Exercise 9.3 A 5-stage RC phase shift oscillator

Consider the RC phase shift oscillator shown below, which consists of 5 identical sections with resistance $R$, capacitance $C$ and a negative voltage gain A.

a)

The circuit schematic of this oscillator is symmetric; this property can be leveraged to simplify calculations. Determine the phase shift per stage, required for harmonic oscillations.

b)

Derive an expression for the (radian) oscillation frequency.

c)

Derive an expression for the amplifier gain A, needed for harmonic oscillation