Common Emitter Voltage Gain Calculator

It uses the emitter-degenerated common-emitter approximation and returns a signed voltage gain in volts per volt, its magnitude, and the degeneration factor. The negative sign identifies the familiar phase inversion at the collector. Use it for quick design checks when transistor output resistance, source loading, and frequency-dependent capacitor effects can reasonably be neglected.

Enter the effective small-signal circuit values

Provide the collector resistance RC in ohms, the unbypassed emitter resistance RE in ohms, and transistor transconductance gm in siemens. RC should represent the resistance seen by the collector in the small-signal model. If the physical collector resistor is loaded by another resistance, such as the input resistance of a following stage, first combine those parallel resistances and enter the effective value. RE should include only the emitter resistance active for the signal frequency being analyzed. A resistor fully bypassed by an ideal capacitor contributes approximately zero at that frequency, so enter zero when the emitter is effectively at AC ground. Transconductance belongs to the selected DC operating point and is often derived from collector current before using this calculator. All three inputs must use base SI units rather than kilohms or millisiemens. For example, enter 4700 for 4.7 kilohms and 0.04 for 40 millisiemens. Consistent units are essential because their products create the dimensionless voltage-gain ratio.

Understand the gain calculation and its sign

The calculation uses Av = -gm × RC / (1 + gm × RE). Without emitter degeneration, the numerator -gm × RC is the idealized common-emitter gain. Adding an unbypassed emitter resistor introduces local negative feedback, represented by the denominator 1 + gm × RE. As that denominator grows, gain magnitude falls, while bias stability, linearity, and input range commonly improve. The result therefore includes the signed voltage gain, its positive magnitude, the gain before emitter degeneration, and the degeneration factor. A result of -37.6 V/V means a sufficiently small positive change at the controlling input produces an output change about 37.6 times as large in the opposite direction. The phase inversion flag makes that interpretation explicit. The ratio has no physical unit, although V/V is conventionally shown to clarify that it relates output voltage change to input voltage change. This is a linear small-signal result, not a prediction that an amplifier can exceed its supply rails or remain linear for arbitrary input amplitude.

Know the approximation limits before applying the result

This calculator intentionally applies a compact midband model. It neglects transistor output resistance, finite beta effects on the source, source resistance, and other loading unless you incorporate loading into the effective RC value yourself. It also assumes gm is valid at the actual bias point and that the transistor remains in its intended active region. At low and high frequencies, coupling capacitors, emitter-bypass capacitors, junction capacitances, and wiring parasitics can change the gain substantially. A partially effective bypass capacitor requires an impedance model rather than a single real RE value. Likewise, a large input can encounter cutoff, saturation, clipping, or nonlinear distortion even when the small-signal gain is correct. Treat the result as a transparent first-order design estimate and compare it with a fuller small-signal model, simulation, or bench measurement when accuracy affects component selection. The formula is especially useful for checking hand calculations, exploring how emitter degeneration trades gain for feedback, and detecting unit-entry mistakes early in an amplifier design workflow.