Common-source (CS) MOSFET amplifier gain control In small-signal analysis of a common-source amplifier (with drain load RD and an optional source resistor RS), which parameter change most directly controls the midband voltage gain magnitude |Av|.

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Solve this multiple-choice question and choose the correct option.

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Introduction / Context:The common-source (CS) MOSFET amplifier is a foundational gain stage in analog electronics. Its midband small-signal voltage gain primarily depends on device transconductance and the effective load seen at the drain. This question probes your understanding of which parameter most directly scales the small-signal voltage gain when the circuit is otherwise biased and loaded consistently. Given Data / Assumptions: A common-source MOSFET stage with drain resistor RD and possibly an unbypassed source resistor RS. We are discussing small-signal midband gain (coupling and bypass capacitors treated as AC shorts unless explicitly unbypassed). Bias point and load are assumed fixed unless the chosen parameter inherently alters them. Linear operation (no clipping or strong nonlinearity). Concept / Approach:For a CS stage without source degeneration, the approximate gain is Av ≈ −gm * (RD || RL). With an unbypassed source resistor, Av ≈ −(gm * (RD || RL)) / (1 + gm * RS). In both forms, gm appears as a direct multiplicative factor that scales the magnitude of Av. Changing gm directly alters how much output voltage develops per unit input small-signal gate voltage. Step-by-Step Solution: Identify the small-signal model: a dependent current source of value gm * vgs feeding the drain load.Express gain: Av = vo / vi ≈ −gm * (effective load) with additional division by (1 + gm * RS) if RS is unbypassed.Note gm’s role: increasing gm increases the dependent current, producing a larger voltage swing across the load.Conclude: gm is the primary lever for small-signal gain scaling under fixed load conditions. Verification / Alternative check:If RD or RL is fixed, doubling gm roughly doubles |Av| (ignoring degeneration). Conversely, halving gm halves |Av|. Supply voltage VDD influences bias headroom but does not directly multiply the small-signal gain unless it shifts the operating point and thereby changes gm indirectly. Why Other Options Are Wrong: the input voltage: changes output amplitude, not the intrinsic small-signal gain.VDD: affects biasing/headroom; gain scaling is not directly proportional to VDD.RS: modifies gain through feedback (denominator 1 + gm * RS); the direct scaling factor is gm.the coupling capacitor value: midband gain is capacitor-independent (they act as shorts in midband). Common Pitfalls:Confusing amplitude with gain, or assuming VDD directly sets gain. Remember that in midband small-signal analysis, gm and the effective load dominate voltage gain. Final Answer:gm (transconductance of the MOSFET)

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