The common-emitter (CE) amplifier is the workhorse voltage gain stage of discrete BJT design. Signal enters the base, exits (inverted and amplified) at the collector, and the emitter is the "common" terminal shared between input and output. It delivers the highest voltage gain of the three BJT topologies (CE, CB, CC) — often 100× or more — which is why it dominated audio preamps, IF strips, and countless op-amp input stages before ICs took over.

How it works: A small AC voltage at the base modulates the base-emitter junction, which exponentially controls collector current. That current flows through a collector resistor R_C, developing a voltage swing that's the amplified (and inverted) copy of the input.

Core design equations (assuming voltage-divider bias and a bypassed emitter resistor):

• Voltage gain: A_v ≈ −g_m · (R_C ∥ R_L), where g_m = I_C/V_T and V_T ≈ 26 mV at room temperature
• Rule of thumb: A_v ≈ −R_C/r_e, where r_e = 26 mV / I_C
• Input impedance: R_in ≈ R₁ ∥ R₂ ∥ (β · r_e) — typically a few kΩ, which loads the previous stage
• Output impedance: R_out ≈ R_C

Worked example — audio preamp: You want a gain of 50 from a 2N3904 running at I_C = 1 mA on a 12 V rail. Then r_e = 26 Ω, so R_C = 50 × 26 Ω = 1.3 kΩ (use 1.3 kΩ or 1.5 kΩ). Set the collector quiescent voltage at 6 V for maximum symmetric swing: V_C = 12 − (1 mA)(1.3 kΩ) = 10.7 V — too high. Drop I_C to 2 mA and recalculate: r_e = 13 Ω, R_C = 650 Ω, V_C = 12 − 1.3 = 10.7 V. Still high — pick R_C = 3 kΩ and accept a gain closer to 230, or add a partially-bypassed emitter resistor to stabilize gain.

The bypass capacitor trap: The unbypassed version (emitter degeneration) gives A_v ≈ −R_C/R_E — predictable, linear, temperature-stable, but low gain. Fully bypassing R_E with a large capacitor restores the high g_m-based gain but reintroduces temperature drift and BJT-to-BJT variation. Split the emitter resistor (small unbypassed R_E1 in series with bypassed R_E2) for the best of both worlds — modest, controlled gain with reasonable linearity.

Watch out for: Miller effect on C_bc multiplies collector-base capacitance by (1 + |A_v|), crushing high-frequency response. That's exactly why cascode topologies exist.