Designing Couplers and Splitters

When to Use

• Designing Wilkinson splitters (equal, unequal, wideband) for power division
• Creating branchline or ratrace couplers for quadrature or sum/difference networks
• Building corporate power dividers for array feed networks
• Designing directional couplers for signal sampling
• Creating SIW splitters or Rotman lenses for beam-forming

When NOT to Use

• Designing transmission lines — use matlab-design-pcb-transmission-line
• Designing filters — use matlab-design-pcb-filter
• Designing passive components (inductors, capacitors, baluns) — use matlab-design-pcb-passive
• Cascading couplers with other components — use matlab-integrate-pcb-circuit
• Optimizing coupler performance — use matlab-optimize-pcb-design

Typical Workflow

1. Before: matlab-manage-pcb-material — set up substrate and conductor
2. This skill: Design the coupler or splitter
3. Check mesh/memory: memoryEstimate(obj, fc, 'RetainMesh', true) — inspect auto-mesh density before committing to a full solve
4. After: matlab-analyze-em — validate S-parameters → matlab-optimize-pcb-design — tune dimensions → matlab-integrate-pcb-circuit — cascade into larger network

Quick Reference — Component Selection

Object	Type	Ports	Best For
wilkinsonSplitter	Equal power divider	3	Standard 2-way equal split
wilkinsonSplitterUnequal	Unequal power divider	3	Asymmetric power distribution
wilkinsonSplitterWideband	Wideband equal divider	3	Multi-octave equal split
couplerBranchline	90° hybrid	4	Quadrature combining/splitting
couplerBranchlineWideband	Wideband 90° hybrid	4	Multi-section wideband quadrature
couplerRatrace	180° hybrid	4	Sum/difference networks
couplerDirectional	Directional coupler	4	Sampling, multi-section symmetric
splitterTee	T-junction	3	Simple reactive split
powerDividerCorporate	N-way corporate	N+1	Array feed networks
SIWSplitter	SIW power divider	3	High-freq waveguide split
rotmanLens	Beam-forming network	N beam + N array	True-time-delay phased arrays

Wilkinson Splitters

Equal Split

ws = design(wilkinsonSplitter, 3e9);
show(ws);
memoryEstimate(ws, 3e9, 'RetainMesh', true);  % Check mesh before solving
sp = sparameters(ws, linspace(1e9, 5e9, 51), 'SweepOption', 'interp');
rfplot(sp);

Key properties: SplitLineLength, SplitLineWidth, Resistance, PortLineLength, PortLineWidth, GroundPlaneWidth.

Unequal Split

ws = wilkinsonSplitterUnequal;
ws = design(ws, 3e9);
show(ws);

The power division ratio is controlled by the impedance transformation arms.

Property reference (2-element vector properties):

Property	Description	Default
SplitLineLength	Length of split lines (m)	0.0279
SplitLineWidth	Width of split lines (m)	[0.0014 0.0049] (2-element vector: one per arm)
MatchLineLength	Length of output matching lines (m)	0.0277
MatchLineWidth	Width of output matching lines (m)	[0.0039 0.0066] (2-element vector: one per arm)
Resistance	Isolation resistor (ohms)	106

Wideband Wilkinson

Multi-section for extended bandwidth:

ws = wilkinsonSplitterWideband;
ws = design(ws, 5e9);
show(ws);
sp = sparameters(ws, linspace(2e9, 8e9, 51), 'SweepOption', 'interp');
rfplot(sp);

Property reference (vector properties scale with NumSections):

Property	Description	Default (3 sections)
NumSections	Number of cascaded sections	3
Shape	Shape of sections	"Rectangular" ("Circular")
SplitLineWidth	Width of quarter-wave transformers (m)	[8.55e-04 0.0014 0.0021] (vector, one per section)
Resistance	Isolation resistor values (ohms)	[100 183.40 141.42] (vector, one per section)

Multi-Layer Wilkinson

ws = design(wilkinsonSplitter, 5e9);
sub = dielectric("FR4", "Teflon");
sub.Thickness = [1e-3 0.5e-3];         % Set Thickness BEFORE assigning to component
ws.Substrate = sub;
ws.Height = 1.5e-3;
show(ws);

Branchline Couplers

Standard (Single-Section)

bl = design(couplerBranchline, 5e9);
show(bl);

freq = linspace(3e9, 7e9, 51);
sp = sparameters(bl, freq, 'SweepOption', 'interp');
rfplot(sp);

Key properties: SeriesArmLength, SeriesArmWidth, ShuntArmLength, ShuntArmWidth, PortLineLength, PortLineWidth.

Wideband (Multi-Section)

blw = couplerBranchlineWideband;
blw.NumSections = 3;
blw = design(blw, 5e9);
show(blw);

Property reference (vector properties scale with NumSections):

Property	Description	Default (2 sections)
NumSections	Number of branchline sections	2
SeriesArmWidth	Width of series arms (m)	0.0051 (scalar or vector)
ShuntArmWidth	Width of shunt arms (m)	[0.00096 0.0029 0.00096] (vector, NumSections+1 elements)
IsShielded	Add metal shielding	false

Branchline with DGS

Adding DGS improves directivity and isolation:

bl = design(couplerBranchline, 5e9);
dgsShape = dumbbell;
dgsShape.SideLength = 3e-3;       % Head size (default Type='Square')
dgsShape.ArmLength = 5e-3;
dgsShape.ArmWidth = 0.3e-3;
bl = dgs(bl, {dgsShape});         % Must capture return value
show(bl);

Analysis Methods for Couplers

freq = linspace(3e9, 7e9, 51);

% Coupling factor (S31 for branchline)
coupling(bl, freq);

% Directivity
directivity(bl, freq);

% Isolation (S41 for branchline)
isolation(bl, freq);

Ratrace Coupler

180° hybrid (sum/difference port):

rr = design(couplerRatrace, 5e9);
show(rr);

freq = linspace(3e9, 7e9, 51);
sp = sparameters(rr, freq, 'SweepOption', 'interp');
rfplot(sp);

% Analysis
coupling(rr, freq);
directivity(rr, freq);
isolation(rr, freq);

Key properties: RingRadius, RingWidth, PortLineWidth, PortLineLength.

Charge and Current on Ratrace

figure; current(rr, 5e9);
figure; charge(rr, 5e9);

Directional Coupler

Multi-section symmetric directional coupler. Note: couplerDirectional does not have a design function — set properties manually:

dc = couplerDirectional;
dc.NumSections = 3;
dc.Width = [2.8e-3 2.8e-3 2.8e-3];       % One value per section
dc.Spacing = [1.3e-3 1.3e-3 1.3e-3];     % One value per section
dc.GroundPlaneLength = 0.15;               % Must accommodate total length
show(dc);

freq = linspace(3e9, 7e9, 51);
coupling(dc, freq);
directivity(dc, freq);

Key properties: NumSections, Length (scalar), Width (vector, one per section), Spacing (vector, one per section), PortLineWidth, GroundPlaneLength.

Tee Junction and Corporate Dividers

Splitter Tee

Simple reactive T-junction. The Shape property controls the junction geometry:

Shape Value	Description
'RectangularMitered'	Rectangular with mitered bends (default)
'RectangularCurved'	Rectangular with curved bends
'Circular'	Circular junction

st = splitterTee;
st = design(splitterTee, 5e9);
show(st);
sp = sparameters(st, linspace(3e9, 7e9, 51), 'SweepOption', 'interp');
rfplot(sp);

% Circular shape variant
st2 = splitterTee(Shape='Circular');
st2 = design(st2, 5e9);
show(st2);

Corporate Power Divider (N-way)

For array feed networks:

cpd = powerDividerCorporate;
cpd.NumOutputPorts = 4;       % 1:4 divider
cpd = design(cpd, 5e9);
show(cpd);
sp = sparameters(cpd, linspace(3e9, 7e9, 51), 'SweepOption', 'interp');
rfplot(sp);

8-Way Corporate Divider

cpd = powerDividerCorporate;
cpd.NumOutputPorts = 8;
cpd = design(cpd, 2.4e9);
show(cpd);

SIW Splitter

siw_s = SIWSplitter;
siw_s = design(siw_s, 10e9);
show(siw_s);

The FeedLine property is a traceTapered object controlling the microstrip-to-SIW transition:

siw_s.FeedLine.InputWidth = 1e-3;
siw_s.FeedLine.OutputWidth = 3e-3;
show(siw_s);

Design Workflow

1. Select topology based on requirements (equal/unequal split, bandwidth, isolation)
2. Design at center frequency: obj = design(ObjectType, fc)
3. Visualize: show(obj)
4. Analyze S-parameters: sparameters(obj, freq, 'SweepOption', 'interp')
5. Check metrics: coupling, directivity, isolation
6. Customize: Adjust properties for specific impedance, substrate, dimensions
7. Optimize if needed (see matlab-optimize-pcb-design)

Coupler-Specific Analysis Functions

These functions are available on 4-port coupler objects: couplerBranchline, couplerBranchlineWideband, couplerRatrace, couplerDirectional.

Function	What It Measures	Signature
coupling(obj, freq)	Coupling factor (dB) — power transferred to coupled port	Plots by default; cVal = coupling(obj, freq) returns values
directivity(obj, freq)	Directivity (dB) — separation of forward vs. backward coupled power	Plots by default; dVal = directivity(obj, freq) returns values
isolation(obj, freq)	Isolation (dB) — power leakage to the isolated port	Plots by default; iVal = isolation(obj, freq) returns values

c = design(couplerBranchline, 2.4e9);
freq = linspace(2e9, 3e9, 101);

coupling(c, freq);              % plots coupling factor
cVal = coupling(c, freq);       % returns numeric values (dB)

directivity(c, freq);           % plots directivity
dVal = directivity(c, freq);    % returns numeric values (dB)

isolation(c, freq);             % plots isolation
iVal = isolation(c, freq);      % returns numeric values (dB)

Port Numbering Convention

3-Port (Splitters)

Port	Function
1	Input
2	Output (through)
3	Output (split)

4-Port (Couplers)

Port	Branchline	Ratrace
1	Input	Input
2	Through (-3dB, 0°)	Sum
3	Coupled (-3dB, -90°)	Difference
4	Isolated	Through

Rotman Lens (Beam-Forming Network)

rotmanLens is an N-beam, N-array true-time-delay beam-forming network.

lens = rotmanLens;
lens.NumBeamPorts  = 4;
lens.NumArrayPorts = 4;
lens.NumDummyPorts = 4;       % Absorb reflected energy at lens edges
lens.BeamPortAngle = 40;      % Angular spread of beam ports (degrees)
lens.MaxScanAngle  = 30;      % Maximum scan angle (degrees)
lens.Height        = 5.08e-4;
lens.Conductor     = metal("Copper");
show(lens);
layout(lens);

Key properties: OnaxisFocalLength, OffaxisFocalLength (auto-computed from scan angle). BeamTaper and ArrayTaper control the tapered feed line shapes (traceTapered objects).

SIW Power Divider

SIWSplitter is a substrate integrated waveguide 1:2 power divider.

s = SIWSplitter;
s.InputLineLength = 0.0155;
s.SplitLineLength = 0.0145;
s.Width           = 0.0125;
s.ViaSpacing      = [0.0017, 0.011];    % [wall via spacing, split via spacing]
s.ViaDiameter     = 5e-4;
s.PostDiameter    = 2.54e-4;
s.PostOffsetX     = 5.5e-3;
s.Height          = 8e-4;
show(s);

Custom feed lines via FeedLine property:

s.FeedLine = traceRectangular(Length=3e-3, Width=2e-3);

Pitfalls

1. Use interpolating sweep for S-parameters: Always use sparameters(obj, freq, 'SweepOption', 'interp') for MoM solves. Direct sweeps solve at every frequency point individually and are significantly slower.

2. Check mesh density before solving: Catalog couplers generate dense auto-meshes that dominate runtime. Always run memoryEstimate(obj, fc, 'RetainMesh', true) before sparameters(). If memory is excessive, coarsen: mesh(obj, 'MaxEdgeLength', lambda/6). See matlab-analyze-em for full mesh inspection workflow.

3. Resistance in Wilkinson: The isolation resistor value defaults to 100 ohm (2×Z0). For non-50-ohm systems, adjust Resistance property accordingly.

4. Port numbering varies: Different coupler types number ports differently. Always check with show(obj) which port is which before interpreting S-parameters.

5. Wideband coupler sections: More sections = wider bandwidth but larger size. Each section adds approximately a quarter-wavelength at center frequency.

6. Corporate divider symmetry: powerDividerCorporate requires NumOutputPorts to be a power of 2 (2, 4, 8, 16...).

7. Corporate divider substrate: powerDividerCorporate.Substrate is read-only. Set the substrate on corp.SplitterElement.Substrate instead — the corporate divider builds from its unit SplitterElement (a wilkinsonSplitter). Note: design() may override the substrate thickness.

8. Corporate dividers have large mesh: Multi-way corporate dividers are physically large structures. Memory requirements can exceed hundreds of GB at high frequencies. Use behavioral S-parameters ('Behavioral', true) for fast amplitude/phase balance verification when full-wave is infeasible.

9. Set substrate BEFORE design(): design(obj, fc) auto-sizes dimensions based on the current substrate. Setting substrate after design() changes the material but does NOT re-compute dimensions — causing incorrect impedance. Always: set Substrate first, then call design().

10. DGS coupling: Adding DGS to couplers can improve directivity by 10-15 dB but slightly shifts center frequency. Re-tune after adding DGS.

11. SplitterTee is reactive: Unlike Wilkinson, the T-junction is a reactive (lossless) split — output ports are not isolated from each other. Use Wilkinson when isolation matters.

12. No design() for couplerDirectional: couplerDirectional does not support design(). Set Length, Width, Spacing, and NumSections manually.

13. couplerDirectional multi-section dimensions: When NumSections > 1, Width and Spacing must be vectors with one element per section. Length remains scalar. Also increase GroundPlaneLength to accommodate the longer structure — the default only fits 1 section.

14. Cascading couplers with stubs/resonators: To physically attach a stub or resonator to a coupler port, use pcbcascade(pcbComponent(coupler), pcbComponent(stub), portA, portB). Match Height, Substrate, and Conductor between the two objects. The connected ports disappear — verify surviving port count with show(combined). See matlab-integrate-pcb-circuit for cascade details.

15. Catalog couplers are MoM-only: Objects like couplerBranchline only support MoM natively. To use FEM, wrap in pcbComponent and set SolverType after construction (not during):

    bl = design(couplerBranchline, 5e9);
    pcb = pcbComponent(bl);
    pcb.SolverType = 'FEM';
    s = solver(pcb);
    s.BoundaryCondition = 'perfectly-matched-layer';
    

    Do NOT pass SolverType as a name-value to pcbComponent(). FEM requires the IDMF solver engine (WSL on Windows) — if idmf_hub is missing, use MoM instead. See matlab-analyze-em for FEM prerequisites and troubleshooting.

Related Skills

• matlab-manage-pcb-material — Substrate configuration
• matlab-analyze-em — S-parameter and field analysis
• matlab-optimize-pcb-design — Optimizing coupler/splitter performance
• matlab-integrate-pcb-circuit — Combining splitters with other components

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