Electromagnetic analysis using FDTD method, Biological Effects Of EM Spectrum

1. T.C
SÜLEMAN DEMİREL UNIVERSITY
FEN BİLİMLERİ ENSTİTÜSÜ
Mühendislik fakültesi
ELEKTRONİK VE HABERLEŞME
MÜHENDİSLİĞİ
Biological Effect of Electromagnetic Waves
COURSE OFFERED
Dr. Selçuk Comlekçi
Electromagnetic Analysis using FDTD Method
Submitted by
MSc. Student
Mohammed Mahdi AboAjamm
Student No. 1330145006

2. Computational Electromagnetics
Maxwell’s equations can be given in differential or
integral form.
Maxwell’s equations can be given in time domain or
frequency domain.
Co

3. Commercial software packages

4. The Finite-Difference Time-Domain Method:
Finite-difference time-domain (FDTD) is a numerical analysis
technique used for modeling computational electrodynamics
(finding approximate solutions to the associated system of
differential equations). Since it is a time-domain method, FDTD
solutions can cover a wide frequency range with a single
simulation run, and treat nonlinear material properties in a
natural way.
The FDTD method belongs in the general class of grid-based
differential numerical modeling methods (finite difference
methods). The time-dependent Maxwell's equations (in partial
differential form) are discretized using central-difference
approximations to the space and time partial derivatives. The
resulting finite-difference equations are solved in either software
or hardware in a leapfrog manner: the electric field vector
components in a volume of space are solved at a given instant in
time; then the magnetic field vector components in the same
spatial volume are solved at the next instant in time; and the
process is repeated over and over again until the desired
transient or steady-state electromagnetic field behavior is fully
evolved.

5. When Maxwell's differential equations are examined, it can be
seen that the change in the E-field in time (the time derivative)
is dependent on the change in the H-field across space (the curl).
This results in the basic FDTD time-stepping relation that, at
any point in space, the updated value of the E-field in time is
dependent on the stored value of the E-field and the numerical
curl of the local distribution of the H-field in space.
The H-field is time-stepped in a similar manner. At any point in
space, the updated value of the H-field in time is dependent on
the stored value of the H-field and the numerical curl of the
local distribution of the E-field in space. Iterating the E-field
and H-field updates results in a marching-in-time process
wherein sampled-data analogs of the continuous electromagnetic
waves under consideration propagate in a numerical grid stored
in the computer memory.
This description holds true for 1-D, 2-D, and 3-D FDTD
techniques. When multiple dimensions are considered,
calculating the numerical curl can become complicated. Kane
Yee's seminal 1966 paper proposed spatially staggering the
vector components of the E-field and H-field about rectangular
unit cells of a Cartesian computational grid so that each E-field
vector component is located midway between a pair of H-field
vector components, and conversely. This scheme, now known
as a Yee lattice, has proven to be very robust, and remains at the
core of many current FDTD software constructs.
To implement an FDTD solution of Maxwell's equations, a
computational domain must first be established. The
computational domain is simply the physical region over which
the simulation will be performed. The E and H fields are
determined at every point in space within that computational
domain. The material of each cell within the computational

6. domain must be specified. Typically, the material is either free-
space (air), metal, or dielectric. Any material can be used as
long as the permeability, permittivity, and conductivity are
specified.
Maxwell’s Equations
The basic set of equations describing the electromagnetic world:

7. FDTD Overview – Cells
A three-dimensional problem space is composed of cells.
FDTD Overview- The Yee Cell
The FDTD (Finite Difference Time Domain) algorithm was first
established by Yee as a three dimensional solution of Maxwell's
curl equations.

8. Three scalar equations can be obtained from one vector curl
equation.

9. Leap-frog Algorithm.

10. SAR Analysis Using FDTD
Recent progress in computer technology enables us to use
FDTD method to numerically calculate the EM interactions of a
inhomogeneous, realistic human head and mobile phone models.
In FDTD, spatial and time derivatives in Maxwell's equations
are replaced with their central difference approximations in
specially organized unit cells. In the unit cell, made up by xy z ,
six components of electromagnetic fields are arranged to
minimize the computational storage needs. The entire
computation domain is obtained by stacking these unit cells into
a larger rectangular volume. FDTD is very easy to implement
and to trace the wave phenomen a and can handle complex
geometries with inhomogeneous materials, either conductors or
lossy dielectrics. FDTD has been applied to a large amount of
EM problems, including planar microstrip analysis, scattering
and inverse scattering problems, antenna simulation together
with near-to-far field transformations, etc. Its comparison with
other powerful time-domain techniques has also been presented.

11. One-dimensional FDTD with MATLAB Example
%Scott Hudson, WSU Tri-Cities
%1D electromagnetic finite-difference time-domain (FDTD) program.
%Assumes Ey and Hz field components propagating in the x direction.
%Fields, permittivity, permeability, and conductivity
%are functions of x. Try changing the value of "profile".
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
close all;
clear all;
L = 4; %domain length in meters
N = 200; %# spatial samples in domain
Niter = 400; %# of iterations to perform
fs = 300e6; %source frequency in Hz
ds = L/N; %spatial step in meters
dt = ds/300e6; %"magic time step"
eps0 = 8.854e-12; %permittivity of free space
mu0 = pi*4e-7; %permeability of free space
x = linspace(0,L,N); %x coordinate of spatial samples
%scale factors for E and H
ae = ones(N,1)*dt/(ds*eps0);
am = ones(N,1)*dt/(ds*mu0);
as = ones(N,1);
epsr = ones(N,1);
mur= ones(N,1);
sigma = zeros(N,1);
for i=1:N
epsr(i) = 1;
mur(i) = 1;
w1 = 0.5;
w2 = 1.5;
if (abs(x(i)-L/2)<0.5)
epsr(i)=4;
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
ae = ae./epsr;
am = am./mur;
ae = ae./(1+dt*(sigma./epsr)/(2*eps0));
as = (1-dt*(sigma./epsr)/(2*eps0))./(1+dt*(sigma./epsr)/(2*eps0));
%plot the permittivity, permeability, and conductivity profiles
figure(1)
subplot(3,1,1);
plot(x,epsr);
grid on;
axis([3*ds L min(epsr)*0.9 max(epsr)*1.1]);
title('relative permittivity');
subplot(3,1,2);
plot(x,mur);
grid on;
axis([3*ds L min(mur)*0.9 max(mur)*1.1]);
title('relative permeabiliity');

12. subplot(3,1,3);
plot(x,sigma);
grid on;
axis([3*ds L min(sigma)*0.9-0.001 max(sigma)*1.1+0.001]);
title('conductivity');
%initialize fields to zero
Hz = zeros(N,1);
Ey = zeros(N,1);
figure(2);
set(gcf,'doublebuffer','on'); %set double buffering on for smoother
graphics
plot(Ey);
grid on;
for iter=1:Niter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%
%The next 10 or so lines of code are where we actually integrate
Maxwell's
%equations. All the rest of the program is basically bookkeeping
and plotting.
%"smooth turn on" sinusoidal source
Ey(3) = Ey(3)+2*(1-exp(-((iter-1)/50)^2))*sin(2*pi*fs*dt*iter);
Hz(1) = Hz(2); %absorbing boundary conditions for left-propagating
waves
for i=2:N-1 %update H field
Hz(i) = Hz(i)-am(i)*(Ey(i+1)-Ey(i));
end
Ey(N) = Ey(N-1); %absorbing boundary conditions for right
propagating waves
for i=2:N-1 %update E field
Ey(i) = as(i)*Ey(i)-ae(i)*(Hz(i)-Hz(i-1));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%
figure(2)
hold off
plot(x,Ey,'b');
axis([3*ds L -2 2]);
grid on;
title('E (blue) and 377*H (red)');
hold on
plot(x,377*Hz,'r');
xlabel('x (m)');
pause(0);
iter
end