The correct answer is D: Barkhausen Criterion.

The Barkhausen criterion is the set of conditions a circuit must satisfy to function as an oscillator and produce sustained oscillations without any external input signal.

Two conditions must be met simultaneously:

1. Loop gain condition: The total loop gain must equal unity — |Aβ| = 1, where A is the amplifier gain and β is the feedback factor.

2. Phase shift condition: The total phase shift around the closed loop must be 0° or an integer multiple of 360°, ensuring the feedback signal is in phase with the input.

Working Principle:

• An amplifier is coupled with a feedback network.

• The amplifier amplifies the signal; the feedback network returns a portion of the output to the input.

• If |Aβ| > 1: oscillations grow until the system saturates.

• If |Aβ| < 1: oscillations die out.

• Only when |Aβ| = 1 and the phase condition is met do oscillations sustain indefinitely.

Applications:

• Signal generators producing sinusoidal, square, or triangular waveforms.

• RF circuits for generating carrier signals in communication systems.

• Frequency generation and modulation circuits.

Limitation: The criterion does not account for real-world non-idealities such as component tolerances, temperature variations, frequency drift, or distortion.