Multipole-based cable braid electromagnetic penetration model: magnetic penetration case
The goal of this paper is to present, for the first time, calculations of the magnetic penetration case of a first principles multipole-based cable braid electromagnetic penetration model. As a first test case, a one-dimensional array of perfect electrically conducting wires, for which an analytical solution is known, is investigated: we compare both the self-inductance and the transfer inductance results from our first principles cable braid electromagnetic penetration model to those obtained using the analytical solution. These results are found in good agreement up to a radius to half spacing ratio of about 0.78, demonstrating a robustness needed for many commercial and non-commercial cables. We then analyze a second set of test cases of a square array of wires whose solution is the same as the one-dimensional array result and of a rhomboidal array whose solution can be estimated from Kley's model. As a final test case, we consider two layers of one-dimensional arrays of wires to investigate porpoising effects analytically. We find good agreement with analytical and Kley's results for these geometries, verifying our proposed multipole model. Note that only our multipole model accounts for the full dependence on the actual cable geometry which enables us to model more complicated cable geometries.