inductance/flux calculations in 2D/3D

[corneliuspaul@xxxxxx]

Dave meeker wrote:

>The discrepancy in inductance between a 2-D and 3-D model is typically much

>smaller than a factor of 2 error.   It sounds like your rationale is that 
>since you have a nearly square cross-section and the end-turns aren't taken

>into account, you'll have about a factor of 2 error in total flux.  It 
>doesn't work quite like that. Think about this terms of magnetic 
>circuits--the only parts of the wire that actually "drive" flux are those 
>that get encircled by the flux path.  The part of the winding that actually

>drives the primary, desirable part of the flux in the transformer is the 
>coils that passes through the "winding window" in the transformer, because 

>the flux flowing through the core circles this part of the winding.  In 
>contrast, the only flux that actually encircles the end turns is leakage 
>flux, traveling on a highly flux reluctant path, mostly through air.    
>Because this end turn leakage path is highly reluctant relative to the 
>primary flux path (hopefully), it doesn't add much inductance to the model.
  
>At least, this is the basic rationale in using a 2-D approximation... 


OK Dave, many thanks for the advice.
I tried out some configurations and it really seems to work 
in practice and I am ready to accept it as the "basic rationale"

Although I still have difficulties understanding WHY it is like that.
A very simple hypothetical experiment:

- take a core with a quadratic cross section

- wind a one turn coil around it. that is, this coil consists of
4 wires, each on every side of the core

- now every wire produces a H-Field around it H = I/(2*pi*r) 
where r is the distance from the wire surface, I is current

- if the core is of linear material then B = mu * H

- flux = integrate B over cross section

THIS IS WHY I "FEEL" EVERY ONE OF THE 4 WIRES PRODUCES ONE FOURTH
OF THE INDUCTION OR FLUX IN THE CORE.

WHERE DOES "the only parts of the wire that actually "drive" flux are those 

that get encircled by the flux path" COME FROM???

what am I missing ?

regards,
Cornelius




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