[sdiy] An Improved Sine Shaper Circuit

mark verbos markverbos at gmail.com
Wed Apr 22 13:44:31 CEST 2020

Thanks for that Phil. I was also wondering what’s wrong with a single J-FET? While viewing that TI Application note I am reminded of how I have always had a soft spot in my heart for piecewise linear, but in something like the Harmonic Oscillator (which has a bunch of sine shapers) a shaper with 1o diodes will really add up quick! I’ll just stick with a J201 and single opamp stage.


> On Apr 22, 2020, at 11:09 AM, Phillip Gallo <philgallo at gmail.com> wrote:
> 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 waveshaper.
> 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.png>
> (Hoping this 200k jpeg displays as graphic inclusions to 'the list' is neat.)
> p
> On Wed, Apr 22, 2020 at 12:23 AM René Schmitz <synth at schmitzbits.de <mailto: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 <mailto:synth at schmitzbits.de>
> http://schmitzbits.de <http://schmitzbits.de/>
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