Question

How can you determine the small-signal input resistance of a common-base BJT amplifier?

Answer 1

To determine the small-signal input resistance of a common-base Bipolar Junction Transistor (BJT) amplifier, you can use the following steps:

Remove the AC signal source and short-circuit all the independent AC voltage sources in the circuit. This simplifies the analysis and allows us to consider only the small-signal parameters of the transistor.

Consider the transistor's small-signal model. In the small-signal model, we replace the transistor with its small-signal equivalent circuit, which includes the transconductance (gm), output conductance (go), and input capacitance (Cπ) components. For a common-base configuration, the small-signal model of the BJT looks like this:

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            +---> Output (Collector) Voltage (v_out)
            |
            |
    R_in    |    R_out
 ---\/\/\---/\/\/\---
    Vin    |         |
            |        ===
            |        --- Cπ
            |
           GND


Disconnect the load resistor (R_out) from the output to find the input resistance (R_in). The input resistance of the common-base amplifier is simply the resistance seen at the input terminals (base-emitter junction).

Apply a small AC voltage signal (v_in) at the input, and analyze the circuit to determine the relationship between v_in and the resulting small-signal input current (i_in). The input current in a common-base configuration is usually a function of the input voltage.

Calculate the input resistance (R_in) using Ohm's law, which is given by the ratio of the small-signal input voltage (v_in) to the small-signal input current (i_in):

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R_in = v_in / i_in


Note that the small-signal input resistance can vary with biasing and load conditions. It also depends on the biasing point of the transistor and the transistor's small-signal parameters (gm, go, and Cπ), which are dependent on the operating point of the BJT.

The specific calculation may involve some circuit analysis depending on the actual circuit you are dealing with, but the general steps mentioned above should guide you in determining the small-signal input resistance of a common-base BJT amplifier.