275 lines
9.0 KiB
Matlab
275 lines
9.0 KiB
Matlab
%
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% Tutorials / horn antenna
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%
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% Describtion at:
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% http://openems.de/index.php/Tutorial:_Horn_Antenna
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%
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% Tested with
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% - Matlab 2011a / Octave 3.4.3
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% - openEMS v0.0.26
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%
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% (C) 2011,2012 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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% horn width in x-direction
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horn.width = 20;
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% horn height in y-direction
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horn.height = 30;
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% horn length in z-direction
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horn.length = 50;
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horn.feed_length = 50;
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horn.thickness = 2;
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% horn opening angle in x, y
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horn.angle = [20 20]*pi/180;
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% size of the simulation box
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SimBox = [200 200 200];
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% frequency range of interest
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f_start = 10e9;
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f_stop = 20e9;
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% frequency of interest
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f0 = 15e9;
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%waveguide TE-mode definition
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m = 1;
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n = 0;
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%% mode functions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% by David M. Pozar, Microwave Engineering, third edition, page 113
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freq = linspace(f_start,f_stop,201);
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a = horn.width;
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b = horn.height;
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k = 2*pi*freq/c0;
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kc = sqrt((m*pi/a/unit)^2 + (n*pi/b/unit)^2);
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fc = c0*kc/2/pi; %cut-off frequency
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beta = sqrt(k.^2 - kc^2); %waveguide phase-constant
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ZL_a = k * Z0 ./ beta; %analytic waveguide impedance
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% mode profile E- and H-field
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x_pos = ['(x-' num2str(a/2) ')'];
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y_pos = ['(y-' num2str(b/2) ')'];
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func_Ex = [num2str( n/b/unit) '*cos(' num2str(m*pi/a) '*' x_pos ')*sin(' num2str(n*pi/b) '*' y_pos ')'];
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func_Ey = [num2str(-m/a/unit) '*sin(' num2str(m*pi/a) '*' x_pos ')*cos(' num2str(n*pi/b) '*' y_pos ')'];
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func_Hx = [num2str(m/a/unit) '*sin(' num2str(m*pi/a) '*' x_pos ')*cos(' num2str(n*pi/b) '*' y_pos ')'];
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func_Hy = [num2str(n/b/unit) '*cos(' num2str(m*pi/a) '*' x_pos ')*sin(' num2str(n*pi/b) '*' y_pos ')'];
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disp([' Cutoff frequencies for this mode and wavguide is: ' num2str(fc/1e9) ' GHz']);
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if (f_start<fc)
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warning('openEMS:example','f_start is smaller than the cutoff-frequency, this may result in a long simulation... ');
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end
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%% setup FDTD parameter & excitation function
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FDTD = InitFDTD( 30000, 1e-4 );
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FDTD = SetGaussExcite(FDTD,0.5*(f_start+f_stop),0.5*(f_stop-f_start));
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BC = {'PML_8' 'PML_8' 'PML_8' 'PML_8' 'PML_8' 'PML_8'}; % boundary conditions
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FDTD = SetBoundaryCond( FDTD, BC );
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%% setup CSXCAD geometry & mesh
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% currently, openEMS cannot automatically generate a mesh
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max_res = c0 / (f_stop) / unit / 15; % cell size: lambda/20
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CSX = InitCSX();
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%create fixed lines for the simulation box, substrate and port
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mesh.x = [-SimBox(1)/2 -a/2 a/2 SimBox(1)/2];
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mesh.x = SmoothMeshLines( mesh.x, max_res, 1.4); % create a smooth mesh between specified fixed mesh lines
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mesh.y = [-SimBox(2)/2 -b/2 b/2 SimBox(2)/2];
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mesh.y = SmoothMeshLines( mesh.y, max_res, 1.4 );
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%create fixed lines for the simulation box and given number of lines inside the substrate
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mesh.z = [-horn.feed_length 0 SimBox(3)-horn.feed_length ];
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mesh.z = SmoothMeshLines( mesh.z, max_res, 1.4 );
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CSX = DefineRectGrid( CSX, unit, mesh );
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%% create horn
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% horn feed rect waveguide
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CSX = AddMetal(CSX, 'horn');
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start = [-a/2-horn.thickness -b/2 mesh.z(1)];
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stop = [-a/2 b/2 0];
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CSX = AddBox(CSX,'horn',10,start,stop);
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start = [a/2+horn.thickness -b/2 mesh.z(1)];
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stop = [a/2 b/2 0];
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CSX = AddBox(CSX,'horn',10,start,stop);
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start = [-a/2-horn.thickness b/2+horn.thickness mesh.z(1)];
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stop = [ a/2+horn.thickness b/2 0];
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CSX = AddBox(CSX,'horn',10,start,stop);
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start = [-a/2-horn.thickness -b/2-horn.thickness mesh.z(1)];
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stop = [ a/2+horn.thickness -b/2 0];
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CSX = AddBox(CSX,'horn',10,start,stop);
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% horn opening
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p(2,1) = a/2;
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p(1,1) = 0;
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p(2,2) = a/2 + sin(horn.angle(1))*horn.length;
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p(1,2) = horn.length;
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p(2,3) = -a/2 - sin(horn.angle(1))*horn.length;
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p(1,3) = horn.length;
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p(2,4) = -a/2;
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p(1,4) = 0;
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CSX = AddLinPoly( CSX, 'horn', 10, 1, -horn.thickness/2, p, horn.thickness, 'Transform', {'Rotate_X',horn.angle(2),'Translate',['0,' num2str(-b/2-horn.thickness/2) ',0']});
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CSX = AddLinPoly( CSX, 'horn', 10, 1, -horn.thickness/2, p, horn.thickness, 'Transform', {'Rotate_X',-horn.angle(2),'Translate',['0,' num2str(b/2+horn.thickness/2) ',0']});
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p(1,1) = b/2+horn.thickness;
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p(2,1) = 0;
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p(1,2) = b/2+horn.thickness + sin(horn.angle(2))*horn.length;
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p(2,2) = horn.length;
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p(1,3) = -b/2-horn.thickness - sin(horn.angle(2))*horn.length;
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p(2,3) = horn.length;
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p(1,4) = -b/2-horn.thickness;
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p(2,4) = 0;
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CSX = AddLinPoly( CSX, 'horn', 10, 0, -horn.thickness/2, p, horn.thickness, 'Transform', {'Rotate_Y',-horn.angle(2),'Translate',[ num2str(-a/2-horn.thickness/2) ',0,0']});
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CSX = AddLinPoly( CSX, 'horn', 10, 0, -horn.thickness/2, p, horn.thickness, 'Transform', {'Rotate_Y',+horn.angle(2),'Translate',[ num2str(a/2+horn.thickness/2) ',0,0']});
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% horn aperture
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A = (a + 2*sin(horn.angle(1))*horn.length)*unit * (b + 2*sin(horn.angle(2))*horn.length)*unit;
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% %% apply the excitation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% xy-mode profile excitation located directly on top of pml (first 8 z-lines)
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CSX = AddExcitation(CSX,'excite',0,[1 1 0]);
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weight{1} = func_Ex;
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weight{2} = func_Ey;
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weight{3} = 0;
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CSX = SetExcitationWeight(CSX,'excite',weight);
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start=[-a/2 -b/2 mesh.z(8) ];
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stop =[ a/2 b/2 mesh.z(8) ];
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CSX = AddBox(CSX,'excite',0 ,start,stop);
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%% voltage and current definitions using the mode matching probes %%%%%%%%%
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%port 1
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start(3) = mesh.z(1)+horn.feed_length/2;
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stop(3) = start(3);
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CSX = AddProbe(CSX, 'ut1', 10, 1, [], 'ModeFunction',{func_Ex,func_Ey,0});
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CSX = AddBox(CSX, 'ut1', 0 ,start,stop);
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CSX = AddProbe(CSX,'it1', 11, 1, [], 'ModeFunction',{func_Hx,func_Hy,0});
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CSX = AddBox(CSX,'it1', 0 ,start,stop);
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%% nf2ff calc
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start = [mesh.x(9) mesh.y(9) mesh.z(9)];
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stop = [mesh.x(end-8) mesh.y(end-8) mesh.z(end-8)];
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[CSX nf2ff] = CreateNF2FFBox(CSX, 'nf2ff', start, stop, [1 1 1 1 0 1]);
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%% prepare simulation folder
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Sim_Path = 'tmp';
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Sim_CSX = 'horn_ant.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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%% postprocessing & do the plots
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U = ReadUI( 'ut1', Sim_Path, freq ); % time domain/freq domain voltage
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I = ReadUI( 'it1', Sim_Path, freq ); % time domain/freq domain current (half time step is corrected)
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% plot reflection coefficient S11
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figure
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uf_inc = 0.5*(U.FD{1}.val + I.FD{1}.val .* ZL_a);
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if_inc = 0.5*(I.FD{1}.val + U.FD{1}.val ./ ZL_a);
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uf_ref = U.FD{1}.val - uf_inc;
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if_ref = if_inc - I.FD{1}.val;
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s11 = uf_ref ./ uf_inc;
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plot( freq/1e9, 20*log10(abs(s11)), 'k-', 'Linewidth', 2 );
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ylim([-60 0]);
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grid on
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title( 'reflection coefficient S_{11}' );
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xlabel( 'frequency f / GHz' );
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ylabel( 'reflection coefficient |S_{11}|' );
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P_in = 0.5*uf_inc .* conj( if_inc ); % antenna feed power
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drawnow
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%% NFFF contour plots %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% calculate the far field at phi=0 degrees and at phi=90 degrees
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thetaRange = (0:2:359) - 180;
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r = 1; % evaluate fields at radius r
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disp( 'calculating far field at phi=[0 90] deg...' );
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[E_far_theta,E_far_phi,Prad,Dmax] = AnalyzeNF2FF( Sim_Path, nf2ff, f0, thetaRange, [0 90], r );
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Dlog=10*log10(Dmax);
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G_a = 4*pi*A/(c0/f0)^2;
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e_a = Dmax/G_a;
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% display some antenna parameter
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disp( ['radiated power: Prad = ' num2str(Prad) ' Watt']);
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disp( ['directivity: Dmax = ' num2str(Dlog) ' dBi'] );
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disp( ['aperture efficiency: e_a = ' num2str(e_a*100) '%'] );
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%%
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% calculate the e-field magnitude for phi = 0 deg
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E_phi0_far = zeros(1,numel(thetaRange));
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for n=1:numel(thetaRange)
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E_phi0_far(n) = norm( [E_far_theta(n,1) E_far_phi(n,1)] );
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end
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E_phi0_far_log = 20*log10(abs(E_phi0_far)/max(abs(E_phi0_far)));
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E_phi0_far_log = E_phi0_far_log + Dlog;
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% display polar plot
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figure
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plot( thetaRange, E_phi0_far_log ,'k-' );
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xlabel( 'theta (deg)' );
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ylabel( 'directivity (dBi)');
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grid on;
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hold on;
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% calculate the e-field magnitude for phi = 90 deg
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E_phi90_far = zeros(1,numel(thetaRange));
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for n=1:numel(thetaRange)
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E_phi90_far(n) = norm([E_far_theta(n,2) E_far_phi(n,2)]);
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end
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E_phi90_far_log = 20*log10(abs(E_phi90_far)/max(abs(E_phi90_far)));
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E_phi90_far_log = E_phi90_far_log + Dlog;
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% display polar plot
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plot( thetaRange, E_phi90_far_log ,'r-' );
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legend('phi=0','phi=90')
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%% calculate 3D pattern
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phiRange = sort( unique( [-180:5:-100 -100:2.5:-50 -50:1:50 50:2.5:100 100:5:180] ) );
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thetaRange = sort( unique([ 0:1:50 50:2.:100 100:5:180 ]));
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r = 1; % evaluate fields at radius r
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disp( 'calculating 3D far field...' );
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[E_far_theta,E_far_phi] = AnalyzeNF2FF( Sim_Path, nf2ff, f0, thetaRange, phiRange, r );
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E_far = sqrt( abs(E_far_theta).^2 + abs(E_far_phi).^2 );
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E_far_normalized = E_far / max(E_far(:)) * Dmax;
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[theta,phi] = ndgrid(thetaRange/180*pi,phiRange/180*pi);
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x = E_far_normalized .* sin(theta) .* cos(phi);
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y = E_far_normalized .* sin(theta) .* sin(phi);
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z = E_far_normalized .* cos(theta);
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figure
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surf( x,y,z, E_far_normalized, 'EdgeColor','none' );
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axis equal
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axis off
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xlabel( 'x' );
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ylabel( 'y' );
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zlabel( 'z' );
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%%
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DumpFF2VTK([Sim_Path '/Horn_Pattern.vtk'],E_far_normalized,thetaRange,phiRange,1e-3);
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