The treatment of geometrically small structures in FDTD by the modification of assigned material parameters

Abstract

Abstract-A number of different improvements to the analysis by finite-difference time-domain (FDTD) of small structures, such as wires, strips and slots have been proposed in the literature. One of these methods takes account of the fringing fields associated with metal edges and wires by empirically modifying the assigned material parameters in neighboring cells. In this contribution it is shown that, in many cases, it is possible to derive these modified assigned material parameters (MAMPs) analytically. In this form, the approach provides an alternative, and novel, way of incorporating Static Field Solutions into the FDTD method which has advantages of simplicity and robustness over existing techniques. Results are presented for a number of structures including wire transmission lines and a microstrip patch antenna.Index Terms-Author, please supply your own keywords or send a blank e-mail to keywords@ieee.org to receive a list of suggested keywords.

The Treatment of Thin Wire and Coaxial Structures in Lossless and Lossy Media in FDTD by the Modification of Assigned Material Parameters

“…The general concept of MAMPs within the FDTD method was described in detail in [4]. So, only the key steps are given here.…”

“…Applying these to an FDTD mesh in the usual way yields (3) and (4), shown at the bottom of the next page, where δx, δy, and δz are the cell sizes, i, j, and k are the serial numbers of the cell, a x is the average of the quantity, a, along an x directed cell edge and a xy is the average of the quantity, a, over an xy cell face. The other four update equations can be obtained by rotating the coordinates.…”

“…In [4], it was shown how, in many situations, MAMPs can be derived analytically, thus avoiding the need for the empirical look-up tables. It was demonstrated that the method was Manuscript effective in the analysis of stripline, wire transmission line, microstrip, and a strip-fed microstrip patch antenna.…”

Analysis of Structures Containing Sharp Oblique Metal Edges in FDTD Using MAMPs

“…It is well known that structures containing sharp metal edges which are aligned to the FDTD mesh can be efficiently analyzed using enhanced FDTD methods. Such enhancements include the use of static field solutions (SFSs), e.g., [3] or modified assigned material parameters (MAMPs), e.g., [4] to account for the singular nature of the field near the edge. In the former case, the FDTD algorithm is expressed as an instance of the method of weighted residuals with singular basis and test functions which take the place of the linear basis functions used in basic FDTD.…”

“…In the latter case, the effect of the singular behavior of the fields near the edge is accounted for by using an appropriately modified value of permittivity and permeability for the material surrounding the edge. The use of MAMPs has been shown to be simple and effective for a variety of situations including patch antennas [4], lossy coaxial structures [5], wires [6], [7] and microstrip transmission lines [4].…”