# What is the way to calculate the Voltage gain of cascade common-emitter BJT amplifier?

I have a problem of calculating the voltage gain of cascade common emitter BJT amplifier using small-signal model

Assume that the reactance of the capacitor is negligible. The circuit is bias at $I_{C1}=0.1mA$ and $I_{C2}=1mA$ and $\beta=100$ for both BJT

simulate this circuit – Schematic created using CircuitLab

$$A_v=\frac{V_{out}}{V_{in}}$$ $$V_{out}=100i_{b2}*R_2=100(\frac{100i_{b1}\frac{R_1r_{be2}}{R_1+r_{be2}}}{r_{be2}})R_2=100(\frac{100\frac{V_{in}}{r_{be1}}\frac{R_1r_{be2}}{R_1+r_{be2}}}{r_{be2}})R_2$$

using $r_{be}=\frac{25\beta}{I_c}$, $r_{be1}=25k\Omega$ and $r_{be2}=2.5k\Omega$

by then I get the result $A_v=1785$

However, the result of my text book says that it's 1765 and $r_{in}=25.25k\Omega$ which I think that $r_{in}=r_{be1}$

Can anybody explain what I missed in calculating or what I did wrong.

• The voltage gain will be somewhat lower than calculated by you because the input resistance of the second stage will be smaller than 2.5kOhms. This is because the resistors biasing the second stage have been forgotten. Without this biasing the circuit will not work. – LvW Oct 14 '15 at 8:04

You should use $25(\beta+1)/I_C$ for the input impedance; the base current also flows through the emitter in addition to the collector current.