By Dragan Poljak
This article combines the basics of electromagnetics with numerical modeling to take on a extensive diversity of present electromagnetic compatibility (EMC) difficulties, together with issues of lightning, transmission traces, and grounding platforms. It units forth a pretty good origin within the fundamentals ahead of advancing to really expert themes, and permits readers to improve their very own EMC computational types for purposes in either learn and undefined.
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Extra info for Advanced Modeling in Computational Electromagnetic Compatibility
In particular, if there is an energy source, then the product EJ is negative for that source and represents energy ﬂow out of the region. The other term on the right-hand side gives the ﬂow in through the domain boundary. 66) Z ~ ÞdV ¼ r Á ð~ E xH V I ~ Þ Á d~ ð~ E xH S ð2:67Þ S the volume integral transforms to the surface integral over the boundary, where d~ S is the outward drawn normal vector surface element. Since all the energy changes must be supplied externally, this term represents the energy ﬂow into the volume per unit time due to a minus sign of the surface integral.
126). There are also many magnetostatic problems concerned with ﬁnding magnetic ﬁelds, in which at least a part of the domain of interest is free of electric currents. For such source-free domains, the curl of the magnetic ﬁeld H is equal to zero, ~¼0 rxH ð2:127Þ Since any zero-curl vector can be represented in terms of the gradient of a scalar function, the magnetic ﬁeld intensity for such cases may be written as ~ ¼ Àrjm H ð2:128Þ where the minus sign is taken to provide a convenient analogy with the case of electrostatic potential.
The magnetic ﬂux ﬂowing through the contour is given by the contour integral of the vector potential A. 8 The interface between two media. 9 Interface at a surface between two different materials. Substituting B in terms of the vector potential A, it follows Z f ¼ rx~ Ad~ S ð2:130Þ S Applying the Stokes theorem, the integration can be performed over the close contour c as follows: I Ad~ s ð2:131Þ f¼ ~ c The surface spanned by the contour can be made arbitrarily small by keeping the two long sides of the contour arbitrarily close to each other while remaining at opposite sides of the material interface.