The purpose of this paper is to provide a tutorial of the FDTD method and its ..... As a second illustration, lets consider the analysis of a. Thermal Conduction .... W. C. Chew and W. H. Weedon, âA 3D perfectly matched medium from modified ...
The Application of the Finite-Difference Time-Domain Method to EMC Analysis StephenD. Gedney University of Kentucky Departmentof Electrical Engineering Lexington, KY 40506-0046 &s&r&. The purposeof this paper is to provide a tutorial of the FDTD method and its application to the full-wave analysis of practical EMC problems. The FDTD method is a versatile techniqueand a powerfbl tool that can allow for the efficient and accurate simulation of electromagnetic interaction and radiation for EMC analysis. The presentationwill begin with an introduction to the FDTD method based on the traditional Yee-algorithm. For the analysis of radiating structures, various absorbing boundary conditions, including the novel Perfectly Matched Layer (PML) absorbingboundary condition, and their relative performanceswill be described. Techniques of computing radiated fields from the time-dependent fields will also be discussed. Included in this discussion will be the limitations of modeling complex structures using regular lattice grids, as well as the benefits of advanced FDTD algorithms that utilize irregular and unstructured grids. Acceleration techniques and the efficient implementation of the FDTD method on high performancecomputerswill also be of concern. Finally, a number of practical EMC problems analyzed using the FDTD method will be presented.
via the FDTD method [3]. Correspondingly, the FDTD method has received extraordinarypopularity over the last 5 years. If the FDTD algorithm is to be a truly viable design tool in industry, it will be necessary to obtain reasonable computational speeds on inexpensive workstations. This will require advancedalgorithms and acceleration techniques, as well as affordable highperformancecomputing.
THE FDTD ALGOFUTHM The FDTD algorithm is traditionally based central difference approximations of the temporal and spatial derivativesof Maxwell’s curl equations:
(1) By staggeringthe discrete electric and magnetic fields in space and time, this leads to a second order accurate approximation,from which an explicit update schemecan be derived. For example, the explicit update expression for Er__is:
E,”i++c
Introduction Over the last decade, the Finite-Difference TimeDomain (FDTD) method has become one of the most widely used computational techniques for the full wave analysis of electromagneticphenomena.Its popularity can be accredited to the simplicity of the algorithm, while providing a robust and accurate analysis of electromagneticfields [l]. Since it is based on a volume discretization, three-dimensionalmaterial inhomogeneities are inherently modeled, allowing for the analysisof planar stratified medium, non-planar devices, devices on finite dielectric substrates and ground planes, and lossy conductors and dielectrics. Lumped or hybrid elements including passiveloads and active elements [2] can also be incorporated into the discrete Maxwell’s equations. Other recent advances in absorbing boundary conditions have provided for the accurate broad-band analysis of printed circuits and antennasin unboundedmedium [ 11. Finally, both broad-bandanalysis and narrow-bandcharacteristics of devices can be obtainedwith a single FDTD simulation. In the last decade,the introduction of inexpensivehighspeed memory, powerful vector processors, high-speed RISC processors,and the maturation of high-performance parallel computers has provided the economical and powerful computational resources that are necessary to perform the analysis of practical engineeringapplications O-7803-3207-5/96/$5.00
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(2) Given the initial condition for the fields, this recursive update scheme can be used to explicitly calculate the vector fields in the entire space in discrete time. The explicit field update expression is stable, provided, the discrete time step satisfies the stability criterion At. . . . . . . . . . . . y..
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Near end (a) and Far end (b) line voltages of the coupled lines in Fig. 5 excited by a 2 V trapezoidalpulse with 50 R matched load and a 30 ps rise time and fall time and 70 ps duration.
