QB_PH_SEC8_003: Semiconductor Devices & Diodes

In a common emitter (CE) BJT amplifier, the collector load resistance is $R_C = 2\text{ k}\Omega$ and the input dynamic resistance is $r_i = 1\text{ k}\Omega$. If the transistor common-emitter current gain is $\beta = 100$, what is the magnitude of the small-signal voltage gain $A_v$?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Small-Signal Model (CE Configuration)**: Output voltage: $v_o = -i_c R_C = -\beta i_b R_C$ Input voltage: $v_i = i_b r_i$ 2. **Voltage Gain Formulation**: $A_v = \frac{v_o}{v_i} = -\frac{\beta i_b R_C}{i_b r_i} = -\beta \frac{R_C}{r_i}$ 3. **Substitution**: $A_v = -(100) \times \frac{2000\,\Omega}{1000\,\Omega} = -200$ 4. **Magnitude Request**: $|A_v| = 200$.