<html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=utf-8"><meta name=Generator content="Microsoft Word 15 (filtered medium)"><style><!--
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--></style></head><body lang=EN-US link=blue vlink="#954F72"><div class=WordSection1><p class=MsoNormal>I remember that this was a big thing for Don Lancaster:</p><p class=MsoNormal><a href="http://www.tinaja.com/magsn01.shtml">http://www.tinaja.com/magsn01.shtml</a></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Take Care,</p><p class=MsoNormal>John</p><p class=MsoNormal><o:p> </o:p></p><div style='mso-element:para-border-div;border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='border:none;padding:0in'><b>From: </b><a href="mailto:Stromeko@nexgo.de">ASSI</a><br><b>Sent: </b>Friday, April 7, 2017 11:32 PM<br><b>To: </b><a href="mailto:synth-diy@synth-diy.org">synth-diy@synth-diy.org</a><br><b>Subject: </b>Re: [sdiy] Square to Sine</p></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>On Tuesday, April 4, 2017 2:26:30 PM CEST rburnett@richieburnett.co.uk wrote:</p><p class=MsoNormal>> I have always wondered about magic sinewaves for something like this.</p><p class=MsoNormal>> For those not familiar they are sinewaves generated digitally using PWM</p><p class=MsoNormal>> techniques but the transitions in the PWM pulse-train are carefully</p><p class=MsoNormal>> chosen using some clever mathematics to force most of the low-order</p><p class=MsoNormal>> harmonics to zero. This *greatly* reduces how much you have to filter</p><p class=MsoNormal>> the signal in order to get a decent sinewave with nice low THD.</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>This is the same working principle as any delta-sigma modulator (ternary in </p><p class=MsoNormal>this case), just with a very low oversampling. There are quite a few papers </p><p class=MsoNormal>that probe the fascinating relationship of various pulse trains vs. the </p><p class=MsoNormal>resulting spectrum in order to determine or eliminate the resulting harmonics, </p><p class=MsoNormal>you could easily keep yourself busy reading about that for a year at least. </p><p class=MsoNormal>For audio, the solution of choice is to just oversample the heck out of it, </p><p class=MsoNormal>chuck all the noise harmonics way up beyond audible and then put an LPF behind </p><p class=MsoNormal>it. For power inverters this doesn't quite work since the energy expended for </p><p class=MsoNormal>each switching cycle will reduce the efficiency and it is generally not </p><p class=MsoNormal>possible to switch really fast even if that wasn't a concern. Please heed the </p><p class=MsoNormal>note about the necessary timing precision (and that actually means down to the </p><p class=MsoNormal>switching waveform, not just the timing of the control signal), which would be </p><p class=MsoNormal>even more demanding a requirement if you were to attempt this for audio </p><p class=MsoNormal>frequencies. I guess it's still possible to do in an FPGA, but if you also </p><p class=MsoNormal>want frequency agility (you still can't do "real" modulation since that undoes </p><p class=MsoNormal>the zeroing of the unwanted harmonics) it gets into rather excessive clocking </p><p class=MsoNormal>requirements.</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Regards,</p><p class=MsoNormal>Achim.</p><p class=MsoNormal>-- </p><p class=MsoNormal>+<[Q+ Matrix-12 WAVE#46+305 Neuron microQkb Andromeda XTk Blofeld]>+</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Wavetables for the Terratec KOMPLEXER:</p><p class=MsoNormal>http://Synth.Stromeko.net/Downloads.html#KomplexerWaves</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>_______________________________________________</p><p class=MsoNormal>Synth-diy mailing list</p><p class=MsoNormal>Synth-diy@synth-diy.org</p><p class=MsoNormal>http://synth-diy.org/mailman/listinfo/synth-diy</p><p class=MsoNormal><o:p> </o:p></p></div></body></html>