|Apr19-11, 06:58 AM||#1|
Solving Dependant Integrals in MATlab
Hi i need to create a MATlab m file solving the following function for 0 to 90 degrees of \theta_0 and for any function F(\theta^').
 dx should be d\theta^', sorry about that.
I managed to do it in MATlab using symbolic maths toolkit and the int() function, but the script breaks for more complex F(\theta^'). I thus need ways of going about it using trapz() or any other recommendable numerical solutions. But I'm really finding it hard to wrap my head around where to start. Any ideas?
Oh just for interest the formula is used for calculating a reflector antenna's aperture efficiency. Where \theta_0 is the subtended angle or f/d ratio (Focus point), and F(\theta^') is the feed used normally in my case, (sin(x/2))^n, (sin(x))^n or 10^((nx^2)/10)
|Apr19-11, 09:40 AM||#2|
Okay I played around a bit and this is what I've ended up. But there is still problems with the amplitude. Any help will still be appreciated. The aperture efficiency for the given problem below should be between 0.8 and 0.83 but the results are out with a factor bigger than 3000. The shap is correct but the amplitude is just out by a factor.
clc clear all theta = 0:89; %Angle range for n= 2:2:8 %Specify range of n % calculate values for all angles of the integral function for i=1:length(theta) angle = theta(i)*pi/180; g =(2*(n+1))*((cos(angle))^n); %The feed int(i) = sqrt(g)*tan(angle/2); % The integral end %Set initial value of iterative integral sum res(1)=int(1); for j=2:length(theta) res(j) = res(j-1)+int(j); %calculate and store integral sum for each case end res = abs(res); %apply absolute value res = res.^2; %square integral %calculate resulting values of complete function for k=1:length(theta) res(k) = res(k)*(cot(k*pi/360))^2; end plot(res) hold on; grid on; end
|integral, matlab, trapz|
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