# LC filter for inverter

I am designing a 1500W inverter. With 24VDC input source and 220VAC 60Hz output voltage. I currently have the topology shown in circuit 1. This results in a square wave at 60Hz. But I need the output to be a pure sinusoid at 60Hz. The M1 and M2 mosfets are driven at 60Hz by PWM and NOT_PWM. To get the output with a pure sinusoid I thought of using an LC filter as shown in circuit 2. I started by trying to calculate the values of L and C through:

F=1/2*pi*sqrt(LC).


However, the values I obtained for L, considering the capacitance value of 10uF and F=60Hz, did not result in a sine wave.

Did I choose the wrong cutoff frequency?

I know that the mosfets switching mode should be SPWM with high frequency, but I have no way to change that at the moment. I have to make this work with switching the switches at 60Hz using LC filter.

simulate this circuit – Schematic created using CircuitLab

simulate this circuit

EDIT

I would like to tell you that I managed to do my project. But it was necessary to change the project topology. I decided to use a full bridge and not a push pull. To make the sine wave I use a sinusoidal pwm signal (with duty cycle variable) and with frequency modulation at 60Hz.

Results in the image below.

simulate this circuit

## 3 Answers

The M1 and M2 mosfets are driven at 60Hz by PWM and NOT_PWM.

No, it will not work very well unless the loading is constant and therefore the Q factor at resonance can be controlled so as not to cause massive reactive currents (leading to serious distortion) and also not produce massive output over-voltage due to inappropriate light loading.

So, even if you got the loading correct and you successfully tailored L and C to have a low-to-moderate Q factor at 60 Hz, you'll then find that you cannot use pulse width modulation control because of the way the output drive push-pull is designed.

Your signals can never be purely $$\PWM\$$ and $$\\overline{PWM}\$$ unless the duty cycle is 50% in this type of circuit regime; it has to be more sophisticated than that to ensure you don't walk the transformer core into heavy saturation.

My advice to you is bite the bullet and design this properly (high frequency PWM) because trying to tune at 60 Hz (coincident with the frequency of the MOSFET control voltages) will end in lots of smoke and disappointment.

This is why we use a higher frequency PWM regime; the LC filters then have a cut-off frequency that sites between 60 Hz and the switching frequency and inherently do not display the problems mentioned above.

• Maybe I expressed myself wrong. PWM and NOT PWM have a dead time between them so the switches don't turn on at the same time. I would like to try to solve the problem with LC filter because I spent a lot of money with an iron core transformer (for low frequencies). But as you said, maybe that's not possible. Commented Mar 28, 2022 at 18:47
• @EduardoCardoso Why not use a higher-frequency PWM (and a suitable transformer) to generate 60Hz at a lower voltage and keep your expensive transformer to step up to 220V? Commented Mar 28, 2022 at 19:23
• @EduardoCardoso you can still use that transformer after you have used a higher speed PWM signal and filtered that signal into a better sinewave. Commented Mar 28, 2022 at 19:34
• I hadn't thought of that, I can switch the mosfets with high frequency (SPWM) and generate a 60Hz signal in the transformer's primary. The high frequency will not reach the transformer. Thanks Andyaka Theodore Commented Mar 28, 2022 at 19:54
• A lot of "pure sine" UPS inverters are exactly like @Andyaka explained: high-frequency PWM, high-frequency LC filter (crossing over way above 60Hz), bulky iron-core transformer and even a small filter at the high voltage side. Commented May 20, 2022 at 12:05

Filtering mains frequencies (50-60Hz) requires heavy iron, especially at such fairly high power levels. In general, you'd only do that if you were designing an old-school vacuum tube circuit where series voltage regulation to reduce ripple was expensive and wasted lots of energy. In semiconductor circuits there's no need for that.

All you need to do is to generate a PWM sinewave at a much higher carrier frequency, carry it through a small high-frequency transformer, and then use a synchronous rectifier switched at line frequency to reconstitute the sine wave on the output. A 1500W inverter transformer for a 1MHz switching frequency easily fits in your palm and doesn't weigh much. You can wind one yourself with Litz wire.

• I'd be very interested to here how you'd get a high frequency PWM'ed version of 60 Hz through a high frequency transformer. Commented Mar 28, 2022 at 21:06

I made a quick LTSpice simulation of an LC circuit with 500 ohm load driven by a "modified sine" wave consisting of 150 volt pulses 8 mSec long, with a 20 mSec period for 50 Hz. I used 100 mH inductor and 33 uF capacitor. X(L) is 34 ohms and X(C) is 96.4 ohms at 50 Hz. The sine wave voltage is about 170 VRMS.

A 100 uF capacitor makes the circuit resonant, so be careful if you build a resonant circuit like this. It stabilizes at about 1000 VRMS!