191 lines
5.6 KiB
Matlab
191 lines
5.6 KiB
Matlab
%
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% EXAMPLE / waveguide / coaxial cable using cylindrical coordinates
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%
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% This example demonstrates how to:
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% - use cylindrical coordinates
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% - setup a coaxial 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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coax_rad_i = 100; %inner radius
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coax_rad_a = 230; %outer radius
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mesh_res = [10 nan 10]; %desired mesh resolution
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N_alpha = 71; %mesh lines in azimuth direction
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physical_constants;
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%excitation
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f0 = 0.5e9;
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epsR = 1;
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%% create sim path %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Sim_Path = 'tmp';
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Sim_CSX = 'coax.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 = InitCylindricalFDTD(numTS,1e-5);
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FDTD = SetGaussExcite(FDTD,f0,f0);
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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);
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%% setup CSXCAD geometry & mesh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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CSX = InitCSX('CoordSystem',1);
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mesh.x = coax_rad_i : mesh_res(1) : coax_rad_a;
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mesh.y = linspace(0,2*pi,N_alpha);
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mesh.z = 0 : mesh_res(3) : length;
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CSX = DefineRectGrid(CSX, unit, mesh);
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%% material
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CSX = AddMaterial(CSX,'fill');
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CSX = SetMaterialProperty(CSX,'fill','Epsilon',epsR);
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start = [mesh.x(1) mesh.y(1) 0];
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stop = [mesh.x(end) mesh.y(end) length];
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CSX = AddBox(CSX,'fill',0 ,start,stop);
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%% apply the excitation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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CSX = AddExcitation(CSX,'excite',0,[1 0 0]);
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weight{1} = '1/rho';
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weight{2} = 0;
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weight{3} = 0;
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CSX = SetExcitationWeight(CSX, 'excite', weight );
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start = [coax_rad_i mesh.y(1) 0];
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stop = [coax_rad_a mesh.y(end) 0];
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CSX = AddBox(CSX,'excite',0 ,start,stop);
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%% define dump boxes... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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CSX = AddDump(CSX,'Et_','DumpMode',0);
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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_','DumpType',1,'DumpMode',0);
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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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CSX = AddProbe(CSX,'ut1',0);
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start = [ coax_rad_i 0 mesh.z(10) ];
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stop = [ coax_rad_a 0 mesh.z(10) ];
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CSX = AddBox(CSX,'ut1', 0 ,start,stop);
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CSX = AddProbe(CSX,'ut2',0);
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start = [ coax_rad_i 0 mesh.z(end-10)];
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stop = [ coax_rad_a 0 mesh.z(end-10)];
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CSX = AddBox(CSX,'ut2', 0 ,start,stop);
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%current calc, for each position there are two currents, which will get
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%averaged to match the voltage position in between (!Yee grid!)
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CSX = AddProbe(CSX,'it1a',1);
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mid = 0.5*(coax_rad_i+coax_rad_a);
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start = [ 0 mesh.z(1) mesh.z(9) ];
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stop = [ mid mesh.z(end) mesh.z(9) ];
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CSX = AddBox(CSX,'it1a', 0 ,start,stop);
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CSX = AddProbe(CSX,'it1b',1);
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start = [ 0 mesh.z(1) mesh.z(10) ];
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stop = [ mid mesh.z(end) mesh.z(10) ];
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CSX = AddBox(CSX,'it1b', 0 ,start,stop);
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CSX = AddProbe(CSX,'it2a',1);
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start = [ 0 mesh.z(1) mesh.z(end-11) ];
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stop = [ mid mesh.z(end) mesh.z(end-11) ];
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CSX = AddBox(CSX,'it2a', 0 ,start,stop);
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CSX = AddProbe(CSX,'it2b',1);
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start = [ 0 mesh.z(1) mesh.z(end-10) ];
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stop = [ mid mesh.z(end) mesh.z(end-10) ];
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CSX = AddBox(CSX,'it2b', 0 ,start,stop);
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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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%%
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freq = linspace(0,2*f0,201);
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U = ReadUI({'ut1','ut2'},[Sim_Path '/'],freq);
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I = ReadUI({'it1a','it1b','it2a','it2b'},[Sim_Path '/'],freq);
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Exc = ReadUI('et',Sim_Path,freq);
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%% plot voltages
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figure
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plot(U.TD{1}.t, U.TD{1}.val,'Linewidth',2);
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hold on;
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grid on;
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plot(U.TD{2}.t, U.TD{2}.val,'r--','Linewidth',2);
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xlabel('time (s)')
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ylabel('voltage (V)')
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legend('u_1(t)','u_2(t)')
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%% calculate incoming and reflected voltages & currents
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ZL_a = ones(size(freq))*Z0/2/pi/sqrt(epsR)*log(coax_rad_a/coax_rad_i); %analytic line-impedance of a coax
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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 = 0.5*(I.FD{1}.val+I.FD{2}.val)./Exc.FD{1}.val;
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if2 = 0.5*(I.FD{3}.val+I.FD{4}.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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