Source follower

The source follower (common-drain amplifier) is the single-MOSFET configuration with the input at the gate, the output at the source, and the drain tied to $V_{DD}$ (AC ground). Voltage gain just below 1, so it doesn’t amplify voltage. It’s a buffer: very high input resistance, very low output resistance, and the output follows the input.

Why the gain is just under 1

A small input change $v_{gs}$ produces a drain (= source) current change $i_d=g_m{v}_{gs}$. That current flows through the source resistor $R_S$, raising the source voltage (the output) by $i_d{R}_S$. But the source voltage is part of $v_{gs}$: with the gate driven by $v_{in}$ and the source at $v_s$,

$v_{gs}=v_{in}-v_s,v_s=g_m{R}_S{v}_{gs}$

Substitute the first into the second and solve for the gain $A_v=v_s/v_{in}$:

$v_s=g_m{R}_S(v_{in}-v_s)\Rightarrow v_s(1+g_m{R}_S)=g_m{R}_S{v}_{in}\Rightarrow A_v=\frac{g_m{R}_S}{1+g_m{R}_S}$

Always less than 1, but for $g_m{R}_S\gg 1$ it’s close to 1. The source follows the gate, hence the name. (Same form as the Source degeneration feedback expression; the source follower is the extreme case where the output is taken at the source itself.)

Output at source follows the gate; gain just below 1, low output impedance.

The point: impedance transformation

A gain of ~1 sounds useless until you look at the impedances:

• Input resistance: near-infinite. The gate is insulated by the Gate oxide, so the stage barely loads whatever drives it.
• Output resistance: $1/g_m$ looking back into the source, low, typically a few hundred ohms.

So it presents a near-infinite impedance to its source and a low impedance to its load, while passing the voltage through nearly unchanged. That’s a Buffer amplifier: drop it between a weak, high-impedance source and a heavy, low-impedance load so the source isn’t loaded down and the load still gets the full signal. It’s the MOSFET analogue of the BJT Emitter follower. Compare the Common-source amplifier (high voltage gain, inverting) and the Common-gate amplifier (current buffer): the source follower is the third of the three single-transistor configurations, and the only voltage buffer.

Source-follower as buffer: high $R_{in}$, near-unity gain, low $R_{out}$.