Source follower

How it works

The bias sink keeps M1's current approximately constant, so its source tracks its gate one V_GS lower. With the bulk grounded, the rising source voltage raises the threshold through body effect. Both transistors' finite output resistances also reduce the gain.

Mb copies I_bias (20 µA by default) from Mr and so fixes M1's current; the output sits V_GS1 below the input, and V_GS1 grows with the output when the bulk is grounded. The ground port returns the bias reference and sink; it is also the input device's default bulk connection.

Signal path

• Follower (M1): Drain on vdd, gate on in, source on out: with its current fixed, its V_GS barely changes, so the source follows the gate one V_GS lower.
• Bias sink (Mr, Mb): Mr, diode-connected, takes the testbench's I_bias; Mb copies it from out to ground as the follower's current.

Key relations

• Small-signal gain: A_v ≈ g_m1 / (g_m1 + g_mb1 + 1/r_o1 + 1/r_ob). below one by construction; with the bulk on its source g_mb1 drops out. The bench checks gain below 0 dB at its stated 1.0 V input point; the rest of the transfer remains visible in the sweep.
• Level shift: V_in − V_out = V_GS1 = V_TH(V_SB) + V_ov. with the bulk grounded V_SB = V_out, so the threshold, and the shift, rise with the output
• Body effect: η = g_mb1/g_m1 = γ / (2 √(2φ_F + V_SB)). the body's share of the transconductance; it shrinks slowly as V_SB rises
• Output resistance: R_out ≈ 1 / (g_m1 + g_mb1). low, which is what a buffer is for; the sink's r_o sits in parallel
• Output floor: V_out > V_ov(Mb). below it Mb leaves saturation and stops copying I_bias

Trade-offs

• Bulk connection: to source removes the body effect, lifting the gain towards one and flattening the shift, but needs an isolated p-well for M1.
• I_bias: more current raises g_m1 and lowers R_out, but increases V_ov, so the level shift grows and the output cannot go as low.
• W: wider lowers M1's V_ov and so the level shift, and raises g_m1, at the cost of input capacitance.
• L_sink: longer raises the sink's output resistance, keeping its current steadier as the output moves, but raises its V_ov at the same W_sink.

Testbenches and limits

• DC transfer

Design variables and defaults

Ports

• in input
• out output
• bn bias
• vdd supply
• 0 ground: bias-sink/reference return and the default NMOS substrate connection

Reference

B. Razavi, Design of Analog CMOS Integrated Circuits, 2nd ed., McGraw-Hill, 2017. Single-Stage Amplifiers - the source follower, and the body effect's contribution to its gain.

The source-follower topology and its small-signal gain. Body transconductance and the output conductances of both the follower and its bias sink reduce the gain; the bulk-connection option isolates the body-effect contribution.