AC equivalent of CE amplifier, unbypassed RE

AC equivalent circuit (RE unbypassed)

With the coupling capacitors shorted and VCC grounded, the circuit is: source vs, bias resistors RB = R1 || R2 from the base to ground, the transistor (T-model: re in the emitter), RE in the emitter lead to ground, and RC (with RL) from the collector to ground.

 vs--+----B--\|C----+---- vo
     |       | |    RC||RL
   R1||R2    re     |
     |       |     GND
    GND      E
             |
             RE
             |
            GND

The T-model: the base current ib = ie/(β+1); the collector current source is α ie ≈ ie.

Input impedance

vb = ie (re + RE) = (β+1) ib (re + RE)
Rib = vb/ib = (β+1)(re + RE)      (or rπ + (β+1)RE)
Zin = R1 || R2 || (β+1)(re + RE)

Voltage gain

Output: vo = -ic (RC || RL) ≈ -ie (RC || RL); input: vb = ie (re + RE). So

Av = vo/vb = -(RC || RL) / (re + RE)

(Exact: Av = -β(RC||RL)/[rπ + (β+1)RE]). If RE ≫ re, Av ≈ -(RC||RL)/RE, which depends only on resistors, so it is stable but lower than with a bypass capacitor (where Av = -(RC||RL)/re).

Other results

• Output impedance (ro neglected): Zo ≈ RC.
• Higher Rin than the bypassed circuit, lower gain, and less distortion because of local negative feedback by RE.