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Area Magnetic materials and components / Magnetic bodies

IEV ref221-04-31

en
effective dimensions (of a magnetic circuit) pl
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.


fr
dimensions équivalentes (d'un circuit magnétique) f pl
dimensions effectives (d'un circuit magnétique) f pl
pour un noyau magnétique de géométrie donnée en un matériau donné, fonctionnant dans le domaine de Rayleigh, longueur du chemin magnétique, section transversale et volume qu'un tore fictif constitué du même matériau et de section droite homogène et radialement mince devrait avoir pour être magnétiquement équivalent au noyau donné

Note 1 – Les dimensions équivalentes sont les suivantes:

section droite équivalente (ou effective)

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

longueur de chemin magnétique équivalente (ou effective)

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

volume équivalent (ou effectif)

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

C1, et C2 sont les coefficients de noyau appropriés; il en résulte:

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 – Ces formules peuvent aussi s'appliquer à un circuit magnétique fonctionnant hors des limites du domaine de Rayleigh si l'aimantation peut être considérée comme uniforme, par exemple dans le cadre d'Epstein.


ar
عامل القلب C2

de
effektive Abmessungen (eines magnetischen Kreises), f, pl

es
dimensiones efectivas (de un circuito magnético)
dimensiones equivalentes (de un circuito magnético)

it
dimensioni equivalenti (di un circuito magnetico)
dimensioni effettive (di un circuito magnetico)

ja
実効(断面積,磁路長,体積), <磁気回路の>

pl
wymiary równoważne obwodu magnetycznego

pt
dimensões equivalentes (de um circuito magnético)

sv
effektiva dimensioner hos magnetisk krets

Publication date: 1990-10
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