transconductance

Transconductance, denoted g_m, is a parameter that measures how effectively a transconductance device converts a small change in input voltage into a change in output current. It is defined for devices such as vacuum tubes and field-effect transistors (JFETs and MOSFETs) as the slope of the output current versus input control voltage, with other terminal voltages held constant.

For a transistor, g_m is commonly expressed as g_m = ∂I_out/∂V_in. In a MOSFET, the input control is the gate-source voltage V_gs and the output current is the drain current I_d, so g_m = ∂I_d/∂V_gs at constant V_ds. The SI unit is siemens (A/V). In small-signal analysis, g_m is a key factor in determining voltage gain, for example in a common-source stage where the approximate gain is A_v ≈ -g_m (R_D || r_o).

Bias-dependent behavior is a feature of transconductance. In a long-channel MOSFET operating in saturation, Id ≈ K (V_gs − V_th)^2, and thus g_m ≈ 2K (V_gs − V_th) = 2 I_d /(V_gs − V_th). For JFETs, Id is often modeled as Id ≈ Idss [1 − (V_gs/V_p)]^2, giving a g_m that varies with V_gs and generally decreases as the device moves toward pinch-off.

Practical notes: g_m increases with drain current, varies with temperature, and is specified at a particular bias point. It is a fundamental parameter in analog circuit design, shaping the performance of amplifiers, mixers, and other voltage-controlled current sources.