Undergrad What causes alternator waveform shape?

[hogshead]

I have a permanent magnet alternator. It does not produce a sine wave output, but rather a sort of distorted triangle wave. I did a frequency analysis on it and it showed a series of harmonics. The strongest was the third, with each odd harmonic getting progressively less powerful. It also had a series of even harmonics at a lesser value that got progressively less powerful.

My question, what causes this and what is it called?

 

[Charles Link]

Just a guess at what might be causing it is the hysteresis curve for the magnetic material of the alternator. Otherwise, perhaps the EMF $\varepsilon=-d \Phi/dt$ simply is non-sinusoidal for geometric reasons. @jim hardy Perhaps you can provide some insight on this.

 

[Khashishi]

I guess it has to do with the shape of the winding of the coils in the stator, and the magnets in the rotor. The magnets alternate polarity around the circumference of the rotor. As it spins past the winding, the changing flux depends on how close the magnets are to the coils. Since the coils have some width, and the magnets have some width, as these two pass each other, the level of "overlap" of a coil with a + end and a - end shifts very roughly linearly in time, giving a triangular pattern. Obviously, this has to do with the details of your generator, and will be different for different generator designs.

 

[hogshead]

Thanks for the help. The alternator has cast-iron pole pieces, so I could see how hysteresis could be a factor. Also I could see how geometric considerations could cause the flux to not be distributed evenly. Why is there a seemingly infinite series of harmonics (at least I assume in theory that there would be as there seems to be a progression going into the noise floor)? What is this phenomenon called?

 

[Charles Link]

Thanks for the help. The alternator has cast-iron pole pieces, so I could see how hysteresis could be a factor. Also I could see how geometric considerations could cause the flux to not be distributed evenly. Why is there a seemingly infinite series of harmonics (at least I assume in theory that there would be as there seems to be a progression going into the noise floor)? What is this phenomenon called?

The waveform is periodic. If it is periodic and a sinusoid, the Fourier transform is a single spike (delta function) at the fundamental frequency. Any other periodic shape can produce some Fourier amplitude at every harmonic of the fundamental frequency. Sharp corners, and quick rises and falls, etc., in the waveform tend to be characterized by significant amplitudes in the higher frequency components of the Fourier transform. Smoother waveforms will be concentrated at the fundamental and lower harmonic frequencies.

 

[NTL2009]

A perfect triangle wave will contain only odd harmonics with the amplitude dropping off sharply (1/n^2). Your imperfect triangle wave seems to fit this pretty closely.

 

[hogshead]

The waveform is periodic. If it is periodic and a sinusoid, the Fourier transform is a single spike (delta function) at the fundamental frequency. Any other periodic shape can produce some Fourier amplitude at every harmonic of the fundamental frequency. Sharp corners, and quick rises and falls, etc., in the waveform tend to be characterized by significant amplitudes in the higher frequency components of the Fourier transform. Smoother waveforms will be concentrated at the fundamental and lower harmonic frequencies.

So, if I am understanding this correctly, the quick rises and falls and sharp corners and such are distorting the wave from being a sine wave? Why are the spikes in the frequency analysis at multiples of the fundamental frequency and not just noise?

 

[Charles Link]

So, if I am understanding this correctly, the quick rises and falls and sharp corners and such are distorting the wave from being a sine wave? Why are the spikes in the frequency analysis at multiples of the fundamental frequency and not just noise?

The distortions you are seeing are not noise. They are a very regular periodic pattern that inherently will show up as harmonics of the fundamental frequency for any repetitive, but non-sinusoidal waveform.

 

[hogshead]

Yes, I can see that they are not noise. What I'm trying to understand is why the distortion is at harmonic intervals and not just noise.

I also want to know the technical name for this so that I can do more research (Google and that kind of thing). It seems to me that since the distortion happens at various harmonics, that this is a form of harmonic distortion, although I have been told that this is an incorrect application of that term. Although I have been told that it is incorrect to call this harmonic distortion, it has not been explained to me why this is incorrect.

 

[Charles Link]

Yes, I can see that they are not noise. What I'm trying to understand is why the distortion is at harmonic intervals and not just noise.

I also want to know the technical name for this so that I can do more research (Google and that kind of thing). It seems to me that since the distortion happens at various harmonics, that this is a form of harmonic distortion, although I have been told that this is an incorrect application of that term. Although I have been told that it is incorrect to call this harmonic distortion, it has not been explained to me why this is incorrect.

I think @Khashishi had a very good explanation in post #3.

 

[NTL2009]

Yes, I can see that they are not noise. What I'm trying to understand is why the distortion is at harmonic intervals and not just noise. ...

Consider a similar type of distortion - if you 'clip' a sine wave, you get a (near) square wave. I think you know that you can construct a square wave by adding odd harmonics (sine waves) at an amplitude of 1/n (do it at 1/n^2 and you get the triangle wave I referenced earlier). If you don't "get" this, use a graphing calculator/program, or an audio editing tool like "Audacity" to do it for yourself - sometimes that is the most illuminating.

So this distortion happens 'in sync' with the sine wave. Caused by clipping, or some sort of non-linear loading on the waveform. It is periodic, and all it can be is harmonics. Anything that is periodic and 'in sync' with the waveform of interest, must be a harmonic, because it is periodic, and it isn't part of the fundamental sinewave. Anything not periodic will appear as 'noise'.

I do think it is correct to refer to this type of wave-shape distortion as "harmonic distortion", I think that is basically by definition. Who disagrees with this? Maybe they are referring to something else?

 

[sophiecentaur]

I have a permanent magnet alternator. It does not produce a sine wave output,

The following expands on what Khashishi wrote in Post #3. The waveform is not important for many applications and I imagine that it's down the list of characteristics of many basic alternators. The emf will be proportional to the rate of change of flux. (That's the basis of Faraday's Laws of Induction) There is no inherent reason why the flux should change sinusoidally because it will depend on the way the magnetic flux changes as the magnet poles and the core pass over each other during the revolution. It is not an important factor for most applications, after all, many appliances will work quite happily on a square wave inverter. If the alternator feeds a transformer it could be important.
The mains waveform needs to be better behaved (more sinusoidal) because many alternators are connected to the grid and Power could be wasted if the waveforms are not all in sync - plus the mains feeds many different transformers. The spec for alternators that feed the grid will include a requirement for low harmonic content, I guess.

 

[Merlin3189]

I was about to ask what SophieC has just said: why does anybody think an alternator output should be a pure sinusoid? Just because textbooks show a single wire moving on a circular path in a uniform magnetic field doesn't mean that people build alternators like that.*

But why are the variations harmonic? Apart from the maths, I'd just like to think about what would happen if there were a non-harmonic component. This component would not stay in phase with the fundamental, but would change from cycle to cycle, peaking at every possible position of the rotor on different cycles. So whatever variation in field or motion caused it would have to be moving relative to both rotor and stator, like maybe a grain of iron bouncing around in the case. But that would be unlikely to move regularly and would generate noise rather than a fixed frequency.
In fact, what property of the alternator could possibly vary cyclically at a constant rate faster than the rotation but completely unconnected with it?

*I think I'm describing a dynamo there. But a single loop of wire with a perfectly symmetrical rotating field is similarly an idealisation.

 

[Cutter Ketch]

But why are the variations harmonic?
.

First let me add my voice to the chorus agreeing with khashishi in post three. It would be hard to construct a real useful alternator (I.e. Something more compact and effective than a small loop rotating in a large uniform field) that produced a perfect sine wave.

However, to answer Merlin the output must be harmonics of the rotation frequency. The system repeats on itself at the rotation frequency. There is no configuration of the system that doesn't recur at the rotation frequency, so the output must repeat on itself at the rotation frequency. That only allows harmonics. To get something not harmonic you would have to introduce an element not at the rotation frequency (which I'm sure happens, say, in an engine compartment where other nearby systems are rotating at different frequencies)

 

[NTL2009]

I was about to ask what SophieC has just said: why does anybody think an alternator output should be a pure sinusoid? Just because textbooks show a single wire moving on a circular path in a uniform magnetic field doesn't mean that people build alternators like that. ...

Well, I guess I always thought of them as being (relatively) pure sine waves. Partly because, as you mention, textbooks show them that way. And I never recall actual putting a scope on one. I just never really thought about it, so just went with the picture in my head.

Also, as SophieC also mentions, a mains alternator does need to put out pure sine waves, so that example sticks in our heads.

But now that I have thought about, due to this thread, it isn't surprising, unusual, or unexpected that alternators for other applications would produce distorted waves. Really no need for them to do be pure, so it would not be a design consideration. I'm guessing the major factor in distortion would be the shape of the magnetic field. Seems like this would need to be carefully designed to reduce distortion. The armature windings are just going in a circle, so probably less distortion from those? Though I suppose differences pole-to-pole would create non-linearity.

 

[sophiecentaur]

text books show them that way.

text books have a lot to answer for.