To calculate the small-signal input resistance of a common-emitter bipolar junction transistor (BJT) amplifier, you can use the hybrid-pi model. The hybrid-pi model is a linear equivalent circuit that simplifies the analysis of the BJT in its small-signal mode of operation. In this model, the BJT is represented by a combination of resistors and a small-signal current source.
Here are the steps to calculate the small-signal input resistance (ri) of a common-emitter BJT amplifier using the hybrid-pi model:
Draw the small-signal equivalent circuit: Begin by representing the BJT with the hybrid-pi model. The small-signal equivalent circuit consists of a voltage source (VĪ) in series with the base terminal and a resistor (ri) connected between the base and emitter terminals. The collector and emitter terminals are left open in this analysis.
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+-------- RĪ -----------+
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Vin (small)----+--- VĪ -- Ri -- BJT --+-- Output
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Vout (small)
Set up the small-signal model parameters:
VĪ: This represents the small-signal voltage across the base-emitter junction, and it is typically denoted as Vbe. In many cases, Vbe is considered to be approximately 0.7V for silicon transistors and 0.3V for germanium transistors.
Ri: This is the small-signal input resistance we want to calculate.
BJT: The transistor represented by the hybrid-pi model.
Apply a small-signal voltage at the input: Apply a small-signal voltage (V_in, small) at the base terminal of the transistor. This small-signal voltage should be much smaller than the DC bias voltage and small enough not to cause significant distortion in the amplifier's output.
Determine the small-signal current (I_in, small) flowing into the base terminal.
Calculate the input resistance (ri):
The small-signal input resistance (ri) can be calculated using Ohm's law as follows:
ri = V_in, small / I_in, small
Keep in mind that this value is an AC (small-signal) resistance, and it represents how the input voltage changes in response to a small AC current at the input.
By following these steps, you can calculate the small-signal input resistance (ri) of a common-emitter BJT amplifier using the hybrid-pi model. Note that the actual value of ri can vary depending on the biasing conditions and the characteristics of the specific BJT used in the circuit.