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NOTICE: When government or other drawings, speci-fications or other data are used for any purposeother than in connection with a definitely relatedgovernment procurement operation, the U. S.Government thereby incurs no responsibility, nor anyobligation whatsoever; and the fact that the Govern-'ment may have formulated, furnished, or in any waysupplied the said drawings, specifications, or otherdata is not to be regarded by implication or other-wise as in any manner licensing the holder or anyother person or corporation, or conveying any rightsor permission to manufacture, use or sell anypatented invention that may in any way be relatedthereto.

USAELRDL Technical Report 2386

STATIC AND DYNAMIC PERFORMANCE OF

MICROPOWER TRANSISTOR LINEAR AMPLIFIERS

R. A. Gilson0. Pitzalis

W. Kissand

J. D. Meindl

September 1963

UNITED STATES ARMY

ELECTRONICS RESEARCH AND DEVELOPMENT LABORATORY

FORT MONMOUTH, N.J.

U. S. ARMY ELECTRONICS RESEARCH AND DEVELOPMENT IABORAT ORIESFOT MONNOUTH, NEW JERSEY

September 1963

USAERDL Technical Report 2386 has been prepared under thesupervision of the Director, Electronic Components Department, andis published for the information and guidance of all concerned.Suggestions or criticisms relative to the form, contents, purpose,oruse of this publication should be referred to the Commanding Officer,U.S. Army Electronics Research and Development Laboratories, FortMonmouth, New Jersey, Attn: Chief, Semiconductor and MicroelectronicsBranch, Solid State and Frequency Control Division.

J. M. K1MBROUGH, JR.Colonel, Signal CorpsCommanding

OFFICIAL:B. B. PAIMMajor, WACAajutant

DTSTRIBUTION:Special

QUALCFIED MBUESTERS MAY OBTAIN COPIES OF 2EIS REPORTFRM DDC.

TIS REPORT HAS UMW RELFASED TO THE OFFICE OF TECHNICALSERVICES, U. S DEPAR14ENT OF COMMERCE, WASHINGTON 25,D. C., OR SALE TO TEE GENERaL PUBLIC.

STATIC AND DYNAMIC PERFORMANCE OF MICROPOWER TRANSISTORLINEAR AMPLIFIERS

R. A. GiLion, 0. lItZaJ., W. Kiss and J. D. Meiudl

DbA -TASK _#1G;622O01AO 5602

ABSTRACT

Silicon planar transistors which exhibit junction reverse currentssmaller than 10 "9 amperes and common emitter current transfer ratiosgreater than 50 for collector currents of 10-6 amperes are now available.An optimum design technique for the application of these devices in linearbroadband amplifiers has been devised. A salient feature of this techniqueis that it provides a unified approach to the DC and large-signal AC design ofa micropower amplifier. Subject to initial constraints, the design technique:(I) provides a specified amplifier output power capability over a wide tem-perature range, (2) minimizes amplifier power drain, and (3) maximizesamplifier power gain. With slight modification, the optimum design techniquealso serves as the basis for a worst case design procedure for linear ampli-fiers considering transistor and resistor tolerance margins. The frequencyresponse of micropower amplifiers can be accurately predicted on the basisof a unilateralized hybrid pi transistor equivalent circuit. Amplifier band-width may be significantly enhanced by means of a cascode circuit. Usinga simple thermistor temperature compensation technique, micropoweramplifiers have been designed whose gain and terminal impedances arevirtually insensitive to large temperature changes.

A common emitter broadband micropower amplifier operating from athree-volt supply with load and source impedances of 5x10 4 ohms can providea 0. 18-v peak AC load voltage over the temperature range -50 4 T t 100oC fora power drain of 23xl0 - 6 w and a power gain of 25 db. If the peak load volt-age capability is reduced to 0. 15 v, this amplifier can accept 10% worst casetolerance margins on all circuit resistors. Depending on transistor barriercapacitances and stray circuit capacitances, amplifier bandwidths vary fromabout 7 KC to 25 KC with two-to five-time increases possible in the cascodecircuit. Further improvements in bandwidth are readily available for largeroperating powers.

U. S. A3M ELECTRONICS RESEARCH AD DEVELOPM T LA0RARESFOR MOlMOU , NEW JERSEr

CONTNTS

Page

ABSTRACT i

INTRODUCTION 1

SECTION 1 - TRANSISTOR CHARACTERIZATION 2

Part 1 - DC Characteristics 2

Part 2 - AC Characteristics 3

SECTION 2 - DESIGN THEORY 6

Part 1 - Basic Design Theory, 6

Part 2 - Saturation, Cut-off and Feedback Refinements 9

Part 3 - Worst Case Tolerance Refinement 10

Part 4 - Amplifier AC Characteristics 11

Part 5 - AC Temperature Compensation 14

Part 6 - Cascode Amplifier 16

SECTION 3 - AMPLIFIER PERFORMANCE 20

CONCUSIONS 24

ACKNOW GMENTS 25

REFE1RECEs 26

APPENDIX 1 27

APPENDIX 2 29

APPEDIX 3 30

i

CONTSPage

TABLES

I. Micropower Transistor Characteristics 31.

II. Worst Case Conditions 32

III. Fourpole H Parameters 33

IV. Amplifier AC Characteristics 33

V. Amplifier Performance Data 34

VI. Worst Case Designs 35

FIGURES

Figures 1 through 26 ........................ .................. 36-59

ii

STATIC AND DYNAMIC PERFORMANCE OF MICROPOWER TRANSISTORLINEAR AMPLIFIERS

INTRODUCTION

Recent advances in semiconductor device technology have producedsilicon planar transistors which exhibit junction reverse currents less thanone nanoampere and common emitter current gains greater than 50 forcollector currents of 1 to 10 microamperes. This collector current rangeis about three orders of magnitude smaller than the normal milliampereoperating current range for low power silicon transistors. Because of theirultra low level operational capabilities, "micropower" transistors are ofgeneral interest in microelectronics and among their possible applicationsoffer a potential solution to the troublesome problem of battery power drainin portable military communications equipment. The purpose of this reportis to describe the results of a feasibility study of the application of micro-power transistors in linear communications circuits.

The discussion is divided into three sections. The first sectiondescribes the salient characteristics of micropower transistors for thecommon emitter mode, including the static base and collector character-istics and the small signal fourpole parameters and equivalent circuit.The second section describes an optimum design theory for linear broad-band micropower amplifiers which provides a unified and worst case treat-ment of the DC and large signal AC design of an amplifier, an analysis ofsmall signal behavior, and an AC temperature compensation technique. Alinear broadband amplifier is considered since it is the most widely en-countered generic communications circuit. The third section of the discus-sion describes the overall performance of broadband micropower amplifiers,including their effective large signal mode of operation, frequency response,temperature behavior and the influence of key design parameters on amplifierperformance.

SECTION 1 - TRANSISTOR CHARACTERIZATION

The purpose of this section is to present characterization data for sixtypical diffused silicon micropower transistors providing useful informationfor device applications in linear communications circuits. The devicesdescribed include three NPN planar transistors (devices, A, B, and C), anNPN planar epitaxial transistor (device D), an NPN mesa transistor (device0,, and a PNP planar transistor (device F) each of which is supplied by.a dif-ferent manufacturer. In Part 1 of the section, the static transistor character-istics are reviewed, and in Part 2 the small signal AC characteristics areconsidered.

Part 1 - DC Characteristics

Figure 1 displays collector characteristic curves for a typical micro-power device for representative operating conditions in the common emitterconfiguration. In their general appearance, these collector characteristicsclosely resemble the familiar transistor behavior for the milliampere rangeof operation. Although not strikingly displayed by the curves of Figure 1,two mild departures from mnilliampere characteristics are the lower satura-tion voltage and the lack of the usual flatness in the active region. In addition,the current transfer characteristics, IC versus IB curves with VCE heldconstant, are relatively nonlinear due to the rapid increase of hFE with ICin the microampere range.

Figure 2 displays typical base-emitter characteristics for the micro-power range. It is evident that the general features of the input behaviorare similar to those of the normal milliampere collector current range. Inessence, Figure 2 illustrates the reason micropower device voltage levelscannot be materially reduced below normal device voltages, although currentlevels are 103 times smaller. The familiar exponential relationship1 betweencurrent and voltage for a semiconductor junction:

I = Is [ exp ( F) -1 101)

where I s = junction reverse saturation current; q = electronic charge =

1. 60 x 10-19 coulombs, k = Boltzmann's constant = 1.38 x 10 - 23 joules/ 0 Kand T = temperature in OK, permits orders of magnitude change in junctioncurrent I for small percentage changes in applied voltage V.

At room temperature junction reverse currents below one nanoampereare common for low power silicon planar transistors. Many devices can befound which exhibit a collector-to-base leakage current ICBO less than 0. 1microampere at 150 0 C. However, at this time the majority of commercialspecifications for micropower transistors quote a maximum value for ICBOat 1500C in excess of 1. 0 ta for collector voltages of 40 v or more. In these

2

devices at temperatures above 100 0 C, ICBO can become significant comparedto base current IB , if not collector current IC , for collector currents in the1 to 10,& a range. Conservative design practice requires that ICBO be con-sidered in the design of the base bias network for a high temperaturemic ropowe r amplifier.

A typical characteristic of silicon micropower transistors is a commonemitter current gain hFE which is more temperature sensitive for collectorcurrents of 1 to 10,.a than for 1 to 10 ma collector currents. Figure 3shows the temperature variation of hE for IC = 10.ta. corrected for ICBO ,

for a typical silicon micropower transistor. Here it is evident that morethan a four-time increase in hFE for -506 T 100 0 C occurs where atIC = 1. 0 ma a three-to-one variation is more typical. This enlarged varia.tion of hFE can be attributed to a shift with current level in the relativeimportance of the various mechanisms which contribute to the base currentin a silicon planar transistor. At low current levels the base current isdominated by surface currents which originate at the surface edge of the

2emitter

The maximum allowable device power dissipation and breakdownvoltages for micropower transistors are far in excess of the requirementsof typical micropower amplifiers. Maximum device ratings are generallyof small concern in micropower circuits. Table I shows a summary of thesalient DC characteristics of devices A through F.

Part 2 - AC Characteristics

The variations with collector current of the small-signal low-frequencycommon emitter fourpole parameters, hle = hie and hgle = hfe, of a typicalmicropower transistor are shown by Figure 4.. These measurements clearlyindicate the drastic changes which occur in the values of the input impedancehlle and forward current transfer ratio h2le as quiescent collector currentis reduced. Table I indicates the marked temperature behavior of the micro-power parameters hll e and h2le. Typical values for the reverse voltagetransfer ratio hle = hre and the output admittance hZ2e = hoe for micro-power transistors are indicated at the bottom of Table I; hl2e and hZ2e cangenerally be neglected in linear micropower circuit analysis.

The frequency behavior of a micropower transistor for the commonemitter mode is most conveniently described by the hybrid pi equivalentcircuit. However, the frequency behavior of the forward current transferratio or current gain h2le is often of special interest. A typical family ofmeasured frequency response curves for h2le is illustrated in Figure 5.

The familiar 6 db/octave roll-off is evident. In addition, it is apparent thatthe gain-bandwidth product for this typical device increases directly withcollector current. Table I gives additional data on the frequency behavior ofh2Ie in terms of f3db and fT"

3

The common emitter hybrid pi equivalent circuit 3 for a micropowertransistor is shown in Figure 6. From an ultra-high frequency immittancebridge measurement, the base spreading resistance of a typical micropowerdevice is rb , ' 50SI and does not vary significantly for 104a4IC 15. 1.0 ma.From audio frequency voltage measurements at room temperature, the com-mon emitter diffusion resistance rble=hlle'z2OO, 000 2 for IC - 10 xa.The calculated value is

(1.02)

rrb+ h h kT 0.026 = 192,000Non0be = b hfe r.hfe IE

where Of ozhfb 2 hZI- is the ccrnrnon base small-signal low-frequencycurrent gain, r- al h.b is the common base diffusion resistance, T = 300 0 Kand IC ! E = 10;" a. The base-to-emitter capacitance Cble is composed ofthe diffusion capacitance CD and the emitter barrier capacitance CTe. Thatis

Cbe = CD + CTe (1.03)

where for homogeneous base transistors

2C qI.E W 2(.4

CD kT (1. 04)

where W = the electrical base width and D = the minority carrier diffusionconstant. For graded base devices CD is also directly proportional to IE .From high-frequency capacitance bridge measurements, the diffusion capaci-tance for a typical micropower transistor was measured as CD2Z 7 . 2 pico-farads for IC = 1.0 ma. Therefore, on the basis of (1.04) one would predictCD = 0. 272 pf for IC = 10.'-a. The typical curves of junction capacitanceversus voltage given by Figure 7 indicate that CTe it 20 pf for a forwardbase bias which produces IC = 10,"a. Here it is obvious that the diffusioncapacitance CD is apparently much less than the emitter barrier capacitanceCTe. CD may be neglected in the micropower transistor equivalent circuitwith no significant loss of accuracy for collector currents less than aboutl0/. a. The data of Table I provide further support for this simplification.The collector capacitance CC is composed virtually entirely of the collectorjunction capacitance with a negligible contribution from collector diffusioncapacitance. Figure 7 indicates the typical variations of the emitter junctioncapacitance CTe as well as CC with applied bias voltage and temperature.The collector current generator has the usual value:

( 0

grmvbWe = r- Vbl e (1.05)

As a check on the accuracy of the proposed equivalent circuit, one maycalculate from Figure 6:

4

1 ~e ( 0o/ (1.06)1+j4) rble [ CTe+Cc+Cs)

and for the cut-off frequency

1f3db ZITrble(CTe+Cc+Cs) (1.07)

where Cs represents 0. 70 pf of transistor stray capacitance including 0. 10 pfof stray base-to-emitter header capacitance and 0. 60 pf stray collector-to-base header capacitance. For Ic = 10A. a, rble = 200,0001., CTe = 22 pfand CC = 7 pf (1. 07) gives f3db = 26.8 KC. This compares favorably withthe measured value of 25 KC, corrected for stray jig capacitance, given byFigure 5. In many applications, the equivalent circuit of Figure 6 may besimplified by neglecting the base spreading resistance rb ,-v 50Q sincerbe. < rble _ 200, 000,Qfor Ic!E 10A a and rb , << j W CTel '-- 500SI forf * 10 MC. A common figure of merit for a transistor is the gain-bandwidthproduct given by:

do 1 Jq' IC(JT=hfe&3db - -o rb1e(CTe+CC+Cs) i. 08)

From (1,08) it is evident that power dissipation may be traded for gain-

bandwidth product by increasing IC . In addition, the transistor barriercapacitances, CTe and CC, and stray capacitance C s should be as smallas possible for a large gain-bandwidth product. The capacitance of a linearlygraded junction may be expressed as

(qa 2J 1/3

CA 2fv J] (1.09)

where A is the junction area, q is the electronic charge, a is the slope of thelinear impurity gradient, E is the material dielectric constant andivj is theabsolute magnitude of the sum of the junction equilibrium potential differenceand the applied voltage. Here it is evident that q is a fundamental constant,( is a material constant, v is virtually constant as described in connectionwith (1. 01) and that allowable decreases in a are largely ineffective in re-ducing C. Obviously, the principal path open to reducing junction barriercapacitance C, in order to increase the gain-bandwidth product of micro-power transistors, is to reduce junction area A. For a given IC, this ofcourse entails an increase in the current density in the device.

5

SECTION 2 - DESIGN THEORY

The schematic diagram of a typical broadband micropower amplifier isshown in Figure 8. Among the more common constraints which must be ob-served in the design of this amplifier are: 1) The supply voltage VCC is fixed.2) The load impedance RL is specified. 3) The peak AC output voltage VL isspecified. 4) The operating temperature range Ty!__Tt-_Tx is fixed. 5) TheDC power consumption of the amplifier PD should be as small as possible.6) The amplifier bandwidth W 3db is specified. Assuming the foregoing con-straints on the design of a micropower amplifier, several problems arisewhich are far less severe or even nonexistent at normal milliwatt powerlevels in silicon transistor linear circuits. With regard to DC operation,transistor bias point stabilization becomes more difficult due to three factors:1) At 1 to 10 microampere collector currents, collector junction reversecurrent ICBO can become significant at temperatures above 100°C. 2) Thetemperature variation of common emitter current gain hpF is comparativelylarge; a five-to-one variation for -500C &T. 100 0C is not unusual. 3) Theeffect of the temperature variation of base-emitter diode conductance gBEbecomes more difficult to counteract at the low battery voltages which usuallyaccompany microwatt power levels.

With regard to AC operation, a major concern derives from the factthat microampere quiescent collector currents severely restrict the dynanicrange of an amplifier and effectively contribute to a large-signal mode ofoperation. In this connection careful attention must be paid to the effects oftemperature as well as saturation and cut-off on the dynamic range of adesign. The influence of both transistor and passive component tolerancesassumes a greater importance in micropower amplifiers, particularly inview of constraints 3) and 5). The lack of high-frequency response of cur-rently available silicon transistors at microwatt power levels seriouslylimits the bandwidth of micropower amplifiers. Finally, the relativelylarge temperature variation of the AC parameters of a micropower transistortends to limit the AC temperature stability of micropower amplifiers. Thissection outlines a design theory which has been found useful in deriving micro-power amplifier designs which adequately satisfy the previously listed con-straints. The section is divided into six parts which present the rudimentsof the design technique in Part 1. the cut-off and saturation off-set refine-ments and the feedback refinement in Part 2, the worst case tolerance refine-ment in Part 3, an analysis of amplifier small-signal AC characteristics inPart 4, an AC temperature compensation technique in Part 5, and the designand analysis of a cascode circuit with improved frequency response in Part 6.

Part I - Basic Design Theory

The DC load line (DC LL) of the micropower amplifier of Figure 8 isgiven by

VCC = ICn RC + VCEn + VRIn (2. 01)

6

at a nominal temperature Tn where VRln = IEnRIWICnRl. In orde. T ,.vide the specified peak AC output voltage VL at Tn for a minimum DC pov'e

dissipation, the amplifier output leg must be designed so that the DC operating

point Qn bisects the AC load line (AC LL) given by

ICn = -(G C + GL) VCEn (Z. 02)

at Tn for Re = 0. Equation (2. 02) represents the AC LL in the DC collectorcharacteristics (Ic, VCE) plane. Although it is properly an AC equation, itis convenient to write it in terms of DC quantities in formulating the designtheory. This technique will be used throughout this section.

The locus of all AC load line midpoints is given by 4

ICn (GC + GL) VCEn . (Z. 03)

In (2. 02) and (2. 03), VCEn must be sufficient to accommodate the specifiedpeak AC output voltage VL. That is, neglecting for the moment the effectsof cut-off and saturation in the transistor

VCEn = VL = IL/GL (2. 04)

where IL is the peak AC output current. Substituting (Z. 04) into (2. 01) and(2. 03) gives

Cn(Vcc - VL - VRI) (2. 05)(VCC - 2 VL - VRln)

and R C (Vcc - ZVL - VRln) (2. 06)VLGL

Given VRln, equations (2. 05) and (2. 06) define the smallest ICn and thelargest RC, respectively, which satisfy the initial design constraints onVCC, RL and VL. This is advantageous since small I C tends to decreasepower dissipation PD and large RC tends to increase amplifier gain. Theproper selection of VRIn in (2. 05) and (2. 06) obviously constitutes a keypoint in the design. VRln=ICnRl represents the DC feedback voltage whichmust be used to stabilize the circuit against transistor DC parameter tem-perature variations for the range TyS T * T x . A practical procedure is tocompute complete designs for several values of VRln and then choose theone giving the desired values of AC power gain and DC power dissipation.This procedure will be illustrated in Section 3.

From Figure 9 it is evident that because the quiescent point bisectsthe AC load line at Tn, operating point drift will limit the output voltageswing to values less than VL when T # Tn. A key feature of the presentdesign theory lies in regulating the DC operating point drift such that thedesired AC output voltage swings at the operating temperature limits

7

(i. e., KyVL at Ty and KxVL at Tx with O< Ky, Kx4 1) are exactly accom-modated. From Figure 9, it is apparent that

KyVL = ICy/GC+GL or ICy = KyVL(GC+GL) at Ty (2.07)

and KxVL = VCE x at T x . (2.08)

(By selecting Ky = = 1/ ' for example, the AC power output capabilityof the amplifier will be 3db below its nominal value at the operating tempera-ture limits. Ty and Tx. of the amplifier. It might also be mentioned herethat if GL varies with temperature it should be reflected in the K valueswhich are selected in (Z. 07) and (2. 08).) The output leg DC equation at Ty,

VCEy = VCC - ICy fR 1 + RC) (2.09)

together with (2. 07) gives the operating point (ICy. VCEy) at Ty. The outputleg DC equation at T x ,

VCC -VCEX (2. 10)Icx = R1 + RC 2 0

together with (2. 08) gives (ICx. VCEx). It is evident here that the selectionof the factors Ky and Kx or the AC dynamic range stability of the amplifiereffectively determines its DC operating point stability.

To complete the design, the input leg must be considered. FromFigure 8,

VCC = (I B + I2) R 3 + I 2 R2 (2. 11)

and 0 = VBE + IER 1 - IZR 2 . (2. 12)

Writing (2. 11) and (2. 12) at both the operating temperature limits (Ty and Tx)and solving the four resultant simultaneous equations yields

R? - LIEXR(2. 13)VC C-IBxR 3 -VBExIExR1

VCC L (IEx-IEy)RI'(VBEy-VBE'x)j

and R3 - (IExIBy.IEyIBX)RI+(VBExIBy.VBEyIBx) (2. 14)

This procedure for determining R 2 and R 3 yields their largest allowablevalues for the associated DC operating point stability and emitter resistanceR1 . This is accomplished due to the fact that IBy, IBx, VBEy and VBExin (2. 13) and (2. 14) effectively take into account the exact overall changesin the transistor parameters ICBO , hFE and gBE for the temperature rangeTy- T ST x . The obvious advantages of large R2 and R 3 are smaller DC

8

power dissipation and larger AC power gain for the amplifier. At this pointit appears that a rudimentary design theory which satisfies the original con-straints on VCC, RL, VL, T and PD has been established.

Part 2 - Saturation, Cut-off and Feedback Refinements

At the relatively low supply and quiescent collector voltage levelsassociated with battery operated micropower circuits, saturation effects inthe transistor may impose a serious limitation on output voltage swing. Inaddition the monotonic fall-off of current gain hFE with decreasing collectorcurrent restricts the AC swing in the low current cut-off region. The distor-tion caused by these two effects as well as the bandwidth of the amplifier canbe improved by providing negative feedback through the emitter resistor Re(Figure 8). The procedure for quantitative consideration of saturation, cut-off and feedback will now be outlined.

The AC LL equation in the DC collector characteristics plane may bewritten as

- ICnVCEn - GC+GL VRen (2. 15)

where VRen is the AC feedback voltage. Considering feedback only, thelocus of AC LL midpoints is given by

Cn +v (2. 16)VCEn -GC+GL Ren

A simple translation of coordinate axes facilitates the desired inclusion ofsaturation and cut-off effects in (2. 16) (see Figure 10).

VCEn- V o ICn o +VRen (2. 17)GC + GL

with VRen = (IEn-lo) Rez (ICn-Io)Re gives the locus of AC LL midpointsconsidering the saturation Vo and cut-off Io offsets. The quiescent collectorvoltage required to accommodate a peak output voltage VL is

VCEn = V L + VRen + V o • (2. 18)

Substituting (Z. 18) into (2. 01) and (2. 17), one may solve for

VcC-VL-VRn-VRen-VoICn = VCCZVLVRlnVRenVo (VLGL+Io) (2. 19)

VCC-ZVL-VRln-VRen-V oand RC = (VLGL+Io) (2.20)

9

In (2. 19) and (2. 20), the values of the DC feedback voltage VR1n, the ACfeedback voltage VRen, and the saturation Vo and cut-off Io offsets may bejudiciously selected to satisfy the overall design constraints of a particularapplication.

The AC output voltage swing is given byKyV Y= Iy-°or

K yVL = or ICy = KyVL(GC+GL) + I o at T (2.21)GC+G L

and KxV L VCEx - Vo KxVRen or

VCEx = Kx(VL + VRen) + Vo at T x (2.22)

Equations (2. 09) and (2. 21) give the DC operating point (ICy, VCEy) at Ty-while (Z. 10) and (2. 22) give the operating point (ICx, VCEx) at T x . Thedesign of the input leg of the amplifier proceeds as described by (2. 11)through (2. 14).

Part 3 - Worst Case Tolerance Refinement

Considerable attention has been given to "worst case" design techniqueswhich assure reliable circuit designs for specified component tolerancemargins particularly for digital logic circuits 6 . While the effects of com-ponent tolerances are generally much more severe in linear circuits than indigital circuits, apparently, practical analytical techniques for worst casedesign of linear circuits are not in wide use at this time. It is felt that thedemonstration of a straightforward worst case design theory for linearcircuits may be of general value and is certainly of particular value in assur-ing that the already minimal dynamic range of a micropower amplifier ispreserved in the face of component tolerances. In the case of broadbandmicropower amplifiers, the critical function of a worst case design techniqueis to insure that the worst possible combination of component toleranceswill not result in ICy less than

ICy = KyVL (I/RC + i/RL) + I o (2. 23)

from (2. 21) and VCEx less than

V.CEx = Kx (VL + VRen) + Vo (2. 24)

from (2. 22). (The symbolism ICy denotes the minimum value of the quantityICy while ICy denotes its maximum value.)

Table II shows the worst case tolerances for the transistor, the biasingresistors and the supply voltage. From Table II and (2. 09) it is evident that

10

VCEy = Vcc --ICy (Rl + Kc) (2. 25).

gives the value of VCEy which accompanies iCy of (2. 23). Also from (2. 10)

ICx VC Vc- CEx_ + Rc

gives the value of ICx which accompanies YCEx of (Z. 24). From Table IIand (2. 11) and (Z. 12)

Vcc = (By + IZy) R 3 + IZy 12 (2. 27)

0 = VBEy + IEyR1 - IzyRz (2.28)

and TY and

Vcc = (jSx + 12x) _R3 + IZx R2 (Z. 29)

0 = VBEx + IEX R, IZx RZ (Z. 30)

at T x yield the values for R 2 and R 3 given in Appendix 1. In (Z. 27) through(2. 30), R 1 = R 1 (i+f R), RI = R 1 (- SR), VCC = VCC (1-,&v) , and so forthwhere, for example, R = 0.05 for a ±5% resistor tolerance margin. Also,

IBy indicates the largest transistor IB at Ty considering both temperatureeffects and manufacturing and aging tolerances. The solutions to (2. 27)through (2. 30) give the nominal values of RZ and R3 which insure that ICyand VCEx will not be less than the required values for the specified dynamicrange, KyVL at Ty and KxVL at T_, for the worst combination of toleranceswhich may arise. This design procedure may be applied to temperature,manufacturing and aging tolerances for all circuit elements including thetransistor, the resistors, and the supply voltage.

Part 4 - Amplifier AC Characteristics

The purpose of Part 4 is to present an analysis of the small-signal ACcharacteristics of broadband amplifiers operating at microwatt power levels.A fourpole network approach as well as an equivalent circuit approach to theAC analysis will be outlined.

From Figure 11, using the familiar low-frequency fourpole "h" para-meters to describe the transistor gives

V= HI Iil + H 1 2 v2

(2. 3 1)and i2 = H2 I i1 +HZ z

II

where the approximate overall amplifier "H" parameters are given byTable III. (The exact values are listed in reference 7.) The amplifier Hparameters are immediately useful in defining the gain and terminal. imped-ances which are specified in Table IV. The H parameter characterizationof the amplifier is valid, of course, only in the midband region.

In order to calculate the frequency response of a broadband micropoweramplifier, it is convenient to utilize the hybrid pi transistor equivalent circuitpreviously developed in Section 1. Figure 12 shows the AC equivalent circuitof a single stage micropower broadband amplifier for its medium and highfrequency ranges with Re = 0. In view of the device impedance levels dis-cussed in Section 1, rb , will be assumed negligible. Following this assump-tion, the principal question to be answered is whether or not the "Millereffect" approximation 8 may be used to unilateralize.the amplifier*.

To determine this. an exact analysis of the circuit of Figure 12' underthe noncritical assumptions that Rg, R 2 3 O a. rbte and R C >. RL yields

rblei-j _ Cc)

A 2 = hfe R (2. 32)i il 1+j3j rbe Cbe+(l+hfe 7- +jj RLCbe)CC3

rb' e

A comparison of the breakpoints of this expression shows that for typicalmicropower amplifiers an accurate approximation over the useful frequencyband of the amplifier is

i 2 1h1l+jfrbe Cble+(1+hfe r ) CC (2.33)

Again under the noncritical assumptions Rg, R 2 3 > > rb'e and RC > > RL, anexact analysis of the circuit of Figure 13 which employs the full Miller effectapproximation also yields the result expressed by (2. 33). Therefore, itappears that the usual Miller effect approximation for unilateralizing broad-band amplifiers remains valid for microwatt power levels.

"The principal value of the Miller effect approximation is that it permitsunilateralization of the amplifier with its accompanying simplification of theanalysis. Referring to Figure 12, to retain accuracy in making this approxi-mation it is necessary that: 1) CC does not load the output generator

grVbe(i. e. , 1C R+R L ) and 2) the direct transmission through

be small compared to gmVble . An additional requirem nt for accuracy ifthe equivalent input capacitance of CC[ i.e., Cc(l+gm

L is shuntedR RT RC RL -i ~+L RCRL)

directly to ground is that Rc+ L-KC-+RL &RC+RL

12

By dropping the simplifying assumptions for Rg, R2 3 , and RC, one

finds from Figure 13 neglecting Cces

i__ hf/ I+RL/RC (.34)

1l+rbe/K3+jj rb'e (Cble+Cb'es)+(1+ CfC)(234)rbl e RC+RL' C+Cs 1

1+rbIe/RZ3

3db hfe RCRL (2.35)rb'e [(Cble+Cbtes)+(l+ rb,e RC+RL) (CCs) ]

For the voltage gain

AV2 - hfe (L/rb'e) (2. 36)Av- v lI+RL/RC+j €.RLCces

where Cb~es, CCs, and Cces are the stray circuit capacitances in parallel

with Cble, CC and RL respectively. (The stray capacitances are not shown

on Figures 12 and 13.) From these equations,. the product of the midband

power gain and the effective bandwidth is, in absolute value,

hfe )z RL/rb e (2.37)

(4~)M. ~i)M. B ~3db +RL/RC Lrl 2 7Wk 3db=_RCM. M.B. rb ,e (Cbe+CbIes)+( + fe RCRL (CC+Cs)

rb,e RC+RL)

As s uming

hfe R C RL 1 RCRL

rbte RC+RL r( RC+RL be CC+C

-L. . B r, (Cc+CCs) I+RL/RC

(2. 38)q Icor G 41 3dbx

3dbkT (Cc+CCs) I+RL/RC

An examination of (2. 38) indicates the gain-bandwidth product of a common

emitter micropower amplifier can be improved by increasing the transistor

collector current IC, which increases power dissipation, and decreasing the

transistor collector-to-base barrier capacitance CC as well as the collector-

to-base circuit stray capacitance CCs. Since CC is usually of the order of 5

picofarads or less, the importance of, minimizing the stray circuit capacitance

13

CCs in order to maximize gain-bandwidth product is quite clear. The fre-quency response of the circuit of Figure 8 when Re 0 is indicated inAppendix 2.

As an additional point of interest, the low frequency cut-off )LF of amicropower amplifier which should be caused by CE will be calculated. FromFigures 8 and 13

ib R s l+j&J RECE (Z.39)ig Rs+rble CRs+rble±(hfe+1)RE]

g R s +rble E

RgR

where R s Rg R23 givesg 23

1 Rs+rbfe+(hfe+l)RE

.LF RECE Rs+rbe

A final parameter which is useful in comparing the performance ofmicropower amplifiers is given by'

F.M. - G3db (2.41)

- VBE+IER,

where PD = VCC [IE+2 V IE + R (2.42)

This quotient of gain-bandwidth product and power dissipation can be con-sidered as a figure of merit, F. M. , for micropower amplifiers. In virtuallyall instances, a major objective in the design of a broadband micropoweramplifier is to achieve a maximum gain and a specified bandwidth for aminimum power dissipation. Therefore, (2. 41) defines a parameter whoserelative magnitude is a useful indication of the quality of a given micropoweramplifier design.

Part 5 - AC Temperature Compensation

Previous parts of this section have been concerned with DC and large-signal AC stabilization of micropower transistor amplifiers. Specifically,the DC operating point and the AC power output capability of an amplifierhave been stabilized against changes with temperature and manufacturingtolerances in the transistor DC parameters ICBO , hFE and gBE, as well asthe values of the resistors R1, R 2 , R 3 and RC and the supply voltage VCC.However, the large temperature variations which occur in the small-signalfourpole h parameters of the transistor can give rise to large changes in thesmall-signal terminal properties of a micropower amplifier. The purpose

14

of Part 5 is to briefly outline a design theory4 which has been developed fortemperature compensation of the current gain, voltage gain, power gain,input impedance and output impedance of micropower amplifiers.

In order to simplify the presentation of the AC temperature compensa-tion technique, component manufacturing and aging tolerances will be neglect-ed and only temperature effects will be considered. A convenient method forhandling the temperature changes is illustrated in Figure 14. The tempera-ture factors or)' factors are used to describe the overall tem rature changesin the resistor values and supply voltage (e.g., R1 a xT ) Since theRI- K at T y "amplifier H parameters determine its terminal properties, compensation

may be sought by imposing the requirements that

HI 1yHI1 x, Hzly=H2lx and HZZy=HZ2x . (Z. 43)

H 12 is neglected since its effect on circuit behavior at the low frequenciesconsidered here is negligible. Substituting the H parameter values listed inTable III gives

(hlley+hzleyRe) R2 3 (hllex+hZlex?"eRe) ?' 2 3R 2 3 (2.44)

(hl ley+hzleyRe)+R23 (hl lex+hZlex )eRe)+ ? 23R23

(h 2 l)R 2 3 (h21ex) ' 2 3R23 (Z. 45)

(hlley+hzleyRe)+R23 (hl lex+hZlexleRe)+ ) 3 Z3

and 1/RC = 1/ )'cRc (2. 46)

where it has been assumed that )? 7= )3 = )'23. A most useful solution to(Z. 44), (2. 45) and (2. 46) results from equating numerators and denominators.From this

123 = hley/halex (2. 47)

Re 23RZ3"hlley requires k 2 3R 2 3 >hlley (2. 48)hZley

le = RZ3-hllex requires R23)hllex (2. 49)R2 3 " h2 lex hlleyhZ ley

and k c 1 . (2. 50)

To simplify the circuit implementation, it is desirable to achieve ),e = 1 in

(2. 49) which requires that hllex- h lex . Since hlle --.hlehllb% hZle rhiley h2-ley

15

hkT

hZle -- , for ke = 1- the relationship

Tcx _ Tx+273

icy Ty+2 7 3 (2. 51)

must be satisfied. In effect, to achieve ' e = 1, the hl le and h 2 le tempera-ture variations must track each other., This can be conveniently achieved bycontrolling the DC collector current change with temperature. so that h l lb

kTr2!- kT is constant. (As (2. 49) indicates, under the special condition

, 23 Z3 h 11., implementation may be further simplified by Re = 0. ) If onethen sefects -v = 1 and )E= 1, all temperature factors for the circuit arespecified with the result that only two temperature sensitive components,R and R 3 , are required for the desired compensation. (&= 1 indicatestemperature invariance.) Furthermore, it is evident that both R2 and R 3should exhibit the same temperature factor, ) 23.

From (2. 51) of the preceding paragraph, it is evident that the AC com-pensation requirements influence the DC stability of the circuit. In this casethe output power capability constraint imposed in Part I must be treateddifferently as indicated in Appendix 3.

Part 6-Cascode Amplifier

Among the broadband micropower amplifier design constraints listedin the introductory portion of this section is the requirement for a specifiedbandwidth bl3db. Equation (2. 35) of Part 4 indicates the value of (J 3db interms of AC circuit parameters. In practice for common emitter cascodesthe "Miller Effect" capacitance (+hfe RCRL ) (Cc+Ccs) largely

rbe R +RL

determines the value of 6) 3db via the multiplying effect ofhfe RRL :0> 1 on (CC+Ccs) . Therefore, presuming the smallest

rb, e RC+RL

practical value of (CC+CCs), if a particular micropower amplifier designdoes not meet the specified U)3db, an expedient approach to this objective

is to reduce ICRL by increasing the current and power drain of the ampli-Rc+RLfier. For example, in the common case where RL represents the input im-pedance of the following stage, an increase in the collector current of thefollowing stage reduces RL and therefore RC by the design procedure ofPart 1. In this manner, one may trade power drain for bandwidth as well asgain-bandwidth product as indicated in (2. 38).

A common-emitter, common-base cascode circuit which has been foundto be particularly effective in reducing the Miller Effect capacitance to pro-duce significantly larger bandwidths for essentially the same power gain andonly a slight increase in power drain, compared with a single common

16

emitter stage, is shown in Figure 15. Referring to the schematic diagramof Part a of Figure 15, it is evident that T 1 and T 2 represent a directcoupled common-emitter, common-base cascode. Cl and C4 serve as by-pass capacitors. The AC equivalent circuit of this cascode is shown inPart b of Figure 15. The stray collector-to-emitter capacitance of T2,Cces2, is neglected since it is not significant within the useful frequencyrange of the amplifier. An analysis of the AC equivalent circuit shows

(2. 52)

i2 (l+rb,el/R2+j W orble p) (/+Ceq)(3+RL/RC 2CRL)

Ordinarily, 1+rb,el/R23 I+RL/RC 1

rbtelCp RLCr r C

hfbZ=l and gmlr 2 -hfbl r1

so that (2. 52) gives

i_ - hfel/1+RL/RC (2.53)

il l+rb'el/R23+jrb'e1 [ (Cb'el+Cb'els)+2(CC l+CCsl)J

with W = l+rblel/R23 (2.54)h3db Wrb~el(Cbel+CbIels)+z(CCl+CCsl).

v 2 hfel(RL/rblel)and -- _ e(2. 55)

Vl I+RL/Rc+jcjRL(Ccz+Ccs2 )

The similarity between the above equations and (2. 34), (2. 35) and (2. 36) isimmediately evident. The key result is that the Miller Effect multiplier has

hfe RC RLbeen reduced from (1+ e RC+RL) , which often exceeds 20, to a value of 2.

This results in substantial increases in W3db while A i and Av are virtuallyunchanged.

The approximate value of the bypass capacitor C4 may be calculatedfrom Figure 15. Since

Vbe2 I+( 1-hfbZ ) R + jej R 4 5 C 4

r( 2 +j f(245 4. 56)glbel Ij4R4C

where R45= R4 R 5

R,4+R 5

17

1 1+(l-h 0 3 2 R45

4 - LF R45

where W"LF is given by (2. 40).

The circuit of Figure 15 is of sufficient interest as a broadband micro-power amplifier that the remaining features of its design will now be outlined,The DC equation for the output leg, analogous to (2. 01) is

VCC = ICZnRC+VCBZn+(VBEZn+VCEln+VRIn) (2. 58)

where VRln = IElnRjICnRl = IE2nRI ICZnRI

The AC LL, analogous to (2. 02), of T 2 is

IC2n = - (GC+GL) VCB2n . (2. 59)

Now, the locus of AC LL midpoints, analogous to (2. 03), of T 2 is

IC2n = (GC+GL) VCBZn (2. 60)

Since VCB2n = VL = IL/GL (2. 61)

analogous to (2. 04), substituting (2. 61) into (2. 58) and (2. 60) gives

On = VLGL fVcc-VL'(VBEZn+VCEln+VRIn)] (2.62)L L VCCZVL_(VBE2n+VCEln+VRln)

]

_ VCC-2VL-(VBE2n+VCE ln+VR in))and VLGL (2.63)

which are analogousto (2. 05) and (2. 06). In order to evaluate (2. 62) and(2. 63), the quantity (VBEZn+VCEln+VRIn) must be assigned a value. Since

IL is known by assuming a minimum nominal operating temperature Tn, aconservative value for VBE2n may be estimated. From Figure 15 it isevident that vceln = vbe2n. The collector-to-emitter AC voltage swing of T 1vcelrisquite small so that VCE1 may be selected at some constant nominalvalue such as 1. 0 v which assures that T 1 remains out of the saturationregion at all temperatures. As in Part 1, a practical procedure for selectingVRIn is to compute and compare complete designs for several values.

With ICn and RC calculated, the amplifier design proceeds in a mannerdirectly analogous to the approach of Part 1. Considering the saturation,cut-off, and feedback refinements of Part 2, the design of the cascodeamplifier again proceeds in a directly analogousmanner with the advantagethat the saturation Vo and cut-off Io offset values may be reduced for the

18

common base connection. Tolerances may be treated in a fashion similar

to the procedure of Part 3' and temperature compensation follows the patternof Part 5. On the basis of simplicity, flexibility and performance, it appearsthat the cascode circuit of Figure 15 may be considered as a general replace-ment of the common emitter amplifier of Figure 8 in micropower applications.

19

SECTION 3 - AMPLIFIER PERFORMANCE

In this section typical experimental and calculated results based on thecharacterization data of Section 1 and the design theory of Section 2 are pre-sented. Table V shows the detailed design and performance of five selectedmicropower amplifiers which illustrate the major features of Section 2. Theassumed initial constraints are indicative of what might be expected from ahigh performance micropower amplifier. The' data indicate that useful oper-ating characteristics can be, achieved at micropower levels and that the agree-ment between calculated and measured performance appears to support thedesign theory of Section 2.

Figure 16 illustrates the temperature behavior of the DC operatingpoint of the circuits of columns 1 and 2 of Table V. As indicated in Table V,the agreement between predicted and measured performance at the operatingtemperature limits appears acceptable, while Figure 16 shows that inter-mediate performance is also well behaved.

The temperature variation of the total percent amplitude distortion %D in the output waveform of the amplifiers of columns 1 and 2 of Table V isillustrated in Figure 17. The measured peak output voltage V2 was main-tained at a constant value for all temperatures. The total distortion is ratherlarge for two reasons. First, the variation of the forward current transferratio hfe with IC is quite pronounced at microampere current levels as illus-trated by Figures 1 and 4. Near the maximum in the hfe versus IC curve,which occurs typically in the milliampere range, hfe varies much moreslowly. The second reason for the large distortion is the fact that the sourceinternal impedance, Rg=50Kfl , used in gathering the data for Figure 17 is notthe optimum value for minimizing the combined input and transfer distortionof the transistor. Due to the monotonic increase in hfe and decrease in hiewith increasing IC at microampere current levels, current source signal,which completely eliminates input distortion, results in the smallest total% D. For example, by increasing Rg from 50K. to 500Kl. , the roomtemperature distortion in the first amplifier (Re=O) with VL=O. 18v is reducedfrom 16% to 13%. Figure 17 shows that a 50% reduction in the actual peakoutput voltage from 0. 6 VL=O. 18v to 0. 3 VL=. 09v causes a nearly equalpercentage reduction in distortion. This response supports the anticipatedresult for the design procedure that primarily input and transfer character-istic nonlinearities in the active region rather than more sharply definedsaturation and cut-off limits cause the distortion. The increased distortionat low temperatures and small collector currents is due to the more rapidrate of change of hfe with IC which occurs under these conditions. The usualreduction in distortion provided by degenerative feedback is readily apparentin Figure 17 for the curves of the second circuit where Re= 3 . 89KZ.

Figures 18 and 19 indicate the variations of mid-band power gain Gand input impedance R with temperature for the amplifiers of columns 1,

20

2 and 4 of Table V. The pronounced temperature sensitivity of the AC ter-minal characteristics of the two noncompensated ( )'Z3= 1. 0) micropoweramplifiers is evident. For the amplifier without feedback, G increases by4. 7 db from 23. 3 db to 28. 0 db and Ri increases 274% from 106K1. to 290K.for -50 T e. 100 0 C. In the feedback case, temperature variations are some-what reduced since G increases with temperature by 3. 4 db from 19. 6 db to23. 0 db and Ri increases 257% from 192KFn to 494KQ from -50 K-T!100 0 C.The variation of power gain with temperature is due primarily to changes incurrent gain Ai , which are in turn due to hZle, since voltage gain Av asdefined in Table IV remains relatively constant for both Re=O and 3. 89Kf..The variation of Ri is caused mainly by the variations of hu 1e and hZleRewhich are in turn also due to hZle since hlle.h21ehl lb.

Figures 18 and 19 also show that the temperature compensated amplifierof column 4 of Table V, with Re= 4 . 4ZK12 and 7'23=0. 28, can provide quiteuseful values of G and Ri which are virtually unchanged for -50 ! T :1000 C.This pronounced temperature insensitivity can be achieved by the simpleexpedient of using a resistor-thermistor combination for R2 and R3 . Inaddition, it is highly predictable as the data of Table V indicate.

The influence of the DC external emitter feedback voltage VRIn at thenominal temperature Tn and the dynamic range constant Kx = Ky = K on theperformance of a micropower amplifier is illustrated by Figures 20 and 21.Figure 20 indicates that for a given K there is an optimum range of valuesof VRln for which upper temperature power gain Gx is essentially a maximumand upper temperature power drain PDx is essentially a minimum. ForK=0. 7, this value of VRIn is approximately 1. 40v. For small VRln, thefall-off of Gx and the increase in PDx are due to the small values for R2 andR 3 which accompany small VRln. For large VRln, increasing IC and de-creasing RC degrade the performance. As K decreases, the curves show thedesirable results that Gx increases and PDx decreases. However, smallervalues of K imply a smaller dynamic range for the amplifier at its tempera-ture limits, Ty and Tx , as well as a larger operating point drift. It is ap-parent from the Gx and PDx curves that high performange circuit designsare more easily obtained at lower K values where the value of VRln is notso critical.

Figure 21 illustrates the dependence on VRln of upper temperatureinput impedance Rix and output impedance Rox. For a constant K, smallVRIn cause low values of Rz and R 3 and therefore low values of Rix. Thefall-off of Rix at large VRln is due to the small values of R 3 necessary tomaintain the required base voltage as well as a smaller hllex due to largerICx values. Rox decreases monotonically with VRln due to decreases in RC .The increase of Rix with decreasing K is due to the greater operating pointdrift which accompanies smaller K and permits larger R 2 and R 3 . Thedecrease of Rox with increasing K is due to the smaller RC values causedby the increases in VRln required to maintain the tight DC stabilitiesassociated with larger K values.

21

The effect of resistor manufacturing tolerances on the design and per-formance of a typical linear broadband micropower amplifier is indicated incolumn 3 of Table V. The measured results were achieved using two 10%worst case design circuits whose resistor values were deliberately chosento be at their worst values at Ty= -50 0 C and at Tx= +100oC as noted inTable II. The agreement between calculated and measured performanceindicated in Table V appears to substantiate the worst case design theory ofPart 3 of Section 2.

In Table VI the calculated effects of tolerances .in the values of R 1 , R2 ,R3 and RC on the design of a micropower amplifier are indicated in detail.The minimum power 0% tolerance (6 R=O, 6 CR=0) design with K=0. 5 cor-responds to the circuit of the first column of Table V while the 6 R=0. 10,

6 CR=0 design corresponds to the circuit of the third column. It is quiteevident from Table VI that the relatively loose DC operating point stabilityassociated with K=0. 5 permits large values of R 2 and R 3 when R=0. Con-sequently, the reductions in R2 and R 3 necessary to combat worst casetolerances up to 10% and above are readily possible with little increase intotal power dissipation. This fact is also illustrated by the SR=0. 02,K=0. 5 and S R=0* 02, K=0. 7 curves of Figure 22. Therefore, the worst caseK=. 5 calculated results of Table VI and Figure 22 indicate that by permittinga sufficiently loose DC stability micropower amplifiers can readily be de-signed to accept 10% worst case resistor tolerances and maintain a reason-able (one half full range) dynamic range for a 150 0 C temperature change.As indicated by the lower portion of Table VI containing the minimum powerdesigns and Figure 22, -by adjusting the value of VRln it is possible to mini-mize the power drain of a circuit designed with a given resistor tolerancemargin. (It should be noted that the worst case conditions assumed in Part 3of Section 2 which form the basis for column 3 of Table V as well as Figure 22and Table VI, are indeed more severe than any physically realizable set oftolerances. The reason for this, obviously, is that any given circuit canhave either one but not both the worst set of tolerances for ICy and VCEx ,

as indicated in Table II. Consequently, the design theory for resistortolerances is highly conservative. )

In microelectronic integrated circuits where the resistors are fabricatedby batch processes such as evaporation of thin films of metals or diffusion ofimpurities into silicon substrates, it is frequently the case that the absoluteresistor values exhibit wide tolerances but the relative values or ratios ofthe resistors to each other are virtually constant. Such constant ratio toler-ances are not as severe as true worst case tolerances, and a comparison ofthe minimum power worst case and constant ratio designs of Table VI showsthis fact. A linear micropower amplifier can withstand worst case tolerancesof 2% or S R=0 ' 02 combined with constant ratio tolerances of 20% or CR=O. 20and larger as indicated by Table VI and Figure 22. With regard to the physi-cal realizability of the constant ratio tolerances assumed in the calculationfor Table VI, the remarks of the previous paragraph again apply.

22

Columns 1 and 5 of Table V and Figures 23 through 26 provide a com-parison. of the vital features of the basic common emitter amplifier and thecascode amplifier with improved frequency response. Figure Z3 shows that,for typical circuits of equal maximum output power capability, the powerdrain of a cascode amplifier is less than twice the drain of a common emitteramplifier. Figure 24 shows that the power gain of a cascode amplifier suf-fers only a slight reduction of about 0. 5 db compared with the common emit-ter amplifier. Figure 25 illustrates the key advantage of the cascode stagewhich is a five-to-ten time increase in cut-off frequency compared with acommon emitter stage. An overall measure of the comparative performanceof the common emitter and cascode amplifiers is indicated in Figure 26. Thegain-bandwidth product divided by power drain provides a Figure of Meritwhich indicates the overall superior performance of the cascode amplifier.

It is evident from Figures 23 through. 26 that the principal advantageof the cascode amplifier is its comparatively large bandwidth. In practice,stray-circuit capacitances which are neglected in Figures 23 through 26severely degrade this bandwidth. For example, the stray capacitances pre-sent in the relatively crude experimental circuits on which Table V is basedwere larger than the transistor capacitances which-are comparable to thoseof device D. In order to determine the device limited frequency potential ofthe circuits, stray circuit capacitance was neglected in the calculated per-formance and the measured performance data were corrected for the effectsof stray circuit capacitance. To illustrate the significance of this correction,the.directly measured or uncorrected bandwidths of the amplifiers of columns1 and 5 of Table V were 15 KC and 50 KC respectively at room temperature.If these results are corrected to remove the influence of measured straycircuit capacitances, the corresponding bandwidths are about 25 KC and120 KC, respectively, at room temperature. Consequently, it is apparentthat the latest advances in microelectronic packaging techniques are neces-sary in order to properly exploit present micropower transistor capabilitiesand approach the predicted behavior of Figure 25.

23

CONCLUSIONS

Thisreport provides a rather comprehensive discussion of the staticand dynamic design and performance of micropower transistor broadbandlinear amplifiers. The initial consideration in an amplifier design is thecharacterization of a micropower transistor. The salient features of themicropower transistors described in Section 1 are:

1. Junction reverse currents less than one nanoampere at roomtemperature.

2. Forward current transfer ratios, hFE and hfe, greater than 50 forcollector currents of 1 to 10/"Aa.

3. Increased sensitivity of the DC forward current transfer ratio hFEand the fourpole parameters h 1 le and, h2le to quiescent collector current andtemperature changes.

4. A relatively limited gain-bandwidth product fT"

5. A simple hybrid pi common emitter small-signal equivalent circuitessentially consisting of the junction barrier capacitances, CTe and CC , thediffusion. resistance, rb'e, and the output current generator gmVble .

Assuming that constraints exist on the supply voltage, load impedance,output voltage swing, operating temperature range, DC power drain andbandwidth of a micropower amplifier, suitable designs can be generated bymeans of the procedure outlined .in Section 2. With regard to DC design,operating point stabilization is affected by: 1) ICBO which may be comparableto IB , if not I C , at temperatures of 100 0 C and above; 2) increased tempera-ture sensitivity of hFE; and 3) large temperature induced changes in VBE.Large-signal AC design is critical' due to the restricted dynamic range im-posed by microampere collector currents and low collector voltages. In thisconnection, DC operating point drift, saturation and cut-off effects in thetransistor and both transistor and resistor tolerances must be considered.Small-signal AC performance is adversely affected by the limited gain-bandwidth product of micropower transistors as well as the increased tem-perature sensitivity of their small-signal fourpole parameters.

A key element in the micropower amplifier design procedure of Section 2is the simple but rather rigorous approach used to unify the DC and large-signalAC design of an amplifier. Subject to initial constraints, the procedure yieldsan optimum circuit design in that it: 1) provides a specified output power ca-pability over the design temperature range, 2) minimizes amplifier powerdrain, and 3) maximizes amplifier power gain. An additional feature of thedesign procedure is its adaptability to a worst case treatment of the effectsof saturation and cut-off in the transistor and manufacturing and aging toler-ances in all circuit elements.

24

In the small-signal analysis and design of broadband micropower ampli-fiers, a unilateralized hybrid pi transistor equivalent circuit can be utilized.Pronounced temperature variations in amplifier low-frequency AC terminalcharacteristics may be accurately compensated by means of a combination ofemitter degenerative feedback and temperature sensitive base voltage-dividerresistors. The bandwidth of common emitter micropower amplifiers islimited by the Miller Effect capacitance and may be enhanced by increasedtransistor quiescent current and by employing common emitter - commonbase cascode circuits to reduce the Miller capacitance multiplier. Thi.s latertechnique may be widely used to extend the bandwidth of micropower circuitswithout sacrificing gain or additional power drain.

On the basis of the results described in this report, it is evident thatthe principal obstacle to be overcome in the application of micropowertransistors in portable military communications equipment is the limitedgain-bandwidth product of micropower devices and circuits. In order toimprove device and circuit frequency response, transistor junction capaci-tances, header capacitances and stray circuit capacitances must be reducedby at least an order of magnitude to about 0. 1 pf. The accomplishment ofthis objective does appear feasible if the latest advances in microelectronicdevice fabrication and packaging are brought to bear on the problem. Furtherreductions in transistor active region lateral dimensions, perfection of sur-face passivation techniques in order to obviate current package forms anddevelopment of passive parts and interconnections with dimensions compar-able to the transistor are the principal necessary steps toward practicalmicropower communications circuits and equipments.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the many invaluable contributionsof Mr. William J. Fox to the final outcome of the work described in thisreport. In addition, the assistance of Mr. Robert Farlee with the transistorcharacterization and Mr. James Oeffinger with the calculation of circuitdesigns is acknowledged.

Z5

REFERENCES

1. "Electrons and Holes in Semiconductors" W. Schockley;

D. Van Nostrand, Princeton, New Jersey, pp 309 - 318, 1950.

2. "LowCurrent Alpha in Silicon Transistors" J. E. Iwerson et al;IRE Transactions on Electron Devices-, Vol.'ED-9, No. 6, pp 474 - 478,November 1962.

3. "Transistor Electronics" DeWitt and Rossoff; McGraw-Hill,New York, pp 112 - 115, 328 - 332, 1957.

4. "Transistor Electronics,' A. W. Lo et al;. Prentice Hall, Englewood,New Jersey, pp 169 - 178, 1955.

5. "Optimum Stabilization Networks for Functional Electronic Blocks;'J. D. Meindl and 0. Pitzalis; Proceedings of NEC, Vol. 16, Chicago, Illinois,pp 576 - 590, October 1960.

6. "Design of Transistorized Circuits for Digital Computers;' A. I.Pressman; J. F. Rider, Inc., New York, pp 93 - 249, 1959.

7. "Power Dissipation in Microelectronic Transmission Circuits"J. D. Meindl, IRE Transactions on Military Electronics, Vol. MIL-5,pp 209 - 215, July 1961.

8. "Transistor Circuit Analysis.' Joyce and Clark; Addison Wesley,Inc. , pp 248 - 257, 1961.

9. "AC Temperature Compensation of Integrated Amplifiers," J. D.Meindl and 0. Pitzalis; IEEE Winter General Meeting, CP63-62, New York,January 1963.

"AC Temperature Compensation of Integrated Amplifiers" J. D.Meindl and 0. Pitzalis; U. S. Army Electronics Research and DevelopmentLaboratory Technical Report 2307, Fort Monmouth, New Jersey, pp 1 - 6,September 1962.

26

APPENDIX 1

The general expressions for the base voltage divider resistors R2 andR3 considering the combined effects of manufacturing and aging tolerancesand temperature variations in the transistor, resistors and supply voltageare

V~~a 1 Rl+dl)+q ( rR +b R +s)3 t3 -3 ?'3 (cZRi+b 2 ) (a

R 3(O 1R1IEY+VBEyan cc20 vVCCGVBEyO R1I Ey03 R 3 1By] Za

where a

I VB Z' vB VBEYlk3Ix 1Ot3#2 ?2k ~2 2 By -Bx 42)Z-x By

b3 1~ 1Ey VBEx +0.l "Ex VBEy

c Jl y x ' P x 'y

2 CC v 3 YBEx ()3102Z'v r'Zv BEy

r C1i rIEX IEY

S BEx VBEy

a nd = (1+ R+~G)P ' 8 1~R

2 = (1RZ+ JC) 192 = (1+3 RZ- CR)

OL 3(1= R3+ CR) IO3 =(1- a 3 4 CR)

O(v= (v) V=(ISv

R at T R Rat Ti R at T j3 R at T

R 2 at Tx -c at Txf2 R 2 at T y v V c at T

In the preceding expressions:

a) R l' S RZ and R3represent the worst case resistormanufacturing and aging tolerances.

21

b) J CR represents the constant ratio resistor manufacturing and

aging tolerances.

c) v represents the worst case supply voltage tolerance.

d) 'v 77 and k3 represent the resistor temperature factors.

e) )v represents the supply voltage temperature factor.

As examples of the evaluation of (la) and (2a):

a) For ±- 5% worst case resistor manufacturing and aging tolerances

SRl = 'R2 = 'R3 = 0.05, 0% constant ratio tolerance 4 CR = 0, 0% supplyvoltage tolerance 'r v = 0 and no resistor or supply voltage temperaturevariation, 1 = ., 2 = )3 = ?v = 1.0.

b) For + 2% worst case resistor manufacturing and aging tolerances

RI = R2 = R = 0. 02, ±_ 10% constant ratio resistor manufacturing andaging tolerancej Cp = 0. 10,' ±5% supply voltage tolerance Sv = 0. 05, a20% increase in all resistor values over the design temperature range

1 1 = 3 = 1. 20 and a 5% decrease in the supply voltage over thedesign temperature range ?V = 0. 95.

In certain cases where temperature behavior is predictable, indicatedin Part 5 of Section 2, it is advantageous to treat resistor manufacturing and

aging tolerances separately from temperature variations via the temperaturefactors )i, ?Z , ) 3 , , . and "v" If the sign of a temperature variation is

unknown, the magnitude must be included in S in the worst case analysis.

28

APPENDIX 2

In the case where Re 'A 0, the current and voltage gain of the circui

Figure 8 are given by

iz _,n g z b 'I1- - Re+(~m~)be b'

il Re + (1+gmR)zble + j) [Re+( l +gmRe) zb'e+gmRLzb'e) (C CCR23 '

v - g m z WeRC ZL

and V1 Re+Z 1 (1+gnRe) RC+ZL (4a)

where zbe rble and ZL RL

w +j rble(Cbte+Cbles ) l+jG0RLCces

APPENDIX 3

When the temperature compensation technique of Part 5 of Section 2 isutilized in an amplifier design, the AC output voltage swing,which is specifiedfor the design, may be achieved as described below.

Assuming the temperature compensation constraints given by (Z. 47)through (2. 51), the design proceeds as described by (2. 15) through (2. 20) ofPart 2 of Section 2. If Ky is selected, Icy is determined by (2. 21). Fromthis, (2. 51) gives ICx for the temperature compensated design. Therefore,(Z. 10) yields VCEX and (Z. 22) then specifies the Value of Kx which accompa-nies the compensated design. If this value of Kx does not provide a suitableoutput voltage swing, another value for VRIn should be selected in (2. 19)and (2. 20) which will yield a new value for Kx . (An alternate approach is toselect several values for Kx = K7 until (2. 51) is satisfied.) R Z and R3 maythen be computed from (la) and (2a) of Appendix I where all Q's,A 's, and

's are unity except ? 2= ?3 = 1'23. Finally, the Re required for AC com-pensation may be computed from (2. 48).

It is important to note that in computing ICn and RC from (2. 19) and(2. 20), a value was selected for VRen which, in effect, determinedRe = Ren/(ICn - Io). If this latter value of Re is greater than the valuerequired by (2. 48), the value given by (2. 48) should be used and the excessamount should be included in R1 to be bypassed by C 1 . In this way the ACdynamic range will be increased somewhat over the design value, and thedesired AC compensation will be affected.

If the value of Re computed from (2. 48) is greater than the valueeffectively assumed in (2. 19) and (2. 20), the recommended procedure is toreturn to (Z. 19) and (Z. 20) and increase the selected value of VRen andtherefore Re in order to precipitate the situation described in the previousparagraph.

30

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300-

E YVCE 3 .0 V

200-

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0.1 0.2 0.3 0.4 0.5 0.6 0.7VBE (VOLTS-)

Figure 2 - Base Characteristics for Common Emitter Configuration; basecurrent IB versus base-to-emitter voltage VBE for variousoperating temperatureb T.

S7

80

160-

140-

120

100- 1IC OUOVCE= 3.OV

80-

60

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-50 -25 0 25 50 75 100

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Figure 3 -Common emitter forward current transfer ratio hEE versustemperature T.

Se

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-80

h21 e~-60

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Figure 4 - Common emitter small-signal short-circuit input impedancehie = hle and forward current transfer ratio hfe = h2le versuscollector current IC .

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1 2 3 4 5 6

VB(V) REVERSE BIAS

Figure 7 - Base-emitter junction capacitance CTe versus base-to-emitter

voltage VBE and base-collector junction capacitance CC versus

collector-to-base voltage VCB for various temperatures.

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'T

Figure 14 -Micropower amplifier schematic diagram indicating circuit

currents, voltages and component values: (a) at the lower

operating temperature limit Ty, and (b) at the upper operating

temperature limit T x .

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Figure 35 - Cascode rnicropower amplifier (a) schematic diagram, (b) ACequivalent circuit.

10- -2.5

8 2.0

6 1.5

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o I I I 0

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Figure 16 -~Micropower amplifier quiescent collector current IC and collector-

to-emitter voltage VCE versus temperature T.

20

15-

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temperature T with AC emitter feedback resistance Re=0, 3. 89KtI

and peak output voltage swing VL=O. 18, 0.09 v.

S.

35

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2~25 8, i z31023.0

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15 t

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Figure 18 - Mid-band power gain G versus temperature T for two noncompen-

sated amplifiers, Re=O, -)Z3=1. 0 and Re=3 . 89Kf1, -" Z3=l 0 and

a compensated amplifier Re=4 . 42Kfl, )'23=0 28.

500- 494

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200

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T( 0 C)

Figure 19 -Mid-band input impedance Ri versus temperature T for twvo

noncompensated amplifiers, Re=O, ' 23="1 0 and Rez 3 . 89KIL,

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