% % EXAMPLE / waveguide / circular waveguide cylindrical coordinates % % This example demonstrates how to: % - use cylindrical coordinates % - setup a circular waveguide defined by the boundary conditions of the % cylindrical coordinate system % - 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 use_MultiGrid = 1; % disable multi-grid for this example 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 nan 15]; %desired mesh resolution N_alpha = 50; %mesh lines in azimuth direction MultiGrid_Level = [50]; % define multigrid radii (if enabled) %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^2,15) '/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,'%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))']; %% define files and path %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Sim_Path = 'tmp'; Sim_CSX = 'Circ_WG_CC.xml'; if (postprocessing_only==0) [status, message, messageid] = rmdir(Sim_Path,'s'); [status, message, messageid] = mkdir(Sim_Path); end %% setup FDTD parameter & excitation function %%%%%%%%%%%%%%%%%%%%%%%%%%%%% if (use_MultiGrid==0) FDTD = InitCylindricalFDTD(numTS,1e-5,'OverSampling',10); else mg_str = num2str(MultiGrid_Level,'%d,'); %create comma-separated string N_alpha = round(N_alpha * 2^numel(MultiGrid_Level)); FDTD = InitCylindricalFDTD(numTS,1e-5,'OverSampling',10,'MultiGrid',mg_str(1:end-1)); end 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('CoordSystem',1); mesh.x = 0:mesh_res(1):rad; %define an odd number of lines in alpha-direction mesh.y = linspace(-pi,pi,N_alpha+mod(N_alpha+1,2))+pi/2; mesh.z = 0 : mesh_res(3) : length; CSX = DefineRectGrid(CSX, unit,mesh); %% apply the excitation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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.x(1) mesh.y(1) mesh.z(1)]; stop = [mesh.x(end) mesh.y(end) mesh.z(1)]; CSX = AddBox(CSX,'excite', 5 ,start,stop); %% define dump boxes... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CSX = AddDump(CSX,'Et_','FileType',0,'DumpMode',2,'SubSampling','2,2,2'); 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','FileType',0,'DumpType',1,'DumpMode',2,'SubSampling','2,2,2'); CSX = AddBox(CSX,'Ht',0 , start,stop); %% define voltage calc boxes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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_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); 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_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-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');