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+%
+% EXAMPLE / microstrip / MSL2
+%
+% This example shows how to use the MSL-port.
+% The MSL is excited at the center of the computational volume. The
+% boundary at xmin is an absorbing boundary (Mur) and at xmax an electric
+% wall. The reflection coefficient at this wall is S11 = -1.
+% Direction of propagation is x.
+%
+% This example demonstrates:
+%  - simple microstrip geometry (made of PEC)
+%  - MSL port
+%  - MSL analysis
+%
+% You may modify the PEC boundary condition at xmax to become a MUR
+% boundary. This resembles a matched microstrip line.
+%
+% Tested with
+%  - Matlab 2009b
+%  - Octave 3.3.52
+%  - openEMS v0.0.14
+%
+% (C) 2010 Sebastian Held <sebastian.held@uni-due.de>
+
+close all
+clear
+clc
+
+%% switches
+postproc_only = 0;
+
+%% setup the simulation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+physical_constants;
+unit = 1e-6; % specify everything in um
+MSL_length    = 10000;
+MSL_width     = 1000;
+substrate_thickness = 254;
+substrate_epr = 3.66;
+
+% mesh_res      = [200 0 0];
+
+%% prepare simulation folder
+Sim_Path = 'tmp';
+Sim_CSX = 'msl2.xml';
+if ~postproc_only
+    [status, message, messageid] = rmdir( Sim_Path, 's' ); % clear previous directory
+    [status, message, messageid] = mkdir( Sim_Path ); % create empty simulation folder
+end
+
+%% setup FDTD parameters & excitation function %%%%%%%%%%%%%%%%%%%%%%%%%%%%
+max_timesteps = 20000;
+min_decrement = 1e-6;
+f_max         = 7e9;
+FDTD = InitFDTD( max_timesteps, min_decrement, 'OverSampling', 10 );
+FDTD = SetGaussExcite( FDTD, f_max/2, f_max/2 );
+BC   = {'MUR' 'MUR' 'PEC' 'PEC' 'PEC' 'PMC'};
+FDTD = SetBoundaryCond( FDTD, BC );
+
+%% setup CSXCAD geometry & mesh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+CSX = InitCSX();
+resolution = c0/(f_max*sqrt(substrate_epr))/unit /50; % resolution of lambda/50
+mesh.x = SmoothMeshLines( [-MSL_length MSL_length], resolution );
+mesh.y = SmoothMeshLines( [-4*MSL_width -MSL_width/2 MSL_width/2 4*MSL_width], resolution );
+mesh.z = SmoothMeshLines( [linspace(0,substrate_thickness,5) 10*substrate_thickness], resolution );
+CSX = DefineRectGrid( CSX, unit, mesh );
+
+%% substrate
+CSX = AddMaterial( CSX, 'RO4350B' );
+CSX = SetMaterialProperty( CSX, 'RO4350B', 'Epsilon', substrate_epr );
+start = [mesh.x(1),   mesh.y(1),   0];
+stop  = [mesh.x(end), mesh.y(end), substrate_thickness];
+CSX = AddBox( CSX, 'RO4350B', 0, start, stop );
+
+%% MSL port
+CSX = AddMetal( CSX, 'PEC' );
+portstart = [          0, -MSL_width/2, substrate_thickness];
+portstop  = [ MSL_length,  MSL_width/2, 0];
+[CSX,portstruct] = AddMSLPort( CSX, 999, 1, 'PEC', portstart, portstop, [1 0 0], [0 0 1], [], 'excite' );
+
+%% MSL
+start = [-MSL_length, -MSL_width/2, substrate_thickness];
+stop  = [          0,  MSL_width/2, substrate_thickness];
+CSX = AddBox( CSX, 'PEC', 999, start, stop ); % priority needs to be higher than 
+
+%% define dump boxes
+start = [mesh.x(1),   mesh.y(1),   substrate_thickness/2];
+stop  = [mesh.x(end), mesh.y(end), substrate_thickness/2];
+CSX = AddDump( CSX, 'Et_', 'DumpType', 0,'DumpMode', 2 ); % cell interpolated
+CSX = AddBox( CSX, 'Et_', 0, start, stop );
+CSX = AddDump( CSX, 'Ht_', 'DumpType', 1,'DumpMode', 2 ); % cell interpolated
+CSX = AddBox( CSX, 'Ht_', 0, start, stop );
+ 
+%% write openEMS compatible xml-file
+WriteOpenEMS( [Sim_Path '/' Sim_CSX], FDTD, CSX );
+
+%% show the structure
+if ~postproc_only
+    CSXGeomPlot( [Sim_Path '/' Sim_CSX] );
+end
+
+%% run openEMS
+openEMS_opts = '';
+openEMS_opts = [openEMS_opts ' --engine=fastest'];
+% openEMS_opts = [openEMS_opts ' --debug-material'];
+% openEMS_opts = [openEMS_opts ' --debug-boxes'];
+% openEMS_opts = [openEMS_opts ' --debug-PEC'];
+if ~postproc_only
+    RunOpenEMS( Sim_Path, Sim_CSX, openEMS_opts );
+end
+
+
+%% postprocess
+f = linspace( 1e6, f_max, 1601 );
+U = ReadUI( {'port_ut1A','port_ut1B','port_ut1C','et'}, 'tmp/', f );
+I = ReadUI( {'port_it1A','port_it1B'}, 'tmp/', f );
+
+% Z = (U.FD{1}.val+U.FD{2}.val)/2 ./ I.FD{1}.val;
+% plot( f*1e-9, [real(Z);imag(Z)],'Linewidth',2);
+% xlabel('frequency (GHz)');
+% ylabel('impedance (Ohm)');
+% grid on;
+% legend( {'real','imaginary'}, 'location', 'northwest' )
+% title( 'line impedance (will fail in case of reflections!)' );
+
+figure
+ax = plotyy( U.TD{1}.t/1e-6, [U.TD{1}.val;U.TD{2}.val;U.TD{3}.val], U.TD{4}.t/1e-6, U.TD{4}.val );
+xlabel( 'time (us)' );
+ylabel( 'amplitude (V)' );
+grid on
+title( 'Time domain voltage probes and excitation signal' );
+legend( {'ut1A','ut1B','ut1C','excitation'} );
+% now make the y-axis symmetric to y=0 (align zeros of y1 and y2)
+y1 = ylim(ax(1));
+y2 = ylim(ax(2));
+ylim( ax(1), [-max(abs(y1)) max(abs(y1))] );
+ylim( ax(2), [-max(abs(y2)) max(abs(y2))] );
+
+figure
+plot( I.TD{1}.t/1e-6, [I.TD{1}.val;I.TD{2}.val] );
+xlabel( 'time (us)' );
+ylabel( 'amplitude (A)' );
+grid on
+title( 'Time domain current probes' );
+legend( {'it1A','it1B'} );
+
+figure
+ax = plotyy( U.FD{1}.f/1e9, abs([U.FD{1}.val;U.FD{2}.val;U.FD{3}.val]), U.FD{1}.f/1e9, angle([U.FD{1}.val;U.FD{2}.val;U.FD{3}.val])/pi*180 );
+xlabel( 'frequency (GHz)' );
+ylabel( ax(1), 'amplitude (A)' );
+ylabel( ax(2), 'phase (deg)' );
+grid on
+title( 'Frequency domain voltage probes' );
+legend( {'abs(uf1A)','abs(uf1B)','abs(uf1C)','angle(uf1A)','angle(uf1B)','angle(uf1C)'} );
+
+figure
+ax = plotyy( I.FD{1}.f/1e9, abs([I.FD{1}.val;I.FD{2}.val]), I.FD{1}.f/1e9, angle([I.FD{1}.val;I.FD{2}.val])/pi*180 );
+xlabel( 'frequency (GHz)' );
+ylabel( ax(1), 'amplitude (A)' );
+ylabel( ax(2), 'phase (deg)' );
+grid on
+title( 'Frequency domain current probes' );
+legend( {'abs(if1A)','abs(if1B)','angle(if1A)','angle(if1B)'} );
+
+%% port analysis
+[U,I,beta,ZL] = calcPort( portstruct, Sim_Path, f );
+%% attention! the reflection coefficient S11 is normalized to ZL!
+
+figure
+plot( sin(0:0.01:2*pi), cos(0:0.01:2*pi), 'Color', [.7 .7 .7] );
+hold on
+plot( 0.5+0.5*sin(0:0.01:2*pi), 0.5*cos(0:0.01:2*pi), 'Color', [.7 .7 .7] );
+plot( [-1 1], [0 0], 'Color', [.7 .7 .7] );
+plot( S11, 'k' );
+plot( real(S11(1)), imag(S11(1)), '*r' );
+axis equal
+title( 'Reflection coefficient S11 at the measurement plane' );
+
+figure
+plot( sin(0:0.01:2*pi), cos(0:0.01:2*pi), 'Color', [.7 .7 .7] );
+hold on
+plot( 0.5+0.5*sin(0:0.01:2*pi), 0.5*cos(0:0.01:2*pi), 'Color', [.7 .7 .7] );
+plot( [-1 1], [0 0], 'Color', [.7 .7 .7] );
+Z = vi.FD.v.val ./ vi.FD.i.val;
+S11_ = (Z-ZL) ./ (Z+ZL);
+plot( S11_, 'k' );
+plot( real(S11_(1)), imag(S11_(1)), '*r' );
+axis equal
+title( {'Reflection coefficient S11 at the measurement plane' 'calculated from voltages and currents'} );
+
+figure
+plot( f/1e9, [real(S11);imag(S11)], 'Linewidth',2 );
+legend( {'Re(S11)', 'Im(S11)'} );
+ylabel( 'amplitude' );
+xlabel( 'frequency (GHz)' );
+title( 'Reflection coefficient S11 at the measurement plane' );
+
+figure
+plotyy( f/1e9, 20*log10(abs(S11)), f/1e9, angle(S11)/pi*180 );
+legend( {'|S11|', 'angle(S11)'} );
+xlabel( 'frequency (GHz)' );
+ylabel( '|S11| (dB)' );
+title( 'Reflection coefficient S11 at the measurement plane' );
+
+figure
+plot( f/1e9, [real(beta);imag(beta)], 'Linewidth',2 );
+legend( 'Re(beta)', 'Im(beta)' );
+ylabel( 'propagation constant beta (1/m)' );
+xlabel( 'frequency (GHz)' );
+title( 'Propagation constant of the MSL' );
+
+figure
+plot( f/1e9, [real(ZL);imag(ZL)], 'Linewidth',2);
+xlabel('frequency (GHz)');
+ylabel('impedance (Ohm)');
+grid on;
+legend( {'real','imaginary'}, 'location', 'northeast' )
+title( 'Characteristic line impedance ZL' );
+
+%% reference plane shift (to the end of the port)
+ref_shift = abs(portstop(1) - portstart(1));
+[U, I,beta,ZL] = calcPort( portstruct, Sim_Path, f );
+%%
+
+figure
+plotyy( f/1e9, 20*log10(abs(S11)), f/1e9, angle(S11)/pi*180 );
+legend( {'abs(S11)', 'angle(S11)'} );
+xlabel( 'frequency (GHz)' );
+title( 'Reflection coefficient S11 at the reference plane (at the electric wall)' );
+
+figure
+plot( sin(0:0.01:2*pi), cos(0:0.01:2*pi), 'Color', [.7 .7 .7] );
+hold on
+plot( 0.5+0.5*sin(0:0.01:2*pi), 0.5*cos(0:0.01:2*pi), 'Color', [.7 .7 .7] );
+plot( [-1 1], [0 0], 'Color', [.7 .7 .7] );
+plot( S11, 'k' );
+plot( real(S11(1)), imag(S11(1)), '*r' );
+axis equal
+title( 'Reflection coefficient S11 at the reference plane (at the electric wall)' );
+
+figure
+plot( sin(0:0.01:2*pi), cos(0:0.01:2*pi), 'Color', [.7 .7 .7] );
+hold on
+plot( 0.5+0.5*sin(0:0.01:2*pi), 0.5*cos(0:0.01:2*pi), 'Color', [.7 .7 .7] );
+plot( [-1 1], [0 0], 'Color', [.7 .7 .7] );
+Z = vi.FD.v.val_shifted ./ vi.FD.i.val_shifted;
+S11_ = (Z-ZL) ./ (Z+ZL);
+plot( S11_, 'k' );
+plot( real(S11_(1)), imag(S11_(1)), '*r' );
+axis equal
+title( {'Reflection coefficient S11 at the reference plane (at the electric wall)' 'calculated from shifted voltages and currents'} );
+
+%% visualize electric and magnetic fields
+% you will find vtk dump files in the simulation folder (tmp/)
+% use paraview to visualize them