matlab: added a microstrip port (with example)
Sebastian Held
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5163c69e7e
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f290fd6db4
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function [CSX,port] = AddMSLPort( CSX, portnr, materialname, start, stop, dir, evec, excitename )
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% [CSX,port] = AddMSLPort( CSX, portnr, materialname, start, stop, dir, evec, excitename )
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%
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% CSX: CSX-object created by InitCSX()
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% portnr: (integer) number of the port
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% materialname: property for the MSL (created by AddMetal() or AddMaterial())
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% start: 3D start rowvector for port definition
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% stop: 3D end rowvector for port definition
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% dir: direction of wave propagation (choices: [1 0 0], [0 1 0] or [0 0 1])
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% evec: excitation vector, which defines the direction of the e-field (must be the same as used in AddExcitation())
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% excitename (optional): if specified, the port will be switched on (see AddExcitation())
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%
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% the mesh must be already initialized
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%
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% example:
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% start = [0 0 height]; stop = [length width 0]; dir = [1 0 0]; evec = [0 0 1]
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% this defines a MSL in x-direction (dir) with an e-field excitation in z-direction (evec)
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% the excitation is placed at x=start(1); the wave travels towards x=stop(1)
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% the MSL-metal is created in xy-plane at z=start(3)
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%
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% Sebastian Held <sebastian.held@gmx.de>
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% May 13 2010
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%
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% See also InitCSX AddMetal AddMaterial AddExcitation calcMSLPort
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% check dir
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if ~(dir(1) == dir(2) == 0) && ~(dir(1) == dir(3) == 0) && ~(dir(2) == dir(3) == 0) || (sum(dir) == 0)
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error 'dir must have exactly one component ~= 0'
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end
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dir = dir ./ sum(dir); % dir is now a unit vector
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% check evec
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if ~(evec(1) == evec(2) == 0) && ~(evec(1) == evec(3) == 0) && ~(evec(2) == evec(3) == 0) || (sum(evec) == 0)
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error 'evec must have exactly one component ~= 0'
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end
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evec0 = evec ./ abs(sum(evec)); % evec0 is a unit vector
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% normalize start and stop
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nstart = min( [start;stop] );
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nstop = max( [start;stop] );
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% determine index (1, 2 or 3) of propagation (length of MSL)
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idx_prop = dir * [1;2;3];
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% determine index (1, 2 or 3) of width of MSL
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idx_width = abs(cross(dir,evec0)) * [1;2;3];
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% determine index (1, 2 or 3) of height
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idx_height = abs(evec0) * [1;2;3];
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% direction of propagation
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if stop(idx_prop)-start(idx_prop) > 0
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direction = +1;
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else
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direction = -1;
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end
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% create the metal/material for the MSL
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MSL_start = start;
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MSL_stop = stop;
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MSL_stop(idx_height) = MSL_start(idx_height);
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CSX = AddBox( CSX, materialname, 999, MSL_start, MSL_stop );
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% FIXME
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% openEMS v0.0.7 does not snap PEC
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% calculate position of the voltage probes
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mesh{1} = sort(CSX.RectilinearGrid.XLines);
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mesh{2} = sort(CSX.RectilinearGrid.YLines);
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mesh{3} = sort(CSX.RectilinearGrid.ZLines);
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meshlines = interp1( mesh{idx_prop}, 1:numel(mesh{idx_prop}), (nstart(idx_prop)+nstop(idx_prop))/2, 'nearest' );
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meshlines = mesh{idx_prop}(meshlines-1:meshlines+1); % get three lines (approx. at center)
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if direction == -1
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meshlines = fliplr(meshlines);
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end
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MSL_w2 = interp1( mesh{idx_width}, 1:numel(mesh{idx_width}), (nstart(idx_width)+nstop(idx_width))/2, 'nearest' );
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MSL_w2 = mesh{idx_width}(MSL_w2); % get e-line at center of MSL (MSL_width/2)
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v1_start(idx_prop) = meshlines(1);
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v1_start(idx_width) = MSL_w2;
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v1_start(idx_height) = nstop(idx_height);
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v1_stop = v1_start;
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v1_stop(idx_height) = nstart(idx_height);
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v2_start = v1_start;
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v2_stop = v1_stop;
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v2_start(idx_prop) = meshlines(2);
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v2_stop(idx_prop) = meshlines(2);
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v3_start = v2_start;
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v3_stop = v2_stop;
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v3_start(idx_prop) = meshlines(3);
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v3_stop(idx_prop) = meshlines(3);
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% calculate position of the current probes
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idx = interp1( mesh{idx_width}, 1:numel(mesh{idx_width}), nstart(idx_width), 'nearest' );
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i1_start(idx_width) = mesh{idx_width}(idx) - diff(mesh{idx_width}(idx-1:idx))/2;
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idx = interp1( mesh{idx_height}, 1:numel(mesh{idx_height}), start(idx_height), 'nearest' );
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i1_start(idx_height) = mesh{idx_height}(idx) - diff(mesh{idx_height}(idx-1:idx))/2;
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i1_stop(idx_height) = mesh{idx_height}(idx) + diff(mesh{idx_height}(idx:idx+1))/2;
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i1_start(idx_prop) = sum(meshlines(1:2))/2;
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i1_stop(idx_prop) = i1_start(idx_prop);
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idx = interp1( mesh{idx_width}, 1:numel(mesh{idx_width}), nstop(idx_width), 'nearest' );
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i1_stop(idx_width) = mesh{idx_width}(idx) + diff(mesh{idx_width}(idx:idx+1))/2;
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i2_start = i1_start;
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i2_stop = i1_stop;
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i2_start(idx_prop) = sum(meshlines(2:3))/2;
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i2_stop(idx_prop) = i2_start(idx_prop);
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% create the probes
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name = ['port_ut' num2str(portnr) 'A'];
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CSX = AddProbe( CSX, name, 0 );
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CSX = AddBox( CSX, name, 999, v1_start, v1_stop );
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name = ['port_ut' num2str(portnr) 'B'];
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CSX = AddProbe( CSX, name, 0 );
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CSX = AddBox( CSX, name, 999, v2_start, v2_stop );
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name = ['port_ut' num2str(portnr) 'C'];
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CSX = AddProbe( CSX, name, 0 );
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CSX = AddBox( CSX, name, 999, v3_start, v3_stop );
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name = ['port_it' num2str(portnr) 'A'];
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CSX = AddProbe( CSX, name, 1 );
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CSX = AddBox( CSX, name, 999, i1_start, i1_stop );
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name = ['port_it' num2str(portnr) 'B'];
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CSX = AddProbe( CSX, name, 1 );
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CSX = AddBox( CSX, name, 999, i2_start, i2_stop );
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% create port structure
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port.nr = portnr;
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port.drawingunit = CSX.RectilinearGrid.ATTRIBUTE.DeltaUnit;
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port.start = start;
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port.stop = stop;
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port.v1_start = v1_start;
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port.v1_stop = v1_stop;
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port.v2_start = v2_start;
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port.v2_stop = v2_stop;
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port.v3_start = v3_start;
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port.v3_stop = v3_stop;
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port.v_delta = diff(meshlines);
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port.i1_start = i1_start;
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port.i1_stop = i1_stop;
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port.i2_start = i2_start;
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port.i2_stop = i2_stop;
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port.i_delta = diff( meshlines(1:end-1) + diff(meshlines)/2 );
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port.dir = dir;
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port.evec = evec;
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port.idx_prop = idx_prop;
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port.idx_width = idx_width;
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port.idx_height = idx_height;
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port.excite = 0;
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% create excitation
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if nargin >= 8
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% excitation of this port is enabled
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port.excite = 1;
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% meshline = interp1( mesh{idx_prop}, 1:numel(mesh{idx_prop}), start(idx_prop), 'nearest' );
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% ex_start(idx_prop) = mesh{idx_prop}(meshline+direction*2); % excitation is placed two cells away from the start of the port (to be able to use the MUR_ABC)
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ex_start(idx_prop) = start(idx_prop);
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ex_start(idx_width) = nstart(idx_width);
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ex_start(idx_height) = nstart(idx_height);
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ex_stop(idx_prop) = ex_start(idx_prop);
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ex_stop(idx_width) = nstop(idx_width);
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ex_stop(idx_height) = nstop(idx_height);
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CSX = AddBox( CSX, excitename, 999, ex_start, ex_stop );
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end
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@ -0,0 +1,90 @@
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function [S11,beta,ZL] = calcMSLPort( portstruct, SimDir, f, ref_shift )
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% [S11,beta,ZL] = calcMSLPort( portstruct, SimDir, [f], [ref_shift] )
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%
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% portstruct: return value of AddMSLPort()
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% SimDir: directory, where the simulation files are
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% f: (optional) frequency vector for DFT
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% ref_shift: (optional) reference plane shift measured from start of port (in drawing units)
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%
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% reference: W. K. Gwarek, "A Differential Method of Reflection Coefficient Extraction From FDTD Simulations", IEEE Microwave and Guided Wave Letters, Vol. 6, No. 5, May 1996
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%
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% See also AddMSLPort
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% check
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if portstruct.v_delta(1) ~= portstruct.v_delta(2)
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warning( 'mesh is not equidistant; expect degraded accuracy' );
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end
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% read time domain data
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filename = ['/port_ut' num2str(portstruct.nr)];
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U = ReadUI( {[filename 'A'],[filename 'B'],[filename 'C']}, SimDir );
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filename = ['/port_it' num2str(portstruct.nr)];
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I = ReadUI( {[filename 'A'],[filename 'B']}, SimDir );
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if (nargin > 2) && ~isempty(f)
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% freq vector given: use DFT
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for n=1:numel(U.FD)
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U.FD{n}.f = f;
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U.FD{n}.val = DFT_time2freq( U.TD{n}.t, U.TD{n}.val, f );
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end
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for n=1:numel(I.FD)
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I.FD{n}.f = f;
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I.FD{n}.val = DFT_time2freq( I.TD{n}.t, I.TD{n}.val, f );
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end
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end
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delta_t = I.TD{1}.t(1) - U.TD{1}.t(1);
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f = U.FD{2}.f;
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Et = U.FD{2}.val;
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dEt = (U.FD{3}.val - U.FD{1}.val) / (sum(abs(portstruct.v_delta(1:2))) * portstruct.drawingunit);
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Ht = (I.FD{1}.val + I.FD{2}.val)/2; % space averaging: Ht is now defined at the same pos as Et
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Ht = Ht .* exp( -1i*2*pi*f * delta_t/2 ); % compensate time shift of Ht with respect to Et
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dHt = (I.FD{2}.val - I.FD{1}.val) / (abs(portstruct.i_delta(1)) * portstruct.drawingunit);
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dHt = dHt .* exp( -1i*2*pi*f * delta_t/2 ); % compensate time shift
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beta = sqrt( - dEt .* dHt ./ (Ht .* Et) );
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beta(real(beta) < 0) = -beta(real(beta) < 0); % determine correct sign (unlike the paper)
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% determine S11
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A = sqrt( Et .* dHt ./ (Ht .* dEt) );
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A(imag(A) > 0) = -A(imag(A) > 0); % determine correct sign (unlike the paper)
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S11 = (A - 1) ./ (A + 1);
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% determine S11_corrected
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delta_e = sum(portstruct.v_delta(1:2))/2 * portstruct.drawingunit;
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delta_h = portstruct.i_delta(1) * portstruct.drawingunit;
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S11_corrected = sqrt( Et .* (dHt ./ (sin(beta.*delta_h*.5)/(beta*delta_h*.5))) ./ ((Ht ./ cos(beta*delta_h*.5)) .* (dEt ./ (sin(beta*delta_e)./(beta*delta_e)))));
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S11_corrected(imag(S11_corrected) > 0) = -S11_corrected(imag(S11_corrected) > 0); % determine correct sign (unlike the paper)
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S11_corrected = (S11_corrected-1) ./ (S11_corrected+1);
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% my own solution...
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temp = sqrt(-dHt .* dEt ./ (Ht .* Et));
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S11 = (-1i * dEt + Et .* temp) ./ (Et .* temp + 1i * dEt); % solution 1
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% S11 = (-1i * dEt - Et .* temp) ./ (-Et .* temp + 1i * dEt); % solution 2
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% % determine ZL
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% Et_forward = Et ./ (1 + S11);
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% Ht_forward = Ht ./ (1 - S11);
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% ZL = Et_forward ./ Ht_forward;
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%
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% % determine ZL_corrected
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% Et_forward_corrected = Et ./ (1 + S11_corrected);
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% Ht_forward_corrected = Ht ./ (1 - S11_corrected);
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% ZL_corrected = Et_forward_corrected ./ Ht_forward_corrected;
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% determine ZL
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ZL = sqrt(Et .* dEt ./ (Ht .* dHt));
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% reference plane shift
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if (nargin > 3)
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% renormalize the shift to the measurement plane
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if (portstruct.stop(portstruct.idx_prop) - portstruct.start(portstruct.idx_prop) > 0)
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dir = +1;
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else
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dir = -1;
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end
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ref_shift = ref_shift - dir*(portstruct.v2_start(portstruct.idx_prop) - portstruct.start(portstruct.idx_prop));
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ref_shift = ref_shift * portstruct.drawingunit;
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S11 = S11 .* exp(2i*real(beta)*ref_shift);
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S11_corrected = S11_corrected .* exp(2i*real(beta)*ref_shift);
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end
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@ -0,0 +1,221 @@
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%
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% microstrip line example
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%
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% this example shows how to use a MSL port
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%
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% The MSL is excited at the center of the computational volume. The
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% boundary at xmin is an absorbing boundary (Mur) and at xmax an electric
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% wall. The reflection coefficient at this wall is S11 = -1.
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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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drawingunits = 1e-6; % specify everything in um
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MSL_length = 10000;
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MSL_width = 1000;
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substrate_thickness = 254;
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mesh_res = [200 0 0];
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max_timesteps = 20000;
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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, 'OverSampling', 10 );
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FDTD = SetGaussExcite( FDTD, f_max/2, f_max/2 );
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BC = [2 0 0 0 0 1];
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FDTD = SetBoundaryCond( FDTD, BC );
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%% setup CSXCAD geometry & mesh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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CSX = InitCSX();
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mesh.x = -MSL_length : mesh_res(1) : MSL_length;
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mesh.y = linspace(-MSL_width/2,MSL_width/2,10); % discretize the width of the MSL with 10 cells
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temp1 = linspace(-4*MSL_width,mesh.y(1),20);
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temp2 = linspace(mesh.y(end),4*MSL_width,20);
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mesh.y = [temp1(1:end-1), mesh.y, temp2(2:end)]; % add coarser discretization
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mesh.z = linspace(0,substrate_thickness,5); % discretize the substrate with 5 cells
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temp1 = linspace(substrate_thickness,2*substrate_thickness,5);
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mesh.z = [mesh.z temp1(2:end)]; % add same space above the strip
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temp1 = linspace(2*substrate_thickness,5*substrate_thickness,10);
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mesh.z = [mesh.z temp1(2:end)]; % coarser discretization
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CSX = DefineRectGrid( CSX, drawingunits, mesh );
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%% Material definitions
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CSX = AddMetal( CSX, 'PEC' );
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CSX = AddMaterial( CSX, 'RO4350B' );
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%% substrate
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CSX = SetMaterialProperty( CSX, 'RO4350B', 'Epsilon', 3.66 );
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start = [mesh.x(1), mesh.y(1), 0];
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stop = [mesh.x(end), mesh.y(end), substrate_thickness];
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CSX = AddBox( CSX, 'RO4350B', 0, start, stop );
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%% MSL port
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CSX = AddExcitation( CSX, 'excite', 0, [0 0 1]);
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portstart = [ 0, -MSL_width/2, substrate_thickness];
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portstop = [ MSL_length, MSL_width/2, 0];
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[CSX,portstruct] = AddMSLPort( CSX, 1, 'PEC', portstart, portstop, [1 0 0], [0 0 1], 'excite' );
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%% MSL
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start = [-MSL_length, -MSL_width/2, substrate_thickness];
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stop = [ 0, MSL_width/2, substrate_thickness];
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CSX = AddBox( CSX, 'PEC', 0, start, stop );
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%% define dump boxes... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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CSX = AddDump(CSX,'Et_','DumpType',0,'DumpMode',0);
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start = [mesh.x(1) , mesh.y(1), substrate_thickness/2];
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stop = [mesh.x(end), mesh.y(end), substrate_thickness/2];
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CSX = AddBox(CSX,'Et_',0 , start,stop);
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CSX = AddDump(CSX,'Ht_','DumpType',1,'DumpMode',0);
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CSX = AddBox(CSX,'Ht_',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 ' --engine=sse-compressed'];
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% openEMS_opts = [openEMS_opts ' --engine=multithreaded'];
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openEMS_opts = [openEMS_opts ' --engine=fastest'];
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Sim_Path = 'tmp';
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Sim_CSX = 'MSL2.xml';
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if ~postprocessing_only
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rmdir(Sim_Path,'s');
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end
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mkdir(Sim_Path);
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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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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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if ~postprocessing_only
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invoke_openEMS(args);
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end
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cd(savePath);
|
||||
|
||||
|
||||
|
||||
%% postproc & do the plots %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
U = ReadUI({'port_ut1A','port_ut1B','et'},'tmp/');
|
||||
I = ReadUI({'port_it1A','port_it1B'},'tmp/');
|
||||
delta_t_2 = I.TD{1}.t(1) - U.TD{1}.t(1); % half time-step (s)
|
||||
|
||||
% create finer frequency resolution
|
||||
f = linspace( 0, f_max, 1601 );
|
||||
for n=1:numel(U.FD)
|
||||
U.FD{n}.f = f;
|
||||
U.FD{n}.val = DFT_time2freq( U.TD{n}.t, U.TD{n}.val, f );
|
||||
end
|
||||
for n=1:numel(I.FD)
|
||||
I.FD{n}.f = f;
|
||||
I.FD{n}.val = DFT_time2freq( I.TD{n}.t, I.TD{n}.val, f );
|
||||
I.FD{n}.val = I.FD{n}.val .* exp(-1i*2*pi*I.FD{n}.f*delta_t_2); % compensate half time-step advance of H-field
|
||||
end
|
||||
|
||||
% interpolate et to the time spacing of the voltage probes
|
||||
et = interp1( U.TD{3}.t, U.TD{3}.val, U.TD{1}.t );
|
||||
|
||||
f = U.FD{1}.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
|
||||
% plotyy(U.TD{1}.t/1e-6,[U.TD{1}.val;U.TD{2}.val],U.TD{1}.t/1e-6,et);
|
||||
% xlabel('time (us)');
|
||||
% ylabel('amplitude (V)');
|
||||
% grid on;
|
||||
% title( 'Time domain voltage probes and excitation signal' );
|
||||
%
|
||||
% 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' );
|
||||
|
||||
|
||||
%% port analysis
|
||||
[S11,beta,ZL] = calcMSLPort( portstruct, Sim_Path, f );
|
||||
|
||||
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( 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( {'abs(S11)', 'angle(S11)'} );
|
||||
xlabel( 'frequency (GHz)' );
|
||||
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' );
|
||||
ylim( [-2*mean(real(ZL)) 2*mean(real(ZL))] );
|
||||
|
||||
% reference plane shift (to the end of the port)
|
||||
ref_shift = abs(portstop(1) - portstart(1));
|
||||
[S11,beta,ZL] = calcMSLPort( portstruct, Sim_Path, f, ref_shift );
|
||||
|
||||
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)' );
|
||||
Loading…
Reference in New Issue