Electromagnetic Behaviour of Metallic Wire Structures by S. T. Chui & Lei Zhou

Author:S. T. Chui & Lei Zhou
Language: eng
Format: epub
Publisher: Springer London, London

with the inverse transform

(5.1a)

Here is the two end of a wire segment, is an integer, and where d is the wire length. Different from the single wire case, the currents at the two ends of a wire segment are no longer symmetrically related to each other. In the Fourier expansion, we have doubled the period to take this into consideration. The issue of padding is well-known in algorithms for fast Fourier transforms. There are different ways by which the function X can be extended to this new region. If one is careful, the result will be the same. One way is to set X to be symmetrically related to that in the original domain: for . We have chosen to set the current and the charge densities to be zero from to x 2 . Thus the range of integration in Eq. (5.1a) is then only of size d for those functions. If only the components with even h are nonzero, we retrieve the result of the previous sections of a single wire. With this choice, there are some mathematical issues which fortunately do not invalidate the final answer. We shall discuss this at the end of this chapter.

As usual the “inductive” and the “capacitive” electric fields can be recast into a matrix form in terms of the wire currents and impedances

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