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# Construct Harmonic Wave Form

02/13/2017 4:27 AM

How it will be possible to construct a wave-form consisting of harmonics. As an input we know only the fundamental frequency of 50Hz and amplitudes at various harmonic frequencies like 100Hz, 150Hz, 200Hz, 250Hz, 300Hz etc.

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Guru

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#1

### Re: Construct Harmonic wave form

02/13/2017 4:39 AM

Use Fourier's theorem.

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#2

### Re: Construct Harmonic wave form

02/13/2017 4:54 AM
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#3

### Re: Construct Harmonic wave form

02/13/2017 5:00 AM

But I do not know the Phase angle difference. Then how it is possible?

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#4

### Re: Construct Harmonic wave form

02/13/2017 5:13 AM

If you are constructing the waveform, then you know the phase angle difference.

No-one else does; you're in charge.

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#5

### Re: Construct Harmonic wave form

02/13/2017 5:42 AM

In any project only harmonic amplitudes are given by equipment manufacturer. How I can consider the phase angles?

Suppose for any arc furnace application furnace supplier gives the list of amplitudes with different frequencies only.

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#6

### Re: Construct Harmonic wave form

02/13/2017 5:53 AM

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#8

### Re: Construct Harmonic wave form

02/13/2017 10:38 AM

In a strict sense you cannot reconstruct the time based signal from knowing only the harmonic amplitudes without the phase relationship. However, a reasonable assumption of zero degrees of phase angle will produce a reasonable waveform for analysis. (Intuitively I believe a zero degree phase for all harmonics will produce the maximum amplitude, too.) Since this is an arc furnace the instant in time that an arc is created cannot be predetermined, thus the uncertainty of which waveform will be produced.

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Guru

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#9

### Re: Construct Harmonic wave form

02/13/2017 11:01 AM

(Intuitively I believe a zero degree phase for all harmonics will produce the maximum amplitude, too.)

Your intuition is correct. All the sinusoids (cosines) would be maximum at time zero and multiples of the fundamental period after that.

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#10

### Re: Construct Harmonic wave form

02/13/2017 11:21 AM

Thanks for the confirmation. It's been awhile since I dealt with the Fourier series theory.

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#12

### Re: Construct Harmonic wave form

02/14/2017 12:42 PM

If you have the actual equipment, you can observe the waveform with a scope. Better yet, an FFT analyzer can measure the waveform AND display the phase of all harmonics.

If you do not have equipment, you must have the phase and amplitude of each harmonic in order to use the inverse FFT to see the source waveform.

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#13

### Re: Construct Harmonic wave form

02/23/2017 6:25 AM

An arc furnace application would only require the amplitudes of harmonics. This is because the supply frequency is 50 Hz, harmonics are a nuisance to power supplier because they cause increased losses in transformers, cables etc and, maybe, trouble to other users of power, telephone circuits etc.

For this purpose, only the amplitudes of harmonics are necessary, they give the harmonic power available and so a comparison of suppliers for potential nuisance of harmonics, cost of reducing them etc. The actual waveform is not much help, you would only have to analyse it to work out the harmonics.

Arc furnaces usually limit the current by an inductive reactance. Harmonics come from saturation of the iron, so your waveform is going to be of that type. Between low starting current and maximum current there is probably a very great change in waveform, adding to your analysis problem. If your furnace is of smaller size, you may also have thyristor control chopping your basic sine wave into phase varied pulses.

So it is far more practical to look at the harmonic levels than worry about the waveform.

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#7

### Re: Construct Harmonic Wave Form

02/13/2017 9:54 AM

If you only know the amplitudes of the frequency components and not their relative phase to the fundamental, then you cannot reconstruct the waveform. There are an infinite number of waveforms that correspond to your amplitude spectrum.

To be able to reconstruct the waveform, you need to take the complex Fourier Transform, which has phase information as well as amplitude information.

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#11

### Re: Construct Harmonic Wave Form

02/14/2017 3:00 AM

They're widely available. Every non pure sinewave waveform, is fundamentally made up of pure sinewaves of different harmonics and amplitudes.

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