To calculate the small-signal transconductance of a common-collector BJT (Bipolar Junction Transistor) amplifier, follow these steps:
Identify the amplifier circuit: Confirm that you are indeed dealing with a common-collector (also known as an emitter follower) BJT amplifier. In this configuration, the emitter is the common terminal between the input and output.
Assumptions: For small-signal analysis, we assume that the signal variations are small enough to linearize the transistor's behavior around the quiescent (DC) operating point. This means we replace the transistor with its small-signal model.
Draw the small-signal model: Replace the BJT with its small-signal equivalent circuit. The small-signal model for a BJT comprises the following parameters:
gm: The small-signal transconductance, which is the change in collector current with respect to the change in base-emitter voltage (ΔIc/ΔVbe).
ro: The small-signal output resistance, which represents the output resistance of the transistor.
The small-signal model of a BJT is a current source connected in parallel with the small-signal output resistance (ro).
Determine the base-emitter voltage change (ΔVbe): Calculate the change in the base-emitter voltage due to the small-signal input. This is usually denoted as ΔVbe.
Calculate the change in collector current (ΔIc): Determine the change in collector current caused by the small-signal input. This is given by ΔIc = gm * ΔVbe, where gm is the transconductance you want to find.
Find the small-signal output current (Iout): The small-signal output current can be considered as the collector current (Ic) itself because the emitter current is assumed to be constant due to the emitter follower configuration.
Calculate the small-signal transconductance (gm): Divide the change in collector current (ΔIc) by the change in base-emitter voltage (ΔVbe) to obtain the transconductance (gm). Mathematically, gm = ΔIc / ΔVbe.
Once you have the value of gm, you can use it to analyze and design the common-collector BJT amplifier's small-signal characteristics, such as voltage gain and input/output impedance.