46 IEEE TRANSACTIONS ON EDUCATION, VOL. E-29, NO. 1, FEBRUARY 1986

In a recent paper, Malik [1] described a method for teaching the +\/cbasic concepts of the differential amplifier (DA) using the approach RL RLof superposition and symmetry [2]. Class experience over a few Ayears convinced me that such an approach could indeed help stu-dents to better comprehend the concepts of differential gain, com-

Q

mon mode gain, differential input resistance, etc. Many students, + ' Qhowever, seem to have difficulty in understanding these new con- 2-cepts as well as the concept of dc amplification. The difficulty can REprobably be attributed to the fact that the preceding relevant coursematerial (small signal amplifiers) does not cover dc coupled ampli- -VEEfiers and is concerned only with single-ended signals. Hence, stu-dents are puzzled, for example, by the fact that no bypass capacitor Fig. 1 Conventional circuit diagram of a DA fed by a differential signalis required on RE (Fig. 1) in a DA. Furthermore, formal derivation d-of the pertinent functions, such as differential gain, does not resolvethe feeling of some students that "something is wrong." To clear cc +vcup the point, I have adopted an approximate analysis which relates

R

the mechanism of amplification in a DA to configurations of small RL RLsignal amplifiers which are more familiar to the students. The basic VOconcepts of this intuitive approach, which is akin to a more accurate I,.Q1 R,n2iVn R12approach given earlier [3], [4], are given here for the benefit of L. RL RL _ Q2 in

those who may wish to adopt it. VC Cc-Rather than drawing the single-ended-output DA in the symmet- 2 RERE + T

rical form (Fig. 1), one can present the amplifier as a cascade of - Re Retwo stages [Fig. 2(a) and (b)]. Applying the simplified h-parameter -VEE -VEEmodel (hre = hoe = hrb = h,b = 0), an approximate expression for (a) (b)the voltage gain function, with respect to Vd/2 and -Vd/2, can bederived by assuming [Fig. 2(a)] Fig. 2. Alternative presentation of the DA for an approximate analysis by

superposition with respect to Vdt2 (a) and - VdI2 (b).R h hi, ~~~~~~~~(1)i1

2 1b_ hfe is zero since the current contributions of Vd12 and VdI2 cancel

and each other.Experience has shown that devoting a few minutes in the class

hie (2) to this approximate analysis saves many questions later when a moreRE » + hfe rigorous analysis, as the one suggested by Malik [1], is pursued.

Hence [Fig. 2(a)], REFERENCES

Re RER_hie [1] N. R. Malik, "Teaching difference amplifier concepts," IEEE Trans.Re = REIIRin2 I ( ) Educ., vol. E-27, pp. 26-30, 1984.

fe [2] E. J. Angelo, Electronics BJTs, FETs, and Microcircuits. New York:By reflecting Re to the base of Ql, one obtains McGraw-Hill, 1969.

[3] J. A. Watson and J. R. Miller, Transistor Circuit Design. New York:Rini -hie + Re(1 + hfe) 2hie. (4) McGraw-Hill, 1963.

Since the emitter signal current of Q, flows into the emitter of Q2 [4] P. J. Comer, Modern Electronic Circuit Design. Reading, MA: Ad-(RE >> Rin2), it follows that the collector signal currents of Q, and dison-Wesley, 1976.Q2 must be equal and of opposite sign (remember that the ratio ofcollector-to-emitter signal current of a BJT transistor is related bya); consequently:

Vd\ Vd hfeRL Comments on "Zero Distortions in Negative Feedback

VO 2) = 2 2hfe (5) Amplifiers"

Similarly, from Fig. 2(b), CARLOS URBINA PACHECO

Vdmllarly from F 2(RLbhfeVo - ) ( 2 (6) Equation (10) in the above paper' is incorrect. The correct form

can be shown to beand by superposition f" i (si)

VO RLhfe g"(Xs) = [1 + 13()]Vd 2hie where the denominator factor [1 + 3'(xi)] is raised to a power of 3

The analysis of the DA differential gain by the redrawn circuits rather than 2.[Fig. 2(a) and (b)] emphasized the fact that each transistor sees asits emitter a rather low dynamic resistance, which, when reflected Manuscript received April 8, 1985.to its base, is equal to hie. Hence, the total input resistance is in- The author is with the Department of Engineering, Institute Technolo-creased from hie to 2hie, thereby reducing the voltage gain by a gico y de Estudios Superiores de Monterey, Unidad Laguna, ITESM, Apdo,factor of 2. The elimination of RE from the analysis is justified by Mexico.the fact that it will always be much larger than the input resistance IEEE Log Number 8407086.Of a common base stage (R,n2) of BJT which is in the order of 10 Q. iD. Wulich and H. Aharoni, IEEE Trans. Educ., vol. E-27, pp. 243-It can be further shown that the residual signal current through RE 245, Nov. 1984.

0018-9359/86/0200-0046$01.00 ©C 1986 IEEE