To calculate the small-signal transconductance (gm) of a common-collector (CC) BJT (Bipolar Junction Transistor) amplifier, you'll need to follow a few steps. The common-collector configuration is also known as the emitter follower.
Identify the small-signal model: The first step is to find the small-signal equivalent model of the common-collector BJT amplifier. In this model, you treat the BJT as a small-signal device and neglect its nonlinearities.
Draw the small-signal model: The small-signal model for the common-collector BJT amplifier consists of a voltage source (Vsig) representing the input signal, a resistor (re) representing the small-signal emitter resistance, and an ideal current source (gm*Vbe) representing the small-signal transconductance.
Apply DC bias conditions: Set up the DC biasing for the BJT to put it in the active region. This involves applying a DC voltage across the base-emitter junction and a load resistor at the collector.
Find the small-signal voltage: Apply a small-signal AC voltage at the input (Vsig) and analyze the circuit to find the small-signal voltage across the emitter resistor (re).
Calculate transconductance: The transconductance (gm) is defined as the change in collector current (ΔIc) divided by the change in the base-emitter voltage (ΔVbe) under small-signal conditions.
gm = ΔIc / ΔVbe
Determine ΔIc and ΔVbe: To find ΔIc and ΔVbe, you can use the small-signal voltage (Vre) across the emitter resistor (re) and Ohm's law. Since Vre = ΔIc * re and ΔVbe = Vsig (input signal voltage), you can calculate ΔIc and ΔVbe.
Calculate gm: Once you have ΔIc and ΔVbe, plug them into the transconductance formula (gm = ΔIc / ΔVbe) to obtain the small-signal transconductance of the common-collector BJT amplifier.
Keep in mind that the value of gm varies with the DC bias point of the BJT and the small-signal conditions, such as the small-signal voltage applied at the input. Therefore, it's essential to consider the specific operating conditions when calculating gm.