Calculation of per-unit-length resistance and internal inductance in 2-D skin-effect current driven problems

The study of two-dimensional (2-D) skin-effect transient problems by means of a formulation based on a magnetic vector potential A and on a scalar potential φ is presented. It is shown that such 2-D problems in the cross-sectional plane of the conductors cannot be treated as voltage driven but only as current driven. As an application of the proposed method, the equivalent per-unit-length resistance and internal inductance of conductors carrying typical switch-mode power supplies nonsinusoidal current waveforms have been evaluated. The analysis clearly reveals that they depend both on switching frequency and duty cycle, and are rather different from dc and ac sinusoidal equivalent parameters. Time-varying instantaneous ohmic resistances and internal inductances can be also defined in sinusoidal steady-state as well as in generic operating conditions.