% % EXAMPLE / antennas / patch antenna % % This example demonstrates how to: % - calculate the reflection coefficient of a patch antenna % % % Tested with % - Matlab 2009b % - Octave 3.3.52 % - openEMS v0.0.14 % % (C) 2010 Thorsten Liebig close all clear clc %% setup the simulation physical_constants; unit = 1e-3; % all length in mm % width in x-direction % length in y-direction % main radiation in z-direction patch.width = 32.86; % resonant length patch.length = 41.37; substrate.epsR = 3.38; substrate.width = 120; substrate.length = 120; substrate.thickness = 1.524; substrate.cells = 5; feed.pos = -4.5; feed.width = 0.5; feed.R = 50; % feed resistance % size of the simulation box SimBox = [200 200 50]; %% prepare simulation folder Sim_Path = 'tmp'; Sim_CSX = 'patch_ant.xml'; [status, message, messageid] = rmdir( Sim_Path, 's' ); % clear previous directory [status, message, messageid] = mkdir( Sim_Path ); % create empty simulation folder %% setup FDTD parameter & excitation function max_timesteps = 30000; min_decrement = 1e-5; % equivalent to -50 dB f0 = 2e9; % center frequency fc = 1e9; % 10 dB corner frequency (in this case 1e9 Hz - 3e9 Hz) FDTD = InitFDTD( max_timesteps, min_decrement ); FDTD = SetGaussExcite( FDTD, f0, fc ); BC = {'MUR' 'MUR' 'MUR' 'MUR' 'PEC' 'MUR'}; % boundary conditions % BC = {'PML_8' 'PML_8' 'PML_8' 'PML_8' 'PEC' 'PML_8'}; % use pml instead of mur FDTD = SetBoundaryCond( FDTD, BC ); %% setup CSXCAD geometry & mesh % currently, openEMS cannot automatically generate a mesh max_res = c0 / (f0+fc) / unit / 20; % cell size: lambda/20 CSX = InitCSX(); mesh.x = [-SimBox(1)/2 SimBox(1)/2 -substrate.width/2 substrate.width/2 feed.pos-feed.width/2 feed.pos+feed.width/2]; % add patch mesh with 2/3 - 1/3 rule mesh.x = [mesh.x -patch.width/2-max_res/2*0.66 -patch.width/2+max_res/2*0.33 patch.width/2+max_res/2*0.66 patch.width/2-max_res/2*0.33]; mesh.x = SmoothMeshLines( mesh.x, max_res, 1.4); % create a smooth mesh between specified mesh lines mesh.y = [-SimBox(2)/2 SimBox(2)/2 -substrate.length/2 substrate.length/2 -feed.width/2 feed.width/2]; % add patch mesh with 2/3 - 1/3 rule mesh.y = [mesh.y -patch.length/2-max_res/2*0.66 -patch.length/2+max_res/2*0.33 patch.length/2+max_res/2*0.66 patch.length/2-max_res/2*0.33]; mesh.y = SmoothMeshLines( mesh.y, max_res, 1.4 ); mesh.z = [-SimBox(3)/2 linspace(0,substrate.thickness,substrate.cells) SimBox(3) ]; mesh.z = SmoothMeshLines( mesh.z, max_res, 1.4 ); mesh = AddPML( mesh, [8 8 8 8 8 8] ); % add equidistant cells (air around the structure) CSX = DefineRectGrid( CSX, unit, mesh ); %% create patch CSX = AddMetal( CSX, 'patch' ); % create a perfect electric conductor (PEC) start = [-patch.width/2 -patch.length/2 substrate.thickness]; stop = [ patch.width/2 patch.length/2 substrate.thickness]; CSX = AddBox(CSX,'patch',10,start,stop); %% create substrate CSX = AddMaterial( CSX, 'substrate' ); CSX = SetMaterialProperty( CSX, 'substrate', 'Epsilon', substrate.epsR ); start = [-substrate.width/2 -substrate.length/2 0]; stop = [ substrate.width/2 substrate.length/2 substrate.thickness]; CSX = AddBox( CSX, 'substrate', 0, start, stop ); %% create ground (same size as substrate) CSX = AddMetal( CSX, 'gnd' ); % create a perfect electric conductor (PEC) start(3)=0; stop(3) =0; CSX = AddBox(CSX,'gnd',10,start,stop); %% apply the excitation & resist as a current source % this creates a "port" CSX = AddMaterial( CSX, 'resist' ); kappa = substrate.thickness/feed.R/feed.width^2/unit; CSX = SetMaterialProperty( CSX, 'resist', 'Kappa', kappa ); start = [feed.pos-feed.width/2 -feed.width/2 0]; stop = [feed.pos+feed.width/2 feed.width/2 substrate.thickness]; CSX = AddBox( CSX, 'resist', 15, start, stop ); CSX = AddExcitation( CSX, 'excite', 0, [0 0 1] ); % excitation in z-direction CSX = AddBox( CSX, 'excite', 0, start, stop ); %% define voltage calc boxes CSX = AddProbe( CSX, 'ut1', 0 ); start = [feed.pos 0 0]; stop = [feed.pos 0 substrate.thickness]; CSX = AddBox( CSX, 'ut1', 0 , stop, start ); %% define current calc boxes CSX = AddProbe( CSX, 'it1', 1 ); start = [feed.pos-feed.width -feed.width substrate.thickness/2]; stop = [feed.pos+feed.width feed.width substrate.thickness/2]; CSX = AddBox( CSX, 'it1', 0, start, stop ); %% dump magnetic field over the patch antenna CSX = AddDump( CSX, 'Ht_', 'DumpType', 1, 'DumpMode', 2 ); % cell interpolated start = [-patch.width -patch.length substrate.thickness+1]; stop = [ patch.width patch.length substrate.thickness+1]; CSX = AddBox( CSX, 'Ht_', 0, start, stop ); %%nf2ff calc [CSX nf2ff] = CreateNF2FFBox(CSX, 'nf2ff', -SimBox/2, SimBox/2); %% write openEMS compatible xml-file WriteOpenEMS( [Sim_Path '/' Sim_CSX], FDTD, CSX ); %% show the structure CSXGeomPlot( [Sim_Path '/' Sim_CSX] ); %% run openEMS openEMS_opts = ''; openEMS_opts = [openEMS_opts ' --engine=fastest']; RunOpenEMS( Sim_Path, Sim_CSX, openEMS_opts ); %% postprocessing & do the plots freq = linspace( f0-fc, f0+fc, 501 ); U = ReadUI( {'ut1','et'}, 'tmp/', freq ); % time domain/freq domain voltage I = ReadUI( 'it1', 'tmp/', freq ); % time domain/freq domain current (half time step is corrected) % plot time domain voltage figure [ax,h1,h2] = plotyy( U.TD{1}.t/1e-9, U.TD{1}.val, U.TD{2}.t/1e-9, U.TD{2}.val ); set( h1, 'Linewidth', 2 ); set( h1, 'Color', [1 0 0] ); set( h2, 'Linewidth', 2 ); set( h2, 'Color', [0 0 0] ); grid on title( 'time domain voltage' ); xlabel( 'time t / ns' ); ylabel( ax(1), 'voltage ut1 / V' ); ylabel( ax(2), 'voltage et / V' ); % 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))] ); % plot feed point impedance figure Zin = U.FD{1}.val ./ I.FD{1}.val; plot( freq/1e6, real(Zin), 'k-', 'Linewidth', 2 ); hold on grid on plot( freq/1e6, imag(Zin), 'r--', 'Linewidth', 2 ); title( 'feed point impedance' ); xlabel( 'frequency f / MHz' ); ylabel( 'impedance Z_{in} / Ohm' ); legend( 'real', 'imag' ); % plot reflection coefficient S11 figure uf_inc = 0.5*(U.FD{1}.val + I.FD{1}.val * 50); if_inc = 0.5*(I.FD{1}.val - U.FD{1}.val / 50); uf_ref = U.FD{1}.val - uf_inc; if_ref = I.FD{1}.val - if_inc; s11 = uf_ref ./ uf_inc; plot( freq/1e6, 20*log10(abs(s11)), 'k-', 'Linewidth', 2 ); grid on title( 'reflection coefficient S_{11}' ); xlabel( 'frequency f / MHz' ); ylabel( 'reflection coefficient |S_{11}|' ); %% NFFF contour plots %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% f0 = freq(find(s11==min(s11))); % calculate the far field at phi=0 degrees and at phi=90 degrees thetaRange = 0:2:359; r = 1; % evaluate fields at radius r disp( 'calculating far field at phi=[0 90] deg...' ); [E_far_theta,E_far_phi,Prad,Dmax] = AnalyzeNF2FF( Sim_Path, nf2ff, f0, thetaRange, [0 90], r ); % display power and directivity disp( ['radiated power: Prad = ' num2str(Prad)] ); disp( ['directivity: Dmax = ' num2str(Dmax)] ); % calculate the e-field magnitude for phi = 0 deg E_phi0_far = zeros(1,numel(thetaRange)); for n=1:numel(thetaRange) E_phi0_far(n) = norm( [E_far_theta(n,1) E_far_phi(n,1)] ); end % display polar plot figure polar( thetaRange/180*pi, E_phi0_far ); ylabel( 'theta / deg' ); title( ['electrical far field (V/m) @r=' num2str(r) ' m phi=0 deg'] ); legend( 'e-field magnitude', 'Location', 'BestOutside' ); % calculate the e-field magnitude for phi = 90 deg E_phi90_far = zeros(1,numel(thetaRange)); for n=1:numel(thetaRange) E_phi90_far(n) = norm([E_far_theta(n,2) E_far_phi(n,2)]); end % display polar plot figure polar( thetaRange/180*pi, E_phi90_far ); ylabel( 'theta / deg' ); title( ['electrical far field (V/m) @r=' num2str(r) ' m phi=90 deg'] ); legend( 'e-field magnitude', 'Location', 'BestOutside' ); %% calculate 3D pattern phiRange = 0:15:360; thetaRange = 0:10:180; r = 1; % evaluate fields at radius r disp( 'calculating 3D far field...' ); [E_far_theta,E_far_phi] = AnalyzeNF2FF( Sim_Path, nf2ff, f0, thetaRange, phiRange, r ); E_far = sqrt( abs(E_far_theta).^2 + abs(E_far_phi).^2 ); E_far_normalized = E_far / max(E_far(:)); [theta,phi] = ndgrid(thetaRange/180*pi,phiRange/180*pi); x = E_far_normalized .* sin(theta) .* cos(phi); y = E_far_normalized .* sin(theta) .* sin(phi); z = E_far_normalized .* cos(theta); figure surf( x,y,z, E_far_normalized ); axis equal xlabel( 'x' ); ylabel( 'y' ); zlabel( 'z' ); %% visualize magnetic fields % you will find vtk dump files in the simulation folder (tmp/) % use paraview to visulaize them