[sdiy] Wave Multiplier-like circuits?

[John Richetta]

On Oct 26, 2009, at 8:55 PM, Adam Schabtach wrote:
> One of my favorite modules is Ken Stone's Wave Multiplier. I love  
> the range
> of timbres it produces from a single oscillator input and the way it
> responds in interesting ways to control voltages. Hence I'm  
> interested in
> finding other circuits that do similar things, and would be  
> delighted if
> anyone has any to recommend to me.
>
> <snip>
>
> Thanks in advance for any suggestions that anyone would like to  
> provide.

Being a not-so-literate amateur hack, who prefers to create from  
scratch, I don't much know about other published circuits.  I am  
fairly sure this topic has been discussed before on this list,  
however, so do the obvious searches, if you haven't.  But this is a  
topic of interest and an ongoing area of exploration for me (on the  
rare occasions I have time for electronics), so, here are some general  
inspirations of mine, from somewhat specific to very vague:

    - piecewise nonlinearities: break up a signal into bands (by  
voltage range, say), and do different things in each band; combine  
different sign/scale versions of the original in each band, and sum;  
shift the limits, gain, etc. for successive bands based on what you  
"learned" about a signal in an earlier one, or based on envelope  
following, or other interesting controls; the obvious approach to  
bands is to make them hard-edged, but consider using smooth windowing  
instead (more difficult, obviously)

    - use any nonlinear regime of your favorite semiconductor device,  
though some are better than others, to distort one or more applied  
signals; my favorite types of curves are smooth but changing "knees,"  
"bumps," and "wiggles" where you can smoothly shift which part of the  
curve is used to distort the "signal" input, by adding more or less  
control signal (or attenuating and then re-amplifying it - harder);  
level conversion before and after nonlinear processing is usually  
necessary; if you care about DC coupling, or tightly controlled gain,  
or output that's mostly free of thumps and DC offsets, this problem  
gets appreciably harder

    - create complementary transformations that are at least  
approximately inverses of one another, transform a signal, insert some  
other conventional processing (ex., filter), and then un-transform the  
result; try to avoid requiring perfect matching of the complementary  
transforms :) - this usually amounts to using not-too-extreme  
nonlinearities

    - depending on what you use to combine linearities, you can  
achieve nonlinear results; balanced multipliers and transconductance  
amps are useful building blocks (though some argue this is  
"cheating" :) ); if you have useful nonlinearities, try to discover  
some judicious ways to blend them - nonlinearly, perhaps - using some  
other control, maybe derived from the signal itself; split, shift, and  
scale, ala wavelets

Apologies for deliberately being very nonspecific, but I hope these  
basic hints might encourage you to invent something interesting.  For  
me, at least, a lot of the fun is thinking up a flexible idea (which  
usually must also past the test of being mathematically nontrivial,  
for it to be musically worthwhile or interesting), and then refining  
it until it works.

Have fun, good luck, and enjoy the sound.  -jar