Wien bridge oscillator realized with op-amp is given in figure bellow.
Simulate Op-amp Wien bridge oscillator.
A Wien bridge oscillator is a type of electronic circuit with electric bridge as feedback. One half of the bridge is selective and it consist of series RC component (R1 and C1) connected to a parallel RC component (R2 and C2). Another half of the bridge is non selective and it is made of resistive network R3 and R4. Selective part forms second order band pass filter with high quality factor Q. This kind of circuit has both positive and negative feedback. Overall feedback is positive and circuit is not stable, but it oscillate in predictive way. Generally, R1 can be different from R2 and C1 can be different from C2. In that case, resonant frequency is (if circuit can oscillate):
From here it is obvious that resonant frequency depends of selective part of the bridge only. On the other hand, to have unstable circuit (so that oscillation can occur on the first place), Barkhausen conditions has to be fulfilled. Barkhausen condition is necessary but not a sufficient condition. It states that in order to have unstable circuit, loop gain AÂ·Î² has to be close to unity i.e.
- Absolute magnitude of the loop gain is one:
- Phase shift of the loop is zero or integer multiply of 2Ï€
For Wien bridge oscillator, Barkhausen conditions is that
So, non selective (resistive) half of the bridge must fulfill necessary condition for oscillations to start. In order to make sufficient condition, parameter Î´ is introduced as:
In here, parameter Î´ shows how good R4 is trimmed to R3. Sufficient condition for initiating oscillations is that A0>Î´, where A0 is open loop gain of op-amp. It means that if R4 is exactly two times higher then R3, Î´ goes to infinity a and A0 is no longer higher then Î´, oscillations will not occur. If parameter Î´ is relatively low, for example, if R4=2.001âˆ™R3, Î´=1000 and A0 is higher then Î´, oscillations will occur, but frequency will not be very stable. On the other hand, if Î´ is high, and A0 is still higher then Î´, oscillations will start and will have stable frequency. So good compromise is to have high value of parameter Î´ and op-amp with very high gain, or to use to op-amps in cascade. Parameters in selective bridge can be mutually different, but for simplicity it is common practice that C1=C2=C and R1=R2=Rf. In that case, frequency of oscillations is: