Common Emitter Amplifier Analysis | Generated by AI
Collector Current \( I_C \)
The input resistance \( R_{in} \) for a common-emitter BJT amplifier with an grounded emitter is approximately the small-signal base resistance \( r_\pi = \frac{\beta V_T}{I_C} \), where \( V_T = 0.026 \) V (thermal voltage at room temperature) and \( \beta = 100 \).
Given \( R_{in} = 1 \) k\( \Omega = 1000 \) \( \Omega \),
\[ r_\pi = \frac{100 \times 0.026}{I_C} = 1000 \]
\[ \frac{2.6}{I_C} = 1000 \]
\[ I_C = \frac{2.6}{1000} = 0.0026 \text{ A} = 2.6 \text{ mA} \]
This bias point yields a collector-emitter voltage \( V_{CE} = V_{CC} - I_C R_C = 12 - (0.0026 \times 2200) \approx 12 - 5.72 = 6.28 \) V, which is near the midpoint of the supply for reasonable linearity.
Voltage Gain \( A_V \)
The small-signal voltage gain for a common-emitter amplifier (with no emitter resistor) is \( A_V = -g_m R_C \), where the transconductance \( g_m = \frac{I_C}{V_T} \).
\[ g_m = \frac{0.0026}{0.026} = 0.1 \text{ A/V (or S)} \]
\[ A_V = - (0.1 \times 2200) = -220 \]
The negative sign indicates phase inversion.