exercise 6.11

c0=298792586                                                      % m/s

mu0=1.256637061435917e-06

e0=8.854e-12

 

f0=11e10

lambda0=c0/f0;

k0=2*pi/lambda0

 

er=3

etha0=120*pi

       

A=1;B=1

       

a=.02;b=.01;d=.1

t=.025

 

dx=a/200;

x=[0:a/200:a];y=[0:b/200:b];z=[0:d/200:d];

 

[X Y Z]=meshgrid(x,y,z);

 

Ey=A*sin(pi*X/a).*sin(pi*Z/d);

Hx=-1j*A/(etha0)*sin(pi*X/a).*cos(pi*Z/d);

Hz=1j*pi*A/(k0*etha0*a)*cos(pi*X/a).*sin(pi*Z/d);

 

% since relative magnetic permeability is null, the integral is limited

% to |Ey| df0(t)/f0

 

df_rel=[]

 

for k=1:1:numel(y)

   

   

    fun1=@(xsym,ysym,zsym)...

 (er-1)*e0*(A*sin(pi*xsym/a)*sin(pi*zsym/d)).^2;

    E1=triplequad(fun1,0,a,0,b,0,z(k));

   

    fun2=@(xsym,ysym,zsym) (e0*(A*sin(pi*xsym/a)*sin(pi*zsym/d)).^2.+...

 mu0*((-1j*A/(k0*etha0*a)*sin(pi*xsym/a).*cos(pi*zsym/d)).^2.+...

                                          (1j*pi*A/(k0*etha0*a)*cos(pi*xsym/a).*sin(pi*zsym/d)).^2));

    E2=triplequad(fun2,0,a,0,b,0,d);

 

    df_rel=[df_rel -E1/E2];

   

end

 

df_rel(1)=[];df_rel(end)=[];

 

figure(1);plot(y([2:end-1]),df_rel);grid on;

xlabel('t');ylabel('df0')

title('frequency relative deviation with integral')

 

% df0(t)/f0 from direct expression

df_rel2=[]

for k=1:1:numel(z)

    E1=(er-1)*e0*A^2*b*z(k)*a/4;

    E2=a*b*d*e0/2*A^2;

 

    df_rel2=[df_rel2 -E1/E2];

 

end

 

figure(2);plot(y,df_rel2);grid on;

xlabel('t');ylabel('df0')

title('frequency relative deviation with direct expression')

 

f0dev=f0+df_rel*f0