Q.With a circuit diagram explain the action of a RC phase shift oscillator. Write the expression for its frequency and feedback factor.

The RC phase-shift oscillator uses an op-amp inverting amplifier with three cascaded RC sections (each giving $60^\circ$) in its feedback path. …

[!TLDR]

Three $60^\circ$ RC sections give $180^\circ$ and the inverting op-amp another $180^\circ$ (total $360^\circ$); the circuit oscillates at $f = \dfrac{1}{2\pi\sqrt{6}\,RC}$ with $\beta = \dfrac{1}{29}$.

Circuit: Figure 6.3.2 shows the RC phase-shift oscillator. It consists of an op-amp as the amplifying stage and three identical RC sections as the feedback circuit that returns a fraction of the output to the inverting input. $R_f$ is the feedback resistor and $R_i$ the input resistor of the inverting amplifier.

Action: The starting voltage is provided by circuit noise. In each RC section the voltage across R leads the applied voltage, and by choosing R suitably each section is adjusted to give a phase shift of $60^\circ$; the three sections together therefore produce $3 \times 60^\circ = 180^\circ$. The op-amp, being an inverting amplifier, introduces a further $180^\circ$. The total phase shift around the loop is $360^\circ$ (equivalently, the feedback voltage is in phase with the input), satisfying the phase condition for positive feedback, so the circuit produces sustained sinusoidal oscillations. …