From 240ed0a3079d4d95ae5aa2226d840e89280167cc Mon Sep 17 00:00:00 2001
From: Thorsten Liebig <Thorsten.Liebig@gmx.de>
Date: Thu, 15 Sep 2011 12:16:54 +0200
Subject: [PATCH] tutorial for a circular waveguide added

---
 Tutorials/Circ_Waveguide.m | 165 +++++++++++++++++++++++++++++++++++++
 1 file changed, 165 insertions(+)
 create mode 100644 Tutorials/Circ_Waveguide.m

diff --git a/Tutorials/Circ_Waveguide.m b/Tutorials/Circ_Waveguide.m
new file mode 100644
index 0000000..13e0559
--- /dev/null
+++ b/Tutorials/Circ_Waveguide.m
@@ -0,0 +1,165 @@
+%
+% Tutorials / Circ_Waveguide
+%
+% Describtion at:
+% http://openems.de/index.php/Tutorial:_Circular_Waveguide
+%
+% Tested with
+%  - Matlab 2009b
+%  - openEMS v0.0.23
+%
+% (C) 2010,2011 Thorsten Liebig <thorsten.liebig@gmx.de>
+
+close all
+clear
+clc
+
+%% setup the simulation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+physical_constants;
+unit = 1e-3; %drawing unit in mm
+numTS = 50000; %max. number of timesteps
+
+% waveguide dimensions
+length = 2000;
+rad = 350;     %waveguide radius in mm
+
+% frequency range of interest
+f_start =  300e6;
+f_stop  =  500e6;
+
+mesh_res = [10 2*pi/49.999 10]; %targeted mesh resolution
+
+%% mode functions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% by David M. Pozar, Microwave Engineering, third edition
+freq = linspace(f_start,f_stop,201);
+p11 = 1.841;
+kc = p11 / rad /unit;
+k = 2*pi*freq/C0;
+fc = C0*kc/2/pi;
+beta = sqrt(k.^2 - kc^2);
+n_eff = (beta/k);
+ZL_a = k * Z0 ./ beta;    %analytic waveguide impedance
+
+% TE_11 mode profile E- and H-field
+kc = kc*unit; %functions must be defined in drawing units
+func_Er = [ num2str(-1/kc^2,15) '/rho*cos(a)*j1('  num2str(kc,15) '*rho)'];
+func_Ea = [ num2str(1/kc,15) '*sin(a)*0.5*(j0('  num2str(kc,15) '*rho)-jn(2,'  num2str(kc,15) '*rho))'];
+
+func_Ha = [ num2str(-1/kc^2,15) '/rho*cos(a)*j1('  num2str(kc,15) '*rho)'];
+func_Hr = [ '-1*' num2str(1/kc,15) '*sin(a)*0.5*(j0('  num2str(kc,15) '*rho)-jn(2,'  num2str(kc,15) '*rho))'];
+
+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
+
+%% setup FDTD parameter & excitation function %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+FDTD = InitCylindricalFDTD(numTS,1e-5,'OverSampling',6);
+FDTD = SetGaussExcite(FDTD,0.5*(f_start+f_stop),0.5*(f_stop-f_start));
+
+% boundary conditions
+BC = [0 0 0 0 3 3]; %pml in pos. and neg. z-direction
+FDTD = SetBoundaryCond(FDTD,BC);
+
+%% setup CSXCAD mesh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+CSX = InitCSX('CoordSystem',1); % init a cylindrical mesh
+mesh.r = SmoothMeshLines([0 rad], mesh_res(1)); %mesh in radial direction
+mesh.a = SmoothMeshLines([0 2*pi], mesh_res(2)); % mesh in aziumthal dir.
+mesh.z = SmoothMeshLines([0 length], mesh_res(3));
+CSX = DefineRectGrid(CSX, unit,mesh);
+
+%% apply the excitation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% ra-mode profile excitation located directly on top of pml (first 8 z-lines)
+CSX = AddExcitation(CSX,'excite',0,[1 1 0]);
+weight{1} = func_Er;
+weight{2} = func_Ea;
+weight{3} = 0;
+CSX = SetExcitationWeight(CSX,'excite',weight);
+start=[mesh.r(1)   mesh.a(1)   mesh.z(8) ];
+stop =[mesh.r(end) mesh.a(end) mesh.z(8) ];
+CSX = AddBox(CSX,'excite',0 ,start,stop);
+
+%% voltage and current definitions using the mode matching probes %%%%%%%%%
+%port 1
+start = [mesh.r(1)   mesh.a(1)   mesh.z(15)];
+stop  = [mesh.r(end) mesh.a(end) mesh.z(15)];
+CSX = AddProbe(CSX, 'ut1', 10, 1, [], 'ModeFunction',{func_Er,func_Ea,0});
+CSX = AddBox(CSX,  'ut1',  0 ,start,stop);
+CSX = AddProbe(CSX,'it1', 11, 1, [], 'ModeFunction',{func_Hr,func_Ha,0});
+CSX = AddBox(CSX,'it1', 0 ,start,stop);
+
+%port 2
+start(3) = mesh.z(end-14);
+stop(3) = mesh.z(end-14);
+CSX = AddProbe(CSX, 'ut2', 10, 1, [], 'ModeFunction',{func_Er,func_Ea,0});
+CSX = AddBox(CSX,  'ut2',  0 ,start,stop);
+CSX = AddProbe(CSX,'it2', 11, 1, [], 'ModeFunction',{func_Hr,func_Ha,0});
+CSX = AddBox(CSX,'it2', 0 ,start,stop);
+
+port_dist = mesh.z(end-14) - mesh.z(15);
+ 
+%% define dump box... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+CSX = AddDump(CSX,'Et','FileType',1,'SubSampling','4,4,4');
+start = [mesh.r(1)   mesh.a(1)   mesh.z(1)];
+stop  = [mesh.r(end) mesh.a(end) mesh.z(end)];
+CSX = AddBox(CSX,'Et',0 , start,stop);
+
+%% Write openEMS compatoble xml-file %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+Sim_Path = 'tmp';
+Sim_CSX = 'rect_wg.xml';
+
+[status, message, messageid] = rmdir(Sim_Path,'s');
+[status, message, messageid] = mkdir(Sim_Path);
+
+WriteOpenEMS([Sim_Path '/' Sim_CSX],FDTD,CSX);
+
+RunOpenEMS(Sim_Path, Sim_CSX)
+
+%% 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_inc - if1; 
+uf2_ref = uf2 - uf2_inc;
+if2_ref = if2_inc - if2;
+
+%% plot s-parameter %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+figure
+s11 = uf1_ref./uf1_inc;
+s21 = uf2_inc./uf1_inc;
+plot(freq*1e-6,20*log10(abs(s11)),'k-','Linewidth',2);
+xlim([freq(1) freq(end)]*1e-6);
+grid on;
+hold on;
+plot(freq*1e-6,20*log10(abs(s21)),'r--','Linewidth',2);
+l = legend('S_{11}','S_{21}','Location','Best');
+set(l,'FontSize',12);
+ylabel('S-Parameter (dB)','FontSize',12);
+xlabel('frequency (MHz) \rightarrow','FontSize',12);
+
+%% compare analytic and numerical wave-impedance %%%%%%%%%%%%%%%%%%%%%%%%%%
+figure
+ZL = uf1./if1;
+plot(freq*1e-6,real(ZL),'Linewidth',2);
+hold on;
+grid on;
+plot(freq*1e-6,imag(ZL),'r--','Linewidth',2);
+plot(freq*1e-6,ZL_a,'g-.','Linewidth',2);
+ylabel('ZL (\Omega)','FontSize',12);
+xlabel('frequency (MHz) \rightarrow','FontSize',12);
+xlim([freq(1) freq(end)]*1e-6);
+l = legend('\Re(Z_L)','\Im(Z_L)','Z_L analytic','Location','Best');
+set(l,'FontSize',12);