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-txline
• 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

matlab
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

matlab
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:

matlab
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

matlab
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)

matlab
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)

matlab
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:

matlab
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

matlab
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):

matlab
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

matlab
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:

matlab
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 |

matlab
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:

matlab
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

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

SIW Splitter

matlab
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:

matlab
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 |

matlab
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.

matlab
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.

matlab
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:

matlab
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.

1. 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.

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

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

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

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

1. 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.

1. 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.

1. 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().

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

1. 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.

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

1. 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.

1. 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.

1. 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):

matlab 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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