# Square wave and sine wave inverter

1. Jan 9, 2012

### hisham.i

Hello,
Suppose we have a square wave inverter, and at the output we put a low pass filter with cut off frequency of 50 Hz, then the output is sinusoidal with frequency 50Hz.
Now lets take a sine wave inverter and at the output we have a low pass filter with cut off frequency of 50Hz, then we get sine wave with frequency of 50Hz.

What is the difference between 2 inverters if we put a low pass filter at the output?
Is it the shape of the current that will be generated on load?

2. Jan 9, 2012

### Staff: Mentor

If you have a sine wave output inverter, you probably don't need to do much additional filtering.

If you put a lowpass filter on a square wave output inverter with the cutoff frequency at 50Hz, you will most definitely not get a sine wave output. Why not?

3. Jan 9, 2012

### hisham.i

If we make fourier series for square wave we will get 50Hz and 3rd, 7th .. harmonic
then if we put a low pass filter we will get the 50hz signal only, so the output will be a sinusoidal signal with 50Hz frequency.

4. Jan 9, 2012

### yungman

Actually we did. It is very hard to generate a pure sine wave. The way I did it is actually use a clock chip through a fast divide by two to get rid of the second harmonics to generate the square wave and use multi-pole filters to filter out all the harmonics. I forgot what type of filter I used. You have second harmonics, it's over, it is 10 times harder to deal with the second harmonics.

5. Jan 10, 2012

### hisham.i

square wave contains only odd harmonics so an lc filter with 50Hz cut off frequency will get rid of all odd harmonics. so we will get a sine wave.
I am working on sine wave inverter using micro controller and H-bridge, but i was thinking about the difference between using a square wave and low pass filter to generate the sine, and the method of using a micro controller to vary the duty cycle in a sinusoidal manner.
In square wave inverter the filter should be able to eliminate the 3rd, 5th,7th.. harmonics, while in sinusoidal pwm inverter the filter will have only to eliminate the switching frequency which can be 10KHZ while odd harmonics are negligible (and maybe not present i don't know).
And this will affect the efficiency of the inverter i think.

6. Jan 10, 2012

### sophiecentaur

Whether Berkman is 'right' or 'wrong' depends on the specification of the filter, I think! But then, how pure is the sine wave from your sine wave inverter?

7. Jan 10, 2012

### yungman

First of all, I did not mean to be disrespectful in the last post, I don't have analytical data. I actually learned this when I was in Seimens Ultra Sound Division where this subject came up about getting a pure sine wave. Filtering a square wave have a lot of limitations, obvious the range is very very limited. It really meant for application on a single frequency. If you need to sweep frequency, you cannot use square wave.

For a single frequency, getting a pure sine wave out of the gate is harder than people realize. You still end up having multi stage low pass filter after that to get a good sine wave. So it make more sense to just start with a pure square wave as I specified using a divide by two fast flip flop. I can say this with some confidence because I have an invention of a multi-stop Time Digital Convertor that time stamp the time of arrival with 70pS resolution. The whole concept depend on a pure sine wave running continuously. When the trigger arrives, it trigger 3 digitizing at 90 deg interval and the data then analyzed and choose the point on the steepest slope, then compare back to a pure sine wave look up table to convert back to linear time.
The project was successful and was implemented into the TOF spectrometer in 97. If the we achieved 70pS resolution with all the ECL delay uncertainty and ADC error included, the sine wave has to be very pure.
Laying out the filter on the pcb can be critical as the inductors do "talk"!!! All inductors has to be in "T" with each other. I don't remember what order anymore or what exactly the filter I used, it is not Bessel or Linear Phase as the rolloff is too mild at 3rd harmonics. In my case, phase shift is not important as long as it stay constant, so I have the free will to use as steep as I want. Also using two 4th order LP with a good buffer in between is much better that an 8th pole filter as you can see in the filter table that higher order filters are not very effective on the frequencies close to the cut off frequency. I used two cascaded filter stages all the time for better filtering.

But again, I never did a spectral analysis on exactly how good the sine wave. I based on the project that I did.

Last edited: Jan 10, 2012
8. Jan 10, 2012

### Antiphon

Best way is to digitally over sample by at least 100x, then your filter frequency is 5khz, not 50 Hz. Just make sure you have enough bits of resolution in the first place. Any harmonics below the first 50 can be made do go away digitally in your lookup table for the sinewave.

9. Jan 10, 2012

### Staff: Mentor

That's more what I had in mind for a sine wave inverter design, but I don't have much experience in inverter designs. It just seemed so brute force to try to filter a square wave into a sine wave, especially with so much power involved.

10. Jan 10, 2012

### Antiphon

Thats the nice thing about the over sampled D/A method. There's almost no harmonic energy until you get up the sampling and even higher switching frequencies. Your filters end up being tiny and efficient (low inductance means lower conduction losses in smaller coils.)

The trade off is digitization error. Before you design this you have to set a spec for the noise floor. My rule of thumb is 10 bits is good to .1% accuracy or a -60dB noise floor. If you need a quieter sinewave then you'll need more bits.

11. Jan 10, 2012

### jim hardy

""It just seemed so brute force to try to filter a square wave into a sine wave, especially with so much power involved.""

that's how it was done in the inverters of my time, capacitors big as paint cans and hundred pound inductors. if you got down to 5% harmonic content you were doing quite well.