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 (2nd order accurate) is employed

Yee Cell (Typically Used for FDTD)

FDTD Background

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FD Approximation

(Central-difference)(Forward-difference)(Reverse-difference)

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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

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Ez in xz-plane radiated by dipole ( l = 2, a = 0.005 ) at timestep = 30

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Dr. Anthony Martin Chaitanya Sreerama

Acknowledgements

Dr. Daniel Noneaker Dr. Xiao-Bang Xu

Antenna Modeling Using FDTDMichael FryeFaculty 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