FET Biasing & Amplifiers: CS, CG, CD, Cascode & Active Loads

Amplifying with FETs. Learn FET bias schemes (fixed gate, self-bias for JFETs, voltage-divider gate bias, current-source bias, source degeneration), the common-source amplifier and its gain with resistive, active and current-source loads, source degeneration, the common-gate stage, the common-drain (source follower) buffer and body effect, the cascode for high gain and bandwidth, and a comparison of topologies by input/output impedance, gain, phase and application — with Python computing CS, degenerated CS, follower and cascode gains.

FET amplifiers mirror the BJT's three configurations — common source ≈ common emitter, common gate ≈ common base, common drain ≈ common collector — but with essentially infinite gate input resistance and lower transconductance.

In CMOS integrated circuits, resistors are replaced by transistors acting as active loads and current sources, enabling very high gain from compact circuits.

An analogy

A common-source amplifier is like a valve controlling water flowing through a narrow outlet pipe: small movements of the valve (gate voltage) cause big pressure changes across the outlet (drain voltage). An active load is an outlet pipe that 'fights back' very strongly, magnifying those pressure changes even more.

Biasing FETs

Bias options:

Three configurations

Common source: inverting voltage gain −g_m R_D, infinite input resistance, output ≈ R_D ∥ r_o. Common gate: non-inverting, low input resistance (~1/g_m) — used as current buffer, in cascodes and RF input matching. Common drain (source follower): gain slightly below 1, low output resistance ~1/g_m, level-shifts by V_GS; body effect lowers gain unless source and body are tied.

Active loads and cascodes

Active (current-source) loads give high gain without large resistors or voltage drops. Cascoding stacks a common-gate device on top of the gain transistor: output resistance rises by ~g_m r_o and the Miller capacitance of the input device is eliminated. Telescopic and folded cascodes are the high-gain stages of CMOS operational transconductance amplifiers.

Design trade-offs

Higher overdrive (V_OV) gives more speed and linearity but less g_m per current and less swing; lower overdrive (moderate/weak inversion) maximises g_m/I_D for low power. Output swing with cascodes shrinks (each device needs V_OV of headroom). Body effect, channel-length modulation, mismatch and 1/f noise (much larger in MOSFETs than BJTs) must be considered. The gm/ID methodology designs analog CMOS directly from simulated device curves.

Formulas

Worked example: JFET self-bias

Given: I_DSS 10 mA, V_P −4 V, target I_D 2.5 mA

Find: R_S.

Answer: 800 Ω

Worked example: Active-load gain

Given: g_m 1 mS, r_o1 = r_o2 = 100 kΩ

Find: A_v.

Answer: −50

Worked example: Follower output resistance

Given: g_m 10 mS

Find: R_out.

Answer: 100 Ω

Common source with current-source (active) load

         V_DD
          │
        ┌─┴─┐  PMOS current source (active load, high r_o)
        │ M2 │── V_bias
        └─┬─┘
          ├────── v_out   A_v = −g_m1·(r_o1 ∥ r_o2)
        ┌─┴─┐
 v_in ──│ M1 │  NMOS gain device
        └─┬─┘
          GND

Replacing R_D with a PMOS current source presents a very high small-signal resistance while still supplying the DC bias current, so gain approaches the intrinsic g_m·r_o/2 — tens to hundreds in one stage. This is the core of CMOS op-amp gain stages.

CS, degeneration, follower and cascode gains

# Common-source amplifier with source degeneration, source follower and cascode gain
gm, ro, RD, RL = 4e-3, 50e3, 4.7e3, 10e3
RDL = 1 / (1/RD + 1/RL + 1/ro)
print(f"CS gain -gm*(RD||RL||ro) = {-gm*RDL:.2f}")
RS = 470
print(f"CS with 470 ohm degeneration: gain = {-gm*RDL/(1+gm*RS):.2f} (Gm = {gm/(1+gm*RS)*1e3:.2f} mS)")
RSf = 2e3
print(f"source follower: gain = {gm*RSf/(1+gm*RSf):.3f}, Rout ~ 1/gm = {1/gm:.0f} ohm")
print(f"intrinsic gain gm*ro = {gm*ro:.0f}; cascode output resistance ~ gm*ro*ro = {gm*ro*ro/1e6:.1f} Mohm")
print(f"cascode with current-source load (Rout 10 Mohm): gain ~ {-gm*1/(1/(gm*ro*ro)+1/10e6):.0f}")
# CS gain -gm*(RD||RL||ro) = -12.02
# CS with 470 ohm degeneration: gain = -4.17 (Gm = 1.39 mS)
# source follower: gain = 0.889, Rout ~ 1/gm = 250 ohm
# intrinsic gain gm*ro = 200; cascode output resistance ~ gm*ro*ro = 10.0 Mohm
# cascode with current-source load (Rout 10 Mohm): gain ~ -20000

A resistively loaded CS stage gains only ~12 because g_m is modest. Degeneration lowers gain to 4.2 but linearises it. A source follower gives 0.89 (not 1 — finite g_m and body effect) with a 250 Ω output. Cascoding multiplies output resistance by g_m·r_o, so a cascode with a cascoded current-source load reaches gains of thousands in a single stage (the idea behind telescopic op-amps).

Common mistakes

Applications

Key takeaways

Going further