The Common Gate Amplifier

In the common gate configuration, the gate is grounded (reference potential), the input is applied to the source, and the output is taken at the drain.

Voltage Gain:

Applying a small-signal voltage $v_{i n}$ at the source results in $v_{g s} = - v_{i n}$ .

The drain current is $g_{m} v_{g s} = - g_{m} v_{i n}$ .

This current flows through the drain resistor $R_{D}$ (ignoring $r_{o}$ ), creating an output voltage:

v_{o u t} = (- g_{m} v_{i n}) \times R_{D} \times (- 1) = g_{m} R_{D} v_{i n}

(Note: The direction of current flow into $R_{D}$ results in a positive gain with respect to the source input).

Input Resistance:

The input resistance is the resistance looking into the source. If the drain resistance is small (or ignored), this is approximately $1 / g_{m}$ .

Application as a Current Buffer:

Because the input resistance ( $1 / g_{m}$ ) is low, the common gate configuration is poor for sensing voltage signals from high-impedance sources. However, it serves as an excellent current buffer.

A current buffer requires low input resistance to accept current and high output resistance to deliver it.
The common gate takes a current at the source and passes it to the drain ( $I_{o u t} \approx I_{i n}$ ).
It effectively decouples the source impedance from the load.