Power gain of a transistor amplifier: Which expression correctly relates the overall power gain (Ap) to the voltage gain (Av) and current gain (Ai)?

Introduction / Context:
Amplifier gain can be defined for voltage, current, or power. Linking these gains helps convert specifications and predict performance when cascading stages. Knowing the correct relationship between power gain, voltage gain, and current gain avoids design errors.

Given Data / Assumptions:

• Small-signal linear operation so gains are meaningful ratios.
• Voltage gain Av = Vout / Vin.
• Current gain Ai = Iout / Iin.
• Power gain Ap = Pout / Pin.

Concept / Approach:
Power is proportional to the product of voltage and current. For linear operation on the same reference impedances: Pout / Pin = (Vout * Iout) / (Vin * Iin) = (Vout / Vin) * (Iout / Iin) = Av * Ai. Thus, power gain is the product of voltage and current gains. Care must be taken with load and source impedances; if they change, gains should be defined consistently.

Step-by-Step Solution:

Verification / Alternative check:
In decibels, Gp(dB) = 10 * log10(Ap) = 20 * log10(Av) + 20 * log10(Ai) when impedances match, consistent with adding dB gains of voltage and current.

Why Other Options Are Wrong:

• Ai^2 (option a) only holds in special cases where Av = Ai and impedances match; it is not the general definition.
• Av * Rout (option c) mixes incompatible quantities and units.
• Ai + Av (option d) is dimensionally meaningless for power gain.

Common Pitfalls:
Forgetting impedance effects or adding linear gains instead of multiplying, and mixing decibel and linear domains.

Final Answer:
Ap = Ai * Av.