Exercise 5.7 An amplfier using a single NPN

Given is the circuit schematic below. For the signal frequencies of interest the capacitors may be considered as low ohmic.

a)

Derive an expression for the collector current $I_C$ (as a function of $V_{\mathit{CC}}$, $R_B$, $R_C$, $\mathit{\beta fe}$). You can assume that the base-emitter voltage of the transistor is $0.6V$.

b)

Draw the small signal equivalent circuit.

c)

Derive an expression for the voltage gain of the circuit.

d)

Derive an equation for the required value of $R_B$ for a collector current of $I_C$. After that calculate the value numerically for $I_C=1\mathit{mA}$, $V_{\mathit{CC}}=3V$, $R_C=2k\mathrm{\Omega }$ and $\mathit{\beta fe}=100$.

e)

If the transistor is replaced by another one with $\mathit{\beta fe}=40$ (without adjusting $R_B$ and $R_C$), how does that affect the collector current?