A transient solver for current density in thin conductors for magnetoquasistatic conditions

Abstract

A computer simulation of transient current density distributions in thin conductors was developed using a time-stepped implementation of the integral equation method on a finite element mesh. A study of current distributions in thin conductors was carried out using AC analysis methods. The study of the AC current density distributions was used to develop a circuit theory model for the thin conductor which was then used to determine the nature of its transient response. This model was used to support the design and evaluation of the transient current density solver.

A circuit model for strip lines was made using the Partial Inductance Method to allow for simulations with the SPICE circuit solver. Magnetic probes were designed and tested that allow for physical measurements of voltages induced by the magnetic field generated by the current distributions in the strip line. A comparison of the measured voltages to simulated values from SPICE was done to validate the SPICE model. This model was used to validate the finite-integration model for the same strip line.

Formulation of the transient current density distribution problem is accomplished by the superposition of a source current and an eddy current distribution on the same space. The mathematical derivation and implementation of the time-stepping algorithm to the finite element model is explicitly shown for a surface mesh with triangular elements. A C++ computer program was written to solve for the total current density in a thin conductor by implementing the time-stepping integral formulation.

Evaluation of the finite element implementation was made regarding mesh size. Finite element meshes of increasing node density were simulated for the same structure until a smooth current density distribution profile was observed. The transient current density solver was validated by comparing simulations with AC conduction and transient response simulations of the SPICE model. Transient responses are compared for inputs at different frequencies and for varying time steps. This program is applied to thin conductors of irregular shape.