Exercise 4.7 An NPN amplifier and bandwidth issues

Given is the circuit schematic of an amplifier, see below.

a)

The amplifier is driven by an ideal voltage source $v_{\mathit{in}}$ and the circuit itself is unloaded. Derive an equation for the frequency dependent voltage gain $a_v=v_{\mathit{out}}(\mathit{j\omega })∕v_{\mathit{in}}(\mathit{j\omega })$. This equation includes the impedance of the capacitances - you cannot assume these to be (near) zero.

b)

Rewrite the previously derived equation into a standard form. This standard form lets you easily get DC-gain, high-frequency gain, poles and zeros from the expression).

c)

Draw a Bode plot (magnitude and phase) of this transfer, indicating the values of poles and zeros (on the x-axis) and the level of the flat part (y-axis).