Dipole Driving Point Impedance Comparison  Dipole antenna modeled: length = 2m, radius = 0.005m  Frequency range of interest: 25MHz=500MHz  Comparison Method: Method of Moments (MoM) patch code  Antenna and EM Modeling with MATLAB -Sergey Makarov  These codes provided a method to quantitatively determine the validity and accuracy of the dipole modeled in FDTD The Finite-Difference Time-Domain Method  Computer-based numerical technique  Models electromagnetic phenomenon (radiation, scattering, etc.) FDTD Modeling Approach  Discrete approximation of Maxwell’s Equations in differential, time-domain form Ampere’s Law Faraday’s Law  First-order derivatives in time and space replaced with finite-difference approximations  “Update equations” developed for the explicit calculation of each field component value at current time step  Once all field values are determined for a given time step, the data is used to determine field values for next time step  In this way, the solution is “marched in time” Finite-difference Approx.  Approximation of first derivative at point ‘b’  For typical FDTD formulations, central-difference (2 nd order accurate) is employed Yee Cell (Typically Used for FDTD) FDTD Background Exact Value FD Approximation (Central-difference) (Forward-difference) (Reverse-difference) Antenna Model in FDTD Uniaxial Perfectly Matched Layer  Reflectionless and conductive material layer surrounding 3D FDTD computational grid  Similar to walls in anechoic chamber  Allows antennas to be simulated as radiating into infinite open space while using a finite grid Gap-Feed Method  Provides problem excitation  Relates incident voltage to E field in feeding gap  Added to tangential E field component along wire length  Shows very little dependence on grid size Contour Path Model for Thin Wires  Sub-cellular technique allowing wire radius to be independent of cell size  Uses integral form of Faraday’s Law to develop special update equations for field components immediately around thin wire  Near-field physics behavior built into field components Basis of 3D FDTD computational grid Field components displaced in space and time E and H field locations interlocked in space Visualization of Dipole Radiation  Graphs below depict the Ez fields in the xy-plane radiated by a z-directed dipole antenna (length 2m, radius 0.005m)  Fields are radiated into a 3D FDTD computational grid completely surrounded by a UPML region  Antenna is excited using the gap-feed method with a Differentiated Gaussian pulse input voltage waveform Ez fields in xy-plane radiated by dipole antenna  Tangential E fields set to zero (shown in green)  Radial E and H fields decay as 1/r, where r is distance from the center of the wire (shown in blue) Dipole Modeling Results  Near Field to Far Field transformation technique  Radiation patterns for modeled antennas  Determination of wideband Far Zone information  Design/analysis of reconfigurable antennas  Modeling of antennas with nonlinear switching devices  Beneficial to be studied with time-domain approach Future Work timestep = 30timestep = 60timestep = 120  Dr. Anthony Martin  Chaitanya Sreerama Acknowledgements  Dr. Daniel Noneaker  Dr. Xiao-Bang Xu Antenna Modeling Using FDTD Michael Frye Faculty Research Advisor: Dr. Anthony Martin Comparison of Driving-Point Impedance Conclusions  Driving point impedance of dipole antenna calculated by the FDTD model compares well to Makarov’s MoM model  The solution is seen to quickly converge to the MoM solution as the number of grid cells per minimum wavelength is increased