197 lines
6.2 KiB
Matlab
197 lines
6.2 KiB
Matlab
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% fake-PML parallel plate waveguide example
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%
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% this example analyzes the reflection coefficient of a vacuum-pml
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% interface
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%
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%
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% currently this example uses a normal material with a certain conductivity
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% profile and not a pml
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%
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close all
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% clear
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clc
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physical_constants
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postprocessing_only = 0;
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%% setup the simulation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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drawingunit = 1e-6; % specify everything in um
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length = 10000;
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epr = 1;
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mesh_res = [200 200 200];
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max_timesteps = 100000;
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min_decrement = 1e-6;
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f_max = 8e9;
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%% setup FDTD parameters & excitation function %%%%%%%%%%%%%%%%%%%%%%%%%%%%
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FDTD = InitFDTD( max_timesteps, min_decrement );
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FDTD = SetGaussExcite( FDTD, f_max/2, f_max/2 );
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BC = [0 0 1 1 0 0];
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FDTD = SetBoundaryCond( FDTD, BC );
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%% mesh grading
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N_pml = 8;
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pml_delta = cumsum(mesh_res(1) * 1.0 .^ (1:N_pml));
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% pml_delta = cumsum([200 200 200 200 200]);
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%% setup CSXCAD geometry & mesh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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CSX = InitCSX();
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mesh.x = 0 : mesh_res(1) : length;
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mesh.x = [mesh.x(1) - fliplr(pml_delta), mesh.x];
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mesh.y = -2*mesh_res(2) : mesh_res(2) : 2*mesh_res(2);
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mesh.z = 0 : mesh_res(3) : 4*mesh_res(3);
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CSX = DefineRectGrid( CSX, drawingunit, mesh );
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%% fake pml %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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g = 2; % 2..3
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R0 = 1e-6; % requested analytical reflection coefficient
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Zm = sqrt(MUE0/(EPS0*epr)); % calculate reflection for substrate/pml interface
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delta = pml_delta(end) * drawingunit;
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deltal = mean(diff(pml_delta)) * drawingunit;
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kappa0 = -log(R0)*log(g)/( 2*Zm*deltal*(g^(delta/deltal)-1) );
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% kappa0 = 1.05;
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CSX = AddMaterial( CSX, 'pml_xmin' );
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CSX = SetMaterialProperty( CSX, 'pml_xmin', 'Epsilon', epr );
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CSX = SetMaterialProperty( CSX, 'pml_xmin', 'Kappa', kappa0 );
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CSX = SetMaterialProperty( CSX, 'pml_xmin', 'Sigma', kappa0 * MUE0/(EPS0*epr) );
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CSX = SetMaterialWeight( CSX, 'pml_xmin', 'Kappa', [num2str(g) '^((abs(x-100)-' num2str(abs(mesh.x(N_pml+1))) ')/(' num2str(deltal) '/' num2str(drawingunit) '))'] ); % g^(rho/deltal)*kappa0
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CSX = SetMaterialWeight( CSX, 'pml_xmin', 'Sigma', [num2str(g) '^((abs(x-100)-' num2str(abs(mesh.x(N_pml+1))) ')/(' num2str(deltal) '/' num2str(drawingunit) '))'] );
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start = [mesh.x(1), mesh.y(1), mesh.z(1)];
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stop = [100, mesh.y(end), mesh.z(end)];
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CSX = AddBox( CSX, 'pml_xmin', 1, start, stop );
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figure
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x = [-fliplr(pml_delta) 50];
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plot( x, kappa0 * g.^((abs(x-50)-abs(mesh.x(N_pml+1)))./(deltal/drawingunit)) ,'x-');
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xlabel( 'x / m' );
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ylabel( 'kappa' );
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figure
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title( 'conductivity profile inside the material' );
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%% excitation
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CSX = AddExcitation( CSX, 'excitation1', 0, [0 0 1]);
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idx = interp1( mesh.x, 1:numel(mesh.x), length*2/3, 'nearest' );
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start = [mesh.x(idx), mesh.y(1), mesh.z(1)];
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stop = [mesh.x(idx), mesh.y(end), mesh.z(end)];
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CSX = AddBox( CSX, 'excitation1', 0, start, stop );
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%% define dump boxes... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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CSX = AddDump( CSX, 'Et_', 'DumpMode', 2 );
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start = [mesh.x(1), mesh.y(1), mesh.z(3)];
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stop = [mesh.x(end), mesh.y(end), mesh.z(3)];
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CSX = AddBox( CSX, 'Et_', 0, start, stop );
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CSX = AddDump( CSX, 'Ht_', 'DumpType', 1, 'DumpMode', 2 );
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CSX = AddBox( CSX, 'Ht_', 0, start, stop );
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% hdf5 file
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CSX = AddDump( CSX, 'E', 'DumpType', 0, 'DumpMode', 2, 'FileType', 1 );
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idx = interp1( mesh.x, 1:numel(mesh.x), length*1/3, 'nearest' );
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start = [mesh.x(idx), mesh.y(3), mesh.z(1)];
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stop = [mesh.x(idx), mesh.y(3), mesh.z(end)];
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CSX = AddBox( CSX, 'E', 0, start, stop );
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% hdf5 file
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CSX = AddDump( CSX, 'H', 'DumpType', 1, 'DumpMode', 2, 'FileType', 1 );
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idx = interp1( mesh.x, 1:numel(mesh.x), length*1/3, 'nearest' );
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start = [mesh.x(idx), mesh.y(1), mesh.z(3)];
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stop = [mesh.x(idx), mesh.y(end), mesh.z(3)];
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CSX = AddBox( CSX, 'H', 0, start, stop );
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%% define openEMS options %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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openEMS_opts = '';
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% openEMS_opts = [openEMS_opts ' --disable-dumps'];
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% openEMS_opts = [openEMS_opts ' --debug-material'];
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% openEMS_opts = [openEMS_opts ' --debug-operator'];
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% openEMS_opts = [openEMS_opts ' --debug-boxes'];
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% openEMS_opts = [openEMS_opts ' --showProbeDiscretization'];
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openEMS_opts = [openEMS_opts ' --engine=fastest'];
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Sim_Path = 'tmp';
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Sim_CSX = 'PML_reflection_analysis.xml';
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if ~postprocessing_only
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[~,~,~] = rmdir(Sim_Path,'s');
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[~,~,~] = mkdir(Sim_Path);
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end
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%% Write openEMS compatible xml-file %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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WriteOpenEMS([Sim_Path '/' Sim_CSX],FDTD,CSX);
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%% cd to working dir and run openEMS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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if ~postprocessing_only
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savePath = pwd;
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cd(Sim_Path); %cd to working dir
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args = [Sim_CSX ' ' openEMS_opts];
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invoke_openEMS(args);
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cd(savePath)
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end
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%% postproc & do the plots %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% E_coords = ReadHDF5Mesh( [Sim_Path '/E.h5'] );
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% H_coords = ReadHDF5Mesh( [Sim_Path '/H.h5'] );
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E = ReadHDF5FieldData( [Sim_Path '/E.h5'] );
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H = ReadHDF5FieldData( [Sim_Path '/H.h5'] );
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E_val = cellfun( @(x) squeeze(x(1,1,:,3)), E.values, 'UniformOutput', false );
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H_val = cellfun( @(x) squeeze(x(1,:,1,2)), H.values, 'UniformOutput', false );
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E_val = cell2mat(E_val);
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H_val = cell2mat(H_val.');
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% pick center point
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Et = E_val(3,:);
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Ht = H_val(:,3).';
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delta_t_2 = H.time(1) - E.time(1); % half time-step (s)
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% create finer frequency resolution
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f = linspace( 0, f_max, 1601 );
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Ef = DFT_time2freq( E.time, Et, f );
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Hf = DFT_time2freq( H.time, Ht, f );
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Hf = Hf .* exp(-1i*2*pi*f*delta_t_2); % compensate half time-step advance of H-field
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% H is now time interpolated, but the position is not corrected with
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% respect to E
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% figure
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% plot( E.time/1e-6, Et );
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% xlabel('time (us)');
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% ylabel('amplitude (V)');
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% grid on;
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% title( 'Time domain voltage probe' );
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%
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% figure
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% plot( H.time/1e-6, Ht );
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% xlabel('time (us)');
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% ylabel('amplitude (A)');
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% grid on;
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% title( 'Time domain current probe' );
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Z0 = sqrt(MUE0/EPS0); % line impedance
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Z = Ef ./ Hf; % impedance at measurement plane
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gamma = (Z - Z0) ./ (Z + Z0);
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plot( f/1e9, 20*log10(abs(gamma)),'Linewidth',2);
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xlabel('frequency (GHz)');
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ylabel('reflection coefficient gamma (dB)');
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grid on;
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title( 'Reflection Coefficient' );
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if exist('ref_1','var')
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hold on
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plot( f/1e9, ref_1,'--','Linewidth',2, 'Color', [1 0 0]);
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hold off
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end
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ref_1 = 20*log10(abs(gamma));
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