Multiple One-Dimensional FDTD Method for Coupled Transmission Lines and Stability Condition

This letter presents the multiple one-dimensional (M1-D) finite-difference time-domain (FDTD) method for coupled transmission lines and its stability condition. The coupled transmission line parameters based on even- and odd-mode approach are incorporated directly into the M1-D FDTD method, whose update equations are provided in detail. Using the M1-D FDTD method, the fine mesh required for the line width and spacing of coupled transmission lines can be omitted. The stability condition of the M1-D FDTD method for coupled transmission lines is determined. It is noted that the time step limit is different from (and usually more restrictive than) that for the single transmission line. To show the usefulness of the M1-D FDTD method for time-domain analysis, the coupled transmission lines are used to illustrate the real-time visualization of electromagnetic fields and to verify the stability condition. Microstrip filters with coupled lines are simulated to further validate the proposed method in frequency domain.