247 lines
8.1 KiB
Matlab
247 lines
8.1 KiB
Matlab
%
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% Tutorials / conical horn antenna
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%
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% Describtion at:
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% http://openems.de/index.php/Tutorial:_Conical_Horn_Antenna
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%
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% Tested with
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% - Matlab 2011a
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% - openEMS v0.0.25
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%
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% (C) 2011 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 radius
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horn.radius = 20;
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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
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horn.angle = 20*pi/180;
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% size of the simulation box
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SimBox = [100 100 100]*2;
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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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%% 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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p11 = 1.841;
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kc = p11 / horn.radius /unit;
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k = 2*pi*freq/C0;
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fc = C0*kc/2/pi;
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beta = sqrt(k.^2 - kc^2);
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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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kc = kc*unit
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func_Er = [ num2str(-1/kc^2,'%14.13f') '/rho*cos(a)*j1(' num2str(kc,'%14.13f') '*rho)'];
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func_Ea = [ num2str(1/kc,'%14.13f') '*sin(a)*0.5*(j0(' num2str(kc,'%14.13f') '*rho)-jn(2,' num2str(kc,'%14.13f') '*rho))'];
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func_Ex = ['(' func_Er '*cos(a) - ' func_Ea '*sin(a) ) * (rho<' num2str(horn.radius) ')'];
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func_Ey = ['(' func_Er '*sin(a) + ' func_Ea '*cos(a) ) * (rho<' num2str(horn.radius) ')'];
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func_Ha = [ num2str(-1/kc^2,'%14.13f') '/rho*cos(a)*j1(' num2str(kc,'%14.13f') '*rho)'];
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func_Hr = [ '-1*' num2str(1/kc,'%14.13f') '*sin(a)*0.5*(j0(' num2str(kc,'%14.13f') '*rho)-jn(2,' num2str(kc,'%14.13f') '*rho))'];
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func_Hx = ['(' func_Hr '*cos(a) - ' func_Ha '*sin(a) ) * (rho<' num2str(horn.radius) ')'];
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func_Hy = ['(' func_Hr '*sin(a) + ' func_Ha '*cos(a) ) * (rho<' num2str(horn.radius) ')'];
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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-5 );
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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 -horn.radius 0 horn.radius 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 = mesh.x;
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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) ];
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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 + waveguide, defined by a rotational polygon
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CSX = AddMetal(CSX, 'Conical_Horn');
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p(1,1) = horn.radius+horn.thickness; % x-coord point 1
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p(2,1) = -horn.feed_length; % z-coord point 1
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p(1,end+1) = horn.radius+horn.thickness; % x-coord point 1
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p(2,end) = 0; % z-coord point 1
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p(1,end+1) = horn.radius+horn.thickness + sin(horn.angle)*horn.length; % x-coord point 2
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p(2,end) = horn.length; % y-coord point 2
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p(1,end+1) = horn.radius + sin(horn.angle)*horn.length; % x-coord point 2
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p(2,end) = horn.length; % y-coord point 2
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p(1,end+1) = horn.radius; % x-coord point 1
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p(2,end) = 0; % z-coord point 1
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p(1,end+1) = horn.radius; % x-coord point 1
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p(2,end) = -horn.feed_length; % z-coord point 1
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CSX = AddRotPoly(CSX,'Conical_Horn',10,0,2,p);
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% horn aperture
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A = pi*((horn.radius + sin(horn.angle)*horn.length)*unit)^2;
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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=[0 0 mesh.z(8)-0.1 ];
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stop =[0 0 mesh.z(8)+0.1 ];
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CSX = AddCylinder(CSX,'excite',0 ,start,stop,horn.radius);
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%% voltage and current definitions using the mode matching probes %%%%%%%%%
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%port 1
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start = [-horn.radius -horn.radius mesh.z(1)+horn.feed_length/2];
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stop = [ horn.radius horn.radius mesh.z(1)+horn.feed_length/2]
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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 ,'--debug-PEC');
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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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%% 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('Conical_Horn_Pattern.vtk',E_far_normalized,thetaRange,phiRange,1e-3);
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