# [sdiy] An Improved Sine Shaper Circuit

Donald Tillman don at till.com
Tue Apr 21 21:45:22 CEST 2020

```> On Apr 17, 2020, at 8:53 AM, Donald Tillman <don at till.com> wrote:
>
>> On Apr 17, 2020, at 1:56 AM, René Schmitz <synth at schmitzbits.de> wrote:
>>
>> Interesting circuit, and a great article.
>> I'm pretty sure I have seen a similar technique before, because I have used it. (cusp canceling)
>
> I am very familiar with cusp cancellation.  I've used it also.  And it's mentioned in the article.
> This is not cusp cancellation.

I'd like to expand on this for a moment...

I think the phrase "cusp cancellation" has, accidentally, been misused a lot.  And that's caused confusion.

"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!

This would be because the transfer curve of the diff amp pair isn't completely flat at the top and bottom.   The tanh() curve is asymptotic, so there will always be a little slope on the peaks.

The most common next step is to apply negative feedback around the diff amp pair.  This could be in the form of a feedback resistor, or by adding small emitter resistors.  The negative feedback plumps up the curve and flattens the slope at the peaks for a better overall fit.  Nice!

But here, with the Colin/Henry/Guest/Tillman (Have I got everybody?  In order?) approach, the output of the diff amp pair isn't remotely close to a sine wave.  Not even trying.  And none of us are using negative feedback to plump out the curve.  We're not in the cusp cancelling business, we're doing something else.

I got here by applying actual cusp cancellation to an actual diff amp pair with negative feedback and a pretty good sine approximation.  Then I refined it with thousands of simulations, which lead me away from cusp cancelling, and toward considering a compound curve of tanh(x) - βx, expressly for the bumps and the sine shape in between.  And the rest as I described.

So I guess Dennis Colin (ARP, Aries) got to the circuit first.

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.

But if the diff amp pair contribution doesn't look like a sine wave, and there's no negative feedback, and the transfer function can be put into the form tanh(x) - βx, then it's this other approach that Dennis Colin pioneered.

-- Don
--
Donald Tillman, Palo Alto, California
http://www.till.com

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