Input and Output Resistance

The input resistance can readily found by recalling Lab 2, where we showed that the input resistance into a common emitter amplifier was $R_{in}=r_{\pi}+\beta R_E$.Well, for a diff-amp, the resistance looking into the base of Q1 is $R_{in}=r_{\pi 1} + \beta_1 R_E'$, where R_E' is the effective emitter resistance of Q1. However, this resistance is actually the resistance looking into the emitter of Q2. Recall that the resistance looking into the emitter is $\frac{1}{g_{m2}}$. So, the input resistance looking into the base of Q1 is

$$R_{in}=r_{\pi 1}+\beta\frac{1}{g_{m2}}=r_{\pi 1}+r_{\pi 2}=2r_\pi$$ (117)

So far in these labs we have considered the BJT collector to be a perfect current source. For now let's continue this approximation. So, if we try to drive the output, which is the collector of Q2, with an independent source, all the current will go through R_C2. Therefore, the output resistance of the diff-amp is just given by

R_o=R_C2