ZIP with MATLAB scripts and note:
exercise 6.7
exercise 6.7 notes:
Correction solutions manual that refers to section 2.2 in [POZAR] for the expressions of the electric and magnetic field inside coaxial:
Both fields show 1/r yet the solutions manual only applies such dependency to the electric field, preventing any numerical attempt to answer the question from reaching a successful result.
On the right hand side, precisely from 2.2, expressions of stationary fields inside coaxial:
c0=298972586
f0=1e9
lambda0=c0/f0
e0=8.854e-12 % [F/m] free space permittivity
mu0=4*pi*1e-7 % [H/m] free space permeability
etha0=120*pi
er=2
mur=1
etha=etha0/er^.5
lambda=lambda0/er^.5
Length=lambda/2 % coaxial electric length
in2m=1e-3*25.4
a=.0855/2*in2m
b=.285/2*in2m
b/a % = 3.33
V0=1 % [V/m] electric field strength
% same b/a as example 3.3 133pg therefore kc*a=.45 and
Kc=549
% in example 3.3 there's a script to generate k*ca over b/a graph
beta=(kc^2-(2*pi/c0*f0*er^.5)^2)^.5
E_rho2=@(rho,phy,z) 4*(V0/(log(b/a)))^2*1./rho.^2.*sin(beta*z).*sin(beta*z)
H_phy2=@(rho,phy,z) (2*V0/(etha*log(b/a)))^2.*1./rho.^2.*(cos(beta*z)).^2
We=e0*er/4*integral3(E_rho2,a,b,0,2*pi,0,Length)
Wm=mu0*mur/4*integral3(H_phy2,a,b,0,2*pi,0,Length)
We/Wm
We = 2.607489720808700e-09
Wm = 2.619286323990977e-09
=
0.995496252901324
tic
We_ov_Wm=[]
for er=1:1:10
for V0=.25:.25:5
lambda=lambda0/er^.5;
Length=lambda/2; % coaxial electric length
beta=(kc^2-(2*pi/c0*f0*er^.5)^2)^.5;
etha=etha0/er^.5;
E_rho2=@(rho,phy,z)...
4*(V0/(log(b/a)))^2*1./rho.^2.*sin(beta*z).*sin(beta*z);
H_phy2=@(rho,phy,z)...
(2*V0/(etha*log(b/a)))^2.*1./rho.^2.*(cos(beta*z)).^2;
We=e0*er/4*integral3(E_rho2,a,b,0,2*pi,0,Length);
Wm=mu0*mur/4*integral3(H_phy2,a,b,0,2*pi,0,Length);
We_ov_Wm=[We_ov_Wm We/Wm];
end
end
toc
figure(1);plot(We_ov_Wm);grid on
title('We/Wm')
the x reference axis is just the iteration sweeping through different values of er and V0, quite 1
