188 IEEE JOURNAL OF sOLID-STATE CIRCLilTS,VOL. SC-7, NO. 2, APRIL 1972

Thus a simple, yet sophisticated integrated-circuit de-sign has been described and s~own to meet the designgoals, The effective current gain from input to output istypically 2.5 x 106 illustrating the control of medium-sizecf currents with rather low-level signals. Applicationsfor whic~ this circuit is particularly well-suited aretimers of long duration with relatively small ~apacitors;high-impedance circuits that would be loaded down withstandard-type circuits; lamp, relay, or solenoid driversup to 100 mA; slowly varyjpg or noisy input signals

where a clean output signal is desirecl (i.e., TTL inter-face circuit to preven~ false triggering) ; squaring cir-cuits; camera exposure controls.

REFERENCES

[11 H. C. Lin, T. B. Tan, G. Y. Chmg, B. Van Der Leest, andN. Formigoni, ‘[Lateral complementary transistor structurefor the simultaneous fabrication of functional blocks,” Proc.IEEE, vol. 52, pp. 1491-1495,Dec. 1964.

[21 A. H. Hoffal$ and R. D. Thornton, “Limitations of tran-sistor de amplifiers,” Proc. IEEE, vol. 52. pp. 179-184,Feb.1964.

Design Analysis of a Gain-Stabilized Transistor Amplifierat Elevated Temperatures Using Passive Elements

RAM S. SHARMA AND 1<. 1{. S. JA~WAL

Abstract—The decrease of the emitter-base and collector-basejunction voltages of a trqpsistor with temperature and the effectof the external cirguit resistances on these voltages are studiedtheoretically and experirn’entally.The influence of the shifting ofthe op~rating poipt with temperature on the gain is discussed. Anew design approach based on V~~ and Vc~ as the stability param-eters is giveh using only passive components. It is found that thisapproach definitely lea’ds to better gain stability with temperaturethan other design techn~ues using NTC elements [1]-[4]. Al-

though work in the early stages was concentrated on germaniumtrarisistors ( – 15 to + 115”C), already some encouraging resultshave also been attained in the study of silicon transistors.

I. INTRODUCTION

T

RANS1~TORS are very much sensitive to varia-

tions in ambient temperature. In the case of the

junction transistor, the most important tempera-

ture-sensitive parameters are the reverse leakage current

(collector’ cutoff current) 1,,o, which flows when the

emitter circuit is open, the emitter and collector currents

lE and l., respectively, current amplification factor ~,

and the emitter–base and collector–base voltages VE~and Vc~, respectively. The reverse leakage current ICBO

is roughly independent of the collector–base voltage and

increases exponentially with temperature doubling for

every 10 or 11“C. If the reverse leakage current changes

by a certain ainount, the entire family of output char-

acteristic curves of the transistor shifts by that amount

parallel to the VCDaxis, whereas the values of the param-

eter IB remain unchanged. This fact is responsible for

making lCDOa parameter of primary concern in transistor

biaiihg [1]. As the ac characteristic values do not change

Manuscript received September 14, 1970; revised April 12,,1971.The authors are with the Department of Physics, University of

K@&ir, Srinags.r,India.

effectively with the change of Ic~o, the emitter current IEis selected for characterization of the operating point and

the design of a stabilized transistor amplifier is based on

the stabilization of lE and VB~ [2], or 1~ and l’c~ [3].

Various other combinations have been tried such as the

stabilization of collector current Ic, against the variationsof lCDO, VE~, and a [4]. Temperature-sensitive resistanceslike thermistors, sensistors, diodes, etc., have been

inserted into the bias circuit of a transistor, so as to pro-duce compensation that completely annuls the lC varia-tions against varying temperatures. The complete dis-cussion of all these approaches is beyond the scope ofthis paper. A design procedure is presented here hasedon the stabilization of emitter–base and collector–basevoltages using only passive elements. The purpose of thispaper is to develop gain-stabilized transistor amplifierswith an extended temperature range between —15 to+ 115°C for germanium transistors without using anyactive or compensating elements. A study of the varia-tions of Vn~ and Vc~ with temperature and their cle-pendence on the external circuit components is conductedto give thorough under~tanding of the choice of thesetwo parameters. The early ~mt of this work was con-centrated mainly on the germanium transistors ( —15 to+1 l~°C), but this has n9w been switched over to thestudy of silicon transistors.

II. VARIATION OF JUNCTION VOLTAGES WITH TEMPERATURE

The voltage across the emitter–base electrode with this

junction forward biased VD~ has a negative temperature

coefficient, i.e., it decreases as the temperature rises. The

precise value of the rate of fall of V~~ depencls on the

nature of the material and its doping. The collector–base\,oltage ~cll, with this junction reverse biased also has a

SHARMA AND JAMWAL : GAIN-STABILIZED TRANSISTOR AMPLIFIER 189

negative temp~rature coefficient. It is observed that therate of fall of t$ese voltages k more in magnitude athigher temperatures than at room temperatures. Therelation developed by Schaffner arid Shea [5] is notadequate to explain these phenomena. Hoffait andThornton [6] derived the relation

(1)

where k, r, and q are independent of temperature, Vgo is

the extrapolated energy gap at T = O K. This relationdoes not seem to satisfy the above bbservations. A1s6 therate of fall of the voltage is independent of the ap~lieclvoltage. The emitter and the collector currents incteasewith temperature, as these voltages fall. A model thatexplains successfully these observations is outlined below.

The diffusion voltage (or tlie height of the potentialbarrier) V~ at temperature T of a p-n junction is repre-sented through the well-knowfi expression

(2)

where CP and u. are the co~ductivities of the p- and n-

type semiconductors, pfl and p. are the nobilities of the

holes and the electrons, respectively, ni is the intrinsic

carrier concentration, k the Boltzmanh’s constant, and q

the electronic charge. If pi is the hole density in thevalence band of the p-type semiconductor then UP =

PP q~p. similarly V. = n. q~~ where n. is the electrondensity in the conduction band of an n-type semicon-ductor. Expression (2) reduces to

(3)

The intrinsic carrier concentration ni increases wi~h tem-perature resulting in a decrease of V~. At a temperaturecorresponding to

ppn. = n,2 (4)

the diffusion voltage reduces to zero and the two typesof semiconductors behave as a single piece of intrinsicsemiconductor. Equation (4) indicates that a heavilydoped silicon device (diode or transistor) should have abetter temperature response.

Consider now the emitter-base junction under an ap-plied forward dc bias El with open collector–base junc-tion. The behavior of this junction against temperaturevariations can be easily understood by assuming athermal voltage generator at the junction with voltageequal to

(5)

where VDT is a constant independent of temperature. Itsvalue is equal to the diffusion voltage at room tempera-ture, Thus the voltage of this generator increases with

temperature, to a maximum value of ;VD~.The equivalentcircuit is given in Fig. 1, and a decrease in the voltageacross the junction VEB accompanied with an increase

of the circuit current with increase in temperature is

evident. The rate of change of this voltage is given by

dv,. _ A(~, – V,b) A VDB , k AT in p~h./rt.2 (6)

dT AT—=—=- AT q AT

where V,gE is the diffusion voltage of emitter–base, ~unc-tion. It is observed that if the collector–base junction isalso biased, a part of the reverse leakage current finds apath across the emitter–base junction, and the rate offall of voltage across tlie emitter–base junction is en-hanced.

Consider now the collector-base junction with appliedreverse dc bias voltage E2, At high temperatures thermalexcitation will takk place resulting in the generation ofnew holes and electrons. These carriers constitute a cur-rent that is attributed to the assumed th:ermal voltagegenerator at the junction. These tlkrmally generatedcarriers are drifted away by the external source Ez. Thedirection of this current and hence, the polarity of thethermal generato~ is governed by the polarity of the ex-ternal source. Thus the polarity of the thermal generatorrevefses in the case of the backward-biased junction. Thedeciease of the voltage V~~ across the junction along

with the increase of the collector current follows from

the equivalent circuit of the junction given in Fig. 2.

Wh?m a transistor is heated, both the junctions lose

their diode properties at a rate given by the decrease

of their corresponding diffusion voltages with tempera-

ture. The external voltage El applied across the forward-biased junctioh is usually small compared to V~~. HenceVBB will be reduced to zero as the temperature rises orevefi reverses its sign. The reverse-bias voltage Ez isnormally very large compared to the diffusion voltageof the collector–base junction V~c. But if the externalapplied voltage Ez is of the order of oi less than VDC,then VCB will reduce to zero or reverse its polarity asthe temperature rises.

111. EFFECT OF EXTERNAL COMPONENTS ON VARIATION

OF JUNCTION VOLTAGES

The exteimal circuit components (i.e., resistances) haveinfluence on the rate of decrease of the junction voltages.As the temperature rises, the circuit current increasesand hence the voltages across these resistances increase,with the result that the rate of decrease of the voltagesacross the junction is enhanced. Also the magnitude ofthe voltage across a junction depends upon the values ofthe external components. The experimentally obtainedresults clarifying the above statements are given in Figs.4-6 for the common-emitter two-battery configuration ofFig. 3. Fig. 4 gives the variations of V~~ and VCBwith

190 IEEE JOURNAL OF SOLID-STATE CIRCUITS,APRIL 1972

IV. CHOICE OF STABILITY PARAMETERSEMITTER 8RSE

b,n

Fig, 1. Equivalent circuit of forward-biased emitter–base junc-tion.

COLLECTOR BRSE

i=ln11

I

I

Fig. 2. Equivalent circuit of reverse-biased collector–base junc-tion.

*Fig. 3. Two-battery emitter-bias transistor amplifier.

temperature for different values of RI, keeping Rz andRL constant. For a high value of l’c~, RI must be small,but this results in a decrease of applied forward voltageV~~. Fig. 5 represents the variations of these two volt-ages with temperature for different values of Rz withfixed RI and RL. A low Rz leads to high values of VEBand Vc~ sitnultaneously. An ideal value of Rz wouldnaturally be zero, but that is undesirable because itwould short circuit the impressed signal to be amplified:Fig. 6 is a representation of the variations of VB~ and

Vc~ with temperature for different loads RL, with fixedvalues of other external components. A high initial valueof VCBis achieved with a. low value of load but then V~Bis reduced. It should be noted from these curves that the

larger the value of the initial voltage, the higher is the

temperature at which it is reduced to zero.

The operating point is determined by the voltagesacross the junctions, the external resistances, and thetransistor characteristics. Since the effective voltagesacross the junctions and the transistor characteristics arechanging with temperature, the operating point usuallyvaries for a given design. To study the effect of the shiftof the operating point on the gain of the transistor ampli-fier the current–voltage characteristics of the reverse-biased collector–base junction and the other junctionforward biased is plotted in Fig. 7 at various tempera-tures for an ac 125 (BEL) dioy junction germaniumtransistor. For a. load RL = 1 k~ and battery voltageE2 = –6.0 V at a temperature of dlOC the load line isAA’ and the operating point is Q1. Since this point liesin the linear part of the curve there is no distortion of thesignal. Suppose that the temperature is varied from i%0to 62°, keeping the current Ic constant. The new operat-ing point will be Q’l. Severe clipping will take place andas a result the gain of the amplifier is reduced. It shouldbe noted here that the collector current can be keptconstant only at the cost of the voltage across the j unc-tion. The voltage across the junction will almost be re-duced to zero, Let us now take the case where there isno restriction on the collector current. Across thejunction the effective battery voltage in the circuit is(.?32– V’,,). The current will be determined by (E2 +V’~~). v’t~ is the effective generator voltage with forward-biased emitter-base junction. The load line will be BB’where B’ is the point corresponding to current (E2 +V’,,) /R, The operating point will be Q“l. At this pointslight clipping can be expected. The gain may also fallslightly, but it will be definitely much better than in thefirst case with Ic = constant, Note that if the load RLis reduced to a value less than 1 k~, then the operating

point will shift from Q“l to some position Q’”, in the

linear part of the curve resulting in a still reduced clip-

ping and a better gain stability. A lower value of load

results in a smaller rate of fall of VCDwith temperature(see also Fig. 6). Thus for the design of a gain-stabilizedamplifier, it is necessary to lay stress on the minimiza-tiol~ of the rate of fall of the collector–base voltage withtemperature and hence VGBshotild be taken as stability

parameter instead of l..

Let us consider the current–voltage characteristics of

the emitter–base junction biased in the forward direction,

with the other junction reverse biased. This is shown in

Fig. 8 at various temperatures. For the ac 125 (BEL)

alloy junction transistor, A is the point on the char-acteristics corresponding to zero external forward-biasvoltage. The current flowing is the thermal current aswell as a part of reverse leakage current, and the voltageacross the junction is negative. If now a small negativevoltage is applied, then there is a sudden fall in currentindicated by AB in Fig. 8. The current is not immediatelyreduced to zero or changes polarity because of the reverseleakage current. Let us choose arbitrarily an operating

SHARMA AND JAMwAL : GAIN-STABILIZED TRANSISTOR AMPLIFIER

RI WIRIRBLE.

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Fig. 6. Effect of variation of RL on

point Qz on the characteristics at T1. If we design theexternal circuit in such a way that the emitter current IEis maintained constant, then the operating point will shift

to Q’a as the temperature is raised to T2. The effective

voltage across the junction corresponding to this operat-

ing point is negative. The impressed sinusoidal signal at

Q’2 will produce an emitter current variation of smaller

magnitude than that at Qz and hence the gain will be

reduced. At a higher temperature T3 the operating point

VEB and V’cB against temperature.

will lie on the steep part of the curve (i.e., portion All)and the gain will increase. With still further rise of tem-perature the gain will decrease as the operating point isshifting to a less steep part of the curve. In addition tothis, the effect of stabilization of 1~ will at least lead to

partial stabilization of l.. This is undesirable as it leads

to the reduction of gain by clipping. On the contrary, if

the circuit is designed in such a manner that the junction

voltage does not fall below zero, the operating point may

192 IEEE JoURNAL OF SOLID-STATE CIRCUITS, APRIL 1972

7

B’

6

5

4

?,,7

Jl

I2

i

h “> &a,0 I I I I I I L

o 1 2 3 4 F 6 7 s s !0

- ‘CEI *VOLTS

Fig. 7. Ic-Vc, characteristics at temperature O, and & 6-600 C,er-20°c) .

have a position such as Q’”z and the voltage gain willnot be affected appreciably. Such a state of affairs ispossible if the circuit current is allowed to change andthe rate of decrease of voltage across the junction isminimized. So far as the effect of temperature is con-cerned, the transistor currents and voltages act as com-plementary parameters. One can either minimize thevariations of the currents or that of the voltage. A gain-stabilizeci transistor amplifier should therefore be de-signed by minimizing the variations in V~E, Hence V~~should be preferred as a stability parameter to IE.

It is obvious from the above discussion that the de-crease of the voltages and the increase of the circuit cur-rents will take place as a natural consequence of thethermal generation of the carriers as a result of the riseof temperature. The fall of the voltages with tempera-tures can be further enhanced by the external circuitcomponents (Figs. 4-6). To minimize the rate of fall ofthe voltages, one can only choose the external circuitcomponents properly. One must take care that the circuitclwrents do not exceed the rated values and so thermalrunaway is prevented. The conditions imposed on thevoltages are thus

v’e~k VCB> V“CB (7)

where single-prime notations denote the values of thevarious quantities at the lower operating temperature T’and the double-prime notations denote the values of theparameters at the higher operating temperature T“. Theanalysis of the two-battery emitter-bias transistor ampli-fier will be taken as an example in Section V.

V. DESIGN ANALYSIS

The emitter-base and collector-base voltages are /3]

v ,. = E, – IcoR, – I,[R, + Ml – a)] (8)

10

‘6

6

74.

H@

2

0–loo -60 -20 0 20 60 130 140 180

vEB ‘ ““v”

l?ig. 8. 1~-VB. characteristics at various temperatures ( 2’,-20° C,2’~60° C, 2’—80°C.

Applying the conditions of (7) to (8) one obtains,

V’., = El – I’GoR2 – I’JR, + R2(1 – a’)] (lo)

V“~~ = E, – I“coR2 – I“,[R, + R,(1 – a“)]. (11)

Subtracting (11) from (10) and solving for RI one

obtains

R = v’m3– V“El+1 II1,–1’,

+ R,[r(l – a’) – 1“.(1 – a“) – (l”co – I’Go)](r’. – I’e) ‘“

The second term in (12) is positive because a“ is either

nearly equal to one or greater than one [8], and so

–1”, (1 – ~“) is either negligibly small or positive. Now

since R2 z O, RI can have a minimum value

V’x, – V“., _ AVEBR1m,n

= ~e – I’e AI.(13)

where A~E~ is the allowed permissible change in VE~ atthe two extreme temperatures, and Al, is the difference

in the current values at these two temperature limits.

Applying the stability condition of (7) to (9) one finds

V’,, = E, – E, + I’.[R1 + a’RL]

i- V’8~ – I’GORL (14)

V“c, = E, – El + 1“.[R, + a“RJ

-t V“~. – I“coRL. (15)

Subtracting (15) from (14) and solving for RI one has

# V’EB– v“,,)+-(v”,, – v’.,)(r’. – I’e)

R. [I“ea” – l’.a’] – [I”co – I’co]—(T” — T’ } (16)vCB = Ez – El + I,[R, + aR,z] + V,, – ICORL. (9)

SHARMAAND JAMWAL: GAIN-STABILIZEDTRANSISTORAMPLI~IER 193

since RL > 0, one can write for the maximum value ofR,, taking consideration of the sign of the voltage,

RAVEB + AVcB

1m.. = AI,(17)

where AVCB z V“cB — V’cB is the allowed difference inthe voltage at the two extremes of the temperatures.Thus RI must lie between

(18)

R2 can be determined from (12) as

R, AI. – AVBB‘2 = r~, – a’) – 1“.(1 – a’}) – (l”.O – I’co) “ (19)

Emitter-bias voltage El can be obtained from (10) as

E, = I’e[R1 + R,(l – a’)] + V~B + I’CORZ. (20)

Single-prime notation has been used in (20) to de-termine El since the battery voltage is also temperaturedependent. It ‘has a negative temperature coefficient andto include this effect a slightly higher value of El isneeded.

RL can be calculated from (16) as

Finally, Ez is obtained from (8) as

– V’xz + ItcoR~ . (22)

The coupling capacitors Cl, CZ and the emitter bypasscapacitor (73 do not figure in the analysis for stabiliza-tion and can be determined from usual considerations offrequency response.

VI. 13XPERIMENTAL DESIGNS AND COMPARATIVE STUDY

A. Present Design

The two-battery common-emitter amplifier of Fig. 3is designed to provide a stabilized gain between thetemperature limits of T’ = – 15°C and T“ = +80°C.The transistor used is an ac 125 germanium alloy junc-tion manufactured by BEL, India, The design is to bemade under the conditions

V’2B(= 110 mV) 2 V.. 2 V“,,(= 50 mV)

V’..(= –5.5V) 2 v., > V“c!,(=–4.5V).

The variations of ~, 100, and the values of emittercurrents are known from the transistor manufacturedspecifications. The emitter current at the highest tem-perature I“. should be selected well below the rated valueto prevent thermal runaway. These parameters are takenas

(2‘= 0.99 o!“ = 1.35

1’.O= –2.0PA l“.O = –600 PA

I’e= 4.0mA I“. = 5.5 mA.

The external resistance and the values of the twobatteries are calculated through the above equation asRI = 600~,Ra = 430 Q,R= = 20 Q,El = 2.5V and

E2 = –5.6 V. The coupling capacitors Cl and CZ aretaken to be 10 pF each. The emitter bypass capacitor Ctis taken to be 100 pF.

A l-kHz sinusoidal signal of amplitude 50 mV is ap-

plied to the input of this amplifier. A voltage gain ofabout 3.6 is observed to be fairly stabilized over a tem-perature range from –15 to + 115°C (Fig. 9, curve 1).It is expected that the gain would remain appreciablyconstant to a temperature much below – 15”C. The dis-tortion is observed at about 85°C [Fig. 10(a)] andabove. Severe clipping takes place at 112°C [Fig. 10(b)]and above till the gain is reduced very abruptly to zero.In order to have a clear understanding of the advantageof the design based on V8B and Vc~ as the stabilityparameters, a few most common design procedures arebriefly mentioned and then a comparative study is made.It should be pointed out here that only the transistoris heated to keep the experimental conditions the samein all the cases under comparison.

B. Bias Stabilization According to Shea [1]

The stabilization is carried out with the aim of keep-ing the collector current Ic constant against the changesin reverse leakage current lc~o. A stability factor S isdefined by the ratio of the change in the collector currentto the change in leakage current,

This factor depends on the circuit configuration and issuch that the lower the value of S, the more stable is thecircuit. A choice of 8 = 2.1, El = 2.0V, and E2 = –9.0V leads to RI = 440Q,R. = 500Q,and RL = 1.0 k~.The collector current in the design is taken to be 4 mA. Itis found that the collector current is fairly stabilized butvoltage gain is very poorly stabilized against the tem-perature variations. (Fig. 9, curve 2). On the oscilloscope[Fig. 10 (c)] it is observed that the amplitude of theoutput voltage falls with temperature as well as severeclipping of the positive cycle of the output wave takesplace, justifying the arguments of Section IV.

C. Bias Stabilization According to Gronner et al. [4], [8]

In addition to the stability factor S’ defined by (23)the additional stability factors- introduced are

al _ dIca VM,

and

~ _ aIca~ (24)

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1—ap-

amm(c) (d) (e)

Fig. 10. Distortion oscillograms of output voltage against tem-perature for various designs. (a) New design at +85°C. (b)New design at + 112°C. (c) Shea’s design at +500C. (d) and(e) Gartner’s design at 00 and 80”C, respectively.

which are the measures of the variation in collector cur-rent to change in VEB and common-emitter current gain

~, respectively. The stress again is laid on keeping thecollector current constant. A circuit with S = 3.8, M =

0.28 mA/V, and N = 8.14 pA/O.01 unit has the externalcomponents as El = 8.0 V, E2 = –9.0 V, RI = 3.3 k~,Rz = 10.0 kQ, ancl RL = 3.0 kQ, and the voltage gainplotted against temperature is shown in Fig. 9, curve 3.

D. G’artner’s Design Approach [3]

The de operating point of a transistor around whichthe voltage and current fluctuate when ac signal is im-pressed is considered to be specified by the emitter cur-rent ~C and the collector voltage VcB. The stability re-quirements for a particular clesign are expressed by

I’. < 1~ < 1“~

IEEE JOURNAL OF SOLID-STATE CIRCUITS, APRIL 1972

V’J@B < VBB < V’CB.

Choosing

I’e = 4.0 mA I“. = 4.2 tnA3

v’.. = –5.5V V“CB = –4..5v

one obtains RI = 2.0 k~, Rz = 200 ~, RL = 200 ~, El =8.5 V, and E2 = –5.0 V. The gain falls from a value of4.7 at –15°C to 3.0 at 85”C, after which it falls veryrapidly to zero at 92°C as is clear from Fig. 9, curve 4.The clipping starts at about 60”C [Fig. 10(d)] and isvery severe as the temperature is 80” C or above [Fig.10 (e)], with the result that the gain falls very rapidlybetween 85 and 92”C. The clipp;g is attributed to the

partial stabilization of Id as a result of the stability re-quirements imposed on 1~, which in turn shifts the op-erating point well below the knee of the IrVO~ curve. Asteady fall of gain from – 15 to +85°C is most likelydue to the currenkvoltage characteristics of the emitter–base junction. The operating point is steadily shiftingtowards a position on the knee of the input charac-teristics as a result of the stability restrictions on ID.

The design approaches based on the stability param-eters I, and T7EBor Ic and T7gBare not studied experi-mentally as they are not expected to result in a bettergain stabilization.

VII. EFFECT OF ~ VARIATIONS

Besides temperature stabilization, the amplifier is alsostabilized against unit-to-unit parameter variations, par-ticularly /3, the short-circuit current gain in a common-emitter configuration. In the amplifier of Fig. 3, withdesign values given in Section VI-A, transistors with ~values of 40, 90, and 130 are used, and the gain is ob-served to remain constant within experimental limits.The low ~ unit is an overused and heat-subjected tran-sistor. The inherent stability of the amplifier against the/3 variation is due to the fact that the concentration islaid on the stabilization of V~B and ~7~Bin the design and

the current variations are tolerated. /3 is essentially a

current transfer factor and hence its variations do not

affect voltage gain performances.

VIII. CONCLUSIONS

The stabilization of the output de current does notlead to the stabilization of output voltage. A better volt-age gain stabilization is possible if the external com-ponents are selected in such a way that the variations ofthe junction voltages are minimized and the currentsare allowed to increase so that the operating point doesnot fall at or below the knee of the characteristics. Thetemperature range of the gain-stabilized amplifier can inthis way be extended from much below – 15 to + 115°Cfor germanium transistors, without using any active ortemperature compensating elements. In the case of a

IEEEJOURNALOFSOLID-STATECIRCUITS,VOL.SC-7, NO.2, APRIL1972

silicon transistor fairly good stabilization has already

been achieved in the range of – 15 to 200”C [10].

ACKNOWLEDGMENT

The authors thank Prof. Dr. N. N. Raina for his keen

interest in their work.

REFERENCES

[11 R. F. Shea, “Transistor operation: Stabilization of operat-ing points,” Proc. IRE, vol. 40, pp. 1435-1437, Nov. 1952.

[2] A. L. Bachmasm, “Stabilisierung des Gleichstromarbeit-spunk tes von ‘Transistoren,” Tech. Mitt. S’chweiz. Post.,‘1’eleph.,Telegraphenbetrieber, vol. 3, pp. 88-89, 1961.

195

[31 W. W. Gartner, Transistors; Principles Design and ApPli-mtion. Frinceton. N. J.: Van Nostrand, 1960, IXJ. 337-364.

[41 A Gronner, Otkine oj Transistor C&cuit ‘D~ekgn. NewYork: Regents, 1966, pp., 354.

[51 J. S. Schaffner and R. F. Shea, ‘The variation of the for-ward characteristics of junction diodes with temperature,”Proc. IRE (Corresp.), vol. 43, p. 101, Jan. 1955.

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High-Frequency Amplifier Design Using Nichols Chart

YOSHIHIRO MIWA, MEMBER, IEEE, KIYOSH1 OKUNO, AND TOSHIHIKO NAMEKAWA

Absfract—In the Lmvilf chart that is used in the design of high-frequency amplifiers, it is not easy to find the stability factors andtransducer gain. To overcome that, the graphical analysis for theactive two-port network using the Nichols chart is described. Thismethod is very useful in the design of high-frequency amplifiershaving a given value for the stability factor, because the stabilityfactors and transducer gain are easily obtained from the Nicholschart and the auxiliary curve overlay. The other basic characteristicquantities for the active two-port network are also given.

NOMENCLATURE

y,,, y,,, y,,, y22 Y parameters of active two-port network.

y,. = g,, + ibis ~,s=lor2.Y* = G, + jB. Source admittance.Y. = (7. + jB. Load admittance.Y, = Y. + y,, = (1, + jB, = lY,le/@,,ml = GJgll, rl = BJG1.

Y, = Y. + g,, = G, + jB, = lY,lei@,,

mz = Gz/g~z, r, = B,/G%.

Yin = y,, – Y1,YM/Y2 Input and output admittances

you, = y,, – y12y,1/Y, of active two-port network.Y,. = $1,~+ Y.

Y Out = gout + YL

K, = 2GlGJJY,zYz,] (1 + cos 00) Stern’s stabilityfactor of termi-nated active two-

port network.K,, = 2g,,g,J\y,,y,,l (1 + cos L9J Sterns’s stability

factor of active two-port network.

k = 2g11g2,/ly12y211 — Cos e.

Manuscript received May 1, 1970; revised May 26, 1971.The authors are with the Faculty of Engineering, Osaka Uni-

versity, Osaka-Fu, Japan.

K,. value of K, under conjugate-matched terminations.Optimum source and load terminationsfor a given value of K,,

Conjugate-matched source and load ter-

minations.Values of m, = m, and ri = r, foroptimum terminations.Values of m, = m, and r, = r, forconjugate-matched terminations.Return ratio of terminated active two-

port network.Return ratios of amplifier with tunedinput and output, input, and output

circuits, respectively.

Return ratio of synchronous tuned am-plifier.

Values of T for Y. = O, YL = O.Gain and phase margins.Minimum values of G~~and 119~1, respec-tively.Angular frequency and frequency.Angular frequency and frequency at

maximum output.Angular frequency at which phase of T is– 180°.

Angular freque<$y at which magnitude ofT is unity.

OT, 190, @M, ~N, @L Phase angles of T, Y12Y21, kf, N, andL, respectively.

M, N, L Linear transformations defined in (17)-(19).G. = 4 Iy,,lz GLGJ[Y, Y, – y,,y,,l’ Transducer gain of

active two-portnetwork.