Definition of signal voltage gain: Which expression correctly defines the small-signal voltage gain of an amplifier?

Introduction / Context:
Amplifier “gain” must be specified by type: voltage, current, transconductance, transresistance, or power. Confusion arises when expressions appropriate to one form (e.g., current gain β = ΔI_C/ΔI_B) are mislabeled as voltage gain. For linear small-signal analysis, the signal voltage gain relates output voltage variation to input voltage variation and is dimensionless (ratio of volts to volts).

Given Data / Assumptions:

• Linear operation around a quiescent point.
• Voltage gain definition requested, not current or power gain.
• Incremental (small-signal) quantities implied.

Concept / Approach:
Voltage gain is defined as A_V = V_out / V_in, often written as ΔV_out / ΔV_in for small-signal derivatives. In a common-emitter BJT stage, A_V can be approximated by −g_m * R_out, but this is a model-based computation, not the definition. Other expressions such as I_C * R_C (voltage across a resistor given a current) calculate a specific voltage, not a ratio of two voltages; ΔI_C/ΔI_B is current gain β; P_out/P_in is power gain; g_m/r_o is not a general definition of voltage gain (though it appears in specific configurations).

Step-by-Step Solution:

Verification / Alternative check:
Data sheets and textbooks consistently specify small-signal voltage gain as a ratio of voltages, often in dB using 20 * log10(|A_V|).

Why Other Options Are Wrong:
I_C * R_C yields a voltage, not a ratio. ΔI_C/ΔI_B is β (current gain). P_out/P_in is power gain, not voltage gain. g_m/r_o is a parameter ratio, not a universal definition of A_V.

Common Pitfalls:
Mixing definitions and computations; using a computed expression as if it were the general definition; ignoring whether gains are specified as magnitude, signed, or in dB.

Final Answer:
A_V = V_out / V_in