In the MOSFET small-signal model, what does gm represent?

• A. The body-effect transconductance, ∂Id/∂Vbs
• B. The transconductance with drain current divided by source resistance
• C. The output conductance, ∂Id/∂Vds
• D. The transconductance, ∂Id/∂Vgs

Answer: (D)

The key idea is how gate voltage controls drain current in the MOSFET’s small-signal model. gm is the transconductance, defined as the derivative of the drain current with respect to the gate-source voltage (holding other voltages fixed): gm = ∂Id/∂Vgs. In small-signal terms, the drain current change is approximately id ≈ gm · vgs, showing how effectively a small gate voltage variation modulates the current through the channel. This parameter captures the gate’s control over current flow, which is exactly what the small-signal model uses gm to describe. The other quantities refer to different sensitivities: body-effect transconductance is ∂Id/∂Vbs, output conductance is ∂Id/∂Vds, and the derivative with respect to Vgs is gm.