The Small-Signal Model and Voltage Gain

Principle of Linearization

Around the quiescent point Q, for a small-amplitude AC signal, the transistor behaves as a linear two-port network. Every quantity is then decomposed into a DC component (uppercase) and an AC component (lowercase): Ic = Ic0 + ic, Vce = Vce0 + vce.

The Simplified Model

At low frequency, the most commonly used small-signal model combines:

• a dynamic input resistance re = Vt/Ie0 (Vt ~ 25 mV at room temperature), which represents the base-emitter junction
• a controlled current source ic = beta*ib

Voltage Gain of the Common-Emitter Amplifier

For a common-emitter amplifier with Rc as the collector resistor and Re decoupled by Ce, the voltage gain is written:

Av = -Rc/re

The negative sign reflects a 180-degree phase shift between the input and the output. re depends directly on the quiescent point: re = Vt/Ic0, so the larger Ic0 is, the smaller re is, and the higher the gain.

Numerical Example

For Ic0 = 1 mA, re = 25 mV / 1 mA = 25 ohms. With Rc = 2.5 kohms, Av = -2500/25 = -100.

Input and Output Impedances

Quantity	Approximate Expression
Ze (input)	R1 // R2 // (beta*re)
Zs (output)	Rc

Common Pitfall

Using a fixed value of Vbe (0.6 V) as if re were constant: re depends on the quiescent current Ic0, not on a universal constant. Another common mistake is forgetting the negative sign of the gain, which reflects a phase inversion that is essential in filtering and negative feedback.