From the below figure, the gain of the amplifier is represented as A. the gain of the amplifier is the ratio of o/p. voltage ($v_o)$ to the input voltage (vi) the feedback network extracts a voltage vf = $\beta vo$ from the output vo of the amplifier.

• The output voltage is added for positive feedback from the signal voltage vs.

$\therefore$ vi = vs + vf

$\therefore$ vi = vs + $\beta vo$ → (1)

The quantity $\beta$ = vf/vo is the feedback ratio

Vo – A (vs + $\beta vo)$

$\therefore$ $\frac{vo}{vs}$ = $\frac{A}{1-A\beta}$

$\therefore$ AF = $\frac{vo}{vs}$ = $\frac{A}{1-A\beta}$

Where A$\beta$ = feedback factor or the loop gain of AB = 1, AF → $\infty$ thus the gain becomes infinity. i.e. there is o/p without any i/p hence we can see this amplifier works as one oscillator.

The condition A$\beta$ = 1 is called barkhausen’s criteria for oscillation.

a) The total phase shift through the amplifier and feedback network must be N x 360 where N = 0, 1, 2 ….

b) The magnitude of the loop gain must be unity.