In an oscillator, for sustained oscillations, Barkhausen criterion is `Abeta` equal to (A = voltage gain without feedback and `beta` = feedback factor)

Options

A. Zero
B. less than 1
C. One
D. Infinity

Answer

C

Explanation

The voltage gain of an amplifier without feedback is given by `A=(V_"output"(V_o))/(V_"input"(V_i))` and the feedback factor `(beta)` is the fraction of the output voltage fed back to the input
`therefore V_i=V_f=betaV_o " " therefore A=V_o/V_i = V_o/(betaV_o)=1/beta`
`therefore Abeta=1`
The voltage gain of the feedback oscillator is `A_f=A/(1-Abeta)`
If for a particular frequency `Abeta`=1, then `A_f=oo` and the circuit begins to oscillate at that frequency .
The condition `Abeta` =1 is known as Berkhausen's criterion for sustained oscillations.