To determine the large-signal voltage gain of a common-collector BJT (Bipolar Junction Transistor) amplifier, also known as an emitter follower, you can follow these steps:
Understand the Common-Collector Amplifier Configuration:
The common-collector amplifier is characterized by having the emitter of the BJT connected to the ground (common terminal). The input is applied to the base, and the output is taken from the collector. This configuration is also known as an emitter follower because the emitter voltage follows the base voltage with a small voltage drop due to the base-emitter junction.
Find the DC Biasing Point:
To start the analysis, you need to find the DC biasing point (also called quiescent point or Q-point) of the transistor. This is done by applying a DC voltage source to the base-emitter junction and setting the values of resistors in the circuit such that the transistor operates in its active region. The active region ensures that the transistor remains linear for the desired input range.
Draw the AC Equivalent Circuit:
To analyze the AC behavior of the amplifier, you need to draw the small-signal AC equivalent circuit. In this circuit, all the DC voltage sources are short-circuited, and all the DC current sources are open-circuited. The capacitors are considered as shorts at the AC frequency.
Identify the Small-Signal Model Parameters:
Identify the small-signal model parameters of the BJT, specifically the transconductance (gm), the output conductance (g0), and the input resistance (re).
Apply Miller Effect (Optional):
If the amplifier has capacitive coupling between the input and output stages, you may need to consider the Miller effect, which affects the overall voltage gain.
Calculate the Large-Signal Voltage Gain:
Once you have the small-signal model parameters, you can calculate the large-signal voltage gain (Av) using the following formula:
Av = -(gm * RL) / (1 + gm * RE)
Where:
Av: Large-signal voltage gain
gm: Transconductance of the transistor
RL: Load resistance (resistor connected to the collector)
RE: Emitter resistance (usually the dynamic resistance, re, of the transistor)
Note that in common-collector configuration, the voltage gain is less than unity (less than 1) due to the negative sign in the formula. The emitter follower acts as a voltage buffer with a voltage gain slightly less than 1.
Keep in mind that this analysis assumes the amplifier operates in its linear region. For accurate results, you may also need to consider factors such as early effect, Early voltage (VA), and load resistance effects.