To calculate the small-signal input resistance of a common-emitter BJT (Bipolar Junction Transistor) amplifier, you need to consider the small-signal model of the BJT and the biasing circuitry associated with the amplifier. The small-signal input resistance is the ratio of the small-signal voltage applied at the input to the corresponding small-signal current that flows into the input of the amplifier.
Here are the steps to calculate the small-signal input resistance:
Draw the Small-Signal Model:
Begin by drawing the small-signal equivalent circuit of the common-emitter BJT amplifier. This includes the transistor and its associated small-signal parameters. The small-signal model typically includes the transistor's transconductance (gm) and output conductance (ro).
Disconnect the Input Signal Source:
Temporarily disconnect the input signal source (e.g., a small-signal voltage source) from the input of the amplifier. This means setting the voltage source to zero.
Find the DC Bias Point:
Analyze the DC biasing circuitry of the common-emitter amplifier to determine the operating point (quiescent point) of the transistor. You need to find the DC collector current (IC) and DC collector-emitter voltage (VCE) at the bias point.
Apply the Small-Signal Input:
Now, apply a small-signal input voltage (v_in) to the input of the amplifier. This is usually done by connecting a small-signal voltage source in series with the input signal path.
Find the Small-Signal Input Current:
Calculate the small-signal input current (i_in) that flows into the base terminal of the BJT due to the small-signal input voltage. This current is usually the base current (i_b) of the transistor.
Calculate the Input Resistance:
The small-signal input resistance (r_in) is given by the ratio of the small-signal input voltage (v_in) to the small-signal input current (i_in):
r_in = v_in / i_in
Keep in mind that the small-signal model of the transistor will include the transconductance (gm) and output conductance (ro). Depending on the frequency range of interest, other parasitic elements like capacitances may also need to be considered.
It's important to note that the actual input impedance of a common-emitter BJT amplifier may not be purely resistive, and it can vary with frequency. For more accurate analysis, you may need to use more detailed small-signal models or consider other effects such as coupling capacitors, parasitic capacitances, and so on. However, the above steps provide a basic outline for calculating the small-signal input resistance.