[sdiy] An Improved Sine Shaper Circuit

Phillip Gallo philgallo at gmail.com
Wed Apr 22 11:09:48 CEST 2020

The latin word 'cuspis' meant a sharp point.
In "Gallic War", it's a spear.
General modern usage tends to a "transition".
The "corner" (cusp) transitioning (joining) two curves, in a Tri to Sine
shaper typically occurs at shaped Sine wave amplitude extremes.

My first exposure to the differential amp waveshaper was upon building an
AR-317 VCO with the late Dennis Colin's waveshaper.

Electronics Magazine Designer's Casebook #6 (compendium 1981-1982) depicted
the differential waveshaper accompanied by cusp cancellation due to
subtracting a portion of the original Tri wave from the result of the diff

I apologetically insert this into an otherwise fascinating discussion due
to bottom tab noting the results of using the technique across 3 common Tri
to Sine methods.
I know, at least, one person (Tim S) who just might argue that the careful
implementation of the FET technique can provide a result equal or better
than the diff amp approach.

[image: image.png]
(Hoping this 200k jpeg displays as graphic inclusions to 'the list' is


On Wed, Apr 22, 2020 at 12:23 AM René Schmitz <synth at schmitzbits.de> wrote:

> On 21.04.2020 21:45, Donald Tillman wrote:
> > I think the phrase "cusp cancellation" has, accidentally, been misused a
> > lot.  And that's caused confusion.
> I don't think there is a formal definition of the term. To me that is
> any method that subtracts a portion of the triangle to the shaped sine
> wave to cancel out the residual slope at the peaks of the sine wave.
> Regardless of how the shaping is accomplished, could be a diff-pair,
> diodes, etc.
> > "Cusp cancellation" should mean that we've already got a pretty good
> > approximation going, but the cusps of the triangle are still coming
> > through a little bit.  And we can cancel those by subtracting a small
> > amount of the original triangle wave.  Sweet!
> There is a continuum of solutions that give you a flat top. Your free
> variable is how hard you drive the tanh function.
> If you start with the best sine you get from tanh shaping alone, you
> just need to add a small fraction of triangle to cancel. But this
> doesn't automatically give you the best sine.
> If you drive the tanh function harder or softer, the proportion of
> triangle you have to mix in for getting a flat top changes, and at some
> point gives you a better sine approximation.
> > So, I'll claim that if a small amount of the original triangle wave is
> > subtracted from a wave that's roughly sinusoidal, then it's actual cusp
> > cancellation.
> In your circuit the cusps are also cancelled, after all you still aim
> for a flat top of the approximated sine at +-pi/2. In that sense one
> could also call this cusp cancelling.
> The way I see it, it is a different set of parameters for the same
> circuit, the math is fundamentally the same.
> So where would you draw the line?
> Best,
>   René
> --
> synth at schmitzbits.de
> http://schmitzbits.de
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