139 lines
3.5 KiB
Matlab
139 lines
3.5 KiB
Matlab
%
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% Tutorials / radar cross section of a metal sphere
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%
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% Describtion at:
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% http://openems.de/index.php/Tutorial:_RCS_Sphere
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%
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% Tested with
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% - Matlab 2013a / Octave 3.8.1
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% - openEMS v0.0.32
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%
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% (C) 2012-2014 Thorsten Liebig <thorsten.liebig@uni-due.de>
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close all
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clear
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clc
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%% setup the simulation
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physical_constants;
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unit = 1e-3; % all length in mm
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sphere.rad = 200;
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inc_angle = 0 /180*pi; %incident angle (to x-axis) in rad
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% size of the simulation box
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SimBox = 1000;
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PW_Box = 750;
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%% setup FDTD parameter & excitation function
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f_start = 50e6; % start frequency
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f_stop = 1000e6; % stop frequency
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f0 = 500e6;
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FDTD = InitFDTD( );
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FDTD = SetGaussExcite( FDTD, 0.5*(f_start+f_stop), 0.5*(f_stop-f_start) );
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BC = [1 1 1 1 1 1]*3; % set boundary conditions
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FDTD = SetBoundaryCond( FDTD, BC );
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%% setup CSXCAD geometry & mesh
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max_res = c0 / f_stop / unit / 20; % cell size: lambda/20
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CSX = InitCSX();
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%create mesh
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smooth_mesh = SmoothMeshLines([0 SimBox/2], max_res);
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mesh.x = unique([-smooth_mesh smooth_mesh]);
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mesh.y = mesh.x;
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mesh.z = mesh.x;
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%% create metal sphere
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CSX = AddMetal( CSX, 'sphere' ); % create a perfect electric conductor (PEC)
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CSX = AddSphere(CSX,'sphere',10,[0 0 0],sphere.rad);
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%% plane wave excitation
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k_dir = [cos(inc_angle) sin(inc_angle) 0]; % plane wave direction
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E_dir = [0 0 1]; % plane wave polarization --> E_z
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CSX = AddPlaneWaveExcite(CSX, 'plane_wave', k_dir, E_dir, f0);
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start = [-PW_Box/2 -PW_Box/2 -PW_Box/2];
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stop = -start;
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CSX = AddBox(CSX, 'plane_wave', 0, start, stop);
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%% dump boxes
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CSX = AddDump(CSX, 'Et');
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start = [mesh.x(1) mesh.y(1) 0];
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stop = [mesh.x(end) mesh.y(end) 0];
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CSX = AddBox(CSX, 'Et', 0, start, stop);
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%%nf2ff calc
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start = [mesh.x(1) mesh.y(1) mesh.z(1)];
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stop = [mesh.x(end) mesh.y(end) mesh.z(end)];
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[CSX nf2ff] = CreateNF2FFBox(CSX, 'nf2ff', start, stop);
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% add 8 lines in all direction as pml spacing
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mesh = AddPML(mesh,8);
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CSX = DefineRectGrid( CSX, unit, mesh );
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%% prepare simulation folder
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Sim_Path = 'Sphere_RCS';
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Sim_CSX = 'Sphere_RCS.xml';
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[status, message, messageid] = rmdir( Sim_Path, 's' ); % clear previous directory
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[status, message, messageid] = mkdir( Sim_Path ); % create empty simulation folder
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%% write openEMS compatible xml-file
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WriteOpenEMS( [Sim_Path '/' Sim_CSX], FDTD, CSX );
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%% show the structure
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CSXGeomPlot( [Sim_Path '/' Sim_CSX] );
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%% run openEMS
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RunOpenEMS( Sim_Path, Sim_CSX);
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%%
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disp('Use Paraview to display the elctric fields dumped by openEMS');
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%%
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EF = ReadUI( 'et', Sim_Path, f0 ); % time domain/freq domain voltage
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Pin = 0.5*norm(E_dir)^2/Z0 .* abs(EF.FD{1}.val).^2;
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%%
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nf2ff = CalcNF2FF(nf2ff, Sim_Path, f0, pi/2, [-180:2:180]*pi/180, 'Mode',1);
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RCS = 4*pi./Pin(1).*nf2ff.P_rad{1}(:);
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polar(nf2ff.phi,RCS);
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xlabel('x -->');
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ylabel('y -->');
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hold on
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grid on
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drawnow
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%%
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freq = linspace(f_start,f_stop,100);
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EF = ReadUI( 'et', Sim_Path, freq ); % time domain/freq domain voltage
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Pin = 0.5*norm(E_dir)^2/Z0 .* abs(EF.FD{1}.val).^2;
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nf2ff = CalcNF2FF(nf2ff, Sim_Path, freq, pi/2, pi+inc_angle, 'Mode',1);
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for fn=1:numel(freq)
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back_scat(fn) = 4*pi./Pin(fn).*nf2ff.P_rad{fn}(1);
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end
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%%
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figure
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plot(freq/1e6,back_scat,'Linewidth',2);
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grid on;
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xlabel('frequency (MHz) \rightarrow');
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ylabel('RCS (m^2) \rightarrow');
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title('radar cross section');
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%%
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figure
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lambda = c0./freq;
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semilogy(sphere.rad*unit./lambda,back_scat/(pi*sphere.rad*unit*sphere.rad*unit),'Linewidth',2);
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ylim([10^-2 10^1])
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grid on;
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xlabel('sphere radius / wavelength \rightarrow');
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ylabel('RCS / (\pi a^2) \rightarrow');
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title('normalized radar cross section');
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