0 \ -r- .H 
 
 3r ■■ h ^, -+- 
 
 -. 1 ^''~ '^ 
 
 + + E* 
 
 -CU. J S. 
 
 
 _. '- l>r "^~ 
 
 t ~^k_ '"*" 
 
 L \ ^' 
 
 JJ^ 
 
 
 r- V 
 
 "1 
 
 ~\ 
 
 \ 
 
 H ' \ 
 
 ^ TO - ' Ju- 
 
 3^ § - " t 
 
 -^=L id ^ 1 
 
 '^ ^ - \ 
 
 T -r-^ S' i 1 ^ " <a « J 
 
 Th ^ , vlTT 3 - ^ «~T~ — 
 
 -l--=i-H r-l _l 
 
 X-£i_sC _cj_ \ 
 
 .3 >v-- C) ■ \ 
 
 -Ja^u^ -■ i 
 
 
 i:J^^^__p., 1 \ 
 
 -CL ° -ti 1 
 
 '^tu-^ . ■" " I 
 
 ^i'^ ^5 -■! ■- ^ V 
 
 l^l< ~ _d_| nv ;j- - - ^ j(^ 
 
 :^Zi \A-ii 11 
 
 2--CI K ^-J 1" 
 
 S - ^ " -f— 
 
 _.:t x\~ I.T - 1 
 
 -H ,=. (3 
 
 a-^i — ' -ii- 
 
 LL_fl' in _il 
 
 _, rj^j-, ^5 
 
 rrrl-S IT --^C i _. i i> 
 
 
 .=L-?.| (5- 
 
 =lJ1i_=1 o 
 
 y fiLf ~\ 13 
 
 ir a; if —^ — 
 
 .^^r ^: -f - ;;# s*- 
 
 i._(]M© -44- 1 
 
 u-^i_3: JL 1 n:^- 
 
 rH tI o ■ 1 
 
 rTi 35 -c" -cr »-■, -t 
 
 ^-(--^tr-H <:) ^^ _P Xl 
 
 ^->;- Mi- I 
 
 b^ t4) fe cl / 
 
 n --' S U4 -f 
 
 I L , ' ^J 
 
 : r ' <f i-- 
 
 1+ '^ r+J 1 
 
 ^ ITi 1 -j-i 1 M 1 Ml 1 M 
 
 3 
 
 - T -I5i- ^ji' 
 
 Wr F tWI » tI -KI I I?M I 
 
 iD f ,-t IT T ! 
 
 Wt k 1 HI t n \""\ \4\\\ 
 
 
 IjL- L ~2^ T 
 
 — S j^ r^ Tw 
 
 IL T ~I/ i 
 
 \\]' M^ ' A \ Yv- U4 
 
 m- JnT L-1 xI r /Trm 
 
 
 L444 LnWi [>fi L-rfn rH:^ 
 
 H44 t±yf\ Tr ^1 L-kI '■ 'yf 
 
 ^+44- HFtT _mi J4^T i. J^I 
 
 _ ^s* ^^"^^J" ^^''^ 
 
 -*^-"-=" "^^^^--■'■^ i>--^r-=^~~"°"° '" 
 
 [tt4 1 1 1 1 1 1 1 1 1 1 1 IfhH-M^I l"'l 1 1 1 1 rlttfflTTTi I ITITI 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 
 
 - 
 
 
 
 
 
 
 
 L-l— LJ 
 
 o 
 o 
 
 o 
 o 
 
 CVJ 
 
 I 
 
 o 
 o 
 
 I 
 
 -22- 
 
-23" 
 

 
 ^c "^ 
 
 Figure 17 
 
 In order to satisfy point (2) o)^ should be as small as possible. 
 This means that the minimum value of R^ should be used. The value of L may 
 be determined in such a way that compensation starts when the real part of 
 the input impedance starts to go negative. The arguments lead to a network 
 which has the following response : 
 
 Ideal 
 
 J'- 
 
 ^Compensator (actual) 
 
 Figure I8 
 
 Examination of Figure 15 reveals the difficulty of compensating 
 several stages. There is no absolute assurance that stability can be maintained 
 for all cases. The resistor R^ would become too large and a slow-down would 
 result. 
 
 -2k- 
 
-25- 
 
1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 S- 
 
 ■ 
 
 
 
 D 
 D — 
 
 
 
 () 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 C 
 
 c 
 
 
 
 
 <) 
 
 
 
 
 
 
 
 
 ^- 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^- 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 S- 
 
 — r — 
 
 
 
 i 
 
 
 
 ;J> 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^- 
 
 — X-V — 
 
 
 
 
 n- 
 
 
 -< 
 
 P 
 
 
 
 
 
 
 
 
 ^ - 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^- 
 
 3 
 
 
 
 1 
 
 iV 
 
 
 
 
 
 
 
 
 
 
 
 S- 
 
 
 
 
 \ 
 
 
 □c 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 "^ 
 
 
 ^ 
 
 ^ 
 
 ^ 
 
 ^ 
 
 ■>t 
 
 
 
 cr — 
 oo - 
 
 
 2 2 2 2 
 
 1— • 1— I i_^ k-i 
 
 "-^ UJ UJ L-^ 
 
 g cc cs: cs: 
 5^ o o a 
 O o o o 
 
 uj ci S ci Lu ci uj d 
 CS <:3 c£ <3 CI ^ c£ a 
 
 2t:2^-2l-2H 
 cl t^ cc ^5 cs: t^ cc t^ 
 
 
 
 
 
 
 ^ 
 
 ^^ 
 
 
 
 
 C 
 
 
 
 
 
 
 
 
 N 
 
 X 
 
 \ 
 
 
 va — 
 
 
 
 
 
 
 
 
 
 NS 
 
 X 
 
 
 ^ - 
 
 
 
 
 
 
 
 
 
 > 
 
 V A 
 
 Y 
 
 '^ — 
 
 
 
 
 
 
 
 
 
 
 \\ 
 
 ^\ 
 
 ro 
 
 + 
 
 
 
 
 
 
 
 
 
 
 A\ 
 
 
 CS. 
 
 o 
 
 1- 
 
 C£ 
 
 <NJ — 
 
 
 
 
 
 
 
 
 
 
 IS 
 
 9DS 
 
 -J 
 
 5 L 
 
 o <3: < 
 
 • 
 1 
 
 O Q 
 
 X 
 
 cr 
 
 -L 
 
 
 ,. 
 
 
 
 
 
 
 
 
 ^ 
 
 <NJ 
 
 <0 
 
 
 EFFECT OF SMUN)T RESISTOR, 
 FIG 2ia 
 
 -27- 
 
o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -<-l 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r- 
 
 ■^ \y 
 
 o 
 
 CSJ 
 
 •r-t 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 } 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 n 
 
 ) 11 
 
 -.-( 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 Q 
 
 
 
 
 
 
 
 
 
 
 
 
 f 
 
 9 
 
 'T 1 
 
 S 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 /_^ 
 
 
 
 s 
 ^ 
 
 ? 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 / / 
 
 
 
 
 
 
 
 
 
 
 
 
 ,/ 
 
 
 / / 
 
 J 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 / 
 
 P ^ 
 
 / 
 
 
 
 
 
 
 
 
 
 ^ 
 
 "^ 
 
 
 / 
 
 / 
 
 / 
 
 o 
 
 JO. 
 
 o 
 
 
 
 1 
 
 
 
 
 
 
 ,-^ 
 
 
 
 / 
 
 / 
 
 ... 
 
 
 
 
 
 
 
 
 
 ^ 
 ^ 
 
 / 
 
 -^ 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 -^ 
 
 <^ 
 
 "V 
 
 
 1 
 
 
 
 
 c^ 
 
 
 
 
 
 
 
 
 
 \ 
 
 . \. 
 
 
 > 
 
 
 
 
 ^<J 
 
 
 
 
 
 
 
 
 
 
 VN 
 
 \ 
 
 
 
 
 LO 
 
 
 
 
 X 
 
 
 
 
 
 
 ^ 
 
 i\ 
 
 ^ 
 
 
 
 
 
 
 
 + 
 
 
 
 
 
 
 
 ^^^ 
 
 \ 
 
 
 
 <t- 
 
 
 
 
 cr 
 
 
 
 
 
 
 
 ^ 
 
 \ 
 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 
 \ 
 
 \\ 
 
 
 
 ro 
 
 
 
 
 h- 
 
 
 
 
 
 
 
 
 N^^ 
 
 
 
 
 
 
 
 C£ 
 S 
 
 
 
 
 
 
 
 
 
 . 
 
 
 CNJ 
 
 
 
 
 LiJ 
 
 — ^ 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 1— ( 
 1- 
 
 o 
 <x 
 
 UJ 
 C£ 
 
 
 
 
 
 
 
 
 
 i 
 
 \ 
 
 t— 1 L 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 CSJ 
 
 O 
 
 C£ 
 
 o 
 
 nCr. 21b 
 
 -28- 
 
-29- 
 
Simple calculations show that if the cutoff frequency of the damper 
 is to be around 12 mc an inductance of a few microhenries is required „ This is 
 best accomplished by the use of a core. An additional benefit results from 
 the RF damping properties of the core material. 
 
 Experiments were performed to study the effects of different core 
 materials^ turns, and shunt resistors (Figures l8, 20, 21a b). 
 
 Figure 22 showg the behavior of the final design: 2i^0 ohms, core 
 CF-lOl-Q-1 (Ferramic-General Ceramics Corporation, Keasbey, New Jersey), ten 
 turns (color code: red-blue). 
 
 For the 2N711 the damper beaomes already too large. If necessary a 
 300 ohm resistor in parallel with ten turns on CF-lOl-H (color code: green) 
 is recommended. However, it will not be possible to stabilize all circuits 
 in this way. 
 
 Evaluation Pulse Tests 
 
 In order to test the pulse response and effectiveness of the damper 
 two pulse tests were performed on intentionally long-wired circuits, 
 a) Series test (GF-^5011), 
 
 -5 
 
 TP No, 3 
 
 o 
 
 1 ^ TP , 
 ^•,7 K>. No, h 
 
 -30- 
 
Results are as shown: 
 
 Figure 24 All horizontal 
 scales 5 nsec/cm; traces are 
 identified along the 3 cm line 
 as TP No. 2^ TP No. 1^ 
 TP No. h, and TP No. 3. 
 
 b) Parallel test 
 
 Figure 25 
 
 3.3 K 
 
 TP No. 7 
 
 o 
 
i 
 
Results are as shown 
 
 Figure 26 All horizontal scale 
 5 nsec/cm; upper traces are 
 TP No. k through TP No. 8; lower 
 traces are TP No. 1 and TP No, 2 
 from top to bottom. 
 
 Machine Test 
 
 Forty-nine 2l+0 ohm/lO turn/Q-1 (red) dampers were installed in 
 Chassis Q-I3 of the new computer. It was known that several instabilities 
 existed in the chassis. After installation no oscillations were observed. 
 Since this chassis contains three levels of non-restoring logic it is felt that 
 the damper will work successfully in nearly all cases. However, if compensation 
 IS used in such a tree structure, stability can be assured only if all emitter 
 followers in the group are compensated, that is, all negative resistances must 
 be removed. 
 
 -32- 
 
and in the coefficients of the other terras. It may be verified that the 
 right hand member of equation (6,l8) is equal to the right hand member of 
 (6.15). This may be done by performing the indicated differentiations. 
 
 Thus we see that in the classical limits the gravitational stress 
 energy tensor E^^ introduced above leads to a conservation of energy equation 
 similar in form to that proposed by Bondi. However, the energy density and 
 the analogue of the Poynting vector, the quantities eJ and eJ differ in detail 
 from those he proposed. 
 
 -21-