Low Distortion and High Thermal Stability in Transistor Audio Power Amplifiers Summary-Two paramount objectives in the design of a high- sary and suficient is the following: There shallbe no quality transistor audio power amplifier are attaining good linearity nonlinearity in the open-loop transfer characteristic at and ensuring good thermal stability. Conflicts frequently arise in realizing these objectives in that steps taken to achieve one tend to any signal level below clipping which causes the incre- worsen the other. This paper examines these two subjects to deter- mental gain, ;.e., the slope of the transfer characteristic, mine the essential conditions which must be fulfilled in order for the to approach zero. Expressed differently, if and y are objectives be met. As a result of this examination the requisite the open-loop input and output, respectively, and B is conditions are found and several useful circuit techniques are de- the closed-loop feedback ratio, one requires that veloped. These techniques provide excellent thermal stability and at the same time permit attaining good linearity with reasonable amounts of negative feedback. Experimental results are given which confirm the validity of the principles and the value of the techniques. B If (1) is satisfied, then the closed-loop incremental gain DISTORTION NONLINEAR will beconstant at 1 / B andthe closed-looptransfer A CHIEVING LOW distortion in anaudio power characteristic will belinear.Theimplications amplifier requires that the over-all transfer char- acteristic exhibit no appreciable nonlinearity in the portion of the characteristic in which normal pro- condition are as follows: 1) class B operation is ruled out, of this class A B operation is acceptable and with eased bias tolerances, and3) nonlinear techniques may be con- gram material spends an appreciable amount of time. sidered for use in the achievement of thermal stability. For music and speech this regionis that around the This last point will now be considered in detail. origin of the transfer characteristic, and for this reason low-level or crossover distortion is of major concern in the design of a high-quality audio power amplifier. As is well known, the thermal stability of a transistor The presence or absence of crossover distortion in a amplifier is governed by the thermal-electrical positive transistor power amplifier depends on the type of bias feedback process whereby heating causes increased col- applied the and effectiveness of distortion-reducing lector current which in turn causes still more heating. feedback. Because class A operation is too inefficient t o For this process to reach a stable equilibrium the “loop be acceptable, push-pull class B or A B operation must gain” for this process must be made less than unity by: beemployed.Sinceitmaybeassumedthatover-all 1) selectingsuitablevalues of the various parameters negativefeedback ill beincorporated in anyhigh- aroundtheloop, , e.g., I c ~ othermal resistance 0, and quality audio power amplifier, the choice between these power supply voltage Vcc, and/or 2) introducing nega- twomodes of operation depends on the way the bias tive feedback to modify one or more of the processes arrangement influences the nature of the open-loop comprising the loop. Since the useful choices for Icno, 6, transfer characteristic and thereby the effectiveness of and VCC usually very limited, and since adequate are the feedback in producing linear closed-loop response. stability can seldom be attained by this means alone, A suficient conditionfor goodclosed-looplinearity the feedback approach is essential in achieving thermal would be to require that the open-loop transfer char- stability.Negativefeedbackcanbeappliedeitheras acteristicbe as linear as possible.On thisbasispure direct electrical feedback or as thermal-electrical feed- class B operationwouldbeexcludedsinceobjectional back. The latter method consists of utilizing tempera- crossover nonlinearities appear even with high-inlped- ture-sensitive bias elements to reduce the bias current A ance drive. On this same basis classB operation would as temperature increases. limitation of this method is A& be acceptable if, but only if, the bias were set at pre- that the temperature influencing thebiaselements is cisely the correct value. This would be a very stringent the ambient or heat sink temperature rather than the requirement. Fortunately this condition is not a neces- transistor junction temperature, the parameter which sary one. A less stringent condition which is both neces- actually determines the electrical characteristics of the transistor. Appreciable time lags occur between changes in thesetemperatures so thatthermal-electricalfeed- Manuscript received April 1964. R. A. Greiner is with the Department of Electrical Engineering, back is ineffective in stopping rapid thermal runaway Lniversity of Vv?sconsin, Madison, IITis. processes. This type of feedback is so slow t h a t i t is D. G. Daugherty is with the Department of Electrical Engineer- ing, University of Kansas, I,aa.rence, Kan. perhaps better not regarded as feedback but rather as Authorized licensd use limted to: IE Xplore. Downlade on May 10,2 at 19:054 UTC from IE Xplore. Restricon aply. Daugherty and Greiner: Distortion and Thermal Xtability in Transistor Amplifiers 27 empirical compensation changes ambient bias for in capacitivebypassing of theseresistances in class A B temperature. rapid The runaway processes must amplifiers is not useful because the emitter signal cur- be sensed and inhibited by electrical means. Direct electri- rentshaveinherentlynonzeroaverageswhichwould cal feedback is thus the primary method for ensuring cause the capacitors to charge and bias the amplifier thermal stability. into cutoff. Accordingly either small emitter resistances T o determine how stability may actually be achieved, mustbeemployedorsomenoncapacitivebypassing i t is necessary to consider the precise mechanisms by arrangement must be found. which thermal instability can occur. A pair transistorsof Suchanarrangementisthat of Fig. 2, wherethe comprising a push-pull class A B amplifier can be con- emitter resistor is bypassed a t large currents by a series nected in essentially two d-c configurations, series and pair of silicon diodes. Since normal silicon diodes require parallel. parellel The arrangement applies trans- to approximately 0.6-volt forward bias before appreciable former-coupledcircuitswhereastheseriesconnection conduction occurs, by suitable selection of RE and the prevails in virtually all output-transformerless circuits. bias current the quiescent operating point may be set In The latter group is of concern here, and a series con- the center of the moderate sloperegion of the trans- figuration will therefore be used as the basis of analysis. conductance characteristic, as shown in Fig. 3. In this Consider the circuit of Fig. 1 and currents il, iz, and case diodebypassing when emitter commences the i ~ . notedabove,thermalrunawayinvolvesanin- As current is driven to twice the quiescent value. This ar- crease in collector current. For an increase in il to occur rangement providesgood bias stability by allowing large there must be an equal increase quiescent RE while at the same time permitting signal in ( i ~ + i 2 ) . Since the output stage is presumably included within a negative operation at highcurrentswithhighgainandsmall feedback loop, an appreciable increase i~ is precluded in losses. An apparentdisadvantage of thisapproach is in t h a t such a n increasewouldconstitutedistortion that it is nonlinear. T h e open-loop transfer character- which would be reduced by the feedback. Thus Qz must istic of a class AB power amplifier using a pair of tran- provide the path for an increase in the collector current sistors connected as in Fig. 2 would be as shown in Fig. of Q1 and vice versa. For examining the collector cur- 4.This transfer characteristic has a slope which is much rent behavior of Q1 and Qz under class A B operation, greater than zero everywhere. Therefore, the necessary we may consider separately near-quiescent the and condition for low closed-loop distortion is satisfied and large-signalphases of operation.Underano-signalor t h e open-loop nonlinearity is not in fact a disadvantage. small-signalconditionclass A operationprevails,and Thus byjudicious application of nonlinear elements itis there is an appreciable collector current flowing due to possible to obtain excellent bias stabilization without the applied bias. Accordingly, quiescent runaway is a causing appreciable amounts of distortion. distinct possibility if the quiescent current is not care- Consider now the large-signal phases of operation of fully controlled.Hence requirement thermal one for the class A B system of Fig. 1, i.e., consider a time when stability is adequate bias stabilization. one transistor is conducting and the other is nominally OFF. If the current Ioff the OFF transistor is actually in zero, then there is no dissipation in that transistor dur- ing its OFF time, and the dissipation in the tran- that sistor is exactly predicted from simpletheory. However, if I o f f # O , excess current flows in both tran- sistors, and there is an excess dissipation per transistor given bylicc(lorr,~+I,tr,2)/2,where V C C is definedin Fig. 1. To prevent thisexcess dissipation from becoming excessive dissipation, (Ioff,~+Iof~,2) small. must be kept Thus the second condition for thermal stability is effec- tive minimiziation of Ioff. Fig. transformerless amplifier circuit for A technique for minimizing I o f t in germanium tran- analyzing thermal stability. sistors (Ioff isnegligible in silicon) is showninFig. 5 where a silicon diode has been added in series with the An effective technique for stabilizing transistor emit- emitter of the germanium transistor. For this arrange- ter and collector current is to apply negative current ment, IoorrgIcBo if the base circuit conditions are such feedback by introducing resistance in the emitter cir- t h a t V B<0.6 volt during the OFF time. Note that this cuit of the transistor. This is of course extensively used circuitdoesnotprovideanybiasstabilization.How- in low-power class A circuits. However, two major ob- ever, by combining this technique with that of Fig. 2, jections to the use of large emitter resistances may be as shown in Fig. 6, an arrangement providing both bias raised in thecaseofpoweramplifiers: 1) the voltage stabilization and Ioff minimization results. In this cir- of and power gains the output stage are severely reduced cuit, as in t h a t of Fig. 2, RE and the quiescent current and 2) power losses in the emitter resistances can be- IQ should be chosen sucht h a t IQRE 0.6 volt. While RE come prohibitively large. It must be further noted that should be large forgood bias stability, some upper limit Authorized licensd use limted to: IE Xplore. Downlade on May 10,2 at 19:054 UTC from IE Xplore. Restricon aply. 28 IEEE TRANSACTIONS O N AUDIO M arch,-April Fig. 6---A stabilization-minimization technique combining Fig. 2-A nonlinear bias stabilization technique. the features of the techniques shown in Figs. 2 and 5. IC must be observed. If RE is too large the slope of the open-loop transfer characteristic becomes too small to sarisfy (1). This occurs both because of the degenera- tion introduced by R E and because the necessarily small quiescentcurrent ( I Q = ~ . ~ / R E ) areduction causes in for small-signal operation. The appropriate upper limit on RE can be determined from analysis of the cir- cuit in which these techniques are to be utilized. This 0 analysisshouldinclude a feedbackstabilityanalysis. 0 The amplifier such be mustdesign over-all the that Fig. 3-The transconductance characteristic smallestslope of the open-loop transfercharacteristic for the circuit of Fig. 2. will satisfy ( l ) ,and at the same time all values of slope between this and the maximum must imply acceptable stability. feedback I t should be noted that in theseseveraltechniques silicondiodeshavebeenemployed in spite of rather than because of theirtemperaturedependence. Ac- cording-ly the diodes should be isolated thermally frotn thepower and be transistors should provided with suitable heat dissipators of their own. EXPERIXEXTAL htPLIFIERS The validity of theprinciplesgivenaboveandthe value of the techniques described are confirmed by the results for two experimental amplifiers. Fig. 7 shows the I output configuration employed in these amplifiers. This Fig. 4-.A typicalopen-looptransfercharacteristicfor Push-pull circuit is basicallS7 the L ~ quasi-complementary ampli- ~ I amplifier using two transistors connected as in Fig.. 2. fier modified to utilize the stabilization techniques de- scribed above. For the compound transistor composed of Q 3 and Q 6 the stabilization-minimization technique of Fig. 5 is employed. resistance For R: thecondition R 5 RL 8 ohms is observed in order to limit the varia- 7 tion in open-loop transfercharacteristicslopeto no more than a factor of two. Since six-ohm resistors were ,7 a t h a n d R is ohms andIQ 100 ma. I n the uppercorn- 7r pound transistor Q2 Q 4 a modification of Fig. 5 is ap- plied t o Q4, and the compound as a whole is stabilized by use of the technique of Fig. 2. Diode D Sminimizes I o f f Fig. off-current effective technique minimization H. C. Lin, complementary amplifier,” “Quasi transistor Elec- for use with germanium transistors. tronics, vol. 29, pp. 173-175; September, 1956. Authorized licensd use limted to: IE Xplore. Downlade on May 10,2 at 19:054 UTC from IE Xplore. Restricon aply. Daugherty and Distortion Greiner: and Stability Thermal in Transistor Amplifiers 29 The excellence of the thermal stability is evidenced by the following data. With the amplifier operating un- der maximum dissipation conditions, the power supply current, and the output transistor heat-sink tempera- ture were recorded a t frequent intervals during a 41- minute test period. The heat-sink temperature varied from an initial value of 30°C to its equilibrium value of this 62OC. During interval was detectable there no change in powersupplycurrent.Fromtheconstancy of this current i t is clear that the dissipation was also constant and that the thermal stability was very good. T h e secondamplifierbasedonFig. 7 employs V g g 2 VCC= volts, CBs= 1000 uf, R1= 100 ohms, and 120 z R 500 ohms. This combination produces 150 watts of sine-wave power in an 8-ohm load and exhibits distor- tion and stability characteristics similar to those given above for the 50-watt unit. As a check on the effective- ness of the diode-resistor networks, this 150-watt am- plifier was “simplified” by omitting several of the diodes and adjusting the bias accordingly. This modified cir- cuit exhibited poor thermal stability and failed destruc- Fig, 7-The basic output configuration used in the two experimental tively at a power level of about 50 watts. From these amplifiers described in the text. All three P-N-P transistors are germanium, both N-P-N transistors are silicon, and all diodes resultsit is seen thatthediode-resistornetworks of are silicon. Figs. 2 and 6 do promote thermal stability and at the same time permit achieving low distortion performance with reasonable amounts of negative feedback. h of Q4 while R6 and D prevent Q 4 from turning off too T h e use of nonlinear techniques is often complicated abruptly and introducing crossover distortion. By sym- and expensive and involves a time-consuming selection s 7 e metry, R R so t h a t R has a value of 6 ohms. andmatching of components.Theapplication of the T h e use of diodes Dl,Dz,and D to provide the base techniques 3 described however, here, is completely bias voltage is a standard practice. The merits of this straightforward. The utilization of the silicon diodes is practice are twofold. One obvious merit is the good bias based on the fact that for appreciable current flow a compensation provided for variations in ambient tem- foward drop of about 0.6 volt is required. Since exactly perature. A second and more important feature of the 0.6 volt is not required, no matching of V-I character- practice is that the diodes exhibit a dynamic resistance istics and/or temperature dependences is involved. The which is much smaller than the static resistance V / I . diodes are never reverse-biased, and therefore reverse Thismeansthattheinstantaneousvariation of bias characteristicsareunimportant.Thusanyhighcon- voltage with signal is much less than would be observed ductance silicon diode of appropriate current rating can if a linear resistance were used in place of the diodes. be used. The constancy of this bias voltage not only improves the symmetry of the transfer characteristic but, more im- CONCLUSION portant, promotes thermal stability by providing ade- Low-distortion amplification requires adequate nega- quate turn off bias for Qz- Q 4 when Q3 Q 6 are driven tive feedback and an open-loop transfer characteristic ON. which has reasonable slope a t all levels other than clip- In the first amplifier based on Fig. 7, VBB 83 volts, ping. Thermal stability requires adequate bias stabiliza- VO= 75 volts, CBS=0, and (Rl+R2) 2000 ohms. tionandeffectiveoff-currentminimization.Thesere- This amplifier delivers 50 watts sine-wave power to an quirements can be met simultaneously by application of 8-ohm load and exhibits open-loop harmonic distortion the techniques of Figs. 2 and 6, as exemplified in Fig. 7, whichvariesbetween 2 and 4 percentasthesignal and including the output stage in an over-all negative level is varied from zero to full power. When a voltage feedback loop. By these means it ispossible to build amplifier is added and 20 t o 26 d b of feedback is applied, verystable,low-distortiontransistorpoweramplifiers the distortion drops by an order of magnitude, as ex- using either silicon orgermaniumtransistorsorany pected, and a stable, low distortion amplifier results. combination thereof. Authorized licensd use limted to: IE Xplore. Downlade on May 10,2 at 19:054 UTC from IE Xplore. Restricon aply.