Contains reports on two research projects

Adler, Richard B.

Blair, J.

Kerk, C. T.

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IX. TRANSISTOR CIRCUITSProf. H. J. Zimmermann J. Blair C. T. KerkProf. R. B. Adler J. B. Cruz R. B. MartindaleProf. S. J. Mason J. Gross R. F. MeyerC. R. HurtigA. VOLTAGE-REGULATED POWER SUPPLIESDesign studies of transistorized voltage-regulated power supplies for transistorcircuits were continued. A circuit which requires no external voltage supplies wasdeveloped and is shown in Fig. IX-1. The regulator employs a pnp power transistor(type 2N57) in series with the rectifier and the load. A two-stage, direct-coupled ampli-fier is used in the feedback loop. The reference voltage is obtained from the reverse-biased breakdown characteristic of silicon-alloy junction diodes. In the supply shown,two silicon diodes (D1 and DZ) are used in series to produce a reference voltage of 15. 6volts.The output voltage may be varied by means of the potentiometer from 20-25 voltswith only small changes in the regulation characteristics of the supply. The quiescentcurrent bias for the power transistor is supplied by the silicon transistor used inthe output stage of the direct-coupled amplifier. The bias for the silicon transistoris obtained by use of the breakdown voltage of silicon diode D3 and the 5. 6K resistorconnected to the base lead of the silicon transistor. The capacitor from the collectorto the emitter of the 1859 transistor suppresses high-frequency oscillations. The fre-quency response of the voltage regulator is essentially flat up to 10, 000 cps.The voltage-regulation characteristic as a function of load current is given inTable IX-1. The variation in the output voltage as a function of line voltage variationis negligible. At a load current of 100 ma the power transistor dissipation is 0. 83 wattand the efficiency of the regulator (excluding rectifier losses) is 66 per cent. At 140 mathe dissipation is 0. 43 watt and the efficiency is 84 per cent. This high efficiency isthe result of the ability of the power transistor to operate close to zero collector voltage.The lower limit upon the input voltage to the regulator (point A) is determined by thedesired output voltage, the peak voltage of the ac ripple, which increases with loadcurrent, and the static characteristics of the transistor at maximum current.IN9 .. .Fig. IX-1. Voltage-regulated power supply9 43 43 A 9 K 7li5V60-'LOAD(IX. TRANSISTOR CIRCUITS)Table IX-1. Voltage Regulation CharacteristicsLoad Current Direct Voltage Ripple Voltage (v)(ma) (v) (peak-to-peak)A B A B(change from nominalvalue of 20 v)0 40 0 0.30 <0.00150 34 -0.02 0.55 <0.001100 28 -0.05 0.70 <0.001140 23 -0.08 0.80 0.001Voltage regulators of this same general configuration having nominal output voltagesfrom 3-25 volts were designed and tested. The lower limit of the output voltage isdetermined by the availability of silicon diodes with low values of reverse breakdownvoltage. The upper limit of the output voltage is determined by the maximum voltageratings of the transistors. In the circuit shown the maximum load current is limitedby the maximum value of the reverse current of the diode D 3 , and the gain of the seriestransistor. The current in the diode is maximum at no-load and its value is determinedby the desired change in load current and the large signal gain of the series transistorover this range.Since the breakdown voltage of the reference diodes has some temperature depend-ence (the ones used varied by about 0. 08 per cent/°C), the output voltage will have atleast an equal temperature dependence. To reduce this temperature dependence, com-pensation by means of thermistors, or by auxiliary forward-biased diodes, may beemployed. Alternatively of course, the diodes may be replaced by batteries having low-temperature coefficients.C. T. KerkB. A MICROSCOPIC INTERPRETATION OF POWER GAIN IN JUNCTIONTRANSISTORSIn amplifiers of the vacuum-tube variety, it is usually possible to understand theprocess of power gain by tracing particles and discussing their energy changes as theymove. While this procedure is not usually the best way to achieve a quantitative des-cription of the device, it often serves as the root of our qualitative understanding of thegain mechanism. In some cases, it may indeed have been the keystone of the inventionof the original device. Peculiarly enough, however, this viewpoint has certainly neverbeen stressed for the transistor, and to the best of our knowledge it has not even beendiscussed. The following compressed outline presents the major features of an attempt(IX. TRANSISTOR CIRCUITS)to treat the junction transistor through a discussion of the particle energies involved (1).We recognize first that "class A" power gain shows up inside a resistive amplifyingdevice as a change in the internal power dissipation. A microscopic view of the dissipa-tion process is therefore required. We achieve this view by writing an energy balancerelation for clouds of holes and free electrons in a semiconductor which is slightly outof thermal equilibrium.In notation which is now standard (2), statistical mechanics leads to the concept ofquasi-Fermi levels for holes and free electrons out of equilibrium= + (kT/q) In (p/n.)p 1(1)S= - (kT/q) In (n/n i )The hole and free electron current densities are then given byP = -q Lp p V p(2)In = -q n V nleading to the notion of generalized nonequilibrium forces Fp, nFp = -q V4p = -q Vi - k V[T In (p/pi)](3)Fn = +q Vqn = + q VY - k V[T In (n/ni)]which are conservative. The potential energies of the carriers at a point s in the non-equilibrium force field are defined in volts asI (s) = F d9 = (s) -p q p p pminmin(4)sI1 (s) = F di = -[(s) - n in]n q n n n minminwhere the zero point is taken at the position where 4 is minimum for each typeof particle. The organized drift velocities are-pVdp qp p p(5)-IVdn qn n Vn(IX. TRANSISTOR CIRCUITS)The assumption of small departures from equilibrium implies that organized transportkinetic energy terms 1/2 m vd are negligible. Therefore the work done by nonequilib-rium forces goes into the lattice as "conductive dissipation"P d -F P Pq 2cp dp pp p l p(6)I n qn7 2Pnp = Vdn Fn n in n n nIf we consider the hole and free electron clouds as open systems, the energy of con-figuration plus thermal energy of each particle can be shown to beEw = 3 /2 kT gp q 2q(7)w = 3/2 +n q 2qwhere E is the energy gap, and hole and free electron masses are taken to be equal.Thus the entire energy per particle isEp = 3/2 kT g + 11p q Zq p(8)Egn 3/ kT + + 1=3/2 -- nWe now note that the energy of a unit volume of a cloud may change by four processes:1. convection of particles, 2. recombination of particles, 3. collision of particleswith the lattice (conductive dissipation), and 4. change of 0 with time at constant par-ticle concentration. The expression of the total energy balance of the clouds per unitvolume then becomesq at (p p) -V. ( p)- qr(np- n p)p + I Vp + qpp at (9)q a (n (In n) - qr(np - n )n Vn + qn0 n n atIf Eqs. 9 are expanded fully, they become nothing but the continuity equations for theflow of holes and free electrons. Expanding only the left side, however, yieldsq -- ( ) - qr(np-  np - P Vpp at p p L 0(10)q n =v. ( n) - [qr(np - noPo) n + n V n](IX. TRANSISTOR CIRCUITS)The term in brackets, as we have seen, is the total dissipation per unit volume, andthe divergence term represents convection of energy into the volume. Thus the leftsides are interpreted as the rate of increase of stored (recoverable) energy per unitvolume.If we treat the temperature T and the gap E as variables independent of thegnonequilibrium potentials HI, since the latter can be altered by light, voltage, and soon, we may write Eqs. 8 as= ' +Ip p p(11)n =  ' + 1nBecause the energy balance relations (Eq. 10) are linear in p and n they can then beseparated into two sets, one in ' and one in II, for each particle type. The equationsinvolving IH have been checked for dissipation in an idealized transistor under quiescentconditions, and as a low-frequency amplifier. In both cases the dissipation checks withcomputations from the equivalent circuit.More work remains to be done on the fully time-varying case, and in connectionwith the equations involving only }'.R. B. Adler for J. BlairReferences1. See J. Blair, Theory of power gain in junction transistors, S. M. Thesis, Depart-ment of Electrical Engineering, M. I. T., Sept. 1, 1955, for further details.2. W. Shockley, Electrons and Holes in Semiconductors (D. Van Nostrand Company,Inc., New York, 1950).

Transistor Circuits

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Transistor Circuits

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