Computing the inductance of a set of coils

[Joe Gwinn]

There seemed to be some interest in the inductance of a set of adjacent interconnected coils. Now, this is fairly easy to compute from measurements of the individual and pairwise inductances. The big deal is managing the bookkeeping well enough to not make any errors. Knowing the computation is also instructive.

Inductance of Adjacent Coils.pdf

[Mike Sulzer]

Very nice, Joe. So if you consider the six coil pickups in the thread below, do the measurements regarding the relative sizes of the total inductances resulting from in phase and alternating phase connections agree with the theory if you assume reasonable mutual inductances? Can you take those measurements and derive a reasonable approximate value for k, the fraction of coupling flux? (Obviously there is actually a set of ks, not all the same, but one could assume that they are identical and see what the implied value is.)

There seemed to be some interest in the inductance of a set of adjacent interconnected coils. Now, this is fairly easy to compute from measurements of the individual and pairwise inductances. The big deal is managing the bookkeeping well enough to not make any errors. Knowing the computation is also instructive.

[ATTACH]17881[/ATTACH]

[CRU JONES]

Thanks Joe! Good stuff!

A value of k for a ceramic humbucker I have recently prototyped is 0.171. Alnico's will have a higher coupling factor. You can, often, sort your magnets this way, BTW Just thought I would throw that k value out there for anyone going through the calculations.

Ethan

[Joe Gwinn]

Very nice, Joe. So if you consider the six coil pickups in the thread below, do the measurements regarding the relative sizes of the total inductance resulting from in phase and alternating phase connections agree with the theory if you assume reasonable mutual inductances?

Thanks. The theory is general, and should work for any set of physically possible mutual inductances. The absolute value of M cannot exceed the harmonic mean of the two coil inductances.

Footnote: The algorithm is based on energy storage, and implicitly assumes that the LR time constant is negligible, which is true of pickup inductance measurements. The basic test of LR time constant in a practical inductor is to establish a current in the inductor and then short it. How long does it take the circulating current to decay? The LR time constant is important only for situations with high inductance and low relative resistance.

Can you take those measurements and derive a reasonable approximate value for k, the fraction of coupling flux? (Obviously there is actually a set of ks, not all the same, but one could assume that they are identical and see what the implied value is.)

Yes, because k is computed from the mutual and self inductances: M=k Sqrt[L1*L2]. It is the self and mutual inductances that are primary, not k, although k is certainly useful.


Inductance - Wikipedia, the free encyclopedia