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IEVref:221-04-31ID:
Language:enStatus: Standard
Term: effective dimensions (of a magnetic circuit) pl
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Definition: for a magnetic core operating within the Rayleigh region, and having given geometry and material properties, the magnetic path length, the cross-sectional area and the volume that a hypothetical toroidal core of the same material properties and of radially thin uniform cross-section should possess to be magnetically equivalent to the given core

Note 1 – The effective dimensions are as follows:

effective cross-sectional area

A e = C 1 C 2 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadgeadaWgaaqcbauaaiaabwgaaKqaGfqaaOGaeyypa0ZaaSaaaeaacaWGdbWaaSbaaKqaGfaacaaIXaaabeaaaOqaaiaadoeadaWgaaqcbawaaiaaikdaaSqabaaaaaaa@3D23@

effective magnetic path length,

l e = C 1 2 C 2 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadYgadaWgaaqcbauaaiaabwgaaKqaGfqaaOGaeyypa0ZaaSaaaeaacaWGdbWaa0baaKqaGfaacaaIXaaabaGaaGOmaaaaaOqaaiaadoeadaWgaaqcbawaaiaaikdaaSqabaaaaaaa@3E0B@

effective volume,

V e = C 1 3 C 2 2 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadAfadaWgaaqcbauaaiaabwgaaKqaGfqaaOGaeyypa0ZaaSaaaeaacaWGdbWaa0baaKqaGfaacaaIXaaabaGaaG4maaaaaOqaaiaadoeadaqhaaqcbawaaiaaikdaaeaacaaIYaaaaaaaaaa@3EA8@

where C1 and C2 are the appropriate core factors hence:

C 1 = l e A e MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadoeadaWgaaqcbawaaiaaigdaaeqaaOGaeyypa0ZaaSaaaeaacaWGSbWaaSbaaKqaGfaacaqGLbaabeaaaOqaaiaadgeadaWgaaqcbawaaiaabwgaaSqabaaaaaaa@3D2E@

C 2 = l e A e 2 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadoeadaWgaaqcbauaaiaaikdaaKqaGfqaaOGaeyypa0ZaaSaaaeaacaWGSbWaaSbaaSqaaiaabwgaaeqaaaGcbaGaamyqamaaDaaajeaybaGaaeyzaaqaaiaaikdaaaaaaaaa@3DCC@

V e = l e A e MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadAfadaWgaaqcbawaaiaabwgaaSqabaGccqGH9aqpcaWGSbWaaSbaaKqaGfaaciGGLbaaleqaaOGaamyqamaaBaaajeaybaGaciyzaaWcbeaaaaa@3D7A@

Note 2 – These formulae can also apply to a magnetic circuit operating outside the limit of the Rayleigh region provided the magnetization can be assumed to be uniform, for example as in an Epstein square.


Publication date:1990-10
Source:
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Internal notes:2017-06-02: Cleanup - Remove Attached Image 221-04-311.gif

2017-06-02: Cleanup - Remove Attached Image 221-04-312.gif

2017-06-02: Cleanup - Remove Attached Image 221-04-313.gif

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2017-08-28: Corrected <mstyle> to </mstyle>. LMO
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