top of page
exercise 1.9
ZIP with MATLAB scripts and note:
example 1.1 notes:
c0=299792458 % [m/s] light speed
eps0=8.854e-12 % [F/m] electric permittivity
er=3 % relative permittivity
mu0=4*pi*1e-7 % [H/m] permeability
mur=1 % [] relative permeability
etha0=120*pi % [Ohm] air intrinsic impedance
E0=100 % [V/m] incident electric field amplitude at z=0
f0=3e9 % [Hz]
lambda0=c0/f0 % [m] wavelength
k0=2*pi/lambda0 % [m^-1] wave number
lambda=lambda0/er^.5
L=.2 % [m] dielectric thickness
tand=.1
% complex propagation constant
g=1j*2*pi*f0*(mu0*eps0*er*(1-1j*tand))^.5
alpha=real(g)
beta=imag(g)
% instrinsic impedance
etha=1j*2*pi*f0*mu0*mur/g
etha=etha0/(er*(1-1j*tand))^.5
% check
abs(etha)
angle(etha)*180/pi
c0 =
299792458
eps0 =
8.853999999999999e-12
er =
3
mu0 =
1.256637061435917e-06
mur =
1
etha0 =
3.769911184307751e+02
E0 =
100
f0 =
3.000000000000000e+09
lambda0 =
0.099930819333333
k0 =
62.875350658550452
lambda =
0.057695085442440
L =
0.200000000000000
tand =
0.100000000000000
g =
5.438330561148803e+00 + 1.090378513375741e+02i
alpha =
5.438330561148803
beta =
1.090378513375741e+02
etha =
2.166978999453002e+02 + 1.080794235536438e+01i
etha =
2.168456168468828e+02 + 1.081530982758087e+01i
ans =
2.171151594715847e+02
ans =
2.855296568749823
a) Si incident wave power density
N1=20 % resolution steps within 1 wavelength
dz=lambda/N1
z=[0:dz:L L];
Ei=E0*exp(-1*real(g)*z).*exp(-1j*imag(g)*z);
% incident Electric field, phasor
% incident wave power at z=0
Si0=abs(real(Ei(1)^2/conj(etha))) % [W/m^2]
R=-1 % reflection coefficient perfect metal at z=L
Er=R*Ei(end)*exp(-real(g)*(L-z)).*exp(-1j*imag(g)*(L-z)); % Reflected field, phasor
% Sr reflected wave power density
% reflected wave power at z=0
Sr0=abs(real(Er(1)^2/conj(etha))) % [W/m^2]
electric field amplitude through lossy dielectric
figure;
plot(z,abs(Ei))
hold on
plot(z,abs(Er))
grid on
title('electric field amplitude through lossy dielectric')
xlabel('z');ylabel('[V/m]')
legend({'|Ei|','|Er|'})
N1 =
20
dz =
0.002884754272122
Si0 =
46.001326178954031
R =
-1
Sr0 =
0.420598524070411
b) Sin(z=0) from total field
Et=Ei+Er;
St0=real(Et(1)^2/conj(etha))
St = Si-Sr?
Si0-Sr0
it's a lossy material, power loss should be included : Sin=Si-Sr-Sloss
St0 =
36.856607391901257
ans =
45.580727654883617
bottom of page