Phase Shift Oscillator

[LvW]

Interesting way to do it indeed. Thanks.

But how did we know that 1.732 identical to SQRT(3) ?
Look at the following derivation (like the one for coupled RC sections in post#2):

1.) For three decoupled RC sections in series we have H(jw)=1/(1+jwRC)^3
2.) This can be expanded easily (polynominal of 3rd degree) and becaue we want H(jw)=real we set Im(denominator)=0
3.) This gives 3*w*RC - [w(RC)]^3=0
4.) Hence: w=SQRT(3)/RC
5.) At this frequency, the Re(denominator)=-1/8. Thus, we need a gain stage with a gain "-8".

 

[Laplace]

I wonder what does making each stage have an impeadance of 10 times more than the last section do? This quite common on cascaded filters without having buffers.

Interesting question, so rather than just 10 times I analyzed this circuit with a parametric factor N. The following graph shows the phase shift for a range of N (N=1 to N=12). The greatest effect occurs for the smaller values of N.