208 lines
6.5 KiB
Matlab
208 lines
6.5 KiB
Matlab
%
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% EXAMPLE / waveguide / circular waveguide
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%
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% This example demonstrates how to:
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% - setup a circular waveguide
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% - use analytic functions for waveguide excitations and voltage/current
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% calculations
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%
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%
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% Tested with
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% - Matlab 2009b
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% - openEMS v0.0.17
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%
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% (C) 2010 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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%% switches & options...
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postprocessing_only = 0;
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use_pml = 0; % use pml boundaries instead of mur
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openEMS_opts = '';
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% openEMS_opts = [openEMS_opts ' --disable-dumps'];
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%% setup the simulation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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numTS = 1e5; %number of timesteps
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length = 1000; %length of the waveguide
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unit = 1e-3; %drawing unit used
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rad = 300; %radius of the circular waveguide
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mesh_res = [10 10 15]; %desired mesh resolution
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%excitation
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f0 = 350e6; %center frequency
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f0_BW = 25e6; %bandwidth: 10dB cut-off frequency
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physical_constants
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%% TE11 mode definitions (Pozar 3rd edition)
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p11 = 1.841;
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kc = p11 / rad /unit;
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k = 2*pi*f0/C0;
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fc = C0*kc/2/pi;
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beta = sqrt(k^2 - kc^2);
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n_eff = (beta/k);
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kc = kc*unit; %functions must be defined in drawing units
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func_Er = [ num2str(-1/kc^2) '/rho*cos(a)*j1(' num2str(kc) '*rho)'];
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func_Ea = [ num2str(1/kc) '*sin(a)*0.5*(j0(' num2str(kc) '*rho)-jn(2,' num2str(kc) '*rho))'];
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func_Ex = ['(' func_Er '*cos(a) - ' func_Ea '*sin(a) )*(rho<' num2str(rad) ')'];
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func_Ey = ['(' func_Er '*sin(a) + ' func_Ea '*cos(a) )*(rho<' num2str(rad) ')'];
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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(rad) ')'];
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func_Hy = ['(' func_Hr '*sin(a) + ' func_Ha '*cos(a) )*(rho<' num2str(rad) ')'];
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%% define files and path %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Sim_Path = 'tmp';
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Sim_CSX = 'Circ_WG.xml';
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if (postprocessing_only==0)
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[status, message, messageid] = rmdir(Sim_Path,'s');
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[status, message, messageid] = mkdir(Sim_Path);
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end
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%% setup FDTD parameter & excitation function %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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FDTD = InitFDTD(numTS,1e-6,'OverSampling',5);
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FDTD = SetGaussExcite(FDTD,f0,f0_BW);
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BC = {'PEC','PEC','PEC','PEC','PEC','MUR'};
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if (use_pml>0)
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BC = {'PEC','PEC','PEC','PEC','PEC','PML_8'};
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end
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FDTD = SetBoundaryCond(FDTD,BC,'MUR_PhaseVelocity',C0 / n_eff);
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%% setup CSXCAD geometry & mesh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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CSX = InitCSX();
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mesh.x = -mesh_res(1)/2-rad:mesh_res(1):rad+mesh_res(1)/2;
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mesh.y = -mesh_res(2)/2-rad:mesh_res(2):rad+mesh_res(2)/2;
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mesh.z = 0 : mesh_res(3) : length;
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CSX = DefineRectGrid(CSX, 1e-3,mesh);
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start = [0,0,0];
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stop = [0,0,length];
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%%% fill everything with copper, priority 0
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CSX = AddMetal(CSX,'copper');
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% CSX = SetMaterialProperty(CSX,'copper','Kappa',56e6);
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CSX = AddBox(CSX,'copper',0,[mesh.x(1) mesh.y(1) mesh.z(1)],[mesh.x(end) mesh.y(end) mesh.z(end)]);
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%%% cut out an air cylinder as circular waveguide... priority 5
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CSX = AddMaterial(CSX,'air');
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CSX = SetMaterialProperty(CSX,'air','Epsilon',1);
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CSX = AddCylinder(CSX,'air', 5 ,start,stop,rad);
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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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CSX = AddCylinder(CSX,'excite', 5 ,[0 0 -0.1],[0 0 0.1],rad);
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%% define dump boxes... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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CSX = AddDump(CSX,'Et_','SubSampling','2,2,2','FileType',0,'DumpMode',2);
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start = [mesh.x(1) , 0 , mesh.z(1)];
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stop = [mesh.x(end), 0 , mesh.z(end)];
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CSX = AddBox(CSX,'Et_',0 , start,stop);
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CSX = AddDump(CSX,'Ht_','SubSampling','2,2,2','DumpType',1,'FileType',0,'DumpMode',2);
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CSX = AddBox(CSX,'Ht_',0,start,stop);
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%% define voltage calc boxes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%voltage calc
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start = [mesh.x(1) mesh.y(1) mesh.z(10)];
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stop = [mesh.x(end) mesh.y(end) mesh.z(10)];
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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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start = [mesh.x(1) mesh.y(1) mesh.z(end-10)];
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stop = [mesh.x(end) mesh.y(end) mesh.z(end-10)];
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CSX = AddProbe(CSX, 'ut2', 10, 1, [], 'ModeFunction',{func_Ex,func_Ey,0});
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CSX = AddBox(CSX, 'ut2', 0 ,start,stop);
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CSX = AddProbe(CSX,'it2', 11, 1, [], 'ModeFunction',{func_Hx,func_Hy,0});
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CSX = AddBox(CSX,'it2', 0 ,start,stop);
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port_dist = mesh.z(end-10) - mesh.z(10);
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%% Write openEMS
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if (postprocessing_only==0)
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WriteOpenEMS([Sim_Path '/' Sim_CSX],FDTD,CSX);
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RunOpenEMS(Sim_Path, Sim_CSX, openEMS_opts);
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end
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%% do the plots %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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freq = linspace(f0-f0_BW,f0+f0_BW,201);
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U = ReadUI({'ut1','ut2'},[Sim_Path '/'],freq);
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I = ReadUI({'it1','it2'},[Sim_Path '/'],freq);
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Exc = ReadUI('et',Sim_Path,freq);
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k = 2*pi*freq/C0;
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kc = p11 / rad /unit;
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beta = sqrt(k.^2 - kc^2);
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ZL_a = Z0*k./beta ;
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uf1 = U.FD{1}.val./Exc.FD{1}.val;
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uf2 = U.FD{2}.val./Exc.FD{1}.val;
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if1 = I.FD{1}.val./Exc.FD{1}.val;
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if2 = I.FD{2}.val./Exc.FD{1}.val;
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uf1_inc = 0.5 * ( uf1 + if1 .* ZL_a );
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if1_inc = 0.5 * ( if1 + uf1 ./ ZL_a );
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uf2_inc = 0.5 * ( uf2 + if2 .* ZL_a );
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if2_inc = 0.5 * ( if2 + uf2 ./ ZL_a );
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uf1_ref = uf1 - uf1_inc;
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if1_ref = if1 - if1_inc;
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uf2_ref = uf2 - uf2_inc;
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if2_ref = if2 - if2_inc;
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% plot s-parameter
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figure
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s11 = uf1_ref./uf1_inc;
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s21 = uf2_inc./uf1_inc;
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plot(freq,20*log10(abs(s11)),'Linewidth',2);
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xlim([freq(1) freq(end)]);
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xlabel('frequency (Hz)')
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ylabel('s-para (dB)');
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% ylim([-40 5]);
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grid on;
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hold on;
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plot(freq,20*log10(abs(s21)),'r','Linewidth',2);
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legend('s11','s21','Location','SouthEast');
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% plot line-impedance comparison
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figure()
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ZL = uf1./if1;
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plot(freq,real(ZL),'Linewidth',2);
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xlim([freq(1) freq(end)]);
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xlabel('frequency (Hz)')
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ylabel('line-impedance (\Omega)');
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grid on;
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hold on;
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plot(freq,imag(ZL),'r--','Linewidth',2);
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plot(freq,ZL_a,'g-.','Linewidth',2);
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legend('\Re\{ZL\}','\Im\{ZL\}','ZL-analytic','Location','Best');
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% beta compare
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figure()
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da = angle(uf1_inc)-angle(uf2_inc);
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da = mod(da,2*pi);
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beta_12 = (da)/port_dist/unit;
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plot(freq,beta_12,'Linewidth',2);
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xlim([freq(1) freq(end)]);
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xlabel('frequency (Hz)');
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ylabel('\beta (m^{-1})');
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grid on;
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hold on;
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plot(freq,beta,'g--','Linewidth',2);
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legend('\beta-FDTD','\beta-analytic','Location','Best');
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%% visualize electric & magnetic fields
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disp('you will find vtk dump files in the simulation folder (tmp/)')
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disp('use paraview to visulaize them');
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