[sdiy] Hopf bifurcation VCOs

[jhaible at debitel.net]

Hi Ian,

I'd love to see this circuit!

Still open for an alternative solution for my new frequency shifter.
(So far, I'm shaping sin and cos from a saw wave, with the obvious glitches
that must then be filtered.)
Can your method be used for really wide frequency sweeps, like 0.1Hz
to 20kHz, with such low distortion?

I was also thinking of a method I've found in Tietze/Schenk, Halbleitertechnik,
where two integrators are used, and the loop gain is controlled by squaring
the two integrator outputs, and comparing x**2 + y**2 with a reference level.
The idea is that, in theory, you don't need a time constant for the amplitude
regulation. I have no idea how well it would work in real live, however.
Your method with zener diodes looks interesting - it should be much less
expensive. -50dB THD, and low sensitivity to parameters? Must see this circuit!

JH.



[...] This is easily done by 
> > > adding a linear slope to the response of a pair of 
> > back-to-back zener 
> > > diodes.  The circuit requires just the zeners, an opamp and four 
> > > resistors.  It is an important circuit, as it can be used 
> > in a variety 
> > > of nonlinear circuit applications including chaos 
> > generation and waveform folding.
> > > 
> > > To build this quadrature oscillator I started by cross-coupling two 
> > > voltage-controlled integrators, similar to what we all use for 
> > > filters, phasors, etc.  These represent the linear terms in 
> > the coupled equations.
> > > Then I added the nonlinear circuit described above around each 
> > > integrator, to implement the nonlinear terms in the equations. This 
> > > may sound complicated, but it only requires two chips: a dual OTA 
> > > (LM3700) and a quad opamp.
> > > 
> > > The result is a very nice circuit.  As far as I can tell it always 
> > > starts up without any latchup problems.  The oscillations 
> > are not at 
> > > all sensitive to circuit parameters.  In fact the coupling of the 
> > > nonlinear elements can be varied over a wide range, with 
> > only a small 
> > > change in distortion.  I recorded the oscillations into Sound Forge 
> > > and did a spectral analysis.  Distortion is very small, with all 
> > > harmonics  down by 50 dB or more.



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