Surface Integral of discrete data sampled in spherical coordinates

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Will Beardell
Will Beardell 2021 年 2 月 18 日
回答済み: darova 2021 年 2 月 19 日
I am calculating far-field radiation patterns using the formula for array factor (in Spherical Coordinates), with a defined Element Factor for each point in theta and phi and element locations X(r) Y(r).
THETA = 0:n_points_theta:pi/2;
PHI = 0:n_points_phi:2*pi;
POWER = zeros(n_points_theta,n_points_phi);
for m = 1:n_points_theta
theta = THETA(m);
for n = 1:n_points_phi
phi = PHI(n);
temp_field=0;
for r=1:nelem
temp_field = temp_field + exp(1i*(2*pi/lambda*(sin(theta)*...
(X(r)*cos(phi) + Y(r)*sin(phi)))));
end
temp_field1 = temp_field*ElementFactor(m,n);
end
POWER(m,n)=abs(temp_field1)^2;
end
The result of this calculation is a matrix "POWER" reflecting the radiated power at each point in (θ,ϕ) space. This matrix is easily plotted in multiple different coordinate systems including 3D surf plots and 2D projections using direction cosines in (x,y) space.
The figure of merit I am looking to determine is the percentage of total power radiated within the first null. I have code to analyze the data output from the above code to determine the theta location of the first null; for all arrays studied the main beam is located at θ = 0.
LogPower = 10*log10(POWER);
min1 = islocalmin(LogPower(:,1));
FNBWidx = find(min1,1);
NullPower = sum(sum(RADIUSch(1:FNBWidx,:)).*sin(THETA(1:FNBWidx)));
TotalPower = sum(sum(RADIUSch).*sin(THETA));
Efficiency = NullPower/TotalPower;
A simple summation of the rows of POWER does not return a correct answer as the polar sampling grid of POWER results in the main beam being significantly over-represented while contributions to the sum for increasing values of θ are attenuated. I am at a loss for how to determine how to weight the matrix properly; I do not believe using the spherical differential operator is correct as it removes the main beam due to its location at θ=0. Any help in properly determining this value is greatly appreciated. As far as I can tell, the answer I'm looking for is the proper scaling factor as a function of θ for each value in the sum.

回答 (1 件)

darova
darova 2021 年 2 月 19 日
I think you forgout about

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