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<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>I just simulated the Thomas Henry
transistor-pair sine shaper, and compared the output to a 90-degree phase
shifted pure sine wave of equal amplitude. It is virtually impossible to
tell the two apart ¨C THD = 0.57% -- light blue is the pure one, orange is the
shaped one.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><img width=545 height=452 id="_x0000_i1026"
src="cid:image002.gif@01D617DE.BA800920"><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Here¡¯s the sine shaper circuit I¡¯m
simulating ¨C this is exactly the circuit I build into all my VCOs (transistors
are 2N3904, opamp is TL07X ¨C the 11k resistors get me closer to 10Vpp than 10k):<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><img width=619 height=494 id="_x0000_i1027"
src="cid:image003.gif@01D617DE.8070E830"><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>In what way does the output of the diff
pair not look like a sine wave?<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<div>
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<hr size=2 width="100%" align=center tabindex=-1>
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<p class=MsoNormal><b><font size=2 face=Tahoma><span style='font-size:10.0pt;
font-family:Tahoma;font-weight:bold'>From:</span></font></b><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'> Synth-diy
[mailto:synth-diy-bounces@synth-diy.org] <b><span style='font-weight:bold'>On
Behalf Of </span></b>Donald Tillman<br>
<b><span style='font-weight:bold'>Sent:</span></b> Tuesday, April 21, 2020
12:45 PM<br>
<b><span style='font-weight:bold'>To:</span></b> Ren¨¦ Schmitz<br>
<b><span style='font-weight:bold'>Cc:</span></b> synth-diy@synth-diy.org<br>
<b><span style='font-weight:bold'>Subject:</span></b> Re: [sdiy] An Improved
Sine Shaper Circuit</span></font><o:p></o:p></p>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<div style='word-wrap: break-word;-webkit-nbsp-mode: space;line-break:after-white-space'>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<div>
<blockquote style='margin-top:5.0pt;margin-bottom:5.0pt' type=cite>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>On Apr 17, 2020, at 8:53 AM, Donald Tillman <<a
href="mailto:don@till.com">don@till.com</a>> wrote:<o:p></o:p></span></font></p>
</div>
<div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><br>
<br>
<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>On Apr 17, 2020, at 1:56 AM, Ren¨¦ Schmitz <<a
href="mailto:synth@schmitzbits.de">synth@schmitzbits.de</a>> wrote:<br>
<br>
Interesting circuit, and a great article.<br>
I'm pretty sure I have seen a similar technique before, because I have used it.
(cusp canceling)<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><br>
I am very familiar with cusp cancellation. I've used it also. And
it's mentioned in the article.<br>
This is not cusp cancellation.<o:p></o:p></span></font></p>
</div>
</div>
</blockquote>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
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<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>I'd like to expand on this for a moment...<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
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<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>I think the phrase "cusp cancellation" has, accidentally,
been misused a lot. And that's caused confusion.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
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<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>"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!<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
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<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>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.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>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!<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>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.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>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) - ¦Âx, expressly
for the bumps and the sine shape in between. And the rest as I described.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>So I guess Dennis Colin (ARP, Aries) got to the circuit first.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>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.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>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) - ¦Âx, then it's this other approach that Dennis Colin pioneered.<o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> -- Don<o:p></o:p></span></font></p>
</div>
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<p class=MsoNormal><font size=1 color=black face=Menlo><span style='font-size:
9.0pt;font-family:Menlo;color:black'>--<br>
Donald Tillman, <st1:place w:st="on"><st1:City w:st="on">Palo Alto</st1:City>, <st1:State
w:st="on">California</st1:State></st1:place><br>
<a href="http://www.till.com">http://www.till.com</a><o:p></o:p></span></font></p>
</div>
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