Consider a BJT  transistor amplifier circuit operating in its active region to provide linear amplification.

The total instantaneous base-emitter voltage, which combines the DC voltage and the input signal, results in an instantaneous collector current.

The exponential term involving the base-emitter voltage is simplified using the small-signal approximation, where the input signal is significantly less than the thermal voltage.

So, the collector current comprises two components: the DC bias current and the signal component.

The ratio of the signal component to the varying base-emitter voltage is known as the BJT transconductance.

Here, the transconductance of the BJT is directly proportional to the DC bias current, which is determined by the slope of the tangent relative to the characteristic curve at the bias point.

So, the voltage gain equals the negative product of the transconductance and the load resistance. The negative sign indicates a 180 degrees phase shift between the amplified and input signals.

When examining the emitter, the small-signal base-emitter resistance is determined by dividing the thermal voltage by the respective DC bias current.