In the small-signal model for a MOSFET operating in saturation, which expression best approximates the drain current variation with small signals?

• A. Id ≈ gm vgs + gmb vbs + (1/ro) vds
• B. Id varies as gm vgs only
• C. Id ≈ gm vds
• D. Id ≈ gmb vbs

Answer: (A)

In small-signal analysis of a MOSFET in saturation, the drain current responds to three independent changes: the gate-to-source voltage, the bulk (body) to source voltage, and the drain-to-source voltage. The gm term captures how ΔId changes with Δvgs, since the gate controls the channel and modulates the current. The gmb term accounts for the body effect: if the bulk is biased differently from the source, a small change in vbs alters the threshold and thus the current by an amount proportional to gmb. The finite output resistance of the channel, due to channel-length modulation, introduces another piece of variation that scales with Δvds, represented as (1/ro) Δvds (often written as gds Δvds with gds = 1/ro). Adding these contributions gives the total small-signal drain current variation: ΔId = gm vgs + gmb vbs + (1/ro) vds.

This explains why just gm vgs or just gmb vbs or only gm vds cannot fully describe ΔId on their own: each term reflects a different physical mechanism affecting Id in saturation. If the bulk is tied to the source, the body term vanishes; and if channel-length modulation is negligible (ro very large), the (1/ro) vds term becomes small.