transconductance (gm)
Transconductance is the single number that says how good a transistor is at its core job: turning an input VOLTAGE into an output CURRENT. It answers "if I wiggle the base-emitter voltage a little, how much does the collector current wiggle?" A big transconductance means a small voltage nudge produces a large current swing — a strong, sensitive control handle. The "trans" means it links two different terminals (input voltage at the base, output current at the collector), and "conductance" because, like conductance, it is current divided by voltage.
Its definition is gm = change in collector current divided by change in base-emitter voltage, and for a BJT it has a beautifully simple value: gm = Ic / VT, where Ic is the bias current and VT is the thermal voltage, about 25 mV at room temperature. So transconductance is set purely by the bias current, not by the transistor type or its beta. At 1 mA, gm = 1 mA / 25 mV = 40 millisiemens (or 40 milliamps per volt). Double the current to 2 mA and gm doubles to 80 mS. Its units are siemens (current over voltage), the reciprocal of ohms — a measure of conductance, which is why a high gm is a 'strong' transistor.
Why you care: the voltage gain of a common-emitter amplifier is simply -gm times the collector load resistance, so transconductance is the very thing that turns into gain. And here is a subtle, important honesty: because gm = Ic/VT depends on the instantaneous current, it is NOT constant as a large signal swings — gm rises on the current peaks and falls in the troughs. That variation is precisely the source of distortion in a simple common-emitter stage, and it is why emitter degeneration (which makes the gain depend on a fixed resistor ratio instead of the wandering gm) linearizes the amplifier. The closely related internal emitter resistance is just its reciprocal, re = 1/gm = VT/Ie.
A transistor biased at 0.5 mA has gm = 0.5/25 = 0.02 S = 20 mS. With a 10 kohm collector resistor the common-emitter gain is -gm times Rc = -0.02 times 10000 = -200. Want more gain at fixed Rc? Run more current to raise gm — but watch the power and the Q-point.
gm = Ic/VT: transconductance is set by the bias current, and gain is gm times the load.
A BJT's gm (Ic/VT) is far higher for a given current than a MOSFET's, which is why BJTs give big gain at low current. But because gm varies with the signal current, raw BJT gain is also less linear unless you add degeneration.