[sdiy] Hopf bifurcation VCOs

[Ian Fritz]

Hi JH --

>I'd love to see this circuit!

Then you shall!  I'll try to get it up in the next few days.

>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?

Don't know yet.  I'll try to have a look today.  There will be offset 
issues, as usual with OTA-based circuits.  My present circuit has a small 
offset on one of the outputs.  The OTA's have been trimmed, but for another 
application; I just rewired that to make the quad osc.

>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.

Ah, that is actually quite similar to what I have.  In my equations 1-x^2 
should reallly be 1-x^2-y^2, and I just arbitrarily dropped the y^2 term to 
see if it would work.  If I had kept it, then my system would also regulate 
x^2 + y^2.  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.

So I guess I have blindly stumbled onto a simplified means to do the 
Tietze/Schenk circuit.  My equations are now:

x' = x(1-x^2) + wy
y' = -wx.

>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!

OK (but you already know the NL part <wink>).

   Ian