To calculate the small-signal input resistance of a common-emitter Bipolar Junction Transistor (BJT) amplifier, you can follow these steps:
Draw the small-signal equivalent circuit: For small-signal analysis, we assume that the transistor is operating in its linear region, and the AC signal is small enough not to cause any significant changes in the DC biasing. In this case, the small-signal equivalent circuit for a common-emitter BJT amplifier looks like this:
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Vin (small signal) Rin
+---||---|>---| |
| C | | hfe * Ib (small signal base current)
| | |
+----[BJT]----+---| <-- Vout (small signal)
| Rc
GND
Identify the components: In the small-signal equivalent circuit, you have the small-signal input voltage (Vin), the input resistance (Rin) that you want to find, the BJT with its current gain (hfe), the base-emitter capacitance (C), and the collector resistor (Rc).
Find the small-signal base current (Ib): To determine Ib, you need to divide Vin by the resistance seen looking into the base-emitter junction (Vbe) of the transistor. Vbe is typically around 0.6 to 0.7 volts for a silicon BJT. So, Ib = Vin / Vbe.
Calculate the small-signal input resistance (Rin): Rin is the ratio of the small-signal voltage Vin to the small-signal base current Ib:
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Rin = Vin / Ib
Substitute the value of Ib: Replace Ib in the equation with the expression you derived in step 3:
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Rin = Vin / (Vin / Vbe) = Vbe
Finalize the value: The small-signal input resistance (Rin) of a common-emitter BJT amplifier is approximately equal to the base-emitter voltage (Vbe) of the transistor.
Keep in mind that this analysis assumes ideal conditions and doesn't account for all parasitic effects or temperature variations. In practical designs, you may need to consider those factors for more accurate results.