Oscillator consist of a amplifier and a positive feedback network, positive feedback network consist of RC or LC network.

Vin = Vs + Vf

But Vf = BVo & A = $\frac{vG}{v_{in}}, v_in = \frac{vo}{17}$

$\frac{vo}{A} = vs + Bvo$

$\frac{vo}{A} - Bvo = Vs$

$V_o (\frac{1}{A}) - B_ = V_s$

$V_o (\frac{1 - AB}{A}) = V_s$

$\frac{vo}{vs} = \frac{A}{1-AB}$

For oscillator $V_s \rightarrow 0$

1 - AB $\rightarrow$ 0

AB = 1 < 0˚ or < 360˚

This conditions are known as Barkhausen's criteria or necessary condition for oscillations.

Barkhausen's criteria.

1] The total gain around the loop must be equal to 1.

2] The total phase shift has to be 0˚ or 360˚.