Solving EM Fields Equations using Finite Difference Method for a 5G Microstrip Patch Antenna Operating at 28 GHz

Abstract

This study aims to analyze and solve the electromagnetic field equations for a rectangular microstrip patch antenna operating at 28 GHz, designed for 5G applications, using both analytical and numerical approached. The study begins with precise mathematical modeling based on Maxwell’s equations to derive a representative equation, applying appropriate boundary conditions for perfect conductors. The analytical solution is obtained using separation of variables, providing a detailed description of the electric and magnetic field distributions within the cavity. On the numerical side, the finite difference method (FDM) is employed to solve the mathematical model of the rectangular microstrip patch antenna, with the Gauss-Seidel method applied for iterative solution. The electric field component  is computed using a second-order central difference approximation, but the magnetic field component  is calculated using a first-order central difference approximation. The numerical results show good agreement with the analytical solution, confirming the accuracy of the implemented algorithm. Furthermore, the study of the effect of segment numbers on accuracy reveals that increasing the number of segments significantly reduces the error. Additionally, the numerical properties are analyzed, including truncation error, accuracy, consistency, convergence, and stability. The analyses indicate that the numerical solution achieves second-order accuracy , is fully consistent, stable, and converges to the analytical solution as the segment size decreases.