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+%
+% EXAMPLE / waveguide / Rect_Waveguide
+%
+% This example demonstrates:
+% - waveguide mode excitation
+% - waveguide mode matching
+% - pml absorbing boundaries
+%
+%
+% Tested with
+% - Matlab 2009b
+% - openEMS v0.0.17
+%
+% (C) 2010 Thorsten Liebig <thorsten.liebig@gmx.de>
+
+close all
+clear
+clc
+
+%% switches
+postproc_only = 0;
+
+%% setup the simulation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+physical_constants;
+unit = 1e-3; %drawing unit in mm
+numTS = 50000; %max. number of timesteps
+
+% waveguide dimensions
+length = 1000;
+a = 1000; %waveguide width
+b = 600; %waveguide heigth
+
+%waveguide TE-mode definition
+m = 1;
+n = 0;
+
+mesh_res = [10 10 10];
+
+%% setup FDTD parameters & excitation function %%%%%%%%%%%%%%%%%%%%%%%%%%%%
+f_start = 175e6;
+f_stop = 500e6;
+
+% dump special frequencies to vtk, use paraview (www.paraview.org) to
+% animate this dumps over phase
+vtk_dump_freq = [200e6 300e6 500e6];
+
+freq = linspace(f_start,f_stop,201);
+
+k = 2*pi*freq/c0;
+kc = sqrt((m*pi/a/unit)^2 + (n*pi/b/unit)^2);
+fc = c0*kc/2/pi; %cut-off frequency
+beta = sqrt(k.^2 - kc^2); %waveguide phase-constant
+ZL_a = k * Z0 ./ beta; %analytic waveguide impedance
+
+disp([' Cutoff frequencies for this mode and wavguide is: ' num2str(fc/1e6) ' MHz']);
+
+if (f_start<fc)
+ warning('openEMS:example','f_start is smaller than the cutoff-frequency, this may result in a long simulation... ');
+end
+
+%% mode functions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% by David M. Pozar, Microwave Engineering, third edition, page 113
+func_Ex = [num2str( n/b/unit) '*cos(' num2str(m*pi/a) '*x)*sin(' num2str(n*pi/b) '*y)'];
+func_Ey = [num2str(-m/a/unit) '*sin(' num2str(m*pi/a) '*x)*cos(' num2str(n*pi/b) '*y)'];
+
+func_Hx = [num2str(m/a/unit) '*sin(' num2str(m*pi/a) '*x)*cos(' num2str(n*pi/b) '*y)'];
+func_Hy = [num2str(n/b/unit) '*cos(' num2str(m*pi/a) '*x)*sin(' num2str(n*pi/b) '*y)'];
+
+%% define and openEMS options %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+openEMS_opts = '';
+% openEMS_opts = [openEMS_opts ' --disable-dumps'];
+% openEMS_opts = [openEMS_opts ' --debug-material'];
+% openEMS_opts = [openEMS_opts ' --engine=basic'];
+
+Settings = [];
+Settings.LogFile = 'openEMS.log';
+
+Sim_Path = 'tmp';
+Sim_CSX = 'rect_wg.xml';
+
+if (postproc_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,'OverSampling',6);
+FDTD = SetGaussExcite(FDTD,0.5*(f_start+f_stop),0.5*(f_stop-f_start));
+BC = [0 0 0 0 0 3];
+FDTD = SetBoundaryCond(FDTD,BC);
+
+%% setup CSXCAD geometry & mesh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+CSX = InitCSX();
+mesh.x = SmoothMeshLines([0 a], mesh_res(1));
+mesh.y = SmoothMeshLines([0 b], mesh_res(2));
+mesh.z = SmoothMeshLines([0 length], mesh_res(3));
+CSX = DefineRectGrid(CSX, unit,mesh);
+
+%% apply the excitation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+start=[mesh.x(1) mesh.y(1) mesh.z(1) ];
+stop =[mesh.x(end) mesh.y(end) mesh.z(1) ];
+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 = AddBox(CSX,'excite',0 ,start,stop);
+
+%% voltage and current definitions using the mode matching probes %%%%%%%%%
+%port 1
+start = [mesh.x(1) mesh.y(1) mesh.z(15)];
+stop = [mesh.x(end) mesh.y(end) mesh.z(15)];
+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);
+
+%port 2
+start = [mesh.x(1) mesh.y(1) mesh.z(end-15)];
+stop = [mesh.x(end) mesh.y(end) mesh.z(end-15)];
+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-15) - mesh.z(15);
+
+%% define dump boxes... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+CSX = AddDump(CSX,'Et','FileType',1,'SubSampling','4,4,2');
+start = [mesh.x(1) mesh.y(1) mesh.z(1)];
+stop = [mesh.x(end) mesh.y(end) mesh.z(end)];
+CSX = AddBox(CSX,'Et',0 , start,stop);
+
+CSX = AddDump(CSX,'Ht','DumpType',1,'FileType',1,'SubSampling','4,4,2');
+CSX = AddBox(CSX,'Ht',0,start,stop);
+
+%% Write openEMS compatoble xml-file %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+if (postproc_only==0)
+ WriteOpenEMS([Sim_Path '/' Sim_CSX],FDTD,CSX);
+
+ RunOpenEMS(Sim_Path, Sim_CSX, openEMS_opts, Settings)
+end
+
+%% postproc %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+U = ReadUI({'ut1','ut2'},[Sim_Path '/'],freq);
+I = ReadUI({'it1','it2'},[Sim_Path '/'],freq);
+Exc = ReadUI('et',Sim_Path,freq);
+
+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)]);
+% ylim([-40 5]);
+grid on;
+hold on;
+plot(freq,20*log10(abs(s21)),'r','Linewidth',2);
+legend('s11','s21','Location','SouthEast');
+ylabel('s-para (dB)');
+xlabel('freq (Hz)');
+
+%% compare analytic and numerical wave-impedance %%%%%%%%%%%%%%%%%%%%%%%%%%
+ZL = uf1./if1;
+figure()
+plot(freq,real(ZL),'Linewidth',2);
+hold on;
+grid on;
+plot(freq,imag(ZL),'r--','Linewidth',2);
+plot(freq,ZL_a,'g-.','Linewidth',2);
+ylabel('ZL (\Omega)');
+xlabel('freq (Hz)');
+xlim([freq(1) freq(end)]);
+legend('\Re(Z_L)','\Im(Z_L)','Z_L analytic','Location','Best');
+
+%% beta compare
+figure()
+da = unwrap(angle(uf1_inc./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');
+
+%% Plot the field dumps %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+dump_file = [Sim_Path '/Et.h5'];
+figure()
+PlotArgs.slice = {a/2*unit b/2*unit 0};
+PlotArgs.pauseTime=0.01;
+PlotArgs.component=0;
+PlotArgs.Limit = 'auto';
+PlotHDF5FieldData(dump_file, PlotArgs)
+
+%% dump frequency to vtk %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% cleanup and create dump folder
+vtk_path = [Sim_Path '/vtk'];
+[status, message, messageid] = rmdir(vtk_path,'s');
+[status, message, messageid] = mkdir(vtk_path);
+
+disp('Dumping to vtk files... this may take a minute...')
+% define interpolation mesh
+mesh_interp{1}=mesh.x * unit;
+mesh_interp{2}=b/2 * unit;
+mesh_interp{3}=mesh.z * unit;
+[field mesh_FD] = ReadHDF5Dump(dump_file,'Interpolation',mesh_interp,'Frequency',vtk_dump_freq);
+
+% dump animated phase to vtk
+for n=1:numel(vtk_dump_freq)
+ phase = linspace(0,360,21);
+ phase = phase(1:end-1);
+ for ph = phase
+ filename = [vtk_path '/E_xz_f=' num2str(vtk_dump_freq(n)) '_p' num2str(ph) '.vtk'];
+ Dump2VTK(filename,real(field.FD.values{n}.*exp(1j*ph/180*pi)),mesh_FD,'E-Field');
+ end
+
+ filename = [vtk_path '/E_xz_f=' num2str(vtk_dump_freq(n)) '_mag.vtk'];
+ Dump2VTK(filename,abs(field.FD.values{n}),mesh_FD,'E-Field');
+end
+
+disp('done... you can open and visualize the vtk-files using Paraview (www.paraview.org)!')