tutorial for a rectangular waveguide added
Thorsten Liebig
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%
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% Tutorials / Rect_Waveguide
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%
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% Describtion at:
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% http://openems.de/index.php/Tutorial:_Rectangular_Waveguide
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%
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% Tested with
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% - Matlab 2009b
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% - openEMS v0.0.23
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%
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% (C) 2010,2011 Thorsten Liebig <thorsten.liebig@gmx.de>
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close all
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clear
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clc
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%% setup the simulation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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physical_constants;
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unit = 1e-3; %drawing unit in mm
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numTS = 50000; %max. number of timesteps
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% waveguide dimensions
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length = 5000;
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a = 1000; %waveguide width
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b = 1000; %waveguide heigth
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% frequency range of interest
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f_start = 300e6;
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f_stop = 500e6;
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%waveguide TE-mode definition
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m = 1;
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n = 1;
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mesh_res = [10 10 10]; %targeted mesh resolution
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%% mode functions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% by David M. Pozar, Microwave Engineering, third edition, page 113
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freq = linspace(f_start,f_stop,201);
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k = 2*pi*freq/c0;
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kc = sqrt((m*pi/a/unit)^2 + (n*pi/b/unit)^2);
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fc = c0*kc/2/pi; %cut-off frequency
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beta = sqrt(k.^2 - kc^2); %waveguide phase-constant
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ZL_a = k * Z0 ./ beta; %analytic waveguide impedance
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% mode profile E- and H-field
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func_Ex = [num2str( n/b/unit) '*cos(' num2str(m*pi/a) '*x)*sin(' num2str(n*pi/b) '*y)'];
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func_Ey = [num2str(-m/a/unit) '*sin(' num2str(m*pi/a) '*x)*cos(' num2str(n*pi/b) '*y)'];
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func_Hx = [num2str(m/a/unit) '*sin(' num2str(m*pi/a) '*x)*cos(' num2str(n*pi/b) '*y)'];
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func_Hy = [num2str(n/b/unit) '*cos(' num2str(m*pi/a) '*x)*sin(' num2str(n*pi/b) '*y)'];
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disp([' Cutoff frequencies for this mode and wavguide is: ' num2str(fc/1e6) ' MHz']);
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if (f_start<fc)
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warning('openEMS:example','f_start is smaller than the cutoff-frequency, this may result in a long simulation... ');
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end
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%% setup FDTD parameter & excitation function %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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FDTD = InitFDTD(numTS,1e-5,'OverSampling',6);
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FDTD = SetGaussExcite(FDTD,0.5*(f_start+f_stop),0.5*(f_stop-f_start));
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% boundary conditions
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BC = [0 0 0 0 3 3]; %pml in pos. and neg. z-direction
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FDTD = SetBoundaryCond(FDTD,BC);
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%% setup CSXCAD mesh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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CSX = InitCSX();
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mesh.x = SmoothMeshLines([0 a], mesh_res(1));
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mesh.y = SmoothMeshLines([0 b], mesh_res(2));
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mesh.z = SmoothMeshLines([0 length], mesh_res(3));
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CSX = DefineRectGrid(CSX, unit,mesh);
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%% apply the excitation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% xy-mode profile excitation located directly on top of pml (first 8 z-lines)
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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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start=[mesh.x(1) mesh.y(1) mesh.z(8) ];
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stop =[mesh.x(end) mesh.y(end) mesh.z(8) ];
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CSX = AddBox(CSX,'excite',0 ,start,stop);
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%% voltage and current definitions using the mode matching probes %%%%%%%%%
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%port 1
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start = [mesh.x(1) mesh.y(1) mesh.z(15)];
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stop = [mesh.x(end) mesh.y(end) mesh.z(15)];
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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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%port 2
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start = [mesh.x(1) mesh.y(1) mesh.z(end-14)];
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stop = [mesh.x(end) mesh.y(end) mesh.z(end-14)];
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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-14) - mesh.z(15);
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%% define dump box... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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CSX = AddDump(CSX,'Et','FileType',1,'SubSampling','4,4,4');
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start = [mesh.x(1) mesh.y(1) mesh.z(1)];
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stop = [mesh.x(end) mesh.y(end) mesh.z(end)];
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CSX = AddBox(CSX,'Et',0 , start,stop);
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%% Write openEMS compatoble xml-file %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Sim_Path = 'tmp';
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Sim_CSX = 'rect_wg.xml';
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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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WriteOpenEMS([Sim_Path '/' Sim_CSX],FDTD,CSX);
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RunOpenEMS(Sim_Path, Sim_CSX)
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%% postproc %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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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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_inc - if1;
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uf2_ref = uf2 - uf2_inc;
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if2_ref = if2_inc - if2;
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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*1e-6,20*log10(abs(s11)),'k-','Linewidth',2);
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xlim([freq(1) freq(end)]*1e-6);
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grid on;
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hold on;
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plot(freq*1e-6,20*log10(abs(s21)),'r--','Linewidth',2);
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l = legend('S_{11}','S_{21}','Location','Best');
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set(l,'FontSize',12);
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ylabel('S-Parameter (dB)','FontSize',12);
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xlabel('frequency (MHz) \rightarrow','FontSize',12);
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%% compare analytic and numerical wave-impedance %%%%%%%%%%%%%%%%%%%%%%%%%%
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figure
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ZL = uf1./if1;
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plot(freq*1e-6,real(ZL),'Linewidth',2);
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hold on;
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grid on;
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plot(freq*1e-6,imag(ZL),'r--','Linewidth',2);
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plot(freq*1e-6,ZL_a,'g-.','Linewidth',2);
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ylabel('ZL (\Omega)','FontSize',12);
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xlabel('frequency (MHz) \rightarrow','FontSize',12);
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xlim([freq(1) freq(end)]*1e-6);
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l = legend('\Re(Z_L)','\Im(Z_L)','Z_L analytic','Location','Best');
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set(l,'FontSize',12);
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%% Plot the field dumps %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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figure
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dump_file = [Sim_Path '/Et.h5'];
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PlotArgs.slice = {a/2*unit b/2*unit 0};
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PlotArgs.pauseTime=0.01;
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PlotArgs.component=0;
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PlotArgs.Limit = 'auto';
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PlotHDF5FieldData(dump_file, PlotArgs)
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