Barkhausen Criterion
Barkhausen Criterion
- 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.
- 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
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