[sdiy] SAW core VCO flyback time

[Richie Burnett]

> You can see the way that increasing amounts of flyback time affect the 
> harmonic structure on this page:
>
> http://electricdruid.net/timbral-evolution-harmonic-analysis-of-classic-synth-sounds/
>
> The bit you want is titled "Ramp-down/Triangle/Ramp-up" in the Phase 
> Distortion section abut half-way down.

A very detailed analysis!

> Up to about 10%, the effect is pretty much a soft roll-off of the higher 
> harmonics...

And a reset time that is 10% of the overall period would be a *very* 
sluggish sawtooth reset!

You can model a non-zero reset time by using a boxcar FIR function (block 
moving average) on an ideal sawtooth to yield a finite slew-rate, and 
achieve the same spectral low-pass filtering effect with notches.  This was 
the motivation behind me asking what typical reset times are for modern 
VCOs.  The point where the high-frequencies start to get rolled-off (-3dB 
point) is at approximately half the reciprocal of the reset time.  So for 
reset times less than about 25us that puts the 3dB point beyond 20kHz where 
any audible effect on the spectrum is marginal at best.  Of course it could 
still have an effect on tuning conformity in an analogue design though.

BTW, I think it's fascinating how the analogue designers strive to achieve 
perfection in the form of "instantaneous" sawtooth resets, low-distortion 
sinewaves, and symmetrical triangle waveforms without the little nipple at 
the peak.  Whilst digital synthesiser designers strive to model the 
imperfections of old analogue oscillators because they are somehow perceived 
to be the reason for their unique character.  Taken to the limit, analogue 
oscillators will become perfect and sterile, whilst VA models will inherit 
all of the "character" ;-)

-Richie,