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Consider the common-collector amplifier in the figure (bias circuitry ensures that the transistor operates in forward active region, but has been omitted for simplicity). Let I_C be the collector current, V_BE be the base-emitter voltage and V_T be the thermal voltage. A I_S, gₘ and rₒ are the small-signal transconductance and output resistance of the transistor, respectively. Which one of the following conditions ensures an early constant small signal voltage gain for a wide range of values of R_E?

1. (A) gₘ R_E << 1
2. (B) I_C R_E >> V_T
3. (C) gₘ rₒ >> 1
4. (D) V_BE >> V_T

Correct answer: (A) gₘ R_E << 1

Solution

The condition gₘ R_E << 1 ensures that the gain of the common-collector amplifier remains relatively constant across varying values of R_E, as it indicates that the transconductance is much smaller than the resistance, minimizing the impact of R_E on the overall voltage gain.

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