Harmonics eliminate from square wave

[shoeb.eee]

even harmonics in a square wave

How can I eliminate harmonics while making inverter. I read a technique in Wikipedia but did not understand. here is the link

http://en.wikipedia.org/wiki/Inverter_(electrical)

the portion need to understand is below
"by inserting a zero-voltage step between the positive and negative sections of the square-wave, all of the harmonics that are divisible by three can be eliminated"


Please make it understandable. Also mention some efficient methods.

 

[E-design]

square duty cycle and harmonics

Your answer in in the next sentence

Changing the square wave as described above is an example of pulse-width modulation (PWM). Modulating, or regulating the width of a square-wave pulse is often used as a method of regulating or adjusting an inverter's output voltage. When voltage control is not required, a fixed pulse width can be selected to reduce or eliminate selected harmonics. Harmonic elimination techniques are generally applied to the lowest harmonics because filtering is more effective at high frequencies than at low frequencies.

https://www.eleinmec.com/article.asp?28

 

[FvM]

eliminate harmonics

You'll find the answer, if you take a look at the fourier series chapter of a mathematical handbook. The said symmetrical square wave with "zero voltage step" has this fourier series:

4h/pi*(cos φ/1 * sin x + cos 3φ/3 * sin 3x + cos 5φ/5 * sin 5x + ...)

φ describes the width of the zero step (on each side of the pulse). A value of 30°, respectively a 67% duty cycle results in cos 3φ = 0, also cos 6φ = 0 etc.

 

[shoeb.eee]

square wave harmonic elimination

Thank you all for your quick reply

@E-design: Please give me a practical example. How can i eliminate 3rd, 9th, 15th harmonic from a square wave output? i.e, divisible by three harmonic less output.

@FvM: Please share the link that you said about fourier series

 

[FvM]

bipolar symmetrical square wave fourier

I was refering to a printed book.

The said 67% duty cycle symmetrical waveform has the requested properties, eliminating 3rd, 6th, 9th ... harmonics.

 

[shoeb.eee]

how harmonics found & eliminate

any practical example and Circuit?

 

[mostafa ahmed]

square wave harmonics

you can read this paper and know one method for reducing THD.
This paper give you the method to reduce THD for any desired value.
If there is any question you can send me your question.
Good luck.

 

[E-design]

how to eliminate harmonics

Here is a display of time and freq to show what happens at 66.6% duty cycle. The harmonics eliminated can be seen marked in red. The fundamental is approx 60Hz (58.6Hz) in this example.

You can see how this figure is obtained by looking at the function (Sinx)/x to describe a repetitive pulsed waveform and analyze where the nulls would occur.

 

[FvM]

harmonics square wave fourier

Yes, a similar result is obtained with a bipolar (0,+1,0,-1) waveform, but in this case, also the even harmonics 2n*f0 are eleminated.

 

[E-design]

fourier series square duty cycle

Like expected plot shows all even harmonics removed due to push-pull action. First significant harmonic component at 300Hz