MOSFET T-model

The T-model is an alternative drawing of the MOSFET small-signal model that places a resistance $1/g_m$ between the gate and the source while routing the same controlled current $g_m{v}_{gs}$ between drain and source. It contains exactly the same physics as the MOSFET hybrid-pi model — it is a rearrangement, not a different model — and 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 is not a real resistor inside the device — the gate is still insulated and draws no current. It is a bookkeeping element that correctly reproduces the relationship between the source-terminal current and $v_{gs}$ when the analysis is done 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 is 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, $R_{in}=1/g_m$, simply is an element you can read off the diagram. The same convenience helps with the Source follower, where the output is at the source.

Because the two models are mathematically equivalent, there is 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.