OFR-14-74 Statistical Evaluation And Mitigation Of Inductive Interference Problems In Portable Power Cables - Section I - Analytical Predictions Of Induced Voltages And Current

1.1 DEVELOPMENT OF INDUCTANCE MATRICES The basic building block in this analytical work is the development of an equivalent circuit. The equivalent circuit for the cable depends on all of the distributed parameters of the cable although the series inductance and resistance are of primary importance. The cable resistances are generally available from handbooks or from cable manufacturers. On the other hand, the cable inductances are not usually available either from handbooks or from the manufacturer's published data. Thus, it is useful to summarize the derivation of the origin of the inductance matrix from basic principles. 1.1.1 Flux Around a Cylindrical Conductor The flux pattern around a cylindrical current carrying conductor can be found by using symmetry in conjunction with Ampere's Law. From symmetry it is clear that the flux lines which always close on themselves must be concentric circles. Thus, from symmetry alone one can get a qualitative picture of the magnetic field. This is shown in Fig. 1.1 where the inner circle represents the solid round conductor and the outer circle represents a flux line. The quantitative picture will now be developed using Ampere's Law.