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exercise 1.9

ZIP with MATLAB scripts and note:

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 example 1.1 notes:

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pozar_01_exercise_09_question.jpg
001.jpg
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
002.jpg
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
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