Simple deterministic solutions for cables over a ground plane or in an enclosure

The use of statistical electromagnetics to determine cable currents in an enclosure consists of two basic parts: (1) determination of the probability density function (PDF) for the ambient electromagnetic fields and (2) substitution of this field PDF in cable-coupling formulas to evaluate the PDF for the cable currents. The application of the work reported here pertains to the second of these operations. Previously, determination of cable-current PDFs was a fairly tedious process involving the solution of finite-difference-like transmission-line equations. Unlike the field-distribution PDFs, the cable-current PDFs could not be expressed, or even approximated, in closed form. The contribution reported here relates the unknown cable-current PDFs to the known field PDFs in closed form and does not require the manipulation of finite-difference entities. Additionally, it turns out that some rather arcane issues concerning the autocorrelation of the electromagnetic cable-driving fields as functions of position or frequency no longer seem to matter.