# [sdiy] An Improved Sine Shaper Circuit

René Schmitz synth at schmitzbits.de
Wed Apr 22 08:22:03 CEST 2020

```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

```