# Basic Harmonics Question

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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

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Doesn't rectification automatically produce only odd harmonics? ...Jim Thompson

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| James E.Thompson                                 |    mens     |
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Because it* is symmetric. Even harmonics indicate "single-endedness"; odd harmonics are clipping or slew-rate derived. *A* half-wave rectifier/diode would have beacoup even harmonics; a bridge would have relatively fewer.

*it being something akin to the transfer function of the DUT...
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Les Cargill```
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Klaus-

With rectification, your ripple frequency is the new "fundamental". Wouldn't that be 300 Hz with 50 Hz 3 phase full wave rectification?

Fred

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Yup. Assuming a constant load, perfect phase spacing (120 degrees), equal phase impedances, and identical diodes, you get 6 identical peaks per input cycle. That means that the only harmonics that can contribute are order 6, 12, 18, ....

Weird loads can cause subharmonic oscillations and stuff, though.

Cheers

Phil Hobbs

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Could you post your schematic (or LT Spice .asc file) ?

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OK, back to school for you -- I'm sure MIT has a spot open in their EE250 class for you to sit in.

Rectification only produces odd harmonics if it's symmetrical (meaning, mostly, that it's full wave). Half-wave rectification produces all harmonics.

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www.wescottdesign.com```
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CRAP CRAP CRAP -- maybe they have room for both of us?

Full-wave rectification would produce odd harmonics in CURRENT, but only even harmonics in VOLTAGE. Think about it (think about it more than I did before I hit "send" last time!)

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www.wescottdesign.com```
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You should see all the 6n +/- 1 harmonics on the AC side and 6n harmonics on the DC side, I'd I recall correctly. All the triplen (ie: 3n) harmonics cancel in the AC side due to the 120 degree shift between the phases.

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I'm not sure what Klaus actually has, since he mentions 250Hz and

350Hz ??

BTW, MIT doesn't have a class EE250... it'd be 6.xxxx ...Jim Thompson

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| James E.Thompson                                 |    mens     |
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I'm thinking that if he's seeing anything sensible at all it's the current in each leg.

I kinda poked at generating the relevant Fourier series, then decided that I'll do it when I don't have chores, or when I'm getting paid.

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www.wescottdesign.com```
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They only do in the distribution transformer which on the HV side is delta connected. And it's not exactly a matter of 'cancellation'. That's where the 3n-harmonic voltages are basically connected in series, forming a short circuit current which isn't seen by the primary feeding circuit, which is good, but which also contribute to additional heating of the transformer, which is bad.

joe

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It's just an extremely simplified model of the current in the individual phase of a load driven by a 3 phase rectifier:

The mains is 50Hz. The harmonics, referred to the 50Hz, is 250Hz (5th) and 350Hz (7th):

I am actually pursuing another thing, just playing around.

I have a circuit where the 5th and 7th are present, and I am trying to see if I could add a 6th harmonic with a certain phase to cancel out the 5th or the 7th.

Like what is done on mains transformers, where adding 30 degrees phase shift to the supply of device 1 will cancel out the 5th harmonic of device 2 (which has 0 degree phase shift). (5 x 30 + 30 = 180)

If I have a 5th and 7th harmonic, can I then add a 6th harmonic with 180 degrees phase shift that would cancel out (180/6 = 30)?

Cheers

Klaus

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The 6th doesn't pop up because the corresonding term in the fourier series comes from integration (of the current times a harmonic sinewave) over a full fundamental cycle. Even harmonics result in a whole number of harmonic cycles within the integration period and that yields zero.

joe

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20PAGE1.pdf

Hey Klaus:

Review your Fourier theory, particularly with regards to orthogonal functions.

No, you cannot add in the m-th harmonic at any amplitude and phase to cancel out the n-th harmonic, unless m = n. It's part and parcel of the definition of orthogonality, and orthogonality is the basis of harmonic theory.

With the right PFC circuit you could not only eliminate nearly all harmonic energy, but you could do it with an output cap on your intermediate rail that would only need to be sized for your switching frequency -- not the mains frequency.

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www.wescottdesign.com```
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If you're talking about eliminating the harmonics in the input current then I have to beg to differ with you. The current in the intermediate rail (18 kHz ripple) is practically DC compared to the 50 Hz mains.

Switching a DC on and off on the input lines does generate harmonics. An intermediate rail capacitor doesn't magically make the current sinusoidal in shape.

A solution could be filtering on the input, or, if that would be too bulky, a PWM controlled bridge rectifier--instead of diodes--*and* a capacitor on the intermediate rail.

joe

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What? If the signal is driving a real load, why would the current and voltage have different harmonics?

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Rick```
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As you are fond of saying...Do The Math ;-)

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