[sdiy] An Improved Sine Shaper Circuit

David G Dixon dixon at mail.ubc.ca
Fri Apr 17 23:12:29 CEST 2020

I've used Thomas Henry's version of the two-transistor sine shaper in all my
VCO designs for years (and did a bit of an optimization study to confirm
that his resistor values were indeed optimum).  Simulation suggests that I
can get as low as 0.57% THD with that shaper, and there is no visual
evidence of the triangle apex leaking through.  At that level, there is
virtually no aural evidence that it isn't a pure sine wave.

How much better is this new shaper in terms of THD?  (If no one answers, I
guess I could simulate it myself.)

-----Original Message-----
From: Synth-diy [mailto:synth-diy-bounces at synth-diy.org] On Behalf Of René
Sent: Friday, April 17, 2020 1:25 PM
To: Donald Tillman
Cc: synth-diy at synth-diy.org
Subject: Re: [sdiy] An Improved Sine Shaper Circuit

Hi Don,

On 17.04.2020 17:53, Donald Tillman wrote:

> I am very familiar with cusp cancellation.  I've used it also.  And it's
mentioned in the article.
> This is not cusp cancellation.  While the circuit looks the same, I'm
subtracting 1 or 2 orders of magnitude more of the original triangle signal
than is necessary to cancel the triangle cusps.

Maybe it would be an addition to do a side by side comparison of your 
circuit with the older method. To emphasize the differences.

> I discovered this using some machine learning tools (Jupyter Notebook,
Numpy) and some of my own software to optimize a classic sine shaper
circuit... one with emitter resistors and with cusp cancellation.   And it
kept pointing me to subtract more and more of the triangle signal.  I
thought something had gone wrong, but what the heck, follow the data.  And
sure enough, the harmonic spectrum really did get better as the transistor's
tanh curve performed a different function.
> Then I realized I was no longer correcting for a little nipple that got
through the sine shaper, I had discovered a new way to approximate the sine
function.   And that it was crazy accurate.  I couldn't find a reference to
this zig-zagging "tanh(x) - beta x" curve mentioned anywhere before.

When I look at the Aries 317 or the Thomas Henry circuit I see that the 
triangle is not just a touch but very substantial in the output. (The TH 
circuit even returns almost all of the OTAs' output current into the 
resistor that connects to the triangle. (Its a high Z node, so if the 
OTA was shut off, it would be just fed through the triangle 100%)
Clearly some form of zig-zagging is happening there too. Whether these 
circuits operate at an/your optimum is another matter.


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