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Mutual Inductance

So, I was wondering, what is the electrical model of mutual inductance?

It's explained in my physics textbook, with no electrical significance as far as I can tell.

Leakage inductance is far simpler to deal with, but I noticed that my textbook doesn't mention it and internet sites deal with cored examples. Air core transformers have leakage inductance too!!

Purpose: wondering what the LL of coupled, concentric solenoids with different diameters is.

Presumably, k (coupling konstant) is roughly the ratio of areas, but I can't find where to get LL from that.

Tim

-- Deep Fryer: A very philosophical monk. Website @

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Reply to
Tim Williams
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OK, don't quote me on this, as "officially" I'm "only" a Tech, but to me it just seems intuitive that the mutual inductance is how much coupling you have left after you subtract out the leakage inductance.

What that means in numbers, I have no idea. I have heard that they're all relatively simple to measure - it has something to do with shorted and open windings and schtuff like that.

Maybe google for "mutual inductance" or "coupling coefficient" or so.

Good Luck! Rich

Reply to
Rich Grise

The transformer equations are

V1 = L1. d I1/ dt + M . d I2/dt

V2 = M. d I1/dt + L2. d I2/dt

where M is less than the geometric mean of L1 and L2, in proportion to the extent that the flux from the two coils is imperfectly coupled. For non-cored solenoids it would have to be close to the area ratio, but then again, the aspect ratio of the solenoids is going to have to come into it.

-- Bill Sloman, Nijmegen

Reply to
bill.sloman

"Tim Williams" schrieb im Newsbeitrag news:3kkHh.47$ snipped-for-privacy@newsfe05.lga...

Hello Tim,

We had a discussion in the LTspice group about coupling factors sometimes ago.

Maybe in appendix-A of this paper is the answer.

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Mr. Lloyd H. Dixon gives an example about the difference of K12, K21 and "K". See Appendix A in this paper.

Best regards, Helmut

Reply to
Helmut Sennewald

I did not even get to appendix A; note on page 4, second column "Thus. the "leakage" flux links the outer winding but not the inner winding." *Very* loud smack in the face that leakage inductance one way is different than the other way. So those "nice" symmetrical looking equations are all lies!

Reply to
Robert Baer

You understand self-inductance, yes? Ignoring winding resistances, given a two winding transformer, if you apply a current to one winding (or to a single winding inductor), the voltage across the inductor is L di/dt. In the case of a sinusoidal AC current i of frequency f in the inductor, the voltage e across the inductor is e = L*2*pi*f*i, or L = e/(2*pi*f*i). L is the ratio of the voltage across the winding to the rate of change of the current in the winding.

Roughly, it's a relationship between the voltage across a winding and the current producing it.

In the case of mutual inductance, it's the ratio of the voltage across a winding to the rate of change of current in *another* winding.

Frederick Grover's book on inductance calculations

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will tell you how to calculate the self-inductance of the solenoids and also their mutual inductance. From this you can calculate the leakage inductance. However, I will tell you that it will probably be easier to build them and measure.

Reply to
The Phantom

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