MOSFET T-model

The T-model redraws the MOSFET small-signal model with a resistance $1/g_m$ between gate and source, routing the same controlled current $g_m{v}_{gs}$ between drain and source. Same physics as the MOSFET hybrid-pi model, just rearranged, so it gives identical answers in any analysis.

The circuit

• A resistance $\frac{1}{g_m}$ connected between gate and source. ($g_m$ is the MOSFET transconductance.)
• The same voltage-controlled current source $g_m{v}_{gs}$ from drain to source.
• The output resistance $r_o$ (from Channel-length modulation) across drain to source when needed.

The $1/g_m$ resistor isn’t a real resistor inside the device; the gate is still insulated and draws no current. It’s a bookkeeping element that reproduces the relationship between the source-terminal current and $v_{gs}$ when you analyze from the source side.

Why it exists: common-gate convenience

The hybrid-π is cleanest when the input is at the gate (common-source). But in the Common-gate amplifier the input drives the source and the gate sits at AC ground, so $v_{gs}=-v_s$ and the controlling voltage is tied to the input node itself. Drawing that with the hybrid-π forces awkward dependent-source manipulations. The T-model puts a resistance $1/g_m$ right where you look into the source, so the low common-gate input resistance $R_{in}=1/g_m$ is an element you read straight off the diagram. Same convenience for the Source follower, where the output is at the source.

Since the two models are mathematically equivalent, there’s never a “correct” choice, only an easier one. Pick the T-model whenever the signal enters or leaves at the source; pick the hybrid-π when it enters at the gate.