% % EXAMPLE / waveguide / coaxial cable % % This example demonstrates how to: % - setup a coaxial waveguide % - use analytic functions for waveguide excitations and voltage/current % calculations % % % Tested with % - Matlab 2009b % - openEMS v0.0.17 % % (C) 2010 Thorsten Liebig close all clear clc %% switches & options... postprocessing_only = 0; use_pml = 0; % use pml boundaries instead of mur openEMS_opts = ''; % openEMS_opts = [openEMS_opts ' --disable-dumps']; %% setup the simulation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% numTS = 5000; %number of timesteps length = 1000; %length of the waveguide unit = 1e-3; %drawing unit used coax_rad_i = 100; %inner radius coax_rad_ai = 230; %inner radius of outer cladding coax_rad_aa = 240; %outer radius of outer cladding mesh_res = [5 5 5]; %desired mesh resolution physical_constants; %excitation f0 = 0.5e9; epsR = 1; %% create sim path %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Sim_Path = 'tmp'; Sim_CSX = 'coax.xml'; if (postprocessing_only==0) [status, message, messageid] = rmdir(Sim_Path,'s'); [status, message, messageid] = mkdir(Sim_Path); end %% setup FDTD parameter & excitation function %%%%%%%%%%%%%%%%%%%%%%%%%%%%% FDTD = InitFDTD(numTS,1e-5); FDTD = SetGaussExcite(FDTD,f0,f0); BC = {'PEC','PEC','PEC','PEC','PEC','MUR'}; if (use_pml>0) BC = {'PEC','PEC','PEC','PEC','PEC','PML_8'}; end FDTD = SetBoundaryCond(FDTD,BC); %% setup CSXCAD geometry & mesh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CSX = InitCSX(); mesh.x = -2.5*mesh_res(1)-coax_rad_aa : mesh_res(1) : coax_rad_aa+2.5*mesh_res(1); mesh.y = mesh.x; mesh.z = 0 : mesh_res(3) : length; CSX = DefineRectGrid(CSX, unit, mesh); %%% coax CSX = AddMaterial(CSX,'copper'); CSX = SetMaterialProperty(CSX,'copper','Kappa',56e6); start = [0, 0 , 0];stop = [0, 0 , length]; CSX = AddCylinder(CSX,'copper',0 ,start,stop,coax_rad_i); CSX = AddCylindricalShell(CSX,'copper',0 ,start,stop,0.5*(coax_rad_aa+coax_rad_ai),(coax_rad_aa-coax_rad_ai)); %% apply the excitation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% start = [0,0,-0.1]; stop = [0,0, 0.1]; CSX = AddExcitation(CSX,'excite',0,[1 1 0]); weight{1} = '(x)/(x*x+y*y)'; weight{2} = 'y/pow(rho,2)'; weight{3} = 0; CSX = SetExcitationWeight(CSX, 'excite', weight ); CSX = AddCylindricalShell(CSX,'excite',0 ,start,stop,0.5*(coax_rad_i+coax_rad_ai),(coax_rad_ai-coax_rad_i)); %% define dump boxes... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CSX = AddDump(CSX,'Et_','DumpMode',2); start = [mesh.x(1) , 0 , mesh.z(1)]; stop = [mesh.x(end) , 0 , mesh.z(end)]; CSX = AddBox(CSX,'Et_',0 , start,stop); CSX = AddDump(CSX,'Ht_','DumpType',1,'DumpMode',2); CSX = AddBox(CSX,'Ht_',0,start,stop); %% define voltage calc boxes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %voltage calc CSX = AddProbe(CSX,'ut1',0); start = [ coax_rad_i 0 mesh.z(10) ]; stop = [ coax_rad_ai 0 mesh.z(10) ]; CSX = AddBox(CSX,'ut1', 0 ,start,stop); CSX = AddProbe(CSX,'ut2',0); start = [ coax_rad_i 0 mesh.z(end-10)]; stop = [ coax_rad_ai 0 mesh.z(end-10)]; CSX = AddBox(CSX,'ut2', 0 ,start,stop); %current calc, for each position there are two currents, which will get %averaged to match the voltage position in between (!Yee grid!) CSX = AddProbe(CSX,'it1a',1); mid = 0.5*(coax_rad_i+coax_rad_ai); start = [ -mid -mid mesh.z(9) ]; stop = [ mid mid mesh.z(9) ]; CSX = AddBox(CSX,'it1a', 0 ,start,stop); CSX = AddProbe(CSX,'it1b',1); start = [ -mid -mid mesh.z(10) ]; stop = [ mid mid mesh.z(10) ]; CSX = AddBox(CSX,'it1b', 0 ,start,stop); CSX = AddProbe(CSX,'it2a',1); start = [ -mid -mid mesh.z(end-11) ]; stop = [ mid mid mesh.z(end-11) ]; CSX = AddBox(CSX,'it2a', 0 ,start,stop); CSX = AddProbe(CSX,'it2b',1); start = [ -mid -mid mesh.z(end-10) ]; stop = [ mid mid mesh.z(end-10) ]; CSX = AddBox(CSX,'it2b', 0 ,start,stop); %% Write openEMS if (postprocessing_only==0) WriteOpenEMS([Sim_Path '/' Sim_CSX],FDTD,CSX); RunOpenEMS(Sim_Path, Sim_CSX, openEMS_opts); end %% freq = linspace(0,2*f0,201); U = ReadUI({'ut1','ut2'},[Sim_Path '/'],freq); I = ReadUI({'it1a','it1b','it2a','it2b'},[Sim_Path '/'],freq); Exc = ReadUI('et',Sim_Path,freq); %% plot voltages figure plot(U.TD{1}.t, U.TD{1}.val,'Linewidth',2); hold on; grid on; plot(U.TD{2}.t, U.TD{2}.val,'r--','Linewidth',2); xlabel('time (s)') ylabel('voltage (V)') legend('u_1(t)','u_2(t)') %% calculate incoming and reflected voltages & currents ZL_a = ones(size(freq))*Z0/2/pi/sqrt(epsR)*log(coax_rad_ai/coax_rad_i); %analytic line-impedance of a coax uf1 = U.FD{1}.val./Exc.FD{1}.val; uf2 = U.FD{2}.val./Exc.FD{1}.val; if1 = 0.5*(I.FD{1}.val+I.FD{2}.val)./Exc.FD{1}.val; if2 = 0.5*(I.FD{3}.val+I.FD{4}.val)./Exc.FD{1}.val; uf1_inc = 0.5 * ( uf1 + if1 .* ZL_a ); if1_inc = 0.5 * ( if1 + uf1 ./ ZL_a ); uf2_inc = 0.5 * ( uf2 + if2 .* ZL_a ); if2_inc = 0.5 * ( if2 + uf2 ./ ZL_a ); uf1_ref = uf1 - uf1_inc; if1_ref = if1 - if1_inc; uf2_ref = uf2 - uf2_inc; if2_ref = if2 - if2_inc; % plot s-parameter figure s11 = uf1_ref./uf1_inc; s21 = uf2_inc./uf1_inc; plot(freq,20*log10(abs(s11)),'Linewidth',2); xlim([freq(1) freq(end)]); xlabel('frequency (Hz)') ylabel('s-para (dB)'); % ylim([-40 5]); grid on; hold on; plot(freq,20*log10(abs(s21)),'r','Linewidth',2); legend('s11','s21','Location','SouthEast'); % plot line-impedance comparison figure() ZL = uf1./if1; plot(freq,real(ZL),'Linewidth',2); xlim([freq(1) freq(end)]); xlabel('frequency (Hz)') ylabel('line-impedance (\Omega)'); grid on; hold on; plot(freq,imag(ZL),'r--','Linewidth',2); plot(freq,ZL_a,'g-.','Linewidth',2); legend('\Re\{ZL\}','\Im\{ZL\}','ZL-analytic','Location','Best');