While I could design a device to do what you wish to do easily enough (It is basically straight out of the engineering manuals, nothing special about it) the cost would be nearly as much as a TSW inverter, the effectiveness likely not as good, it would not solve all the problems and it would be kind of bulky.

All in all a new inverter is indicated.

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While I could design a device to do what you wish to do easily enough (It is basically straight out of the engineering manuals, nothing special about it) the cost would be nearly as much as a TSW inverter, the effectiveness likely not as good, it would not solve all the problems and it would be kind of bulky.

All in all a new inverter is indicated.

I'm interested in this circuit, will you share it?

A three pole L(series) C(shunt) L(series) low pass filter would go a long way in reducing the higher order harmonics which would result in a much smoother waveform. You could also try a 60Hz bandpass filter design as an alternate trade solution. The design challange would be to hold the insertion loss to a minimum. That would require large low resistance inductors and some analysis would have to be done to see if the rms voltage was still at acceptable levels after filtering. There would also be some concern about how the inverter would work with the harmonices being reflected back into the inverter. This would be an interesting Spice analysis. You might have to follow the filter with an autoformer to get the voltage levels back if the filter reduces the amplitude too much. This would imapact overall efficiency but that might be an OK trade.

With the voltage peaks of the starting MSW being a nominal 140, IMO a perfect filter would yield a sine wave with 140 volt peaks, or 99 volts RMS. A further complication is the behavior of MSW inverters varying the peak voltage and pulse width as the RMS voltage regulation method. A good filter would totally defeat the inverter's voltage regulation. The output voltage would be directly proportional to the DC input voltage, which typically varies by at least 10%. So you might be looking at an output voltage range of roughly 90 to 100. With that in mind, I think even a good filter is infeasible for the application.

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If you do a Fourier transform on a square wave you find that it is composed of an infinite series of odd harmonic sine waves with decreasing co-efficients.
See HERE

I suspect that by the time enough of the harmonics are removed with a filter to get a pure sine wave or anything close to one, there will be very little power left - not enough to provide anything usable.

There is a nifty animation showing the way the square wave is generated by adding odd harmonic sine waves HERE

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Depending on the Q of the filter which is dependent on the load you can get most any voltage that you want. For instance take a series resistor, inductor, and capacitor that is resonant at 60 Hz. Put it across the output and the voltage across the capacitor and the inductor will be a sine wave and try to go to infinite voltage as the resistance is reduced! DON'T TRY THIS IT MAY BLOW UP! Used this method many times to charge capacitor banks.

With the voltage peaks of the starting MSW being a nominal 140, IMO a perfect filter would yield a sine wave with 140 volt peaks, or 99 volts RMS. A further complication is the behavior of MSW inverters varying the peak voltage and pulse width as the RMS voltage regulation method. A good filter would totally defeat the inverter's voltage regulation. The output voltage would be directly proportional to the DC input voltage, which typically varies by at least 10%. So you might be looking at an output voltage range of roughly 90 to 100. With that in mind, I think even a good filter is infeasible for the application.

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Please explain more about how a MSW regulates the AC output voltage. I would expect the peak voltage and positive and negative pulses to be constant duration regardless of load just like a sinewave inverter. A DC to DC converter would exhibit a varying pulse width based on load as you described.

If you do a Fourier transform on a square wave you find that it is composed of an infinite series of odd harmonic sine waves with decreasing co-efficients.
See HERE

I suspect that by the time enough of the harmonics are removed with a filter to get a pure sine wave or anything close to one, there will be very little power left - not enough to provide anything usable.

There is a nifty animation showing the way the square wave is generated by adding odd harmonic sine waves HERE

As I recall the third harmonic of a square wave is down 13 dB from the fundamental and the other harmonics go down in amplitude as the harmonic count goes up. The harmonics follow a sin x/x amplitude. The fundamental will be the largest component in the Fourier series but as I indicated you might have to bring the amplitude back to 120 V RMS with an autoformer due to elimination of the higher order harmonics.

MSW output voltage regulation:
The inverter has a DC-to-DC converter that steps the 12 volt input up to about 140 volts. The 140 volts is then switched positive and negative onto the AC output to form the output waveform. The DC-to-DC converter is unregulated. The output voltage is directly proportional to the input voltage. The device that controls the switching to make the AC waveform (microprocessor or PWM controller) has no control over the DC-to-DC converter's output voltage. It does, however, have full control over switching this DC voltage to make the AC output, and regulates the output at 120 volts RMS by controlling the width of the positive and negative pulses. When the inverter's DC input is at the top of it's input voltage range, the AC waveform has relatively tall and narrow + and - pulses. As the inverter's input voltage goes lower, the AC output pulses become shorter and wider, maintaining 120 volts RMS all the time. One side-effect of this is that microwave ovens, being peak voltage sensitive, have more cooking power when the battery powering the inverter is fully charged, and the cooking power goes down as the battery discharges, even though the RMS voltage is constant.

If you do a Fourier transform on a square wave you find that it is composed of an infinite series of odd harmonic sine waves with decreasing co-efficients.
See HERE

I suspect that by the time enough of the harmonics are removed with a filter to get a pure sine wave or anything close to one, there will be very little power left - not enough to provide anything usable.

There is a nifty animation showing the way the square wave is generated by adding odd harmonic sine waves HERE

If you do a Fourier analysis on a square wave you find that it can be represented by that series of sinewaves.

That is a pretty cool animation, but it is not the way the square wave in a MSW inverter is generated.

The output of the MSW inverters doesn't initially start off as a sine wave, I don't see how you can filter harmonics out of that waveform and be left with a sinewave?

But then again, there are LOTS of things "I don't see how"