Question

How do you calculate the input impedance and current gain of a common-collector BJT amplifier?

Answer 1

To calculate the input impedance and current gain of a common-collector (CC) BJT (Bipolar Junction Transistor) amplifier, you'll need to follow these steps:

Identify the common-collector amplifier circuit: The common-collector amplifier is also known as the emitter follower. It consists of an NPN transistor with the emitter connected to the ground, the base as the input, and the collector as the output.

Obtain the small-signal equivalent circuit: Replace the BJT with its small-signal equivalent model. For an NPN BJT, the small-signal equivalent circuit consists of a current source representing the base current (Ib), a voltage source representing the base-emitter voltage (Vbe), and a current source representing the collector current (Ic) controlled by the base-emitter voltage.

Draw the small-signal equivalent circuit: Here's a simplified diagram of the small-signal equivalent circuit for a common-collector amplifier:

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        V_in
         |
         R_in
         |
         +-----> Vbe
         |      |
        ---    /\/\/  Ib
         |      \ /\
         |       |
         +-------+
         |
        ---     Rc
         |      /
         +----|<|-----> V_out
         |      \
         -      Ic
         |
         Vee (Emitter supply voltage)

V_in: Input voltage (signal source)
R_in: Input resistance (to be calculated)
Vbe: Base-emitter voltage (small-signal)
Ib: Base current (small-signal)
Rc: Collector resistor
V_out: Output voltage (across Rc)
Ic: Collector current (small-signal)
Vee: Emitter supply voltage
Calculate the input impedance (R_in):

The input impedance of the common-collector amplifier is given by the ratio of the change in the base-emitter voltage (Vbe) to the change in the base current (Ib):

R_in = ΔVbe / ΔIb

Typically, the base current (Ib) can be approximated as the change in the input voltage (ΔV_in) divided by the input resistance (R_in):

Ib = ΔV_in / R_in

Solving for R_in:

R_in = ΔVbe / (ΔV_in / R_in)
R_in = R_in * (ΔVbe / ΔV_in)

Calculate the current gain (β):

The current gain (β) of the common-collector amplifier is defined as the ratio of the change in the collector current (Ic) to the change in the base current (Ib):

β = ΔIc / ΔIb

In many common-collector amplifiers, the relationship between Ic and Ib is given by:

Ic = β * Ib

Therefore, the current gain (β) is simply the ratio of the change in the collector current (ΔIc) to the change in the base current (ΔIb).

Keep in mind that real-world amplifier circuits may have additional components, such as bypass capacitors, coupling capacitors, and biasing resistors, which can affect the actual values of input impedance and current gain. The calculations provided here are based on a simplified small-signal equivalent circuit for educational purposes. In practice, it's essential to consider the complete circuit and its specifications for accurate results.