156 lines
5.1 KiB
Matlab
156 lines
5.1 KiB
Matlab
%
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% Tutorials / CRLH_Extraction
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%
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% Description at:
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% http://openems.de/index.php/Tutorial:_CRLH_Extraction
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%
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% Tested with
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% - Matlab 2011a / Octave 4.0
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% - openEMS v0.0.33
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%
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% (C) 2011-2015 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-6; % specify everything in um
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feed_length = 30000;
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substrate_thickness = [1524 101 254];
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substrate_epsr = [3.48 3.48 3.48];
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CRLH.LL = 14e3; %CRLH totel (line) length
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CRLH.LW = 4e3; %CRLH unit cell width (without the stubs)
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CRLH.GLB = 1950; %CRLH gap width bottom layer
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CRLH.GLT = 4700; %CRLH gap width top layer
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CRLH.SL = 7800; %CRLH stub length (bottom layer, both sides)
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CRLH.SW = 1000; %CRLH stub width (bottom layer, both sides)
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CRLH.VR = 250; %CRLH via hole radius (stub -> ground)
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CRLH.TopSig = sum(substrate_thickness); %top layer height
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CRLH.BottomSig = CRLH.TopSig - substrate_thickness(end); %bottom layer height
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% frequency range of interest
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f_start = 0.8e9;
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f_stop = 6e9;
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%% setup FDTD parameters & excitation function %%%%%%%%%%%%%%%%%%%%%%%%%%%%
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FDTD = InitFDTD();
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FDTD = SetGaussExcite( FDTD, (f_start+f_stop)/2, (f_stop-f_start)/2 );
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BC = {'PML_8' 'PML_8' 'MUR' 'MUR' 'PEC' 'PML_8'};
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FDTD = SetBoundaryCond( FDTD, BC );
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%% Setup a basic mesh and create the CRLH unit cell
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CSX = InitCSX();
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resolution = c0/(f_stop*sqrt(max(substrate_epsr)))/unit /30; % resolution of lambda/30
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mesh.x = [-feed_length-CRLH.LL/2 0 feed_length+CRLH.LL/2];
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mesh.y = [-30000 0 30000];
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substratelines = cumsum(substrate_thickness);
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mesh.z = [0 cumsum(substrate_thickness) linspace(substratelines(end-1),substratelines(end),4) 20000];
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% create the CRLH unit cell (will define additional fixed mesh lines)
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[CSX mesh] = CreateCRLH(CSX, mesh, CRLH, resolution/4);
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% Smooth the given mesh
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mesh = SmoothMesh(mesh, resolution, 1.5, 'algorithm',[1 3]);
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CSX = DefineRectGrid( CSX, unit, mesh );
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%% Setup the substrate layer
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substratelines = [0 substratelines];
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for n=1:numel(substrate_thickness)
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CSX = AddMaterial( CSX, ['substrate' int2str(n)] );
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CSX = SetMaterialProperty( CSX, ['substrate' int2str(n)], 'Epsilon', substrate_epsr(n) );
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start = [mesh.x(1), mesh.y(1), substratelines(n)];
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stop = [mesh.x(end), mesh.y(end), substratelines(n+1)];
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CSX = AddBox( CSX, ['substrate' int2str(n)], 0, start, stop );
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end
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%% add the feeding MSL ports
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CSX = AddMetal( CSX, 'PEC' );
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portstart = [ mesh.x(1) , -CRLH.LW/2, substratelines(end)];
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portstop = [ -CRLH.LL/2, CRLH.LW/2, 0];
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[CSX,port{1}] = AddMSLPort( CSX, 999, 1, 'PEC', portstart, portstop, 0, [0 0 -1], 'ExcitePort', true, 'FeedShift', 10*resolution(1), 'MeasPlaneShift', feed_length/2);
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portstart = [ mesh.x(end) , -CRLH.LW/2, substratelines(end)];
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portstop = [ +CRLH.LL/2, CRLH.LW/2, 0];
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[CSX,port{2}] = AddMSLPort( CSX, 999, 2, 'PEC', portstart, portstop, 0, [0 0 -1], 'MeasPlaneShift', feed_length/2 );
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%% write/show/run the openEMS compatible xml-file
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Sim_Path = 'tmp';
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Sim_CSX = 'CRLH.xml';
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[status, message, messageid] = rmdir( Sim_Path, 's' ); % clear previous directory
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[status, message, messageid] = mkdir( Sim_Path ); % create empty simulation folder
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WriteOpenEMS( [Sim_Path '/' Sim_CSX], FDTD, CSX );
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CSXGeomPlot( [Sim_Path '/' Sim_CSX] );
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RunOpenEMS( Sim_Path, Sim_CSX );
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%% post-processing
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close all
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f = linspace( f_start, f_stop, 1601 );
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port = calcPort( port, Sim_Path, f, 'RefPlaneShift', feed_length);
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s11 = port{1}.uf.ref./ port{1}.uf.inc;
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s21 = port{2}.uf.ref./ port{1}.uf.inc;
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plot(f/1e9,20*log10(abs(s11)),'k-','LineWidth',2);
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hold on;
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grid on;
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plot(f/1e9,20*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 (GHz) \rightarrow','FontSize',12);
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ylim([-40 2]);
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%% extract parameter
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A = ((1+s11).*(1-s11) + s21.*s21)./(2*s21);
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C = ((1-s11).*(1-s11) - s21.*s21)./(2*s21) ./ port{2}.ZL;
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Y = C;
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Z = 2*(A-1)./C;
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iZ = imag(Z);
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iY = imag(Y);
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fse = interp1(iZ,f,0);
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fsh = interp1(iY,f,0);
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df = f(2)-f(1);
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fse_idx = find(f>fse,1);
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fsh_idx = find(f>fsh,1);
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LR = 0.5*(iZ(fse_idx)-iZ(fse_idx-1))./(2*pi*df);
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CL = 1/(2*pi*fse)^2/LR;
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CR = 0.5*(iY(fsh_idx)-iY(fsh_idx-1))./(2*pi*df);
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LL = 1/(2*pi*fsh)^2/CR;
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disp([' Series tank: CL = ' num2str(CL*1e12,3) 'pF; LR = ' num2str(LR*1e9,3) 'nH -> f_se = ' num2str(fse*1e-9,3) 'GHz ']);
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disp([' Shunt tank: CR = ' num2str(CR*1e12,3) 'pF; LL = ' num2str(LL*1e9,3) 'nH -> f_sh = ' num2str(fsh*1e-9,3) 'GHz ']);
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%% calculate analytical wave-number of an inf-array of cells
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w = 2*pi*f;
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wse = 2*pi*fse;
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wsh = 2*pi*fsh;
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beta_calc = real(acos(1-(w.^2-wse^2).*(w.^2-wsh^2)./(2*w.^2/CR/LR)));
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%%
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figure
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beta = -angle(s21)/CRLH.LL/unit;
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plot(abs(beta)*CRLH.LL*unit/pi,f*1e-9,'k-','LineWidth',2)
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grid on;
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hold on;
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plot(beta_calc/pi,f*1e-9,'c--','LineWidth',2)
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plot(real(port{2}.beta)*CRLH.LL*unit/pi,f*1e-9,'g-','LineWidth',2)
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ylim([1 6])
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xlabel('|\beta| p / \pi \rightarrow','FontSize',12)
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ylabel('frequency (GHz) \rightarrow','FontSize',12)
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l = legend('\beta_{CRLH, 1 cell}','\beta_{CRLH, \infty cells}','\beta_{MSL}','Location','East');
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set(l,'FontSize',12);
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