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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| under a fixed load and bias point? Choose the factor whose variation most directly scales |Av| in the small-signal model.

Difficulty: Easy

Correct Answer: gm (transconductance of the MOSFET)

Explanation:


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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