Hello!

I have to find the minimum required value of Rf for oscillations to start in this circuit. R=1k e C=80nF

I know that for oscillations to start, Vo/Vf has to be over 29. But I can't find that expression.

I wrote these equations:

(V1/R)+(V1-V0)*(sC+1/Rf)+(V1-V2)sC=0

V2/R+(V2-V3)sC+(V2-V1)sC=0

Vf/Rf+(V3-V2)sC=0

Since the ampop is ideal, I admitted that v-=0, so the third resistance is connected to the ground through the virtual short circuit.

What am I doing wrong?

Thank you for your help!

 

There's some discussion in Wikipedia, but no description of how to derive the expressions:

http://en.wikipedia.org/wiki/Phase_shift_oscillator

Have a look here:

http://home.earthlink.net/~doncox/wec/Oscillators.html

http://www.aikenamps.com/PhaseShiftOscillators.html

http://www.crbond.com/papers/ent23.pdf

 

I think the oscillator section in this free ebook may be of help www.ti.com/lit/an/slod006b/slod006b.pdf

 

Thank you so much, I'll check those websites to see if I can get to the solution