# how can i calculate summation over two limits and that too inside a for loop for different values of x & z to have a graph as shown in figure that varies with change in frequency ?

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ben. on 26 Jan 2018
Answered: Eric on 1 Feb 2018
```clear
a=3.6;
b=4;
d=5.8;
k=(4*pi)/3;
w=12.5716e08;
e0=8.85e-12;
y=1.35;
x=[linspace(10,50,5)];
z=[linspace(10,50,5)];
x1=0.45;
y1=1.4;
z1=1.37;
e0n=2;
m = [linspace(4,100,97)];
n = [linspace(4,100,97)];
kx=(m*pi)/a;
ky=(n*pi)/b;
beta=sqrt(kx.^2+ky.^2-k^2);
E0=1/(w*e0);
E1=(2*e0n*sin(kx*x1).*cos(ky*y1))/(a*b*beta.*sin(beta*d));
E2=sum(E1);
E4=zeros(6);
E=zeros(6);
for x=10:10:50
for z=10:10:50
E3=(kx.*ky.*cos(kx.*x).*sin(ky*y).*sin(beta*z1).*sin(beta.*(d-z)))+((ky.^2-k^2).*sin(kx.*x).*cos(ky*y).*sin(beta*z1).*sin(beta.*(d-z)))+(ky.*beta.*sin(kx.*x).*sin(ky*y).*(-sin(beta*z1)).*cos(beta.*(d-z)));
E4(x,z)=sum(E3);
end
end
E(x,z)=E0*E2.*E4(x,z);
plot3(z,x,E)
```

(please let me know the corrections to make.thanks)

Eric on 1 Feb 2018
Okay, so there seem to be a lot of things going on (i.e. wrong) here, too much for someone else to solve for you. So a few points to get you started:
• When you calculate E3, it appears you have taken all three E-field directions and smashed them into the same equation. You probably only want the y hat part of (2.21), namely ( z' here is "z prime")
% if z > z'
E3_y = (ky.^2-k^2).*sin(kx*x).*cos(ky*y) .* sin(beta*z ).*sin(beta*(d-z'));
% if z < z'
E3_y = (ky.^2-k^2).*sin(kx*x).*cos(ky*y) .* sin(beta*z').*cos(beta*(d-z ));
• In your for loops, you'll want to use indexing, for example:
for i_x = 1:length(x)
for i_z = 1:length(z)
% Equations use x(i_x) and z(i_z), for example,
E4(i_x,i_z) = x(i_x).*z(i_z);
end
end
• m and n in the photo start at 0 and go to infinity. Why did you choose 4:100? (Note: You might have issues if the equation doesn't converge quickly.)
• m and n have separate indexing, so you need to separate them somehow, by indexing for example: (There are other, probably better, ways to do this though.)
for i_kx=1:length(kx)
% f(x,z,kx,ky) is the part in the summation
E_whatever(i_kx) = sum(f(x(i_x),z(i_z),kx(i_kx),ky;)
end
• Add more points to x and z (make it about 100, at least) to get a better surface.
• You'll eventually want to use meshgrid instead of your current linspace of x and z, and surf or mesh instead of your current plot3.
After you try all that, come back with your latest problems and maybe someone can get you a better answer. Good luck!