Computer-Aided Design in Electromagnetics - the Case for Surface Impedance Boundary Conditions

Abstract

Surface impedance boundary conditions (SIBCs) have been successfully used for over 70 years in both analytical and numerical computation. With the need to model increasingly complex geometries and smaller artifacts, its importance in computer-aided design of electromagnetic devices has become prominent. High frequency SIBCs have been particularly successful because of the minimal penetration of electromagnetic fields in conductors and lossy dielectrics. SIBCs based on the skin depth have also been used although these have been limited to the first order (Leontovich) condition and Leontovich-like conditions. Little has been done in incorporating second order SIBCs and higher. A general method of derivation of SIBCs of arbitrary order is presented here and shown to apply to low frequency power structures including electric machines, transmission lines and nondestructive testing of materials. The proposed SIBCs are universally applicable and the order of the SIBC allows control of errors in design. Whereas low order SIBCs apply to classical flat surfaces and perpendicular diffusion, higher order conditions take into account curvatures and lateral diffusion of fields as well. Results shown include transmission line parameters, eddy current testing and other power applications in which they contribute to speed and accuracy of the design. In some cases, the use of SIBCs is not only possible but rather is critical to the very ability to obtain an acceptable design.

Keywords

• boundary element methods
• diffusion processes
• electromagnetics
• numerical analysis
• surface impedance boundary conditions