[sdiy] Hopf bifurcation VCOs

[Ian Fritz]

At 08:41 AM 11/11/05, jhaible at debitel.net wrote:
> > I think it is OK to just regulate just x^2, because then the
> > correct y must follow because of the integration!  In fact, I didn't
> > mention it yesterday, but I have found that only one of the NL circuits is
> > needed. Same reason.
>
>But isn't THD at low frequencies much better if you use both terms?
>
>(I'm just speaking of the Tietze/Schenk version here, as I haven't seen your
>implementation yet.)
>
>Normally, when you control the loop gain of a sine VCO, you have some device
>for mearuring the amplitude, which has some ripple, which will either cause
>some THD in your sine wave, or - if you smooth it with long time constants -
>will react slowly. So for low oscillator frequencies, it's always a tradeoff
>between THD and regulation time.

My circuit doesn't work that way.  There is no rectification and time 
constant and loop gain control.  There is only the the nonlinearity acting 
on the signal and fed back. So I guess in that sense it is not so close to 
Tietze/Schenk. If the peak signal is greater than x=1, then the fed back 
signal is x(1-x^2)<0.  If the peak is less than x=1 then x(1-x^2)>0. So the 
peak is kept at x=1. This is the sense in which the amplitude is regulated.

The mystery to me is why the distortion is so low.  I think two things 
contribute: first, the required feedback is very small (and if it is 
increased the distortion increases); second, the feedback is to the 
integrator input, so the error signal is integrated (filtered) before 
reaching the signal output.

Sorry if my remarks about similarity to the Tietze/Schenk circuit were 
confusing.  The regulation mechanism is different in the two cases.

   Ian