antenna modeling using fdtd sure program 2004 clemson university michael frye faculty advisor: dr....
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Antenna Modeling Using FDTD
SURE Program 2004Clemson University
Michael FryeFaculty Advisor: Dr. Anthony Martin
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Presentation Outline
General Finite-Difference Time-Domain Method (FDTD) Modeling Approach
Formulation of Antenna Model in FDTD
Dipole Driving-Point Impedance Comparison
Future Work
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What is FDTD?
Numerical technique Computer based (computationally intensive) Time-domain solution
Modeling of electromagnetic phenomenon Radiation, scattering, etc.
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One FDTD Application
Specific absorption rate distribution of 1,900MHz cell phone held against tilted head model
Comp. Electrodynamics Taflove and
Hagness
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FDTD Modeling Approach
Approximation of Maxwell’s Curl Equations Faraday’s Law and Ampere’s Law
Differential, time-domain form
First-order derivatives (time and space) replaced with finite-difference approximations
“Update equations” developed for calculation of field values in a discrete 3D grid
1
t
H
E1
t
E
H
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Simple Finite-Difference Example Exact Value
FD Approximation
(Central-difference)
(Forward-difference)
(Reverse-difference)
lim0( ) ( )( )
xc abx
ƒ ƒƒ
( ) ( )( ) c abx
ƒ ƒƒ
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Development of update equations Consider Ex component equation of Ampere’s Law
Simply problem by reducing to 2D (for illustration)
Choose to evaluate at time: t=n and location: x=i, y=j
1Ex Hz Hy
t y z
1Ex Hz
t y
, ,
,
| |1
|
n ni j i j
i j
Ex Hz
t y
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Development of update equations Approx. time derivative with central-difference
Resulting expression (Ex and Hz displaced in time)
Hz evaluated at integer time-steps Ex evaluated at integer +/- ½ time-steps
1/ 2 1/ 2, , ,| | |n n ni j i j i jEx Ex Ex
t t
1/ 2 1/ 2, , ,
,
| | |1
|
n n ni j i j i j
i j
Ex Ex Hz
t y
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Development of update equations Approx. spatial partial derivative with central-difference
Result: Ex and Hz also displaced in space
Hz evaluated at integer +/- ½ y points along grid Ex evaluated at integer y points along grid
, 1 2 , 1 2, | || n nni j i ji j Hz HzHz
y y
1/ 2 1/ 2, 1 2 , 1 2, ,
,
| || | 1
|
n nn ni j i ji j i j
i j
Hz HzEx Ex
t y
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Development of update equations Resulting update equation for Ex for 2D case
Fully explicit solution for each Ex point on grid Only information at previous time steps needed No matrix inversion needed (Implicit solution)
Introduces stability issues (Courant condition) Species maximum ratio of spatial and time step
Remaining update equations derived similarly Faraday’s law provides H component update equations
1/ 2 1/ 2, , , 1 2 , 1 2
,
1| | | |
|n n n ni j i j i j i j
i j
tEx Ex Hz Hz
y
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Yee Cell (Typically Used for FDTD)
Basis of 3D computational grid Builds lattice of Yee cells
Field components displaced in space and time
E and H field locations interlocked in space
Solution is “time-stepped”
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Antenna model in FDTD
Basic elements for FDTD antenna model Open region
Infinite computational grid Contains antenna, modeled structures, etc.
Representation of antenna structure in FDTD grid Thin-wire model (one example)
Voltage feed Provides antenna excitation
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Uniaxial Perfectly Matched Layer Problem: FDTD grid cannot be “infinite”
Implies unlimited computational time and resources
Solution: Truncate with conductive material layer Similar to walls in anechoic chamber Allows antennas to be simulated as radiating into open space
with a finite FDTD grid
Desired characteristics Reflectionless boundary regardless of incident field polarization
or angle Incident fields attenuated to zero (through conductivity) Reasonably small addition to computational grid
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3D FDTD Grid Truncated by UPML
The PML on the Top
The PML on the Left
PEC wall
UPML region
Free space region
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Thin-wire FDTD model
Consider modeling a very thin wire Needed for dipole, monopole, etc.
Option 1: Decrease cell size fit wire into cell Diameter of wire equals cell width Significantly increases computation time Cubic approx. of circular cross-section
Option 2: Use sub-cellular modeling techniques Modeled features can be smaller than FDTD grid size Cell size independent of wire radius
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Faraday’s Law contour path model Uses integral form of Faraday’s Law
Results not obvious from differential FD approach Special update equations developed
Affects field components immediately around wire
Near-field physics behavior built into field values immediately around wire Tangential E set to zero (along wire) Circulating H and radial E fields decay as 1/r
Radial distance away from center of wire
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Implementation of wire in FDTD grid
Components set to zero Components set to zero
Components which decay as 1/r
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Faraday’s Law contour path model
Faraday’s Law
Applied to contour C and surface S
New update equations derived for circulating H components
Yee grid illustrates both differential and integral forms
1
C S
dd d
t
H
E l s
y
x
z
Ez
0y
Ey
Hx
Thin wire
C
a
Ey
Ez
S
y y
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Antenna Feeding
Gap-feed method Provides problem excitation Relates incident voltage to E-field in feeding gap
Added to tangential E-Field component Shows very little dependence on grid size
Acts like infinitesimal feed gap Important for consistent results
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Visual Results Dipole ( l=2m, a=0.005m ) radiating into a 3D FDTD grid
terminated by UPML, pulse excitation
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Driving-Point Impedance Comparison Need quantitative verification of FDTD model
Antenna and EM Modeling with MATLAB, Sergey N. Makarov
Method of Moments patch code (freq. domain) Dipole Driving Point Impedance compared
Dipole parameters: length 2m, radius 0.005m Frequency range: 25MHz-500MHz
How can freq. information be determined from time-domain results?
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Driving-Point Impedance Comparison Antenna excited with wideband voltage source
Differentiated Gaussian Pulse chosen Known spectrum, zero DC content
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Driving-Point Impedance Comparison Energy radiates into grid
Voltage and current calculated for each time step Transients allowed to “die-out”
Discrete Fourier Transform Compare directly to frequency information
FDTD Solution convergence Spatial cell size dictated by desired frequencies
10 or more cells per wavelength Computation time increases as spatial size decreases Finer grids typically result in higher accuracy
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Comparison Results
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Comparison Results
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Future Work
Development of Near Field to Far Field transformation Currently in progress FDTD intrinsically Near Field technique Radiation patterns Wideband Far Zone information
Design/analysis of reconfigurable antennas Nonlinear switching devices
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Acknowledgments
Dr. Anthony Martin
Chaitanya Sreerama
Dr. Daniel Noneaker
Dr. Xiao-Bang Xu
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Thank You