Derive the approximate voltage gain of a CE amplifier with emitter degeneration and resistor values RE and RC.

• A. Av ≈ -RC / (r_e + (β+1)RE); with a bypass capacitor across RE, the gain increases toward -RC / r_e.
• B. Av ≈ -RC / (r_e + RE).
• C. Av ≈ RC / (r_e + (β+1)RE).
• D. Av ≈ -RC * (β+1)RE / r_e.

Answer: (C)

Main idea: emitter degeneration adds negative feedback that increases the effective emitter resistance in the small-signal path, which lowers the gain.

In a common-emitter stage, the small-signal emitter current is about (β+1) times the base current. The resistor RE then introduces a voltage drop of (β+1)RE due to that emitter current. Along with the intrinsic emitter resistance r_e, the total emitter impedance faced by the signal is r_e + (β+1)RE. The collector current is roughly β times the base current, so the voltage change at the collector is v_C ≈ - i_C RC ≈ -β i_B RC. Putting these together gives an approximate base-to-collector gain Av ≈ - RC / (r_e + (β+1)RE). If you report the magnitude of gain, you drop the minus sign, yielding Av ≈ RC / (r_e + (β+1)RE). This aligns with the chosen option, which expresses the magnitude of the gain in that form. The bypass case across RE removes the (β+1)RE term, moving the gain toward -RC/r_e, illustrating how AC degeneration reduces the gain.