Question

the transistor parameters in the circuit are: are β1 = β2 = 100, va1 = va2 = ∞, and icq1 = 0.5 ma, icq2 = 2 ma. determine the small - signal voltage gain av2 = vo2/vo1.

Explanation:

Step1: Calculate $r_{\pi 1}$ and $r_{\pi 2}$

The formula for the trans - resistance $r_{\pi}$ is $r_{\pi}=\frac{\beta V_T}{I_{CQ}}$, where $V_T = 26\ mV$ at room temperature.
For transistor $Q_1$: $r_{\pi 1}=\frac{\beta_1V_T}{I_{CQ1}}=\frac{100\times26\ mV}{0.5\ mA}= 5.2\ k\Omega$.
For transistor $Q_2$: $r_{\pi 2}=\frac{\beta_2V_T}{I_{CQ2}}=\frac{100\times26\ mV}{2\ mA}=1.3\ k\Omega$.

Step2: Analyze the small - signal model of the second - stage

The small - signal voltage gain of the second stage $A_{V2}=\frac{V_{o2}}{V_{o1}}=-\frac{\beta_2R_{E2}}{r_{\pi 2}}$.
Substitute $\beta_2 = 100$, $R_{E2}=4\ k\Omega$ and $r_{\pi 2}=1.3\ k\Omega$ into the formula.
$A_{V2}=-\frac{100\times4\ k\Omega}{1.3\ k\Omega}\approx - 307.69$.

Answer:

$-307.69$