Common Emitter Amplifier

The common emitter amplifier is the most widely used BJT amplifier configuration in analog electronics. It provides both voltage gain and current gain simultaneously, making it the preferred choice when signal amplification is the primary objective. Understanding its small signal behavior, input-output impedance, and phase relationship is a core requirement for GATE analog electronics.

Core Concept: CE Configuration

The circuit diagram below shows the complete CE amplifier with voltage divider biasing and all essential components including coupling and bypass capacitors.

In the common emitter configuration, the emitter terminal is common to both the input loop (base-emitter) and the output loop (collector-emitter). The input signal is applied at the base through a coupling capacitor, and the amplified output is taken at the collector. The emitter may have a bypass capacitor CE across the emitter resistor RE to short circuit RE at signal frequencies while retaining DC stability.

The CE amplifier is the only BJT configuration that provides both voltage gain greater than 1 and current gain greater than 1. This makes its power gain the highest among the three configurations (CE, CB, CC). The voltage gain is negative, meaning the output signal is 180 degrees out of phase with the input. This phase inversion occurs because when Vin increases, IB increases, IC increases, the voltage drop across RC increases, and therefore Vout equals VCC minus IC times RC decreases.

Mathematical Expression: Voltage Gain and Impedances

Using the small signal hybrid-pi model, the voltage gain AV of the CE amplifier (with CE bypassing RE) is given by the expression negative gm multiplied by RC parallel RL, where gm is the transconductance equal to IC divided by VT, and VT is the thermal voltage approximately 26 mV at room temperature. The negative sign confirms the 180 degree phase inversion.

The input resistance Rin of the CE amplifier is the parallel combination of R1, R2, and the small signal input resistance looking into the base, which is denoted rpi and equals beta divided by gm. Since R1 and R2 are typically in the tens of kilohms range and rpi is in the kilohms range, the effective input resistance is moderate. The output resistance Rout is approximately RC in parallel with the output resistance ro of the transistor, where ro equals VA divided by IC, and VA is the Early voltage.

When RE is not bypassed, the voltage gain magnitude reduces to gm times RC divided by (1 plus gm times RE), which approaches RC divided by RE for large gm times RE. This is the degenerated CE stage, where gain is traded for stability and linearity. The input resistance with unbypassed RE is R1 parallel R2 parallel (rpi plus (1 plus beta) times RE), which is significantly higher than the bypassed case.

Practical Understanding: Frequency Response

At low frequencies, the coupling capacitors Cin and Cout have high impedance and block the AC signal, causing the gain to fall off below the lower 3 dB frequency fL. At high frequencies, the internal junction capacitances of the BJT, especially the base-collector capacitance Cmu, reduce gain through the Miller effect. The Miller effect multiplies Cmu by (1 plus gm times RC) at the input node, creating a dominant pole that limits the bandwidth. This is one reason the CE amplifier has lower bandwidth compared to the CB configuration.

Given:
IC = 2 mA, VT = 26 mV, RC = 3.3 kohm, RL = 10 kohm, R1 = 33 kohm, R2 = 10 kohm, beta = 100

Why this formula applies:
Small signal analysis of CE amplifier with CE bypass capacitor active (RE shorted for AC).

Formula:
gm = IC / VT
rpi = beta / gm
Rin = R1 || R2 || rpi
AV = -gm x (RC || RL)

Substitution:
gm = 2 mA / 26 mV = 76.9 mA/V
rpi = 100 / 76.9 mA/V = 1.3 kohm
RC || RL = (3.3 x 10) / (3.3 + 10) = 33 / 13.3 = 2.48 kohm
R1 || R2 = (33 x 10) / 43 = 7.67 kohm
Rin = 7.67 || 1.3 = (7.67 x 1.3) / (7.67 + 1.3) = 9.97 / 8.97

Calculation:
gm = 76.9 mA/V
rpi = 1.3 kohm
Rin = 1.11 kohm
AV = -76.9 mA/V x 2.48 kohm = -190.7

Final Answer:
Voltage Gain AV = -190.7 (magnitude 190.7, phase inverted)
Input Resistance Rin = 1.11 kohm
Output Resistance Rout = RC = 3.3 kohm (approximately)

Exam Tip: In GATE, phase inversion is a guaranteed feature of the CE amplifier. The voltage gain with bypassed CE is -gm(RC||RL). Without CE, gain magnitude drops to approximately RC/RE. Do not confuse input resistance rpi with the overall Rin (which includes R1 and R2 in parallel).

Quick Revision

• CE amplifier: input at base, output at collector, emitter common. Provides AV > 1, AI > 1, highest power gain of all three BJT configurations.
• Voltage gain AV = -gm x (RC || RL). Negative sign means 180 degree phase inversion of output with respect to input.
• Transconductance gm = IC / VT = IC / 26 mV at room temperature. Higher IC gives higher gm and higher gain.
• Input resistance Rin = R1 || R2 || rpi. Moderate value (typically 1 to 10 kohm range).
• CE bypass capacitor CE: shorts RE at AC frequencies, restores full gain while DC stability is maintained by RE.
• Miller effect through Cmu limits high-frequency bandwidth. CE configuration has lowest bandwidth of the three BJT configurations.
• GATE trap: Phase inversion is unique to CE configuration. CB and CC do not invert phase.