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Suppose I'm using a 3.6 kHz carrier to reproduce a 60 Hz sine wave. To properly design a filter for this application to hit a specific harmonic distortion target, I need to know the harmonic content of the PWM signal. How can I predict what that harmonic content is? Is it going to vary dramatically with the pulse widths? Or will there be certain simplifying assumptions I can make?

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  • \$\begingroup\$ 60Hz + the Fourier series of a square wave with a fundamental of 3.6kHz \$\endgroup\$
    – Matt Young
    Jun 25, 2015 at 15:01
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    \$\begingroup\$ PWM is just a series of pulses. Rectangular pulse function is represented by the sinc function in the Fourier domain. So it has an infinite number of harmonics. The "narrower" is the pulse, the wider is the sinc. \$\endgroup\$
    – Eugene Sh.
    Jun 25, 2015 at 15:03
  • \$\begingroup\$ Aww, fudge. I was thinking of the resulting harmonics on the 60Hz signal, not the harmonics content of the PWM. I've deleted my other comment. \$\endgroup\$
    – JRE
    Jun 25, 2015 at 15:34
  • \$\begingroup\$ Stephen, are you done with this Q and A now? If not, please leave a comment explaining your thoughts. \$\endgroup\$
    – Andy aka
    Feb 10, 2021 at 13:11

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If you have 50:50 mark space ratio you are dealing with a square wave and this should be a good start (this is for a 1kHz square wave): -

enter image description here

When it comes to other duty cycles try this for size: -

enter image description here

Presumably your filter might be a 2nd order low-pass type made from L and C. Keep the resonant point at least 50% above 60Hz to prevent catestrophic series resonance at 60Hz. You can easily simulate this to see what current this filter might be taking an an unloaded 60Hz supply and I would recommend simulation to furnish you with the total harmonic distortion.

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