Question

How do you calculate the small-signal voltage gain of a common-collector BJT amplifier?

Answer 1

To calculate the small-signal voltage gain of a common-collector (CC) BJT (Bipolar Junction Transistor) amplifier, also known as an emitter follower, you can follow these steps:

Identify the Small-Signal Model: First, determine the small-signal equivalent circuit for the common-collector amplifier. The small-signal model for a BJT typically consists of a hybrid-pi (π) model. In the common-collector configuration, the emitter terminal is the input, and the collector terminal is the output.

Draw the Small-Signal Equivalent Circuit: The small-signal equivalent circuit for a common-collector BJT amplifier using the hybrid-pi model looks like this:

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           Rs    Rb
Vin ----/\/\/----|----|\
                  |   | \
                  |   / / C
                 | |  \ \_
                 | |   ---  Rc
                 | |   ---  RL (Load Resistance)
                 | |  / /
                  \ \ / / Ib (Base current)
                  /  \ \_
                  \  /  E
                  /\/\  (Transistor)
                  Rg  Re (Emitter Resistance)
                   |    |
                   ------ GND
                    Vout


Where:

Vin: Input small-signal voltage
Vout: Output small-signal voltage
Rs: Source resistance (if applicable)
Rb: Base bias resistor
Rc: Collector resistor
RL: Load resistance
Ib: Base current (small-signal)
Re: Emitter resistance (small-signal)
Rg: Internal resistance of the signal source

Set up the small-signal AC equations: Apply small-signal AC analysis to the equivalent circuit. Replace all the DC bias voltages and currents with their small-signal AC counterparts, represented by lowercase symbols (e.g., Vbe, Ic, Ib). Use linear approximations for the transistor's characteristics around its operating point.

Write the small-signal AC equations: Write the KVL (Kirchhoff's Voltage Law) equation around the input and output loops to relate the small-signal AC voltages and currents.

Calculate the Voltage Gain: The small-signal voltage gain (Av) is the ratio of the output voltage variation (ΔVout) to the input voltage variation (ΔVin) while assuming all other small-signal parameters remain constant:

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Av = ΔVout / ΔVin

Simplify and solve for Av: By solving the small-signal AC equations, you should be able to determine the value of Av.

Note: The common-collector BJT amplifier is primarily used for impedance matching and not for voltage amplification. As a result, its voltage gain is slightly less than unity (Av ≈ 1).

Keep in mind that this is a basic overview of the calculation process. In practice, the hybrid-pi model and other transistor models may need to be refined based on specific transistor parameters and conditions. Also, ensure that the transistor remains in the active region for accurate small-signal analysis.