Barkhausen Criterion

Sustained oscillation needs a loop gain of exactly one with zero (or 360°) phase shift.

Intermediate

For an amplifier $A$ with feedback network $\beta$ :

$|A\beta| = 1 \qquad \angle A\beta = 0^\circ \ (\text{or } 360^\circ)$

In practice the loop gain is set slightly above 1 so oscillation starts from noise, then something non-linear (amplitude limiting, a lamp, a diode or AGC) brings it back to exactly 1 so the amplitude stays stable.

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