Barkhausen Criterion

Consider a basic inverting amplifier with an open loop gain A.


• As basic amplifier is inverting, it produces a phse shift of 180* between input and output.
• The feedback network attenuation factor β is less than unity.
• Now the input Vi applies to the amplifier is to be derived from its output Vo using feedback network.
• But the feedback must be positive i.e. the voltage derived from output using feedback network must be in phase with Vi. Thus the feedback network must introduce a phase shift of 180* while feeding back the voltage from output to input. This ensures positive feedback.

The arrangement shown


• Consider a fictitions voltage Vi applied at the input of the amplifier. Hence we get,
Vo = A Vi
• The feedback factor β decides the feedback to given input,
Vf = β Vo
• Substituting these two
Vf = A β Vi
• For the oscillator, we want that feedback should drive the amplifier and hence Vf act as Vi. we can write that, Vf sufficient to act as Vi when,
|Aβ|=1
• And the phase of Vi is same as Vi i.e. feedback network should introduce 180* phase shift in addition to 180* phase shift introduced by inverting amplifier. This ensures positive feedback. So total phase shift around a loop 360*
• In this condition, Vf drives the circuit and without external input circuit works as an oscillator
• The two conditions discussed above, required to work the circuit as an oscillator are called Barkhausen criterionfor oscillator
• Satisfying these conditions, the circuit works as an oscillator producing sustained oscillations of constant frequency and amplitude

sustained oscillations