<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">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.<div class=""><br class=""></div><div class=""><br class=""></div><div class="">Mark</div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Apr 22, 2020, at 11:09 AM, Phillip Gallo <<a href="mailto:philgallo@gmail.com" class="">philgallo@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class=""><div dir="ltr" class="">The latin word 'cuspis' meant a sharp point. </div><div dir="ltr" class="">In "Gallic War", it's a spear. </div><div dir="ltr" class="">General modern usage tends to a "transition".</div><div dir="ltr" class="">The "corner" (cusp) transitioning (joining) two curves, in a Tri to Sine shaper typically occurs at shaped Sine wave amplitude extremes.<br class=""></div><div dir="ltr" class=""><br class=""></div><div dir="ltr" class="">My first exposure to the differential amp waveshaper was upon building an AR-317 VCO with the late Dennis Colin's waveshaper.</div><div dir="ltr" class=""><br class=""><div class="">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.<br class=""></div><div class=""><br class=""></div><div class="">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.</div><div class="">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.</div><div class=""><br class=""></div><div class=""><div class=""><span id="cid:ii_k9b31j2z0"><image.png></span><br class=""></div></div><div class="">(Hoping this 200k jpeg displays as graphic inclusions to 'the list' is neat.)</div><div class=""><br class=""></div><div class="">p</div><div class=""><br class=""></div><div class=""><br class=""></div></div></div><br class=""><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Apr 22, 2020 at 12:23 AM René Schmitz <<a href="mailto:synth@schmitzbits.de" class="">synth@schmitzbits.de</a>> wrote:<br class=""></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">On 21.04.2020 21:45, Donald Tillman wrote:<br class="">
<br class="">
> I think the phrase "cusp cancellation" has, accidentally, been misused a <br class="">
> lot. And that's caused confusion.<br class="">
<br class="">
I don't think there is a formal definition of the term. To me that is <br class="">
any method that subtracts a portion of the triangle to the shaped sine <br class="">
wave to cancel out the residual slope at the peaks of the sine wave.<br class="">
Regardless of how the shaping is accomplished, could be a diff-pair, <br class="">
diodes, etc.<br class="">
<br class="">
> "Cusp cancellation" should mean that we've already got a pretty good <br class="">
> approximation going, but the cusps of the triangle are still coming <br class="">
> through a little bit. And we can cancel those by subtracting a small <br class="">
> amount of the original triangle wave. Sweet!<br class="">
<br class="">
There is a continuum of solutions that give you a flat top. Your free <br class="">
variable is how hard you drive the tanh function.<br class="">
<br class="">
If you start with the best sine you get from tanh shaping alone, you <br class="">
just need to add a small fraction of triangle to cancel. But this <br class="">
doesn't automatically give you the best sine.<br class="">
<br class="">
If you drive the tanh function harder or softer, the proportion of <br class="">
triangle you have to mix in for getting a flat top changes, and at some <br class="">
point gives you a better sine approximation.<br class="">
<br class="">
> So, I'll claim that if a small amount of the original triangle wave is <br class="">
> subtracted from a wave that's roughly sinusoidal, then it's actual cusp <br class="">
> cancellation.<br class="">
<br class="">
In your circuit the cusps are also cancelled, after all you still aim <br class="">
for a flat top of the approximated sine at +-pi/2. In that sense one <br class="">
could also call this cusp cancelling.<br class="">
<br class="">
The way I see it, it is a different set of parameters for the same <br class="">
circuit, the math is fundamentally the same.<br class="">
<br class="">
So where would you draw the line?<br class="">
<br class="">
Best,<br class="">
René<br class="">
<br class="">
--<br class="">
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</blockquote></div>
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