Re: [femm] Comparing inductance predictions: femm vs standard formula

[David Meeker <dmeeker@xxxxxxxx>]

Dan Haronian wrote:

> Hi David
>  
> I wonder if you could help me with the following question:
>  
> Self inductance of wire with rectangular cross section is given by
>  
> 2*L[Ln(2*L/(w+t)+0.5+0.22*(w+t)/L]
>  
> L is the length of the inductor, W and t are the width and height.
>  
> I was expecting to see the inductance to go to zero when w or t go to 
> zero but this is not the case. 
>  
> Do you have a more accurate equation?
>  
> Thanks
>  
> Dan Haronian
> Israel
>  

The inductance of a single wire with no return isn't a well-defined 
problem. There are some formulas (which I think were cribbed from 
Grover) at:
http://home.san.rr.com/bushnell/self_inductance.htm
but don't use the one for the various single conductor cases unless you 
know what you are doing. I also haven't verified that these formulas 
have been _accurately_ cribbed from Grover....

At any rate, one can't model a single-conductor inductance problem by a 
2D planar analysis in FEMM.  Some return path for the current is always 
implied by the boundary conditions that you draw for the finite element 
solution -- the per-unit-length inductance of a single conductor in a 
truly unbounded 2D planar domain is infinite.

Inductance converges to finite, nonzero values if a coil is thin in one 
dimension.  Inductance is infinite for a 2D or axisymmetric point 
current.  If you try to simulate a point current in FEMM, the inductance 
that you obtain is strongly dependent on mesh density, with the 
inductance going to infinity as the mesh size goes to zero.

--
David Meeker
dmeeker@xxxxxxxx
http://femm.berlios.de/dmeeker