Interconnected Multi-1-D FADI- and FLOD-FDTD Methods for Transmission Lines With Interjunctions

This paper presents the interconnected multi-1-D (IM1-D) fundamental alternating-direction-implicit finite-difference time-domain (FADI-FDTD) and fundamental locally 1-D finite-difference time-domain (FLOD-FDTD) methods for transmission lines with interjunctions. The proposed methods are unconditionally stable and capable of treating multiple main transmission lines and stubs interconnected at various interjunctions using time step larger than Courant-Friedrichs-Lewy limit. Fundamental scheme-based IM1-D FADI- and FLOD-FDTD methods are derived to enhance the efficiency with matrix-operator-free right-hand sides. The methods involve one-step update procedure optimized for simulation of main transmission lines and stubs on mobile device. Using proper treatments at the interjunctions for various interconnection conditions, the electromagnetic fields in all interconnected main transmission lines and stubs can be updated cooperatively and efficiently to solve practical problems. A microstrip line loaded with stubs and a branch-line coupler are simulated to show the accuracy and efficiency of the proposed methods. To extend the applicability for handling the couplings between two transmission lines via gaps, a microstrip circuit with gaps is simulated using the proposed methods incorporated with equivalent circuit models involving capacitances. Real-time simulations of these numerical examples provide much intuitional insight for one to observe the electromagnetic waves propagation in time domain on computer or mobile device.