Explain the Wien bridge oscillator principle and the condition for sustained oscillation.

Explain the Wien bridge oscillator principle and the condition for sustained oscillation.

• A. The Wien network yields zero phase shift at a resonant frequency; the op-amp must have a gain of 3; amplitude stabilization needed
• B. The Wien network yields zero phase shift at all frequencies; the op-amp must have a gain of 1
• C. The Wien network yields 180-degree phase shift at resonance; the op-amp must have a gain of 2
• D. The Wien network yields zero phase shift at all frequencies; the op-amp must have a gain of 10

Answer: (A)

The Wien bridge oscillator relies on a frequency-selective feedback path that, at a specific resonant frequency, adds no phase shift and attenuates the signal by a fixed amount (1/3). This lets the op-amp, wired as a non-inverting amplifier, supply just enough gain so that the overall loop gain is unity, which is what sustains oscillations. At the resonant frequency, the Wien network’s magnitude is 1/3 and its phase is zero. To satisfy the Barkhausen criterion (loop gain = 1 with zero net phase shift), the op-amp’s non-inverting gain must be three. With that, the loop gain is 3 × (1/3) = 1, so oscillations can persist. In practice, amplitude stabilization is needed because any small mismatch or nonlinearity can cause the amplitude to grow or decay. A stabilization element (like a lamp or diodes) reduces the effective gain as the output grows, bringing the loop gain back to 1 and keeping the output steady. So the correct description is: zero phase shift at the resonant frequency, the op-amp gain of three, and a mechanism for amplitude stabilization to maintain steady oscillations. The other statements fail because the network does not provide zero phase shift at all frequencies, the phase at resonance is zero (not 180), and the required gain is not one (and a higher gain would need stabilization to avoid runaway).

The Wien bridge oscillator relies on a frequency-selective feedback path that, at a specific resonant frequency, adds no phase shift and attenuates the signal by a fixed amount (1/3). This lets the op-amp, wired as a non-inverting amplifier, supply just enough gain so that the overall loop gain is unity, which is what sustains oscillations.

At the resonant frequency, the Wien network’s magnitude is 1/3 and its phase is zero. To satisfy the Barkhausen criterion (loop gain = 1 with zero net phase shift), the op-amp’s non-inverting gain must be three. With that, the loop gain is 3 × (1/3) = 1, so oscillations can persist.

In practice, amplitude stabilization is needed because any small mismatch or nonlinearity can cause the amplitude to grow or decay. A stabilization element (like a lamp or diodes) reduces the effective gain as the output grows, bringing the loop gain back to 1 and keeping the output steady.

So the correct description is: zero phase shift at the resonant frequency, the op-amp gain of three, and a mechanism for amplitude stabilization to maintain steady oscillations. The other statements fail because the network does not provide zero phase shift at all frequencies, the phase at resonance is zero (not 180), and the required gain is not one (and a higher gain would need stabilization to avoid runaway).