Multiple LOD-FDTD Method for Inhomogeneous Coupled Transmission Lines and Stability Analyses

A multiple locally 1-D (MLOD) finite-difference time-domain (FDTD) method for inhomogeneous coupled transmission lines and stability analyses are presented. The method is aptly called the MLOD coupled line (CL)-FDTD method. Various split matrices are proposed, and the corresponding update equations are formulated and discussed. All the proposed split matrices yield implicit electric field update equations with tridiagonal or block tridiagonal matrices on the left-hand sides. For more efficiency, the block tridiagonal matrices for implicit electric field may be reformulated and replaced with tridiagonal matrices for implicit magnetic field. The stability analysis is first performed using the von Neumann method in the Fourier domain. It is shown that the von Neumann method alone may not be sufficient to ascertain stability for inhomogeneous media. To include media inhomogeneity, the two-media reduced-matrix stability analysis is proposed. It allows us to efficiently analyze the key stability characteristics in inhomogeneous media and is useful for quick detection of any potential instability that is not apparent via the von Neumann method. The stability characteristics with variation of media parameters are also investigated and discussed. The numerical results are provided to validate the stability and accuracy of the proposed MLOD CL-FDTD method with various split matrices.