1961 IRE TRANSACTIONS ON MILITARY ELECTRONICS 209 Power Dissipation in Microelectronic Transmission Circuits* JAMES D. MEINDLt, MEMBER, IRE Summary--The interrelationship of power dissipation, gain, pedance values, dynamic range, and efficiency may be stability, terminal impedance values, dynamic range and effici- convenienti investigated. ency is investigated for small-signal amplifiers in the middle y range of frequencies. Utilizing a novel circuit-design theory CIRCUIT ANALYSIS which treats a transistor along with its biasing resistors as a single entity, amplifier designs are derived which combine opti- In the fabrication and application of microelectronic mum ac performance and minimum dc power dissipation. The product of ac power gain and dc-to-ac efficiency is found to be circuits, it is appropriate to treat a generic circuit type as a useful figure of merit for microelectronic transmission circuits. an entity. Fig. 1 shows the schematic diagrams of the three amplifiers considered in this paper. Fig. 2 shows the ac INTRODUCTION equivalent circuit of the amplifier of Fig. 1 (a). The dotted C ONSIDERING the subject with all its ramifica- blocks enclose the two-port active networks treated as (t tions, power dissipation may well be the problem entities. On the basis of this two-port characterization, a of singular importance in microelectronics. Aside rather novel design theory directed toward small-signal from its broad influence on over-all equipment character- microelectronic amplifiers has been devised in order to istics' such as size, weight, reliability, and cost, power dis- pursue more effectively the goals of this investigation. In sipation is inherently related to many aspects of circuit essence the theory provides a means for optimizing the ac performance. To some extent the influence of dissipation performance of an amplifier-a transistor and its asso- on the performance of digital circuits has been clarified ciated biasing resistors-while minimizing its dc power by recent investigations.2-5 However, the corresponding dissipation. Specifically, the product of ac power gain and effects of dissipation in transmission circuits have received dc-to-ac efficiency is maximized. relatively little attention.6 The purpose of this paper is to It is convenient to present the design theory as a suc- report the results of a study of the effects of total circuit cession of enumerated steps: power dissipation on certain general properties of trans- 1) Anticipate the lower and upper operating tempera- mission circuits. tures Ty and T$,, respectively, of the circuit. Knowledge of In order to generate information of broad significance, a these limits is necessary in order to provide circuit designs careful choice of the generic circuit function to be ana- with adequate temperature stability. lyzed is necessary. Perhaps the most universal circuit 2) Select the transistor dc operating point at Ty (i.e., the function in military communications equipments is small- values of Icy and Vc,y) and T, (i.e., the values of Icx and signal amplification. Because the circuit configuration of a VCEX) Collectively, the two operating points should reflect small-signal amplifier varies considerably depending on a reasonable amount of dc drift, AIC 'C7-'Cy and which of it:s many properties are emphasized, further defi- AVCE-VCEX- VCEy, over the anticipated temperature nition of a circuit type is necessary. By concentrating on range Individually, an operating point should be selected the mid-band performance of a wide-band amplifier, the to accommodate the required ac collector voltage and cur- interrelationship of the commonly more critical amplifier rent amplitudes. properties--power dissipation, gain, stability, terminal im- 3) With the transistor at temperature T, and dc operat- ing point Icy and VCEY, measure the dc quantities IBy and VBEY and the ac quantities h11y, h12y, h21y, and h22y at any * Received by the PGMIL, April 6, 1961. mid-band frequency. Equivalent measurements should be t U. S. Army Signal Research and Development Laboratory, made at T5, Ic, and VCEx1. The need for these measure- Fort Monmouth, N.J. 'A. P. Stern, "Some general considerations of microelectronics," ments is obviated if equivalent information is available Proc. Natl. Elefctronics Coanf., vol. 16, pp. 194-198; October, 1960. from transistor data sheets. 'D. F. Allison, et al., "KMC Planar Transistors in Microwatt Logic Circuitry," Solid-State Circuits Conf., Philadelphia, Pa.; Feb- 4-a) Write two sets of Kirchhoff equations describing uary, 1961. the dc behavior of the circuit, one at Tx and one at Ty. 'J M. Early, "Speed, Power and Component Density in Multi- element High-Speed Logic Systems," Solid-State Circuits Conf. This yields a set of four simultaneous equations6 contain- Philadelphia, Pa.; February, 1960.inthtrnitrdcurnsadvlge IyVCYI,, 4H. Raillard and J. J. Suran, "Speed vs circuit power dissia *n th rnitrd urnsadvlae I,,Vs,'x tion in flip flops," PRoc. IRE, vol. 47, (Correspondence), pp. 96-97- and so forth] and the dc stabilization network elements January, 1959. [R1, R2, R3, RC~, and Vcc for Fig. l (a)] . J. J. Suran. "Circuit considerations relating to microelectronics," b rt w eso ichofeutosdsrbn PROC. IRE, vol. 49, pp. 420-426; February, 1961.b)WtewossofKrhf quinsdciig 6J. D. Meindl and 0. Pitzalis, "Optimum stabilization networks the ac behavior of the circuit, one at Tx and one at Tg. for functional electronic blocks," Proc. Nati. Electronics Conf., vol.Thseqaincotntecrntacurnsadvl- 16, pp. 576-590; October, 1960.Ths qaon otnthcrutacuresadvl-
Transcript
1961 IRE TRANSACTIONS ON MILITARY ELECTRONICS 209
Power Dissipation in Microelectronic Transmission Circuits*JAMES D. MEINDLt, MEMBER, IRE
Summary--The interrelationship of power dissipation, gain, pedance values, dynamic range, and efficiency may bestability, terminal impedance values, dynamic range and effici- convenienti investigated.ency is investigated for small-signal amplifiers in the middle yrange of frequencies. Utilizing a novel circuit-design theory CIRCUIT ANALYSISwhich treats a transistor along with its biasing resistors as a
single entity, amplifier designs are derived which combine opti- In the fabrication and application of microelectronicmum ac performance and minimum dc power dissipation. Theproduct of ac power gain and dc-to-ac efficiency is found to be circuits, it is appropriate to treat a generic circuit type asa useful figure of merit for microelectronic transmission circuits. an entity. Fig. 1 shows the schematic diagrams of the three
amplifiers considered in this paper. Fig. 2 shows the ac
INTRODUCTION equivalent circuit of the amplifier of Fig. 1(a). The dotted
C ONSIDERING the subject with all its ramifica- blocks enclose the two-port active networks treated as(ttions, power dissipation may well be the problem entities. On the basis of this two-port characterization, a
of singular importance in microelectronics. Aside rather novel design theory directed toward small-signalfrom its broad influence on over-all equipment character- microelectronic amplifiers has been devised in order toistics' such as size, weight, reliability, and cost, power dis- pursue more effectively the goals of this investigation. Insipation is inherently related to many aspects of circuit essence the theory provides a means for optimizing the acperformance. To some extent the influence of dissipation performance of an amplifier-a transistor and its asso-on the performance of digital circuits has been clarified ciated biasing resistors-while minimizing its dc powerby recent investigations.2-5 However, the corresponding dissipation. Specifically, the product of ac power gain andeffects of dissipation in transmission circuits have received dc-to-ac efficiency is maximized.relatively little attention.6 The purpose of this paper is to It is convenient to present the design theory as a suc-report the results of a study of the effects of total circuit cession of enumerated steps:power dissipation on certain general properties of trans- 1) Anticipate the lower and upper operating tempera-mission circuits. tures Ty and T$,, respectively, of the circuit. Knowledge of
In order to generate information of broad significance, a these limits is necessary in order to provide circuit designscareful choice of the generic circuit function to be ana- with adequate temperature stability.lyzed is necessary. Perhaps the most universal circuit 2) Select the transistor dc operating point at Ty (i.e., thefunction in military communications equipments is small- values of Icy and Vc,y) and T, (i.e., the values of Icx andsignal amplification. Because the circuit configuration of a VCEX) Collectively, the two operating points should reflectsmall-signal amplifier varies considerably depending on a reasonable amount of dc drift, AIC 'C7-'Cy andwhich of it:s many properties are emphasized, further defi- AVCE-VCEX- VCEy, over the anticipated temperaturenition of a circuit type is necessary. By concentrating on range Individually, an operating point should be selectedthe mid-band performance of a wide-band amplifier, the to accommodate the required ac collector voltage and cur-
interrelationship of the commonly more critical amplifier rent amplitudes.properties--power dissipation, gain, stability, terminal im- 3) With the transistor at temperature T, and dc operat-
ing point Icy and VCEY, measure the dc quantities IBy andVBEY and the ac quantities h11y, h12y, h21y, and h22y at any
* Received by the PGMIL, April 6, 1961. mid-band frequency. Equivalent measurements should bet U. S. Army Signal Research and Development Laboratory, made at T5, Ic, and VCEx1. The need for these measure-
Fort Monmouth, N.J.'A. P. Stern, "Some general considerations of microelectronics," ments is obviated if equivalent information is available
Proc. Natl. Elefctronics Coanf., vol. 16, pp. 194-198; October, 1960. from transistor data sheets.'D. F. Allison, et al., "KMC Planar Transistors in Microwatt
Logic Circuitry," Solid-State Circuits Conf., Philadelphia, Pa.; Feb- 4-a) Write two sets of Kirchhoff equations describinguary, 1961. the dc behavior of the circuit, one at Tx and one at Ty.'J M. Early, "Speed, Power and Component Density in Multi-
element High-Speed Logic Systems," Solid-State Circuits Conf. This yields a set of four simultaneous equations6 contain-Philadelphia, Pa.; February, 1960.inthtrnitrdcurnsadvlge IyVCYI,,
4H. Raillard and J. J. Suran, "Speed vs circuit power dissia *n th rnitrd urnsadvlae I,,Vs,'xtion in flip flops," PRoc. IRE, vol. 47, (Correspondence), pp. 96-97- and so forth] and the dc stabilization network elementsJanuary, 1959. [R1, R2, R3, RC~, and Vcc for Fig. l(a)] .
J. J. Suran. "Circuit considerations relating to microelectronics," b rt w eso ichofeutosdsrbnPROC. IRE, vol. 49, pp. 420-426; February, 1961.b)WtewossofKrhf quinsdciig
6J. D. Meindl and 0. Pitzalis, "Optimum stabilization networks the ac behavior of the circuit, one at Tx and one at Tg.for functional electronic blocks," Proc. Nati. Electronics Conf., vol.Thseqaincotntecrntacurnsadvl-16, pp. 576-590; October, 1960.Ths qaon otnthcrutacuresadvl-
210 IRE TRANSACTIONS ON MILITARY ELECTRONICS July
tVCC ___tvcc
eq~~~~~~~~~~~~~~~~~~~~~~~~~~~~R
r r ---,| R3 *~~~~~~Rc l IRiIC IC I
VCE VCfVE
RI RR RLl lB
RI-R RI-R~~~~~R-
77P77 77777
(c)
Fig. 1-Schematic diagrams of circuits with dc currents and voltagesindicated. (a) Circuit 1. (b) Circuit 2. (c) Circuit 3.
eIR3 Re V R
IC-
LH 21 H-22Fig. 2-AC equivalent circuit for Fig. 1(a).
1961 Meindi: Power Dissipation in Microelectronic Transmission Circuits 211
ages, the transistor small-signal h parameters, and the b) Since the transistor h parameters are known from 3stabilization network elements. and the stabilization network elements from 5-a, the sets
5-a) Since the transistor dc currents and voltages are of equations in 4-b may be solved for the H parametersknown frorn 2 and 3, the set of simultaneous equations of of the circuit at both T, and T,. From Fig. 2,4-a may be solved in terms of these quantities and any oneof the five stabilization network elements (e.g., R1). The V, = Hili-+ H12V2tabulated solutions for the circuits of Fig. 1 are given inTables I and II. i2 H21il + H22V2 (1)
may be used to define the H parameters. Their values are the input impedancegiven in Table III. For practical computation the approxi- Hi, + AIHRLmate expressions may be used. R= H11 (3)
6-a) Select an allowable value of R16 and compute the 1 + H22RLvalues of the remaining stabilization network elements and the output impedanceusing the equations of Table II. Rg + Hi 1
b) From the results of 6-a and the equations of Table Ro = -- - Rc (4)III, the H parameters may be used in familiar formulas7 8 H22R9 + AH H92to give the power gain of the circuits within the dotted blocks of Fig. 1. The
H212RL indicated approximations are valid for AH-.HniH22(1 + H= RL)(Hll + AHRL) which requires 1/Rc>>h22.
7) The value of R1 selected in 6-a should be chosen toH212 RL achieve small total dc power dissipationi in the circuit at
Hi, (1 + RL/Rc)2 the upper temperature (i.e., P,) and large ac power out-
TABLE IIIAC CIRCUIT PARAMETERS
Circuit 1 Circuit 2
The exact values of the functional component H parameters are
r (1 -h12)(121) R R2,2 + (-11)2) (I +1_21_ R,_ +R23
H1 _ 1 + h22Ret H = +R+ 112R + + 1 + h R2 RRJA A
F[1 - A-1 112)R/122e] R (1-112)h9Re2 (1 - h 12)(I A __- _e]L#1)1 A- =h22Re ____ R 1 A1122Re)RR L 1+_- 22RejR
( 1 11222 A 1 F / (1h-212)(1 A 121) 1+(1-h2)(I +A- R12h22A- Re3 11111A . Re A-.1, 2
2 Rc 1A-iRe R3 (1 +h22Re) R e R1 1 + h22R(#1) H22=----- A-----_ ___ __________ _____
1[1Ah A (1 - 12) (1+/21) RRA- A+R[( - 1h122+ -.A-e Hhi, + R, +- L- A-R22H2 A- A-R+ h 22RR23 (1A 1 22Re Rc+ e)R2R3(122 _ ( +2) + - A Re R23
(1 - h112)(1 A 112) __R2RA1A- . Re A R2[ and R23 = _]--1 + h22Rean R2 A Rl2
The approximate values of the above quantities are
1961 Meindl: Power Dissipation in Microelectronic Transmission Circuits 213
put (i.e., PLX). That is, the dc-to-ac efficiency 'q,=PL,1P, should be maximized. To obtain qi,, the equa- 35 \ \ 36tioni for the AC load line on the DC collector character- P,(mw)istics planie is approximately93'
Permitting the output signal swing to extend to either axis !of the collector characteristics fixes the output voltage |\ 21amplitude as the smaller of the two quantities 15229
Ic7~~~ ~ ~ ~ ~ ~ ~ ~ ' '-. .C= -16
Iand VCEx- 10 -17 231/Rc + 1/RL
5Thus, the ac load power is
Icx 2 901__ 1 1_ ,0rlI0,_ __1 _ _1 11 11
PLx 112RL)\1 XRc + 1/RL7 R1 (Fig. 3-Total circuit power dissipation at 100WC (P.) for Fig. l(a)
or vs external emitter resistance (Ri) at various dc stabilities.
PLX = (1t2RL)(VCEx)2. (6)
In additioni to maximizing 7x, R1 should be selected to TABLE IVmaximiize the power gain (G,). A practical compromise DC STABILITY INDEXfor approaching both objectives is to maximize the gain- Stability*efficiency product (Gx7x) of the circuit. Identi- 1c,(ma) Icx(ma) VCEx(V) VCEX(V) AMc(ma) AVCE(V)The results of utilizing the foregoing design theory to fication
investigate the amplifier properties previously listed are Nu_mbernow discussed. 1 0.30 2.0 8.00 3.00 1.7 5.0
4 6.00 4.00 2.0The results presented are based on the behavior of a 5.50 4.50 1.06 5.25 4.75 0.5
typical small signal diffused siliconi transistor. The tem-perature range of interest is Ty = --30°C < T < 8 7.00 3.00 4.0100°C = T. In order to provide sufficient data to gener- 9 6.50 3.50 3.0ate a meaningful group of curves describing circuit be- 11 5.50 4.50 1 .0havior, computations were performed for the set of dc 12 5.25 4.75 0.5operating points given in Table IV. In this table, for ex- 13 0.70 1.30 8.00 3.00 0.6 5.0ample, dc stability identification No. 21 indicates that the 14 7.00 3.00 4.0
15 6.50 3.50 3.0limiting transistor dc operating points are Icy - 0.80 ma, 16 |600 4.00 2.0VCEY = 6.50 v and Icz = 1.20 ma, VCEZ = 3.50 v. From 17 5.50 4.50 1.0measurements made at the limiting temperatures and dc 18 5.25 4.75 0.5operating points for case 21, IBV 59.7,ua, VBE2= 20 0.80 1.20 7.00 3.00 4 .00.759 v and IBm = 38.2sta, VBEZ 0.494 v describe the (dc 21 6.50 3.50 3.0behavior cof the transistor. The corresponding ac param- 22 6.00 4.00 2.0eters are hi,, = 1260 ohms, h12,= 3.6 X 10-4, h21 = 22.5, 24 5.25 4.75 0.5h22y = 12.5 X 10-6 (ohms)-' and h1i, = 2070 ohms, h12 =
1.1 X 10-4, h2= 35.4, h-22 48 X 10-6 (ohms)-' at a 25 0.90 1.10 8.00 3.00 0 4.250frequency of 1000 cps. The stabilization network resistors 27 6.50 3.50 3.0
28 6.00 4.00 2 .0and powei- supply are assumed independent of tempera- 29 5.50 4.50 1.0ture. 30 l 5.25 4.75 L 0.5
Based on the experimental data referred to in the pre- 31 0.95 1 .05 8.00 3 .00 0. 1 5.0ceding par-agraph and the dc design equations of Tables 32 7.00 3.500 4.0I and II, Fig. 3 illustrates the power dissipation at T, re- 34 6.00 4.00 2.0quired to maintain various fixed dc operating point sta- 36 5.50 4.750 l 1 .0bilities for the circuit of :Fig. 1(a). The curves are num -___________________________
bered to correspond with Table IV. as will be the case with * Note that the stability identification number is merely an identi-fying symbol and does not in itself indicate the degree of stability of acirculit.
9A. W. LO, et al., "Transistor Electronics," Prentice-Hall, Inc.,Englewood Cliffs, N.J.; 1955.
214 IRE TRANSACTIONS ON MILITARY ELECTRONICS July
forthcoming figures. Considering the family of curves of 35rFig. 3, power dissipation (PF) increases with increasingcurrent stability (smaller LAIc) and decreasing voltage sta- 30' G7(db) - - -bility (larger zAVCE). However, if AIc becomes excessivelylarge, P1 does not continue to decrease but begins increas-ing since Ic is then forced to drift through an over-ex- / ' \ 2 \tended range.6 Curves 4 and 5 on the left of Fig. 3 illus-trate this. Furthermore, for a fixed dc stability Px may 20vary significantly depending on the circuit design. As in- /dicated, for a fixed dc stability, designs with relatively I \large R, require smaller power dissipation. Similar curves ' 22329for the circuit of Fig. l(b) show the minimum values of 2 36P1 for a given stability are about 2 per cent to 3 per cent 10 I-
400 1000 10QOOOsmaller compared with Fig. 1(a) with less dependence on RI (a)R1. For the circuit of Fig. 1(c), Fr is typically 10 per centRi. For th.irutfFi.cPitpcal ercn Fig. 4-Amplifier ac power gain at 100'C (G.) for Fig. 1 (a) withto 50 per cent smaller compared with Fig. 1(a), and in- image-matched terminations vs external emitter resistance (Ri)creases slightly with increasing R,. According to Fig. 3, at various dc stabilities.PF, may be minimized by choosing an intermediate currentstability and a tight voltage stability such as case 17 (see current gain (h2l) with temperature is largely counter-Table IV), and designing the circuit for a relatively large acted in most circuits by the increase of the input imped-value of R1. The effect of this effort to minimize Px on ac ance (h,,) with temperature, which causes more signalperformance is considered below. current to be shunted to ground through the external base
In calculating ac performance, the external emitter re- resistors. For the circuit of Fig. 1(b), the G, maximasistance (RK) is assumed to be completely bypassed (i.e., typically run several decibels less than for Fig. 1(a) andRe = 0), which is a special case of the general set of equa- show somewhat better temperature stability due to the neg-tions of Table III. Three separate sets of terminal condi- ative ac voltage feedback through R3. For Fig. 1(c) thetions are considered. The first condition assumes that the G. maxima are essentially the same as for Fig. 1(a). Fromamplifier terminal impedances are image matched by the Figs. 3 and 4 it is obvious that minimum dc power dissi-source and the load (i.e., Rg - Ri and RL - Ro). The pation and maximum ac power gain cannot be achievedsecond condition assumes that the amplifier is an iterative simultaneously. Before proposing a solution to the dissipa-stage (i.e., Rg = Ro and RL= Ri). The third condition tion vs gain problem, several other points are considered.assumes that Rg- 1000Q and that Rc is the total load on The definition of a circuit power gain is meaninglessthe amplifier. In this case proper adjustments must be unless ac stability or the capacity to avoid breaking intomade in the formulas of Table III (1/Rc 0O here) and oscillation exists. Since amplifier behavior is under inves-in (2) through (6) [RL- RC here] to achieve meaning- tigation only for the middle range of frequencies, allful results. In general the discussion is limited to the case equivalent circuit elements are real, and unconditional acof image-matched terminations, except for instances where stability prevails.the results are radically different from the two remaining The variation of amplifier ac input impedance at thecases. upper temperature (Ri,) for the circuit of Fig. 1 (a) with
Based on measurement data, the equations of Table III, image-matched terminations is shown in Fig. 5. It is evi-and (2), Fig. 4 shows the ac power gain at T. for the cir- dent that Rix is virtually independent of dc stability butcuit of Fig. 1(a) with image-matched terminations. Power that it increases rapidly with increasing R1 for a given dcgain (G,) increases with increasing current stability stability, which is due to larger R2 and R3. Rix approaches(smaller AIJ) and decreasing voltage stability (larger the approximate value h11x as R2 and R3 or R1 becomesAVCE), primarily due to accompanying increases in Rc relatively large for a fixed dc stability. Typically, Ri isRL. This trend will reverse itself, of course, when 1/Rc + smaller and more sensitive to load variations for the cir-1/IRL equals and then becomes smaller than h92.x. For a cuit of Fig. 1(b) than in the circuits of Fig. 1 (a) and (c),fixed dc stability there is a noticeable maximum in a G, whose input impedances behave quite similarly. Since Rifunction. The initial low values of C1 are due to excessive is composed essentially of temperature-sensitive hl1 ininput signal loss in the small R2 and R3 which accompany parallel with temperature-insensitive K2 and K3, the tem-small R1. The final low values of C1 are due to the small perature stability of RX improves for small R2 and R3 andK0 which accompany large R1. The temperature variation deteriorates for large R9 and R3. Typical changes in Kiof the power gain C may not be monotonic and depends range up to 50 per cent for the cases considered in thison dc stability as well as the circuit design. Howvever, it investigation.remains within reasonable limits (-0.20 db to +2.00 db) The variation of amplifier ac output impedance at thefor otherwise acceptable circuit designs. This stability is upper temperature (R01) for the circuit of Fig. 1(a) isdue partly to the fact that the increase of the transistor shown in Fig. 6. For typical circuits K0S RC. Therefore
1961 Meindl: Power Dissipation in Microelectronic Transmission Circuits 215
400z 1000 Rlo,ooo' 0(a46hlaemthe emntsv etra mte e
400 lowmoFig. 5-Amplifier ac input impedance at 1000C (Rix) for Fig. 1 (a) RI (-'-
with imnage-matched terminations vs external emitter resistance Fig. 7-Amplifier dc-to-ac efficiency at 1000C (mi.) for Fig. 1(a)(R1) at various dc stabilities. with image-matched terminations vs external emitter resistacce
temperature. Fig. 8-Amplifier gain-efficiency product at 100TC(Gxia x) feor Fig.400 1000 Iooo 1(a) with image-matched terminations vs external emitter re-
RI Fig. l(b) taithcrusoFgla ad() onsistance (Ri) at various dc stabilities.
Fig. 6-Amplifier ac Output impedance at100v C (R w) for Fig. 1(a)with image-matched terminations vs external emitter resistance
(R1) at variousdc stabilities.point, Ic. and VCE. Greater values of Ic and VCE permit a
larger dynamic range. Operating point stability is neces-sary to maintain a stable dynamic range. For a given dc
Ro0, is very sensitive to the dc design of the circuit. Pri- stability the maximum load power is derived for circuitmanily, increasing aAVCeor decreasing Alc permits larger designs with Ri somewhat smaller than it is for maximumRc values. SinceRd is insensitive to temperature, Ro typi- power gain.cally varies less than 10 per cent for -30 < T < 1000C. The dc-to-ac efficiency of an amplifier cx PLX/1Px in-However, if Re is moved outside the dotted blocks of Figy. dicates the degree of utilization of itS potential dynamic
216 IRE TRANSACTIONS ON MILITARY ELECTRONICS July
1) The continuing increase in P, with increasing ACVE, CONCLUSIONSas demonstrated by the reversal in curves 29, 28, and 27.^n ~~The relationships between de powrer dissipation and ac
power gain, both dc and ac stability, ac terminal impedance2) The decreaseinhPe brought about when 1/Rc + values, dynamic range, and dc-to-ac efficiency have been
l/R-eusa th bem smset forth for the nmost common small signal transmissionThe c s ocircuits. The results indicate that by careful design it is
Tpossble to achieve a small signal amplifier wtih both pre-manner with regard to efficiency. The maximum per cent miefficiency achieved for Fig. 1 (a) is about 1 per cent smaller accm ped tili a novel designthor. whichthan for Fig. 1(c) and about 1 per cent larger than for a
treats a transistor and its biasing resistors as a signal en-titv in maximizing the gain-efficiency product of the am-
On the basis of the results discussed up to this point, it.' plifier. This product, which interlocks the demands forappears that a useful figure of merit for comparing micro- ellent ac anddctdeigs isueflo fge ofmerit for
electronic small signal amplifier designs is the product of excellent anc ldesigns, S a useful figure ofr ers t forrZ . . . ~~~~~~microelectronic small signal amplifiers. Perhaps the mo-st
power gain and efficiency (G,,,r,,,). From a relative point vital improvements still necessary for enhanced amplifierof view a maximum value for ( requires a large acpoferv aie amaximum vynalucranefo oreqaclaerg ac performance are improved temperature stability of the acpower gain, a large dynamic range or ac powver output
' . . p~~~~roerties, power gain, and input impedance. Also, the(PLX), and a small dc power dissipation (P,). Fig. 8 pp . Ashows the gain-efficiency product for the circuit of Fig.
effects of pore dissipation on sensitivity, bandwidth, andnoise figure are of interest. Additional investigation of
1(a) with image-matched terminations. The optimum am- ths rbls sncsaythese probelms is necessarv-.plifier design represented in this figure is the maximumpoint on the curve for dc stability No. 21. The circuit de- ACKNOWLEDGMENTsign is R1 =1320Q, R2 = 13700Q, R3 = 54200Q, R, The author would like to thank PFC. 0. Pitzalls for6250Q, and V0= 12.5 v. The performance data is Px - performing the measurements necessary for this paper.17.5 mw, G2 = 28 db, Ri. = 1730Q, Ro= 48303Q, and The assistance of Mrs. M. Tate with the computations is
-~X 6.28 per cent. gratefully acknowledged.
A Thermal Design Approach for Solid-State EncapsulatedHigh-Density Computer Circuits*
A. E. ROSENBERGt ASSOCIATE MEMBER IRE, AND T . C. TAYLOR+.
Summary-This paper considers the thermal problems asso- INTRODUCTIONciated with the design of high component-density encapsulatedcircuits, constructed with small solid-state components. The posIHE practlce of plastic encapsulation of circuits com-thermal resistance to the dissipation of component-generated A posed of small components and their associated wir-heat is shown to consist of that of the encapsulating medium, ing has achieved wide acceptance recently. By theplus that of the external circuit cooling process. Because the use of this practice, a circuit, or inulticomponent portionexternal cooling becomes more difficult as the size of an en- thereof, is concentrated into a single, component-like struc-capsulated circuit is reduced, a method of constructing such .circuits is proposed which minimizes the thermal resistance due ture. The use of such structures in building more complexto the encapsulating medium. This construction makes a large circuits offers many possible advantages, including simpli-fraction of the allowable component temperature rise available fied circuit testing and maintenance, simplified chassis andfor use in the external heat dissipation process by providing hardware design, saving of space, improved structural re-high thermal conductance paths for the transfer of heat from .liabi.ithe surfaces of the components to one surface of the circuit ty an imroe fucioa reiblt in cetiestructure. Analytical models are developed for the most im- spects. Wi1th the increasing availability and use of micro-portant heat transfer processes in the proposed circuit structure. ininiatulre components, it seems likely that circulit encapsu-The equations based on these models are arranged in a form lation techniques, or their equivalents, will be used moresuitable for design use, and example designs are presented. widely than heretofore. This conclusion is derived from
the fact that it is necessary to accomplish the hookup wir-* Received by the PGMJL, April 12, 1961. ing and structural fabrication of a circulit in an amount oft Epsco, Inc., Cambridge, Mass.I Raytheon Co., Semiconductor Div., Newton, Mass. space xvhich iS in keeping with the component dimensions,
