Wien Bridge Oscillator

This is the Popular wein Bridge Osciallator which uses a Opamp in Non-inverting Configuration as shown above.The question is what should be the values of R and C .And also values of R6 and R5 for the above circuit to oscillate.

The condition for oscillation is Absolute value of  AB=1 ,angle should be 0 or 360 degree.Where A is the  gain of the OpAmp and B=Feedback network

. Consider only the Feedback network.

Put S=jW in the above equation

The non inverting amplifier produces  Zero phase shift.So the feedback network also should contribute zero phase shift in order to satisfy barkhausen criteria for Phase .This is possible only when W=1/RC in the above equation. 

 In that case , The feedback network has transfer function H(S)=1/3 which has zero  phase.

Now the phase of whole network is 0.

However closed loop gain is not equal to one.

i.e AB!=1. 

A here refers to amplifier gain.The opamp is in Non inverting stage.So we should consider the gain of Non inverting stage, not of openloop gain of opamp

so A= 1+(R6/R5).

B=1/3

So minimum value of A=1

So if R6=2k and R5=1k.

A will be 3 and the circuit will oscillate.

.

The circuit will oscillate at the frequency which is determined by the values of R and C. Because At W=1/RC

the circuit will follow Barkhausen criteria for oscillation.So the frequency can be calculated by substituting W=2*pi*f.

 f=1/2*pi*R*C.Which  is the frequency of oscillation.

So anyone who wants to build this circuit should make sure that gain is 3.And you can decide at which frequency the oscillations should occur and choose R and C  values respectively