Finite-difference time-domain modeling of longitudinally periodic boundary stripline based on Floquet's theorem

Abstract

An efficient numerical method for full-wave analysis of waveguiding structure constructed by longitudinally periodic boundary condition was presented and employed to study several periodic structures. The wave propagation property in periodic waveguide can be considered just by solving electromagnetic problem in a single unit-cell. In the second chapter of this dissertation, two original contributions are presented. Firstly, for the first time, a concrete formulation for time-domain representation of Floquet’s propagation mode is derived in this work. The relation between the frequency-domain and the time-domain representation of the Floquet’s propagating mode in longitudinally periodic (LP) structure is carefully presented. It is also well explained why time-domain complex variables exists in Floquet’s propagation mode representation. Secondly, a new spatial grid scheme is invented. In the presented spatial grid scheme, the real part and the imaginary part of each field component are staggered by a half of longitudinal spatial increment, which results in the reduction of the computation time in the finite-difference time-domain (FDTD) simulation employing LP boundary condition. In addition, the numerical accuracy of the presented FDTD scheme is also carefully discussed based on spatial harmonic analysis, from which the effect of numerical parameter such as size of the spatial grid and size of time step is evaluated. In the third chapter, the effective electrical delay by employment of meander delay line is evaluated. In particular, the meander effect on the propagation delay and the characteristic impedance is carefully discussed. To guarantee the best quality of the transmitted signal, the stop-band frequency of the employed meander line must be larger than the cut-off frequency of signal. The manufacturing tolerance is also discussed. The presented stop-band characteristic of meander line is very useful in filter design. As well known, meander line is very ...