The Non-uniform Finite-Difference Time-Domain Method

The principles and applications of the finite-difference time-domain method (FDTD) with the emphasis on non-uniform FDTD and contour-path integral method are studied in detail in this paper. And the non-uniform FDTD method is adopted to analyze some microwave circuits with some nonstandard structures. First, we reviewed the finite-difference time-domain Yee?s method. The difference equations, the stability condition, numerical dispersion characteristic and absorbing boundary condition are discussed. Second, general non-uniform difference equations are discussed. Contour-path law with integral model is applied in non-uniform grid, so we can obtain the integral equations on the boundary of different grid length. Then non-uniform difference equations are derived by numerical central differences in time and space domain. Based on the non-uniform FDTD algorithm, the stability condition, non-physics reflections and absorbing boundary condition (ABC) include Mur ABC and perfectly matched layers (PML) in non-uniform mesh are studied. As a special example named expanding grid, numerical dispersion characteristic is derived. Finally, the calculations of the scattering parameters about microstnp low-pass filter and thin film capacitance show the merit of the non-uniform FDTD algorithm. Finally, for thin media or narrow slot, the contour-path concept is illustrated. The contour-path integral comes from Ampere and Faraday's laws. The principles and applications of the contour-path method are interpreted by two examples. One is a narrow slot penetrating a planar PEC screen of finite size. Other is the thin planar material sheet. Finally, the calculations of the scattering parameters about thin film capacitance show this method clearly.