BJT Amplifier Configurations: CE, CB, CC, Darlington & Cascode

The three basic transistor amplifiers and their combinations. For each — common emitter, common base and common collector (emitter follower) — learn the schematic, biasing, small-signal model, voltage/current/power gain, phase, input and output resistance, frequency behaviour, practical uses and limitations; then emitter degeneration and bypassing, collector loading, and compound stages (Darlington, Sziklai, cascode) — with Python computing gains and impedances for bypassed and degenerated CE stages and an emitter follower.

Grounding (for AC) a different terminal of the transistor produces three configurations with very different properties: CE gives high voltage gain with inversion, CB gives low input impedance and wide bandwidth, CC (emitter follower) gives unity gain with low output impedance for driving loads.

Real amplifiers combine stages to get gain, impedance and bandwidth together — and the same trio reappears as common source, common gate and common drain for FETs.

An analogy

CE is a lever that multiplies motion but flips direction (inverting gain); CC is a strong but faithful helper that copies your motion while carrying heavy loads (buffer); CB is a wide-open door that passes current quickly with little resistance (fast, low input impedance).

Three configurations

Which terminal is common (AC ground) decides behaviour:

Emitter degeneration

Unbypassed emitter resistance adds local negative feedback: gain becomes ≈ −R_C/R_E (resistor ratio), input resistance rises by (β + 1)R_E, distortion falls (the nonlinear r_e matters less), and bandwidth improves. The price is lower gain. Designers often split R_E and bypass part of it to set gain independently of bias.

Compound configurations

Darlington (two emitter followers in cascade): β ≈ β₁β₂, very high input resistance, but V_BE doubles (~1.4 V), slower turn-off and higher V_CE(sat). Sziklai (complementary feedback pair): high gain with only one V_BE drop and better thermal behaviour. Cascode (CE feeding CB): the CB device shields the CE collector from voltage swings, eliminating Miller multiplication — wide bandwidth and very high output resistance (used in RF and op-amp gain stages).

Practical limits

Output swing is limited by saturation and cutoff on the AC load line; large signals distort because g_m depends on I_C (keep v_be ≪ V_T, ~10 mV, for < 10% distortion without degeneration). Gain is limited by r_o (intrinsic gain V_A/V_T). Input capacitance (Miller) limits bandwidth in CE; source impedance matters in CB. Stages are usually combined: e.g. CE gain stage + emitter-follower output.

Formulas

Worked example: Bypassed CE gain

Given: I_C 1 mA, R_C ∥ R_L = 4 kΩ

Find: A_v.

Answer: ≈ −155

Worked example: Degenerated CE

Given: R_C ∥ R_L 4 kΩ, R_E 390 Ω, r_e 26 Ω

Find: A_v.

Answer: ≈ −9.6

Worked example: Darlington β

Given: β₁ = 100, β₂ = 50

Find: β_total.

Answer: ≈ 5150

Common-emitter amplifier

        +VCC
          │        │
         R1       RC 5.6k
          │        ├──||── C_out ──► v_out  [R_L 10k]
 v_in ─||─┤ B      │ C
    C_in  │      NPN
         R2        │ E
          │       R_E1 220 Ω   (unbypassed: sets gain ≈ −R_C∥R_L/(r_e + 220))
          │        │
          │       R_E2 1k ─┬─ C_E (bypass)
         GND       GND ────┘

Splitting the emitter resistor lets the unbypassed part set a stable, predictable gain while the bypassed part only affects DC bias. Coupling capacitors block DC between stages and set the low-frequency corner.

Gains and impedances of CE and CC stages

# Common-emitter amplifier small-signal gains: bypassed, degenerated, and emitter follower
VT, IC, beta = 0.02585, 1.074e-3, 150              # IC from the bias design (beta 100 case)
gm = IC / VT
rpi = beta / gm
RC, RL, RE, R1, R2, Rs = 5600, 10e3, 1200, 82e3, 18e3, 1e3
RB = R1 * R2 / (R1 + R2)
RCL = RC * RL / (RC + RL)
Av_bypassed = -gm * RCL
Rin_b = RB * rpi / (RB + rpi)
print(f"gm = {gm*1e3:.1f} mA/V, r_pi = {rpi:.0f} ohm")
print(f"CE, RE bypassed: Av = {Av_bypassed:.1f}, Rin = {Rin_b/1e3:.2f}k, overall from 1k source: {Av_bypassed*Rin_b/(Rin_b+Rs):.1f}")
re_ = 1 / gm
RE_unbyp = 220                                     # partially bypassed: 220 ohm unbypassed
Av_deg = -RCL / (re_ + RE_unbyp)
Rin_deg = 1 / (1/RB + 1/(rpi + (beta + 1) * RE_unbyp))
print(f"CE with 220 ohm degeneration: Av = {Av_deg:.1f}, Rin = {Rin_deg/1e3:.2f}k (gain set by resistors)")
# Emitter follower driving 100 ohm
RE_f, RL_f = 1000, 100
REL = RE_f * RL_f / (RE_f + RL_f)
Av_cc = (beta + 1) * REL / (rpi + (beta + 1) * REL)
print(f"emitter follower into 100 ohm: Av = {Av_cc:.3f}, Rout ~ re + Rs/(beta+1) = {re_ + Rs/(beta+1):.1f} ohm")
# gm = 41.5 mA/V, r_pi = 3610 ohm
# CE, RE bypassed: Av = -149.1, Rin = 2.90k, overall from 1k source: -110.9
# CE with 220 ohm degeneration: Av = -14.7, Rin = 10.54k (gain set by resistors)
# emitter follower into 100 ohm: Av = 0.792, Rout ~ re + Rs/(beta+1) = 30.7 ohm

Fully bypassed, the CE stage gives huge gain (−149) but it depends on g_m (current and temperature), distorts and has low input resistance (2.9 kΩ) that loads the source. Leaving 220 Ω unbypassed trades gain for stability: −14.7 set by resistors, higher input resistance (10.5 kΩ) and lower distortion. The emitter follower's 31 Ω output resistance lets it drive a 100 Ω load with little loss.

Common mistakes

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Key takeaways

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