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+%
+% EXAMPLE / waveguide / circular waveguide
+%
+% This example demonstrates how to:
+% - setup a circular waveguide
+% - use analytic functions for waveguide excitations and voltage/current
+% calculations
+%
+%
+% Tested with
+% - Matlab 2009b
+% - openEMS v0.0.17
+%
+% (C) 2010 Thorsten Liebig <thorsten.liebig@uni-due.de>
+
+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 = 1e5; %number of timesteps
+length = 1000; %length of the waveguide
+unit = 1e-3; %drawing unit used
+rad = 300; %radius of the circular waveguide
+mesh_res = [10 10 15]; %desired mesh resolution
+
+%excitation
+f0 = 350e6; %center frequency
+f0_BW = 25e6; %bandwidth: 10dB cut-off frequency
+
+physical_constants
+
+%% TE11 mode definitions (Pozar 3rd edition)
+p11 = 1.841;
+kc = p11 / rad /unit;
+k = 2*pi*f0/C0;
+fc = C0*kc/2/pi;
+beta = sqrt(k^2 - kc^2);
+n_eff = (beta/k);
+
+kc = kc*unit; %functions must be defined in drawing units
+func_Er = [ num2str(-1/kc^2) '/rho*cos(a)*j1(' num2str(kc) '*rho)'];
+func_Ea = [ num2str(1/kc) '*sin(a)*0.5*(j0(' num2str(kc) '*rho)-jn(2,' num2str(kc) '*rho))'];
+func_Ex = ['(' func_Er '*cos(a) - ' func_Ea '*sin(a) )*(rho<' num2str(rad) ')'];
+func_Ey = ['(' func_Er '*sin(a) + ' func_Ea '*cos(a) )*(rho<' num2str(rad) ')'];
+
+func_Ha = [ num2str(-1/kc^2,'%14.13f') '/rho*cos(a)*j1(' num2str(kc,'%14.13f') '*rho)'];
+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))'];
+func_Hx = ['(' func_Hr '*cos(a) - ' func_Ha '*sin(a) )*(rho<' num2str(rad) ')'];
+func_Hy = ['(' func_Hr '*sin(a) + ' func_Ha '*cos(a) )*(rho<' num2str(rad) ')'];
+
+%% define files and path %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+Sim_Path = 'tmp';
+Sim_CSX = 'Circ_WG.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-6,'OverSampling',5);
+FDTD = SetGaussExcite(FDTD,f0,f0_BW);
+BC = {'PEC','PEC','PEC','PEC','PEC','MUR'};
+if (use_pml>0)
+ BC = {'PEC','PEC','PEC','PEC','PEC','PML_8'};
+end
+FDTD = SetBoundaryCond(FDTD,BC,'MUR_PhaseVelocity',C0 / n_eff);
+
+%% setup CSXCAD geometry & mesh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+CSX = InitCSX();
+mesh.x = -mesh_res(1)/2-rad:mesh_res(1):rad+mesh_res(1)/2;
+mesh.y = -mesh_res(2)/2-rad:mesh_res(2):rad+mesh_res(2)/2;
+mesh.z = 0 : mesh_res(3) : length;
+CSX = DefineRectGrid(CSX, 1e-3,mesh);
+
+start = [0,0,0];
+stop = [0,0,length];
+
+%%% fill everything with copper, priority 0
+CSX = AddMetal(CSX,'copper');
+% CSX = SetMaterialProperty(CSX,'copper','Kappa',56e6);
+CSX = AddBox(CSX,'copper',0,[mesh.x(1) mesh.y(1) mesh.z(1)],[mesh.x(end) mesh.y(end) mesh.z(end)]);
+
+%%% cut out an air cylinder as circular waveguide... priority 5
+CSX = AddMaterial(CSX,'air');
+CSX = SetMaterialProperty(CSX,'air','Epsilon',1);
+CSX = AddCylinder(CSX,'air', 5 ,start,stop,rad);
+
+CSX = AddExcitation(CSX,'excite',0,[1 1 0]);
+weight{1} = func_Ex;
+weight{2} = func_Ey;
+weight{3} = 0;
+CSX = SetExcitationWeight(CSX, 'excite', weight );
+CSX = AddCylinder(CSX,'excite', 5 ,[0 0 -0.1],[0 0 0.1],rad);
+
+%% define dump boxes... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+CSX = AddDump(CSX,'Et_','SubSampling','2,2,2','FileType',0,'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_','SubSampling','2,2,2','DumpType',1,'FileType',0,'DumpMode',2);
+CSX = AddBox(CSX,'Ht_',0,start,stop);
+
+%% define voltage calc boxes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%voltage calc
+start = [mesh.x(1) mesh.y(1) mesh.z(10)];
+stop = [mesh.x(end) mesh.y(end) mesh.z(10)];
+CSX = AddProbe(CSX, 'ut1', 10, 1, [], 'ModeFunction',{func_Ex,func_Ey,0});
+CSX = AddBox(CSX, 'ut1', 0 ,start,stop);
+CSX = AddProbe(CSX,'it1', 11, 1, [], 'ModeFunction',{func_Hx,func_Hy,0});
+CSX = AddBox(CSX,'it1', 0 ,start,stop);
+
+start = [mesh.x(1) mesh.y(1) mesh.z(end-10)];
+stop = [mesh.x(end) mesh.y(end) mesh.z(end-10)];
+CSX = AddProbe(CSX, 'ut2', 10, 1, [], 'ModeFunction',{func_Ex,func_Ey,0});
+CSX = AddBox(CSX, 'ut2', 0 ,start,stop);
+CSX = AddProbe(CSX,'it2', 11, 1, [], 'ModeFunction',{func_Hx,func_Hy,0});
+CSX = AddBox(CSX,'it2', 0 ,start,stop);
+
+port_dist = mesh.z(end-10) - mesh.z(10);
+
+%% Write openEMS
+if (postprocessing_only==0)
+ WriteOpenEMS([Sim_Path '/' Sim_CSX],FDTD,CSX);
+
+ RunOpenEMS(Sim_Path, Sim_CSX, openEMS_opts);
+end
+
+%% do the plots %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+freq = linspace(f0-f0_BW,f0+f0_BW,201);
+U = ReadUI({'ut1','ut2'},[Sim_Path '/'],freq);
+I = ReadUI({'it1','it2'},[Sim_Path '/'],freq);
+Exc = ReadUI('et',Sim_Path,freq);
+
+k = 2*pi*freq/C0;
+kc = p11 / rad /unit;
+beta = sqrt(k.^2 - kc^2);
+
+ZL_a = Z0*k./beta ;
+
+uf1 = U.FD{1}.val./Exc.FD{1}.val;
+uf2 = U.FD{2}.val./Exc.FD{1}.val;
+if1 = I.FD{1}.val./Exc.FD{1}.val;
+if2 = I.FD{2}.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');
+
+% beta compare
+figure()
+da = angle(uf1_inc)-angle(uf2_inc);
+da = mod(da,2*pi);
+beta_12 = (da)/port_dist/unit;
+plot(freq,beta_12,'Linewidth',2);
+xlim([freq(1) freq(end)]);
+xlabel('frequency (Hz)');
+ylabel('\beta (m^{-1})');
+grid on;
+hold on;
+plot(freq,beta,'g--','Linewidth',2);
+legend('\beta-FDTD','\beta-analytic','Location','Best');
+
+%% visualize electric & magnetic fields
+disp('you will find vtk dump files in the simulation folder (tmp/)')
+disp('use paraview to visulaize them');