The hybrid-π model is the default form of the MOSFET small-signal model: it draws the linearised transistor with the gate–source port left open and the controlled source plus output resistance hung across the drain–source port.
The circuit
- Gate to source: open circuit. No DC or AC gate current flows, because the gate is insulated by the Gate oxide. The full small-signal appears across this open port and is the controlling variable.
- Drain to source: a voltage-controlled current source in parallel with the output resistance . The current source is the linearised MOSFET square-law (slope , the MOSFET transconductance); models Channel-length modulation.
That is the entire model: and , with an open input.
Why it is the natural choice for common-source
In a Common-source amplifier the input drives the gate and the output is taken at the drain, with the source at AC ground. The hybrid-π lines up with that topology: the input source connects straight across the open gate–source port (so the controlling is the input voltage), and the output port (drain to source) already has and in it. The gain falls out in one line:
No rearrangement needed. For configurations where the source moves with the signal (the Common-gate amplifier in particular) the MOSFET T-model is usually tidier, but it is the same model: the hybrid-π and the T-model contain identical elements and always give the same answer. Use whichever makes the chosen topology least messy.