Hi Ratch - yes, here are the results of my "fresh start:":
With reference to your post#14 (calculation in blue):
Third line from the bottom:
* Left side of the equation is imaginary and right side is complex (imag. plus real).
This requires to set the REAL part of the right side equal to zero.
This would immediately lead to w=1/[SQRT(3)*RC].
* Alternative: Continuing your approach:
Shifting the left imag. part to the right side of the equation, we get: 0=Im + Re.
In the second line from the bottom you have set all the imaginary parts equal to zero (Im=0).
The result is given in the last line of your calculation.
* However, this is only the "first half of the story“.
Because the left side is zero you also must set Re=0.
Hence, we get as a second equation again: w=1/[SQRT(3)*RC].
* Finally, both equations must be fulfilled at the same time (because of 0=Re+Im)).
Equalizing both w expressions gives the condition: R2=8R. After inserting this requirement into
your w expression, we again get: w=1/[SQRT(3)*RC].
* Comment: To me, it was clear from the beginning that w cannot depend on R2 because only the
CR sections determine the phase properties of the loop gain. So - how can we interpret your
result (involving R2) - even if it is only 50% of the calculations?
If you - from the beginning - replace the ratio R2/R by the gain A you will see that A will be not
part of the imaginary part and, hence, R2 would not appear as part of your result.
Why this surprising fact?
Because the resistor R at the inv. input node of the opamp plays a double role: It is part of the
CR network and, at the same time. part of the gain determining resistor ratio. Therefore, it is
good to use the term A instead of R2/R (and not to combine this ratio with the other R terms).
* Final comment: The oscillation frequency is determined by the time constant RC only.
That means: The resistor R2 determines the gain only with the requirement: R2>8R.
Of course, the oscillation amplitude will rise until it is limited by the supply voltage or by any
additional non-linear part.