Hi..

Please can someone kindly explain only these parts :

In the first image : Ic2, the capacitor and diodes... like why 1uF, IC2 part of the circuit

In the 2nd image : Ic3, the diodes

Just these part of the circuits I'm trying to understand... I'm guessing it's straightforward

I understand the wien bridge, Jfet in linear region calculations

Thanks alot

 

Capacitors included between the output and the inverting input to filter the DC voltage. There could very well be a smaller capacitor, but the designer was not sorry for 1 µF. The larger the capacitor the better the filtering. I recommend you to simulate these circuits in LTspice using my collection of models. Then you can do experiments, namely change the values and observe what happens.
In the second image, one diode is the detector and the second diode is for thermal compensation.

 

An oscillator with a fairly clean sinewave output is a Bubba oscillator that uses four op amps (often found in one IC package) and simple diode limiting to control the voltage amplitude (LTspice simulation below), thus requiring no complex AGC feedback.

The three low-pass filters (3-pole total) after U3 effectively filter the distortion at the output from the soft diode limiting.

The four phase-shift filters that determine the oscillator frequency help minimize the effect of the RC tolerances since the four RC values will tend to average.

 

Because we want to stabilize (set) the output amplitude, we need some variable gain circuit. So, as part of a variable gain stage, we use a JFET (as a voltage-controlled resistor). But we need a DC voltage at the gate to "set" the stage gain. So, we need a rectifier and the RC filter (low pass filter). The D1 is just a rectifier diode. And this diode will "charge" the capacitor and this creates negative-going voltage at the output needed for the JFET. But we can't keep charging the capacitor with positive pulses from the rectifier. We need a discharge path too. So we add a D2 diode to provide a (slow) discharge path for an integrator capacitor. And in both circuits, the diodes have the same task to do.
https://forum.allaboutcircuits.com/...ct-in-amplifier-circuits.137016/#post-1147554