Exercise 4.1 Signal sources, loads and overall gain

A signal source with output resistance $R_g$ of $600\mathrm{\Omega }$ is connected to an amplifier circuit. We can choose from two amplifiers: one with a voltage gain $a_{v1}=30$ and an input resistance $r_{\mathit{in}1}=6k\mathrm{\Omega }$, the other with a voltage gain $a_{v2}=60$ and an input resistance $r_{\mathit{in}2}=600\mathrm{\Omega }$. The output of the amplifier remains unloaded (open).

a)

Calculate the gain from input voltage to output voltage, for both amplifier configurations.

We now place a coupling capacitor $C_c$ between the output of the signal source and the input of the amplifier.

b)

Calculate the value of capacitor $C_c$ to get a (low frequency, -3dB) cutoff frequency equal to 20 Hz. Provide the answer as a function of among others $r_{\mathit{in}}$ and $R_g$.

c)

Draw a Bode plot (magnitude and phase) of the transfer function of the amplifier configuration including capacitor $C_c$. You may assume that $r_{\mathit{in}}=r_{\mathit{in}2}=600\mathrm{\Omega }$ and that $a_v=a_{v2}=60$ for this plot.