Why is the phase shift through the RC feedback circuit in a phase-shift oscillator 180°?

The phase shift in an RC feedback circuit in a phase-shift oscillator is 180° due to the combination of the amplifier and the feedback network. Here's a step-by-step explanation:

1. The phase-shift oscillator consists of an inverting amplifier and a feedback network composed of resistors and capacitors.

2. The inverting amplifier alone provides a phase shift of 180°. This is because the output signal is 180° out of phase with the input signal.

3. The feedback network is designed to provide an additional phase shift of 180° at the desired frequency of oscillation. This is achieved by using a network of three RC sections. Each RC section provides a phase shift of up to 60°, and three sections together provide a phase shift of up to 180°.

4. Therefore, the total phase shift through the oscillator circuit is 360° or 0°, which is the condition required for sustained oscillations.

5. The phase shift of 180° through the feedback network also ensures that the feedback is positive, which is another condition for sustained oscillations.

So, the 180° phase shift through the RC feedback circuit in a phase-shift oscillator is a result of the design of the oscillator circuit to meet the conditions required for sustained oscillations.