Bipolar transistor amplification biased

bjttransistors

This exercise is about a BJT transistor common emitter circuit, with a biasing resistor between the base and the collector. I am supposed to compute the signal amplification of the circuit \$V_o/V_s\$ (\$V_o\$ being at node1). I am given that the transistor has \$\beta = 50\$ and \$r_{\pi} = 1.1\$ for the \$\pi\$ equivalent model.
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Best Answer

There are, in principle, two ways for solving the task. Please understand that I do not intent to present the solution for you. However, I will try to give you some hints to find the solution by yourself.

1.) Application of the superposition theorem

Supplementing the transistor Pi-model with the external resistors results in a circuit which contains two sources: A voltage source Vin and the controlled current source of the Pi-model. Thus, after applying the superposition principle you get two equations for finding the two unknown quantities: Vo/Vin and Vbe. (Please note that the transconductance of the Pi-model can be expressed by the two known values for beta and Rpi).

2.) Application of the general gain formula for negative feedback

The closed-loop gain is Vo/Vin=Acl=AoHf/(1-AoHr). (Note that Ao will be negative).

Gain without feedback Ao=Vout/V(base) (simple gain formula for common emitter);

Forward (damping)factor Hf=V(base)/Vin for Vout=0;

Return (feedback) factor Hr=V(base)/Vout for Vin=0.

Both factors are calculated using simple voltage divider rules.