The conditions necessary for sustained oscillation can be summarized as follows:

1. There should be a positive feedback.

2. The loop gain of the circuit must be equal to or greater than 1 i.e. Aβ<=1.

3. The phase shift around the circuit must be zero or 360 degrees.

The non-sinusoidal oscillation at steady state can happen at 2 states:

1. β is not exactly 1.

2. Due to saturation.

And α decimal signal or noise voltage can provide a measurable output voltage and the circuit can act as oscillator even without an input signal.