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Question relating to parallel inductors.

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Ash Small

Tue Dec 06 2016, 12:35PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

I've read the laws applying to series and parallel inductors, and it makes perfect sense.

My question is do these laws still hold if the inductors are wound on a common core?

Kizmo

Tue Dec 06 2016, 12:50PM

Registered Member #599 Joined: Thu Mar 22 2007, 07:40PM
Location: Northern Finland, Rovaniemi
Posts: 624

Ash Small wrote ...

I've read the laws applying to series and parallel inductors, and it makes perfect sense.

My question is do these laws still hold if the inductors are wound on a common core?

Short answer is no, i think only parameter that does behave the same way in both cases is DC resistance.

Ash Small

Tue Dec 06 2016, 12:57PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Thanks Kizmo, I suspected as much.

What's the slightly longer answer?

hen918

Tue Dec 06 2016, 02:39PM

Registered Member #11591 Joined: Wed Mar 20 2013, 08:20PM
Location: UK
Posts: 556

The slightly longer answer is that if they are wound on the same core you have yourself a transformer. If they are wound in phase (in the same direction) and connected in parallel, you will have just doubled up the copper on what is essentially one winding (this is to be avoided though, because and discrepancy in the number of turns, or more specifically amount of flux cut through, causes inefficiencies as electrically turns are shorted due to their being a difference in voltage between them). The inductance *should* be the same.

If your (same length) windings are connected in series you will have doubled the length of the windings and the inductance will increase proportional to the square* of the turns. (voltage will increase linearly, of course).

If your windings are in anti-phase and in series the number of turns will have to be subtracted and this "n" used to find the new inductance.
In anti-phase parallel, you will have effectively shorted turns on your inductor.

Care should also be taken not to locate unshielded power inductors near each other when the windings (as they are slightly coupled by their proximity) are in anti-phase, for the same reason.

*Edited, meant square, not square root.

Dr. Slack

Tue Dec 06 2016, 02:41PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

The longer answer includes the mutual inductance of the inductors, the voltage induced in one because of the dI/dt in the other. In fact one way to calculate the mutual inductance is to measure the individual inductors, measure the combined inductance, and whack the measurements into a suitable formula.

For instance, consider the windings on a common mode choke. Each would measure some finite value, but because of their mutual inductance, when put in series, their inductance is 4x that of one, and when in anti-series their inductance is approximately zero.

Ash Small

Tue Dec 06 2016, 05:13PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Thanks for the replies. I've been doing some research elsewhere, and found something similar, and found a reference to mutually coupled inductors, and a formula relating the total inductance and the mutual inductance. I don't think it was explained exceptionally well though.

I can see how wiring, say, the primary and secondary of a step down transformer in parallel would create issues.

I also remember something about shorting out the secondary, or leaving it open circuit when measuring different parameters, so am I correct in assuming that if I short the secondary, the primary would be the only measurable inductance? (ie, would the secondary no longer have any effect on the inductance of the primary? )

2Spoons

Tue Dec 06 2016, 09:43PM

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM
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Posts: 615

With partial coupling of different parallel inductances you can have some very odd things happening. I found one scenario where current would flow backwards in one inductor, due to coupling from the other. This all came about from me trying to find the best way to construct high power, low loss PCB coils.
Try it in a simulator : 1:2 turns ratio, and coupling >0.5. Inductors in parallel.

hen918

Tue Dec 06 2016, 10:09PM

Registered Member #11591 Joined: Wed Mar 20 2013, 08:20PM
Location: UK
Posts: 556

Ash Small wrote ...

...
I also remember something about shorting out the secondary, or leaving it open circuit when measuring different parameters, so am I correct in assuming that if I short the secondary, the primary would be the only measurable inductance? (ie, would the secondary no longer have any effect on the inductance of the primary? )

By shorting out the secondary and measuring the primary, you are measuring the total leakage inductance. This is the inductance that is not coupled to the transformer / inductor. It is drawn in models of real transformers as a separate inductor in series with the primary, as this is effectively what it is.

By leaving the secondary open, and measuring the primary, you are measuring the magnetising inductance. This is the inductance that's effectively in parallel with the primary, and is drawn as such on the real diagram of a transformer. Whatever is driving the transformer has to cope with the current flowing through the magnetising inductance even when the transformer is unloaded. This is why large power supplies are very inefficient at low loads.

Ash Small

Tue Dec 06 2016, 11:32PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Thanks for the reply. Do I take it then, that if leave one coil unconnected, in a situation where two inductors share a common core, that it no longer interacts with the other inductor?

klugesmith

Wed Dec 07 2016, 05:14AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

If you leave one coil unconnected, it can still resonate with its self-capacitance and affect the "black box" behavior of the other coil. Might be easier to measure in an air-core design.

There are inductive devices called variometers, unrelated to aviation instruments with the same name. Arrange two coils that can be rotated with respect to each other, to sweep the coupling factor k between almost 1 and almost -1.

Suppose each coil alone has inductance L, and they are connected in series. Then the combined inductance ranges from almost 4L (max positive k), through 2L (k=0, e.g. orthogonal orientation), to almost 0 (max negative k). I think a parallel connection would behave in a similar way.

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