Q.Draw the circuit diagram of a Wein bridge oscillator and explain its working. Write the expression for its frequency and feedback factor.

The Wein bridge oscillator uses an op-amp with a Wein bridge (series $R_1C_1$ arm, parallel $R_2C_2$ arm and resistors $R_3$, $R_4$) connected between its output and input as the frequency-selective feedback network. …

[!TLDR]

The Wein bridge (series $R_1C_1$ + parallel $R_2C_2$ + $R_3,R_4$) gives zero phase shift only at balance, so the op-amp oscillates at $f = \dfrac{1}{2\pi RC}$ with $A = 3$ and $\beta = \dfrac{1}{3}$.

Circuit: Figure 6.3.4 shows the Wein bridge oscillator, in which the Wein bridge is connected between the amplifier's input terminal and its output terminal. The bridge has a series $R_1C_1$ network in one arm and a parallel $R_2C_2$ network in the adjoining arm; the remaining two arms carry the resistors $R_4\ (=R_i)$ and $R_3\ (=R_f)$. The op-amp is connected as a non-inverting amplifier and its output $V_o$ drives the bridge.

Working: The phase-angle criterion for oscillation is that the total phase shift around the circuit must be $0^\circ$. This condition is satisfied only when the bridge is balanced, i.e. at resonance, so oscillations occur exactly at the resonant frequency of the balanced Wein bridge. The series–parallel RC (lead–lag) network passes the maximum voltage with zero phase shift at this frequency and attenuates all other frequencies, making the oscillation frequency highly selective. At balance,

and for $R_1=R_2=R,\ C_1=C_2=C$ this gives $\dfrac{R_3}{R_4} = 2$. …