The Barkhausen criteria should be satisfied by an amplifier with positive feedback to ensure the sustained oscillations. For an oscillator circuit there is no input signal “V”,hence the feedback signal Vf  itself should be sufficient to maintain the oscillations. An oscillator is basically an “amplifier” which does not have any ac input but it operates on the principle of positive feedback to generate an ac signal at its output. Thus it is clear that an amplifier can work as an oscillator if positive feedback is made to exist. However positive feedback not always guarantees oscillations. An amplifier will work as an oscillator if and only if it satisfies a set of conditions called the ‘Barkhausen Criterion’

The Barkhausen criterion states that:

• An oscillator will operate at that frequency for which the total phase shift introduced, as the signal proceeds from the input terminals, through the amplifier and feedback network and back again to the input is precisely 0˚ or 360˚ or integral multiple of 360˚.
• At the oscillator frequency, the magnitude of the product of open loop gain of the amplifier A and the feedback factor (β) is equal to or greater than unity.

Therefore, |Aβ|≥1

The product Aβ is called as the “loop gain”.