Draw the circuit diagram of a Wien's bridge oscillator and explain its operation.

Circuit Diagram of a Wien's Bridge Oscillator:

Explanation of Wien's Bridge Oscillator Operation:

The Wien's bridge oscillator is a sinusoidal electronic oscillator that generates frequencies from a few hertz to several hundred kilohertz. It consists of a Wien bridge network, which is a four-terminal electrical network that exhibits a phase shift of 180 degrees at a specific frequency. This frequency is called the resonant frequency of the Wien bridge network.

The Wien bridge oscillator uses the Wien bridge network in a positive feedback loop to create a stable sinusoidal oscillation. Here's how it operates:

1. Wien Bridge Network:

• The Wien bridge network consists of two resistors (R1 and R2) and two capacitors (C1 and C2).
• Resistors R1 and R2 form the upper arms of the bridge, while capacitors C1 and C2 form the lower arms.
• The diagonal of the bridge connects the input voltage (Vin) to the output voltage (Vout).

2. Phase Shift:

• At low frequencies, the capacitors act as open circuits, and the bridge behaves as a voltage divider.
• As the frequency increases, the capacitors start to act as conductors, causing a phase shift between Vin and Vout.
• At the resonant frequency (f_r), the phase shift reaches 180 degrees, and the bridge becomes balanced.

3. Positive Feedback:

• In the Wien's bridge oscillator, the output of the Wien bridge network is fed back to the input through an amplifier with a gain of A.
• When the phase shift in the Wien bridge network is 180 degrees, the positive feedback causes the oscillation to start and sustain.
• The amplifier provides the necessary gain to overcome losses in the Wien bridge network and sustain the oscillation.

4. Oscillation Frequency:

• The oscillation frequency (f_osc) of the Wien's bridge oscillator is determined by the values of R1, R2, C1, and C2.

• The resonant frequency (f_r) of the Wien bridge network is given by:

  • f_r = 1 / (2π√(R1R2C1C2))

• In practice, f_osc is slightly lower than f_r due to the non-ideal behavior of components.

5. Waveform:

• The Wien's bridge oscillator produces a sinusoidal waveform because the positive feedback is phase-shifted by 180 degrees at the resonant frequency.
• This phase shift ensures that the feedback signal is in phase with the input signal, which results in a stable sinusoidal oscillation.

Adjustable Frequency:

• The oscillation frequency of the Wien's bridge oscillator can be adjusted by varying the values of R1, R2, C1, and C2.
• Changing the values of these components changes the resonant frequency of the Wien bridge network, which in turn changes the oscillation frequency.

The Wien's bridge oscillator is a versatile circuit that is widely used in electronic applications such as frequency generators, function generators, and audio test equipment. Its stability, adjustable frequency, and sinusoidal waveform make it a popular choice for various electronic applications.