Stripline to MSL Transition
Simulate the transition between a balanced stripline and an unbalanced microstrip line (MSL) and extract the S-parameters of the two-port transition. Simulation time: ~2 min.
This tutorial covers:
Stripline port setup (balanced, ground planes above and below)
Microstrip line (MSL) port setup in the same simulation
Transition via (cylinder) with a circular cutout in the ground plane
Inhomogeneous mesh for improved accuracy and simulation speed: fine cells near the via gap, coarser cells elsewhere
S-parameter extraction and insertion loss analysis
Octave/Matlab Script
Setup the Simulation
Both conductors share an RO4350B substrate stack (εr = 3.66, lossy via Kappa at 2.45 GHz). The stripline is buried at z = 0 between two ground planes while the MSL runs on top; matching their impedances at the same trace width determines the via radius and surrounding clearance gap.
physical_constants;
unit = 1e-6; % specify everything in um
line_length = 15000; % line length of strip line and microstrip line
substrate_width = 10000;
air_spacer = 4000; % air spacer above the substrate
msl_width = 500;
msl_substrate_thickness = 254;
strip_width = 500;
strip_substrate_thickness = 512;
connect_via_rad = 500/2;
connect_via_gap = 1250/2;
substrate_epr = 3.66;
substrate_kappa = 1e-3 * 2*pi*2.45e9 * EPS0*substrate_epr; % substrate losses
f_max = 10e9;
resolution = 250;
edge_res = 25;
feed_shift = 2500;
meas_shift = 5000;
Setup FDTD Parameters & Excitation Function
A Gaussian pulse centered at f_max/2 with half-bandwidth f_max/2 sweeps near-DC to 10 GHz in a single simulation run. PML_8 on the ±x port faces cleanly absorbs guided modes; MUR handles the open lateral and top sides; the PEC bottom is the stripline reference ground.
FDTD = InitFDTD();
FDTD = SetGaussExcite( FDTD, f_max/2, f_max/2);
BC = {'PML_8' 'PML_8' 'MUR' 'MUR' 'PEC' 'MUR'};
FDTD = SetBoundaryCond( FDTD, BC );
Setup CSXCAD Geometry & Mesh
The 1/3-2/3 edge offset distributes two mesh lines per conductor edge to resolve near-singular fringe fields without over-refining. The x-mesh is built in two passes: first a fine zone around the via clearance gap, then coarser lines out to the port ends. Two polygon halves form the shared reference plane at z = strip_substrate_thickness with a circular cutout (radius = connect_via_gap) that prevents a short to the via conductor.
CSX = InitCSX();
edge_mesh = [-1/3 2/3]*edge_res; % 1/3 - 2/3 rule for 2D metal edges
mesh.x = SmoothMeshLines( [-connect_via_gap 0 connect_via_gap], 2*edge_res, 1.5 );
mesh.x = SmoothMeshLines( [-line_length mesh.x line_length], resolution, 1.5);
mesh.y = SmoothMeshLines( [0 msl_width/2+edge_mesh substrate_width/2], resolution/4 , 1.5);
mesh.y = sort(unique([-mesh.y mesh.y]));
mesh.z = SmoothMeshLines( [linspace(-strip_substrate_thickness,0,5) linspace(0,strip_substrate_thickness,5) linspace(strip_substrate_thickness,msl_substrate_thickness+strip_substrate_thickness,5) 2*strip_substrate_thickness+air_spacer] , resolution );
CSX = DefineRectGrid( CSX, unit, mesh );
% Create Substrate
CSX = AddMaterial( CSX, 'RO4350B' );
CSX = SetMaterialProperty( CSX, 'RO4350B', 'Epsilon', substrate_epr, 'Kappa', substrate_kappa );
start = [mesh.x(1), mesh.y(1), -strip_substrate_thickness];
stop = [mesh.x(end), mesh.y(end), +strip_substrate_thickness+msl_substrate_thickness];
CSX = AddBox( CSX, 'RO4350B', 0, start, stop );
% Create a PEC called 'metal' and 'gnd'
CSX = AddMetal( CSX, 'gnd' );
CSX = AddMetal( CSX, 'metal' );
% Create strip line port (incl. metal strip line)
start = [-line_length -strip_width/2 0];
stop = [0 +strip_width/2 0];
[CSX,port{1}] = AddStripLinePort( CSX, 100, 1, 'metal', start, stop, strip_substrate_thickness, 'x', [0 0 -1], 'ExcitePort', true, 'FeedShift', feed_shift, 'MeasPlaneShift', meas_shift );
% Create MSL port on top
start = [line_length -strip_width/2 strip_substrate_thickness+msl_substrate_thickness];
stop = [0 +strip_width/2 strip_substrate_thickness];
[CSX,port{2}] = AddMSLPort( CSX, 100, 2, 'metal', start, stop, 'x', [0 0 -1], 'MeasPlaneShift', meas_shift );
% transitional via
start = [0, 0, 0];
stop = [0, 0, strip_substrate_thickness+msl_substrate_thickness];
CSX = AddCylinder(CSX, 'metal', 100, start, stop, connect_via_rad);
% metal plane between strip line and MSL, including hole for transition
x0 = mesh.x(1); x1 = mesh.x(end);
y0 = mesh.y(1); y1 = mesh.y(end);
theta_l = linspace(-pi, 0, 11);
p_l = [x0, 0, connect_via_gap*sin(theta_l), 0, x0 ;
y0, y0, connect_via_gap*cos(theta_l), y1, y1 ];
CSX = AddPolygon( CSX, 'gnd', 1, 'z', strip_substrate_thickness, p_l);
theta_r = linspace(0, pi, 11);
p_r = [0, x1, x1, 0, connect_via_gap*sin(theta_r) ;
y0, y0, y1, y1, connect_via_gap*cos(theta_r) ];
CSX = AddPolygon( CSX, 'gnd', 1, 'z', strip_substrate_thickness, p_r);
Write/Show/Run the openEMS compatible xml-file
Serializes the geometry and FDTD settings to XML, optionally previews the structure in AppCSXCAD to verify the transition geometry, then launches the solver. A clean simulation directory avoids stale HDF5 field data corrupting the S-parameter extraction.
Sim_Path = 'tmp';
Sim_CSX = 'strip2msl.xml';
CleanupSimPath(Sim_Path);
WriteOpenEMS( [Sim_Path '/' Sim_CSX], FDTD, CSX );
CSXGeomPlot( [Sim_Path '/' Sim_CSX] );
RunOpenEMS( Sim_Path, Sim_CSX );
Post-Processing
calcPort performs a DFT on the time-domain probe recordings and de-embeds incident and reflected wave voltages referenced to 50 Ohm. S11 reveals the impedance match at the excitation port; S21 shows the total insertion loss of the stripline-to-MSL transition across the 0-10 GHz band.
close all
f = linspace( 0, f_max, 1601 );
port = calcPort( port, Sim_Path, f, 'RefImpedance', 50);
s11 = port{1}.uf.ref./ port{1}.uf.inc;
s21 = port{2}.uf.ref./ port{1}.uf.inc;
plot(f/1e9,20*log10(abs(s11)),'k-','LineWidth',2);
hold on;
grid on;
plot(f/1e9,20*log10(abs(s21)),'r--','LineWidth',2);
legend('S_{11}','S_{21}');
ylabel('S-Parameter (dB)','FontSize',12);
xlabel('frequency (GHz) \rightarrow','FontSize',12);
ylim([-40 2]);
Images
S-parameters (S11, S21) of the stripline to microstrip transition