self inductance calculation.. need advice

[corneliuspaul@xxxxxx]

Dear all,

I have a question about calculating self inductances in a 
transformer coil in 2D models. 
could you please comment on my understanding of the situation?

the standard magnetostatic method is to drive the winding in question 
with a current of one ampere and let FEA calculate the total energy E.
once you have calculated the total field energy you easily compute
the inductance L by the formula:
E = 0.5 L * I^2 --> L = 2E/I^2 --> L=2E for I=1amp

so far so good...
but what happens when we model the geometry in 2D?
consider we have a core with a quadratic cross section 
(width a * depth a millimeters)
and a quadratic coil wound around it 
(width b * depth b millimeters). 
let the coil and core be of height c millimeters.

our 2D model shows the core as a rectangle of c * a millimeters 
(and infinite depth into the z direction). 
the coil wires can only be modeled as their cross sections on either 
side of the core, spaced b millimeters apart. They also extend into
infinite depth.
that is, in reality I do not model a coil but I model an infinetely long
transmission line with a ferrite core in between the 2 conductors.
the other 2 coil wires do not show up in the model at all: going from 
left to right in front of the core and from right to left behind the core.

if I calculate the field energy of this model and compute the inductance
by the formula given above, the resulting Inductance is in Henries per
unit depth (normally Henries per meter). 

the question is: how do I compute the inductance for the real coil
from this value for the inductance/meter of the transmission line model?

do I multiply by core depth a or by coil depth b?

and much more of interest: am I not missing out the field (energy) that
is generated by the other 2 coil wires that do not show up in the model at
all??
if the coil depth into z direction is much bigger than the coil width this
does not matter, but in my case the coil depth and coil width are equal 
b=b.

so do I have to multiply the value by 2?

this, of course becomes even more interesting if the core has a quadratic
cross section and the coil has a circular cross section.
by which factor k do I multiply then? 
k = (circumference of circular coil)/2b...?

the same questions arise when calculating the flux density in the core:
my feeling is that by using the infinitely long transmission line model
I am calculating too low a flux density in the core, because I am missing
out on the flux generated by the missing wires in the model.

you see, I am a bit confused. 
any comments would be helpful.


have a nice weekend!
regards, cornelius





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