Basic Harmonics Question

Because the part I didn't mention is that the current is in the power line, and the voltage is at the output of the diode bridge.

It's kinda implied in the thread, but it's not really knock-you-out obvious, I suppose.

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I missed the part about it being three phase. That will have a huge impact on the line current relative to output voltage, I agree. Anyone know how to show the harmonics are all odd or even with three phase?

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Rick

Because there is a three phase rectifier sitting in between the (output) current and (input) voltage. The diodes don't conduct during the full 180 degrees of the half cycles; they 'commutate', i.e. are forced off when the next phase's voltage supersedes the voltage of the currently conducting diode's phase. Something like that, graphically it's much easier explained. :)

joe

No no, not at all, there is nothing to be angry about and sorry if I seem to express anger, because that was not my emotion at that time. I thought I stated it quite friendly: "...then I have to beg to differ with you." Please point to any other indication of anger if you'd please?

Sorry about misunderstanding you. What exactly did you mean by 'right PFC'? I thought you wanted to put an additional device (the PFC) in front of the rectifier or on the intermediate link.

The former would (imho) be less optimal than replacing the diode rectifier with a PWM one, the latter wouldn't fix the problem. It's three phase.

Yes, that was what I said: too bulky. :)

cheers, joe

Yes, I knew that, but I stumbled across this article:

And I wanted to see if I could use a similar technique..

But, I have a problem visualizing how they achieve the cancelling effect, won't it be no-optimal?

Regards

Klaus

In an N-pulse rectifier, harmonics up to N/2, and multiples thereof, are either not generated (e.g., even), or cancel out (by leaving neutral voltage in delta, or drawing neutral current in wye).

The Fourier excuse is, if the phase shift between fundamentals is 1/N (of a full cycle), then the phase shift of the Kth harmonic is K * 1/N. Both phase and frequency multiply by the harmonic, in short. If K/N is a full circle (or zero, or multiple full circles..), then the phase wraps around.

At least, it works at N=6. I forget if that's an orthogonality thing (i.e., it only works for the fact that you're using more than two wires, with some phase shift, to transfer power -- higher phase counts are linearly dependent so can't do anything nicer) or a phase thing (which would be general in N).

I've been very slightly tempted, from time to time, to build an amplifier with three phase output. Two phase is common -- push-pull -- and this has the apparent effect of canceling even harmonics. The rub is, three phase requires complicated wideband phase shift networks. Properly implemented, though, it should indeed cancel 3rd and multiples, leaving 5th and 7th as the primary components.

Tim

Seven Transistor Labs, LLC Electrical Engineering Consultation and Contract Design Website:

Hi

I was just playing with a simulation of a 6 diode rectifier (3 phase input)

Mains freqeuency is 50Hz, the harmonics are 250 and 350Hz. The theory is way to long away for me to remember. Why does the 5th and 7th harmonic pop up and no 6th?

Thanks

Klaus

All odd or all even are easy, and are treated in the Fourier literature: If a complete cycle has odd symmetry* around some point in the cycle then the harmonics are all odd. If a complete cycle has even symmetry around some point in the cycle then the harmonics are even.

So determining if all the harmonics are odd or even is an "at a glance" sort of thing, at least if you remembered to let out the clutch on your brain before you glance (see my first response to JT, above).

• Odd symmetry around x = 0 means that f(-x) = -f(x). Even symmetry around x = 0 means that f(-x) = f(x).

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I was speaking without experience of what is actually used in the 3-phase drive market (if someone wanted me to design 3-phase power equipment for them my first -- and probably second and third -- recommendation would be "hire someone else").

Your PWM diode is a member of what I would call PFC devices -- whether or not that's how industry terminology goes.

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Thanks.

Actually it's not a PWM diode, but a Pulse Width Modulation controlled rectifier bridge which consists of transistor or thyristor type controlled devices. Like a PWM inverter, but then used 'the other way around' as a rectifier.

cheers, joe

6 is an even number..

Jamie

Not correct. Odd functions have only sine Fourier terms. Even functions only cosine terms. One can trivially see that sin(2x) is an odd function even though it's an even harmonic.

If you need still more convincing, consider that you can change a symmetrical square wave from odd to even by just time-shifting it by a quarter period, but the harmonics remain all odd!

Yes.

Jeroen Belleman

}snip{

Maybe with a DSP? I just don't know whether algorithms exist for this. In the complex plane (or frequency domain) it would plainly be a matter of multiplying with e^j2pi/3 and e^-j2pi/3. Actually I have no idea how to do this.

How many speakers were you thinking of, 3? If that's the case I think the harmonics will be there anyway, coming out of the speakers and those harmonics that you're targeting at will only cancel out as the soundwaves meet each other in the air. So positioning of the speakers will be a problem, and it will have directional effects, I'm afraid.

Or if you're talking about a three phase speaker then you've lost me.

I can see now why you're only _slightly_ tempted.

joe

Oh, dammit. Yup, I need to go back to school.

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I was leading myself down the garden path because I can just look at a square wave or a triangle wave and know that it's all odd harmonics, and I can look at full-wave rectified sine wave and know it's all even harmonics.

But I don't think there's a simple rule (consider a square wave passed through a ringing filter -- it's all odd harmonics, but that's not necessarily apparent from glancing at the wave form -- or is it? Dammit, I can't think tonight.)

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Tim Wescott 
Wescott Design Services 
http://www.wescottdesign.com

That works on the input side, but getting it out to a speaker requires a power phase shift network (and assumes the speakers have known constant impedances... that'd be the day..). As you note, possibly a three phase array or mechanism could be used as well, but it would only cancel in places.

This works well at RF, where you only have to do it for a narrow band of frequencies (even "wideband" is usually just meaning 100s of MHz, rather than "a sizable percentage of the center frequency"). You can split and combine amplifiers using phase shift networks, and do this to help harmonic distortion (though distortion should already be low due to filtering it in the first place).

The basic structure is an LC lowpass ladder network, L-C-L, but where the L's are tightly coupled. At low frequency, the L's act as shorts and the phase shift is zero; at high frequency, the C shorts the L like it's a CT winding (it is!), and phase shift is 180 degrees. Phase walks a circle inbetween, and reaches 90 degrees at resonance. Resonance needs to be dampened well enough to the system impedance, so that it doesn't actually resonate at all, but transitions as gradually as possible. Finally, a bunch of these are cascaded, because an amplifier -- an audio amplifier -- covers ideally three orders of magnitude in frequency, 20Hz to 20kHz. The coupled inductors need to have low enough leakage to keep the phase shift strong up to the top of bandwidth; a 20Hz choke being any good at 20kHz is a challenge!

Phase shifters have been used in radio tech, like the phasing SSB modulator/detector. These are usually limited to signal processing, and therefore done cheaply: resistors and capacitors. The classic four-way RC lattice filter has a large and variable phase shift from input to output, but preserves a useful phase shift between outputs, so it can be useful.

Tim

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Seven Transistor Labs, LLC 
Electrical Engineering Consultation and Contract Design 
Website: http://seventransistorlabs.com

Oooh! Oooh! There is a simple rule (see, it's morning and I've had a good slug of caffeine, and now I can think)!

For the "only even harmonics" case, then it's just a matter of noting that the output is perfectly cyclical at twice the input frequency -- in effect, the output's "fundamental" is doubled. That's almost too easy.

For the "only odd harmonics" case then if the first half-cycle of the wave is exactly duplicated, with polarity reversed, in the second half- cycle, then the wave only has odd harmonics.

I'm 99 & 44/100 percent sure I've got this right, but critiques are welcome.

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Tim Wescott 
Wescott Design Services 
http://www.wescottdesign.com