What is the formula for Common-Emitter Voltage Gain?

The Common-Emitter Voltage Gain formula is Av = −Rc / re, where Av—Voltage gain (negative = inverting); Rc—Collector load resistance (Ω); re—Small-signal emitter resistance (Ω).

What does Av mean in the Common-Emitter Voltage Gain formula?

Av is Voltage gain (negative = inverting).

Common-Emitter Voltage Gain

Q: How do you calculate Common-Emitter Voltage Gain?

Use the formula Av = −Rc / re. The voltage gain of an undegenerated common-emitter amplifier is the collector load resistance divided by the small-signal emitter resistance, with a minus sign because the stage inverts. Enter the values you know in the calculator above and it solves for the remaining variable.

Av = −Rc / re

Calculator

Voltage Gain

Collector Resistor

Emitter Resistance

Result

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Formula

Av = −Rc / re

Description

The voltage gain of an undegenerated common-emitter amplifier is the collector load resistance divided by the small-signal emitter resistance, with a minus sign because the stage inverts. Since re is set by bias current, the gain rises with collector resistance and bias current. Adding an external emitter resistor RE changes this to −Rc/(re+RE), trading gain for stability and linearity.

Variables

Av — Voltage gain (negative = inverting)
Rc — Collector load resistance (Ω)
re — Small-signal emitter resistance (Ω)

Practical Notes

With an emitter degeneration resistor RE, Av ≈ −Rc/RE, which is stable and bias-independent. The undegenerated gain here is the maximum achievable but varies with temperature and current.

Related Concepts

All Discrete Amplifiers formulas →

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