Calculation Methods for Single-Conductor Transmission Lines

Single-conductor transmission lines represent fundamental components in electromagnetic field and microwave technology, commonly used for analyzing key parameters such as characteristic impedance and propagation constants. These problems typically involve numerical solutions of Maxwell's equations, where MATLAB serves as an ideal computational tool due to its robust matrix operation capabilities. When implementing single-conductor transmission line calculations in MATLAB, several core aspects require consideration: First, establishing the geometric model of the transmission line, including physical characteristics like conductor dimensions and dielectric layer parameters. Then selecting appropriate numerical methods such as Finite Difference Method (FDM) or Method of Moments (MoM) to transform continuous electromagnetic field problems into discrete matrix operations. For single-conductor configurations, the absence of coupling effects allows simplification to two-dimensional electrostatic field solutions using MATLAB's PDE Toolbox or custom matrix solvers. Special attention must be paid to boundary condition handling during computation, particularly the conditions satisfied at conductor surfaces. Typically, conductor surfaces are treated as equipotential surfaces, while external boundaries of the computational domain require appropriate absorbing boundary conditions or truncation methods implemented through MATLAB's boundary condition functions. During results analysis, extraction of key parameters like characteristic impedance and propagation constants can be achieved through post-processing of computed field distributions using impedance calculation algorithms and field integration techniques. This computational approach not only applies to ideal conductor scenarios but can be extended to accommodate conductor losses and dielectric losses through complex permittivity modeling. By modifying parameter configurations in MATLAB scripts, researchers can efficiently investigate how different geometric dimensions and material parameters affect transmission characteristics, which holds significant value for antenna design and transmission line optimization. Code implementation typically involves matrix assembly for discretized domains, iterative solvers for large linear systems, and impedance extraction routines based on voltage-current relationships or field-based calculations.