Finding the resultant of 3 perpendicular complex vectors

Hi,

I want to find the resultant vector of 3 perpendicular complex vectors in x-, y-, and z-direction.

Please see the code below:

MATLAB CODE:

%% Define parameters
N = 8;
r = 0.075;
l = 2;
%% Feed Locations OR Element Position
for n = 1: N
    pos(n,:) = [r*cos(2*pi*(n-1)/N) r*sin(2*pi*(n-1)/N) 0];
end

%% Phase Shift assigned on each element (depends on l)
phs_element = NaN(N,1);
for n = 1 : N
    phs_element(n,:) = (2*pi*n*l/N)*(180/pi);
end

%% Define array
arr = conformalArray;
dip = dipole;
dip.Length = 0.058709;
dip.Width = 0.0012491;
arr.Element = dip;
arr.ElementPosition = pos;
arr.PhaseShift = phs_element;
%% Calculate Fields on x-y plane
x = [0.5:0.5:1];
y = [0.5:0.5:1];
[X,Y] = meshgrid(x,y);
p = [X(:)';Y(:)';1*ones(1,prod(size(X)))];
[E,H] = EHfields(arr,2.4e9,p);
p

p = 3×4

0.5000 0.5000 1.0000 1.0000 0.5000 1.0000 0.5000 1.0000 1.0000 1.0000 1.0000 1.0000

E

E = 
  -0.4004 + 0.0972i  -0.1881 + 0.2145i   0.2803 + 0.4538i  -0.3156 + 0.2068i
  -0.3306 + 0.0795i  -0.3316 + 0.3810i   0.1221 + 0.2002i  -0.2966 + 0.1952i
   0.3819 - 0.0301i   0.4552 - 0.4620i  -0.3063 - 0.5734i   0.6283 - 0.3766i

The E field vector is a 3x4 matrix, where 1st column of E represents the x-, y-, and z- component respectively at position given by the 1st column of the "p" matrix.(NOTE: The column of matrix "p" represent the x-, y-, and z- coordinates)

How do I find the resultant of E field at those points on p?

Thank You.

Biplob Biswas

Research Scholar

Answer 1

[Aakash]

To calculate the magnitude of the resultant E field at each point in p, sum up the components and divide by magnitude at each point.

You can try the code below:

E_mag = vecnorm(E); % Calculates the magnitude of each E field vector

E_res = sum(E)./E_mag; % Sums up the x-, y-, and z- components and divides by the magnitude

[Biplob]

Thank you Aakash.