total inductance of bucking coils

[Brett Holden]

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
a variable, so I am grasping thin air. Can somebody please help me out?

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?
(headache)

Thanks for your help!

 

[Shaun]

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

You not one of those free energy nuts are you?

 

[Brett Holden]

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

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

You not one of those free energy nuts are you?

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
a variable, so I am grasping thin air. Can somebody please help me out?

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?
(headache)

Thanks for your help!

 

[Brett Holden]

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

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

You not one of those free energy nuts are you?

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
a variable, so I am grasping thin air. Can somebody please help me out?

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?
(headache)

Thanks for your help!

 

[Brett Holden]

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.

 

[General Patron]

Brett Holden said the following on 2009-02-05 17:05:

What are you, the Usenet police?

No he is not, that would be me.

Thanks for NOTHING.

YW.