186 lines
6.5 KiB
Matlab
186 lines
6.5 KiB
Matlab
%
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% EXAMPLE / microstrip / MSL
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%
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% Microstrip line on air "substrate" in z-direction.
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%
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% This example demonstrates:
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% - simple microstrip geometry
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% - characteristic impedance
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% - material grading function
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% - geometric priority concept
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%
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%
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% Tested with
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% - Matlab 2009b
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% - Octave 3.3.52
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% - openEMS v0.0.14
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%
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% (C) 2010 Thorsten Liebig <thorsten.liebig@uni-due.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-3; % all length in mm
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% geometry
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abs_length = 100; % absorber length
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length = 600;
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width = 400;
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height = 200;
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MSL_width = 50;
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MSL_height = 10;
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%% prepare simulation folder
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Sim_Path = 'tmp';
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Sim_CSX = 'msl.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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%% setup FDTD parameter & excitation function %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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max_timesteps = 2000;
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min_decrement = 1e-5; % equivalent to -50 dB
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f0 = 2e9; % center frequency
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fc = 1e9; % 10 dB corner frequency (in this case 1e9 Hz - 3e9 Hz)
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FDTD = InitFDTD( max_timesteps, min_decrement );
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FDTD = SetGaussExcite( FDTD, f0, fc );
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BC = {'PMC' 'PMC' 'PEC' 'PMC' 'PEC' 'PEC'};
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FDTD = SetBoundaryCond( FDTD, BC );
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%% setup CSXCAD geometry & mesh
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% very simple mesh
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CSX = InitCSX();
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resolution = c0/(f0+fc)/unit /15; % resolution of lambda/15
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mesh.x = SmoothMeshLines( [-width/2, width/2, -MSL_width/2, MSL_width/2], resolution ); % create smooth lines from fixed lines
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mesh.y = SmoothMeshLines( [linspace(0,MSL_height,5) MSL_height+1 height], resolution );
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mesh.z = SmoothMeshLines( [0 length], resolution );
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CSX = DefineRectGrid( CSX, unit, mesh );
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%% create MSL
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% attention! the skin effect is not simulated, because the MSL is
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% discretized with only one cell!
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CSX = AddMaterial( CSX, 'copper' );
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CSX = SetMaterialProperty( CSX, 'copper', 'Kappa', 56e6 );
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start = [-MSL_width/2, MSL_height, 0];
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stop = [ MSL_width/2, MSL_height+1, length];
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priority = 100; % the geometric priority is set to 100
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CSX = AddBox( CSX, 'copper', priority, start, stop );
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%% add excitation below the strip
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start = [-MSL_width/2, 0 , mesh.z(1)];
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stop = [ MSL_width/2, MSL_height, mesh.z(1)];
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CSX = AddExcitation( CSX, 'excite', 0, [0 -1 0] );
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CSX = AddBox( CSX, 'excite', 0, start, stop );
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%% fake pml
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% this "pml" is a normal material with graded losses
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% electric and magnetic losses are related to give low reflection
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% for normally incident TEM waves
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finalKappa = 1/abs_length^2;
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finalSigma = finalKappa*MUE0/EPS0;
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CSX = AddMaterial( CSX, 'fakepml' );
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CSX = SetMaterialProperty( CSX, 'fakepml', 'Kappa', finalKappa );
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CSX = SetMaterialProperty( CSX, 'fakepml', 'Sigma', finalSigma );
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CSX = SetMaterialWeight( CSX, 'fakepml', 'Kappa', ['pow(z-' num2str(length-abs_length) ',2)'] );
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CSX = SetMaterialWeight( CSX, 'fakepml', 'Sigma', ['pow(z-' num2str(length-abs_length) ',2)'] );
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start = [mesh.x(1) mesh.y(1) length-abs_length];
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stop = [mesh.x(end) mesh.y(end) length];
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% the geometric priority is set to 0, which is lower than the priority
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% of the MSL, thus the MSL (copper) has precendence
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priority = 0;
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CSX = AddBox( CSX, 'fakepml', priority, start, stop );
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%% define dump boxes
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start = [mesh.x(1), MSL_height/2, mesh.z(1)];
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stop = [mesh.x(end), MSL_height/2, mesh.z(end)];
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CSX = AddDump( CSX, 'Et_', 'DumpMode', 2 ); % cell interpolated
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CSX = AddBox( CSX, 'Et_', 0, start, stop );
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CSX = AddDump( CSX, 'Ht_', 'DumpType', 1, 'DumpMode', 2 ); % cell interpolated
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CSX = AddBox( CSX, 'Ht_', 0, start, stop );
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%% define voltage calc box
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% voltage calc boxes will automatically snap to the next mesh-line
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CSX = AddProbe( CSX, 'ut1', 0 );
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zidx = interp1( mesh.z, 1:numel(mesh.z), length/2, 'nearest' );
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start = [0 MSL_height mesh.z(zidx)];
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stop = [0 0 mesh.z(zidx)];
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CSX = AddBox( CSX, 'ut1', 0, start, stop );
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% add a second voltage probe to compensate space offset between voltage and
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% current
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CSX = AddProbe( CSX, 'ut2', 0 );
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start = [0 MSL_height mesh.z(zidx+1)];
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stop = [0 0 mesh.z(zidx+1)];
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CSX = AddBox( CSX, 'ut2', 0, start, stop );
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%% define current calc box
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% current calc boxes will automatically snap to the next dual mesh-line
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CSX = AddProbe( CSX, 'it1', 1 );
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xidx1 = interp1( mesh.x, 1:numel(mesh.x), -MSL_width/2, 'nearest' );
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xidx2 = interp1( mesh.x, 1:numel(mesh.x), MSL_width/2, 'nearest' );
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xdelta = diff(mesh.x);
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yidx1 = interp1( mesh.y, 1:numel(mesh.y), MSL_height, 'nearest' );
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yidx2 = interp1( mesh.y, 1:numel(mesh.y), MSL_height+1, 'nearest' );
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ydelta = diff(mesh.y);
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zdelta = diff(mesh.z);
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start = [mesh.x(xidx1)-xdelta(xidx1-1)/2, mesh.y(yidx1)-ydelta(yidx1-1)/2, mesh.z(zidx)+zdelta(zidx)/2];
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stop = [mesh.x(xidx2)+xdelta(xidx2)/2, mesh.y(yidx2)+ydelta(yidx2)/2, mesh.z(zidx)+zdelta(zidx)/2];
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CSX = AddBox( CSX, 'it1', 0, start, stop );
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%% write openEMS compatible xml-file
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WriteOpenEMS( [Sim_Path '/' Sim_CSX], FDTD, CSX );
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%% show the structure
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CSXGeomPlot( [Sim_Path '/' Sim_CSX] );
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%% run openEMS
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openEMS_opts = '';
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openEMS_opts = [openEMS_opts ' --engine=fastest'];
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% openEMS_opts = [openEMS_opts ' --debug-material'];
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% openEMS_opts = [openEMS_opts ' --debug-boxes'];
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RunOpenEMS( Sim_Path, Sim_CSX, openEMS_opts );
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%% postprocess
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freq = linspace( f0-fc, f0+fc, 501 );
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U = ReadUI( {'ut1','ut2','et'}, 'tmp/', freq ); % time domain/freq domain voltage
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I = ReadUI( 'it1', 'tmp/', freq ); % time domain/freq domain current (half time step offset is corrected)
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% plot time domain voltage
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figure
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[ax,h1,h2] = plotyy( U.TD{1}.t/1e-9, U.TD{1}.val, U.TD{3}.t/1e-9, U.TD{3}.val );
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set( h1, 'Linewidth', 2 );
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set( h1, 'Color', [1 0 0] );
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set( h2, 'Linewidth', 2 );
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set( h2, 'Color', [0 0 0] );
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grid on
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title( 'time domain voltage' );
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xlabel( 'time t / ns' );
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ylabel( ax(1), 'voltage ut1 / V' );
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ylabel( ax(2), 'voltage et / V' );
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% now make the y-axis symmetric to y=0 (align zeros of y1 and y2)
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y1 = ylim(ax(1));
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y2 = ylim(ax(2));
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ylim( ax(1), [-max(abs(y1)) max(abs(y1))] );
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ylim( ax(2), [-max(abs(y2)) max(abs(y2))] );
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% calculate characteristic impedance
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% arithmetic mean of ut1 and ut2 -> voltage in the middle of ut1 and ut2
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U = (U.FD{1}.val + U.FD{2}.val) / 2;
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Z = U ./ I.FD{1}.val;
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% plot characteristic impedance
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figure
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plot( freq/1e6, real(Z), 'k-', 'Linewidth', 2 );
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hold on
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grid on
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plot( freq/1e6, imag(Z), 'r--', 'Linewidth', 2 );
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title( 'characteristic impedance of MSL' );
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xlabel( 'frequency f / MHz' );
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ylabel( 'characteristic impedance Z / Ohm' );
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legend( 'real', 'imag' );
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%% visualize electric and magnetic fields
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% you will find vtk dump files in the simulation folder (tmp/)
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% use paraview to visualize them
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