Quasi-Static Analysis of Multilayer Dielectrics Filled Coaxial Line Using Conformal Mapping Method

Abstract

Analytical solutions for characteristic impedance and effective permittivity of coaxial line filled with multilayer dielectrics are presented. Using the conformal mapping approach, the cross section of coaxial line filled with multilayer dielectrics in z-plane is mapped into cross section of parallel-plate filled with multilayer dielectrics in the t-plane. The capacitance per unit length keeps the same after conformal mapping. The capacitance per unit length is calculated in the t-plane using the classic parallel-plate capacitance calculation equation. Based on the capacitance per unit length, characteristic impedance and effective permittivity of coaxial line filled with multilayer dielectrics can be derived using transmission line theory. Finally, two examples are given to verify the results. The presented analytical solutions are accurate as well as efficient and are useful for transmission line theory and computer-aided design in microwave engineering.