CE bypassed amplifier Rin, Rout, Av, Ai

Small-signal model

For the CE amplifier with voltage divider bias and RE bypassed by CE (so the emitter is at ac ground), the hybrid-π model has: rπ between B and E, the source gm vπ with ro between C and E, the bias resistors RB = R1 || R2 at the input, and RC || RL at the output.

 vs--Rs--+--B--rπ--E(gnd)      C--+--+
         |       vπ  gm vπ(ro)----+  RC||RL
       R1||R2                         |
         GND                         GND

gm = IC/VT, rπ = β/gm.

Input resistance

Rin = R1 || R2 || rπ

Output resistance

Set vs = 0: then vπ = 0 and the dependent source is zero, so

Rout = RC || ro  ≈ RC

Voltage gain

vo = -gm vπ (RC || RL || ro) ,   vπ = vi (neglecting Rs)

Av = -gm (RC || RL)  ≈ -(RC || RL)/re

With a signal source: Avs = Av · Rin/(Rin + Rs).

Current gain

Ai = io/ii = (vo/RL)/(vi/Rin) = Av · Rin/RL

Ai = -gm (RC||RL) Rin/RL

When RB ≫ rπ, Rin ≈ rπ and gm rπ = β, so Ai ≈ -β RC/(RC + RL); this approaches -β when RL ≪ RC.