Q.What should be the capacitance value of the capacitor required for a phase shift oscillator of frequency $120\,\text{Hz}$, if the resistor has a value of $220\,\Omega$?

The RC phase-shift oscillator is a low-frequency oscillator that replaces the inductor of an LC circuit with resistor-capacitor sections. It rests on the phase-shift property of a single RC section: with a series capacitor $C$ and a shunt resistor $R$, the output taken across $R$ leads the applied voltage by an angle $\phi$ where

The value of $\phi$ depends on $R$ and $C$: if $R = 0$ the lead is $90^\circ$; if $R = \infty$ it is $0^\circ$. In practice $R$ is chosen so each section gives a convenient $60^\circ$, and three such sections in cascade produce a total of $3 \times 60^\circ = 180^\circ$.

An op-amp connected as an inverting amplifier supplies the amplification and adds another $180^\circ$. The RC network's $180^\circ$ plus the amplifier's $180^\circ$ make the total loop shift $360^\circ$ — the phase condition for positive feedback — so the circuit oscillates. Its frequency is …