tri 2 saw modualtion

[Kimmo Koli]

On Mon, 27 Oct 1997, Eli Brandt wrote:

> Don Tillman wrote:
> > If you look at the harmonic spectra of the waveform you'll see for the
> > triangle case that every even harmonic is nulled out, and as you
> > change the symmetry, those "nulls" will slide up in frequency over the
> > harmonics and move farther apart, up until the wave is a full sawtooth
> > shape where there are no more nulls.  A Bessel function describes the
> > amount of each harmonic.
> > 
> > (This is a guess from the harmonic spectra of a PWM square wave -- I
> > haven't done the actual math.  The same mechanism applies though.)
> 
> A triangle-saw sweep is the integral of a square-pulse sweep (if all
> of your pulse waves have the DC properly stripped out), so the nulls
> are in the same place and all.  But the spectrum is tilted 6dB/oct.
> 
I've been working on a normal tri and square wave integrator and
hysteresis oscillator (funtion generator) where you could modulate the
triwave symmetry and therefore also the symmetry of the square wave. This
simultaneuous  tri/saw- and PWM-modulation can easily produce a double saw
waveform by multiplying the triwave with the square (basically multiplying
by +1 or -1). With symmetrical triangle wave the result is a saw with
doubled frequency and with an more and more unsymmetrical triwave the
result is one shorter and shorter saw and one longer and longer saw. Then
the spectrum shifts back to the fundamental frequency and simultaneusly a
high frequency peak is added to the spectrum. Should sound interesting
with a suitable resonance filter (prefebrably with overdrive).

If a counter is added to the circuit also different sequences of
unsymmetrical triwaves and double saws could be generated.

Unfortunately I have no time to finish the VCO design while the writing of
my PhD-thesis takes all of my time. The other drawback (apart that the
VCO is very complex) is that needed integrator input current
multiplier/dividers need a linear control voltage. I was thinking of
building one heated exp-converter a la National AN-XXX (fill in the number
I forgot) to drive two or more of my VCOs. 
        
Best regards,
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   Kimmo Koli                         Helsinki University of Technology 
   kimmo at ecdl.hut.fi                  Electronic Circuit Design Laboratory
   http://www.ecdl.hut.fi/~kimmo      P.O.Box 3000
   Tel:  +358 9 451 2273              FIN-02015 HUT
   Fax:  +358 9 451 2269              Finland 
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