OK, here goes. This is a very complex task to provide a complete and accurate simulation for various modulation indices, switching frequencies, and load impedances. However, for a first pass, I found an example where someone calculated the spectra for a 100% modulation sinewave.
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https://www.wpi.edu/Pubs/E-project/...-190851/unrestricted/PWM_Techniques_final.pdf)
The purpose of the filter is to reduce the amplitude of the harmonics to a specified maximum level. People normally only look at the first one-to-three large, low order harmonics since usually the high order harmonics are smaller amplitude and also easier to filter. In the Crowley & Lueng paper hypertexted above, figure 9 shows a third harmonic equal to about 15% of the fundamental (160V for the fundamental, 25V for the third harmonic). To reduce the third harmonic to 3% of the fundamental (for a THD of something like 5%, which is about as ugly a waveform as most sensitive circuits can stand) you need a filter that reduces the third harmonic by a factor of 5 (3%/15%). A double-pole filter like the LC reduces the amplitude by a factor of 4 for every octave, so your filter has to have a corner frequency of slightly less than 1.5*fundamental frequency.
Now here's the really nasty part of your LC filter: It's so close to the fundamental frequency (less than an octave), that it will be boosting the fundamental (peaking) instead of having a flat characteristics.
This is a clear case of what one of my friends calls the "Conservation of Misery Principle". You can make the waveform cleaner with a lower frequency filter but it will make your output unstable. You can make the output stable, but your waveform won't be something you want to show your kids.
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I may have not answered your question properly. I answered the question - "What frequency should I choose for a resonant frequency for the filter?" If the question was: "I need to build an LC filter with a resonant frequency of 80 Hz for example. How do I pick the L's and C's?"
The answer to the second question is: (2*pi*80Hz)squared = 1/LC or 252,000 = 1/LC in this example.
Let's try a 1uf capacitor first: L = 1/(252,000*C) = 1/(252,000*1uf) = 3.96H.
OK that inductor is pretty big. Let's pick the L as 396uH instead (1/10000 the size of the the 3.96H we first calculated), now the C is 10000uF. That's a pretty big capacitor. How about something in the middle? How about 39mH and 100uF? or 50 mH and 80uF? or 25mH and 160uF?
Where does the 25mH (or other value) inductor come from? take apart an old power transformer from an old TV (not LCD TV) and start winding turns on it until you get the L you want.
I hope this helps.