In the following op-amp circuit:
Rf here is replaced by the following:
What do the anti-parallel diodes here serve? This is a Wien Bridge oscillator circuit and I am showing only the negative terminal of the op-amp. Once the diodes are removed the output is very unstable and I am not sure why. Maybe explaining what they do will help me.
Edit: Another question I should ask is: why are the diodes necessary when there is a parallel resistance with Rf but not when it's on its own in series?
The purpose of anti-parallel diodes in a Wien bridge oscillator is to provide non-linear feedback. For stable oscillator operation, the closed-loop gain must be 1. If it is greater than 1, the oscillations will increase with time. If it is less than 1, the oscillations will decay.
By using a non-linear feedback element, as the signal increases in amplitude, the gain decreases. If the signal decreases in amplitude, the gain increases. This permits there to be a level for the signal where the gain is exactly 1, and the oscillator is stable.
Diodes have an exponential/logarithmic voltage/current relationship. Although their use to automatically adjust gain in a Wien bridge oscillator leads to some distortion of the output so that it is not exactly sinusoidal, in practice, the distortion is often small enough for the purposes at hand. If not, another method of gain regulation is needed, or a different oscillator topology.
Your question can best be answered through the extremely simple and intuitive concepts of "dynamic resistor", "dynamic voltage divider" and "dynamic gain".
In the first figure, a "static voltage divider" R1-R2 with a transfer ratio of R1/(R1 + Rf) is connected in the negative feedback of the op-amp. The op-amp increases its output voltage (R1 + Rf)/R1 times to overcome this "disturbance"... thus transmuting into a non-inverting amplifier with a constant inverting gain of K = (R1 + Rf)/R1. So this is achieved by the mechanism of the negative feedback.
In the Wien bridge oscillator, the magnitide of the voltage oscillations at the op-amp output (simply put, Vout) has to be constant. This is achieved by an inverting gain K(-) about 3 (Rf = 2R1) by the mechanism of something like another "negative feedback" as follows.
The Rf-R1 voltage divider is made "dynamic" (self-adjusting) by replacing the "static" resistor Rf with a "composite dynamic resistor" in the second figure. Its main part is a diode acting as a "dynamic resistor" and a few ordinary "static" resistors. This arrangement acts as follows.
If Vout tries to increase its peak value, the diode begins conducting more... ie, the dynamic resistor Rfd decreases its resistance. The Rfd-R1 voltage divider increases its transfer ratio... the inverting gain K(-) decreases... and Vout decreases as well (restores its previous value).
A few years ago, I asked an RG question about this legendary circuit (and particularly, about this part of the circuit). It provoked a lively discussion which I suppose will be interesting to you.
