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CC amplifier small-signal model, Rin and gain

Short answer

The small-signal model has rπ between base and emitter, with a dependent source gm vπ from collector to emitter. Input resistance Rin = R1||R2||[rπ+(β+1)(RE||RL)]. Voltage gain Av = (β+1)R'E/[rπ+(β+1)R'E] ≈ R'E/(re+R'E) ≈ 1.

Draw the small signal model for Common Collector Amplifier and find its input resistance and voltage gain.

Small-signal (hybrid-π) model of the common collector amplifier

The collector is tied to VCC (ac ground). The base is the input, and the emitter the output (with RE || RL).

 vs--Rs--+----B--rπ--E-----+---- vo
         |     |           |
       R1||R2  +-( ) gm vπ-+   (current source from C(gnd) to E)
         |                RE||RL
        GND                |
                          GND

Here vπ = vb - vo, and the controlled source gm vπ feeds the emitter.

Input resistance

The emitter current is ie = ib + gm vπ = (β+1) ib. Let R'E = RE || RL. Then

vb = ib rπ + ie R'E = ib [rπ + (β+1) R'E]
Rib = rπ + (β+1) R'E  = (β+1)(re + R'E)       [rπ = (β+1) re]
Rin = R1 || R2 || [rπ + (β+1)(RE || RL)]

Voltage gain

vo = ie R'E = (β+1) ib R'E ,   vb = ib [rπ + (β+1) R'E]

Av = vo/vb = (β+1) R'E / [rπ + (β+1) R'E]  = R'E/(re + R'E)  ≈ 1

Including the source resistance: Avs = Av · Rin/(Rin + Rs).

Example

IE = 1 mA (re = 25 Ω), β = 100, R'E = 2 kΩ: Rib = 101 × 2025 = 204.5 kΩ, Av = 2000/2025 = 0.988.

✓ Answer checked by Claude Opus 5.5 (high effort)

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