Q.With a circuit diagram, explain the principle of phase shift in RC circuit.

In a single RC section the output taken across the resistor leads the input voltage, because the current through the capacitor leads the applied voltage; the amount of lead is the phase shift.

[!ANSWER]

For one RC section $\tan\phi = \dfrac{X_C}{R} = \dfrac{1}{\omega C R}$; by choosing R suitably each section is made to give a phase shift of $60^\circ$, so that three such sections together provide the $180^\circ$ needed by a phase-shift oscillator.

[!TLDR]

An RC section makes its output (across R) lead the input by an angle $\phi$ with $\tan\phi = 1/(\omega C R)$; three $60^\circ$ sections give the required $180^\circ$.

A phase-shift circuit is basically an RC network. Consider one section (Figure 6.3.1a): the input voltage $V_i$ is applied through a series capacitor C, and the output $V_o$ is taken across the resistor R connected from the junction to the return line.

Because the same current flows through C and R, and the current in a capacitor leads the voltage across it, the voltage developed across R (which is in phase with the current) leads the applied voltage $V_i$ by an angle $\phi$. From the phasor relation of the series RC section,

The value of $\phi$ depends on R and C. If $R = 0$, $V_o$ leads $V_i$ by $90^\circ$; if $R = \infty$, $\phi = 0^\circ$. In practice R is varied to a value that makes each section produce a lead of $60^\circ$.

When three such identical RC sections are cascaded, the total phase shift becomes $3 \times 60^\circ = 180^\circ$; i.e. the network output leads its input by $180^\circ$. An inverting amplifier adds a further $180^\circ$, giving $360^\circ$ around the loop, which is exactly the phase condition needed for oscillation. This is the principle used in the RC phase-shift oscillator.

[!ANSWER]

The voltage across R leads the input because capacitor current leads its voltage, the lead being $\tan\phi = 1/(\omega C R)$. R is set so each RC section gives $60^\circ$, and three sections together produce the $180^\circ$ phase shift required for phase-shift oscillation.