total inductance of bucking coils

Discussion in 'General Electronics' started by Brett Holden, Jan 31, 2009.

1. Brett HoldenGuest

I need to be able to calculate the total inductance of two coupled coils
when one coil is wound in reverse. I have a Boylestad's Introductory Circuit
Analysis (old - 6th edition) that has a section covering this but I have run
into a problem because there seems to be some circular reasoning in defining
the equation (#1). (I have used brackets in place of subscripts.)

Inductance of two coupled, bucking coils:
1) L[T-] = L[1] + L[2] - 2M[1,2]

2) M = .25( L[t+] - L[t-] )

3) L[t+] = L1 + L2 + 2M[1,2]

4) L[t-] = L1 + L2 - 2M[1,2]

I can't use subscripts here, so formula 1 is supposed to read:
"total inductance of two reverse wound (coupled) coils equals
inductance L1 plus inductance L2, minus (two times their mutual
inductance)".

OK, if we can define the mutual inductance "M", then all is well.

To define M, formula 2 seems simple enough but introduces two more
variables, L[t+] and L[t-].

In formulas 3 and 4, variables L[t+] and L[t-] are defined, but M is used as

Also, formula 1 seems to ignore the influence of coeffecient of coupling
between the coils but maybe that is accounted for in equations 3 and 4?

2. ShaunGuest

What's your application, what do you want to know that for.

You not one of those free energy nuts are you?

3. Brett HoldenGuest

No free energy. Want to build Induction Balance metal detector. Coplanar
coils often use a bucking coil arrangement. Transmit coil has one segment
wound in reverse. The receive coil is positioned so as to have a null in the
absence of target. Target detection occurs when target upsets the balance.

http://www.deeptech-bg.com/round_coils/coplanar.pdf

4. Brett HoldenGuest

What are you, the Usenet police? I thought maybe you'd have an answer.
Thanks for NOTHING.

5. Brett HoldenGuest

I have found the problem. Not only did I manage to mangle the equations, I
was trying to read something into the problem that isn't there.

M will be an unknown between 0 and 1, depending on permeability of the
medium and physical proximity of coil sections. Equation 1 can stand alone.

Equations 2,3,and 4, relate M to the total inductances of two series coils
by taking measurments with coils in series wound and bucking configurations.
There is where the circular logic jumps up which I will happily ignore.

6. General PatronGuest

Brett Holden said the following on 2009-02-05 17:05:
No he is not, that would be me.

YW.