For an RC phase shift oscillator, which of the following statements is INCORRECT?

Concept:

An RC phase shift oscillator is a type of sinusoidal oscillator that uses an amplifier (usually a transistor or op-amp) and a phase-shift network made up of resistors and capacitors to produce continuous waveforms without any input signal.

For sustained oscillations, the circuit must satisfy the Barkhausen criterion, which states:

• The total phase shift around the loop must be 360° or 0°.
• The loop gain (product of amplifier gain and feedback network gain) must be ≥ 1.

Evaluation of Options:

Option 1: The total phase shift of the RC network is 180°

This is Correct. A 3-stage RC network produces a total phase shift of 180° (each stage contributes 60°). The amplifier, being inverting, provides another 180°, resulting in a total phase shift of 360° (i.e., 0° phase shift), satisfying the phase condition of Barkhausen's criterion.

Option 2: The magnitude of the gain of the RC network is > 1/29

This is Incorrect. In a 3-stage RC network used in the oscillator, the gain of the RC network is approximately \( \frac{1}{29} \). Hence, it is wrong to say the gain is greater than 1/29. This is the incorrect statement we are looking for.

Option 3: The magnitude of gain of the amplifier must be ≥ 29

This is Correct. Since the RC network attenuates the signal by a factor of 29, the amplifier must compensate by providing a gain of at least 29 to maintain unity loop gain (\( A \cdot \beta = 1 \)).

Option 4: The oscillation frequency of the oscillator is \( \frac{1}{2\pi RC \sqrt{6}} \)

This is Correct. This is the standard formula for the oscillation frequency of a 3-stage RC phase shift oscillator.