| It has been a great challenge for years to accurately solve complicated electromagnetic problems, especially using analytical approaches. With the aid of modern computer technology, finding a complete full-wave solution of the Maxwell's equations has become achievable using various numerical techniques. The Finite Difference Time Domain (FDTD) algorithm, introduced by K. S. Yee in 1966, is a generalized time domain Maxwell's solution tool that can, in principle, solve a wide category of practical electromagnetic problems. The FDTD algorithm utilizes the direct discretization of the time-dependent Maxwell's equations by expanding the time and spatial derivatives in a central difference format while retaining the second-order accuracy. It requires the electric and magnetic fields to be updated separately at halftime steps, and to be offset from one another in space. The updated time-stepping equations are explicit so that they are easily implemented in computer programming. This research work is to develop a generalized FDTD Maxwell's solver, based on the FDTD approximations of the Maxwell's equations in the Cartesian coordinate system, and to further apply it to the analysis of diverse monolithic millimeter-wave integrated circuit (MMIC) structures for predicting their corresponding characteristics. Various types of boundary conditions, including three types of absorbing boundary conditions (ABCs), are fully studied for mesh truncations in the computational space-domain. The research includes an extensive validation for a number of integrated structures through comparisons with the available results published in literature, and an intensive design of practical MMIC structures, such as integrated printed filters and planar inverted-F antennas (PIFAs).; It has been demonstrated in this research that the FDTD is a powerful, robust, and full-wave tool due to its flexibility for describing and modelling complex-shaped geometry, broad frequency band computation with only a single run, straightforward time-stepping algorithm without matrix operations, and a great capability for handling a huge amount of field unknowns. |
