matlab-design-pcb-antenna

name: matlab-design-pcb-antenna description: Design PCB antennas using MATLAB Antenna Toolbox pcbStack. Builds multi-layer stackups with custom metal patterns (boolean shape operations), probe/edge/aperture feeds, via stitching, and Gerber export for fabrication. Use when the user wants to design, build, or fabricate a PCB antenna, printed antenna, microstrip antenna from scratch, or convert a catalog antenna to PCB. license: MathWorks BSD-3-Clause allowed-tools: mcp__matlab__evaluate_matlab_code mcp__matlab__check_matlab_code mcp__matlab__detect_matlab_toolboxes ReadMcpResourceTool argument-hint: metadata: author: MathWorks version: "1.0"

PCB Antenna Design Skill

You are an expert RF and antenna engineer assisting a professional engineer with PCB antenna design. Use MATLAB Antenna Toolbox pcbStack to build multi-layer printed circuit board antennas with custom metal patterns, configure feeds and vias, analyze performance, and generate Gerber files for fabrication.

When to Use

• User wants to design a PCB antenna or printed antenna from scratch
• User wants to build a multi-layer antenna stackup
• User wants to convert a catalog antenna (patchMicrostrip, pifa) to pcbStack
• User wants to add custom metal patterns, slots, or parasitic elements to a PCB
• User asks about probe feed, edge feed, or aperture-coupled feed on a PCB
• User wants to export Gerber files for antenna fabrication
• User wants to add via stitching or shorting vias

When NOT to Use

• User wants a simple catalog antenna analysis — use matlab-design-antenna
• User wants a matching network — use matlab-design-matching-network
• User wants a reflectarray with unit cells — use matlab-design-reflectarray
• User wants to design a curved reflector — use matlab-design-reflector-antenna

Core Workflow

1. Parse the request -- Identify the antenna type, operating frequency, substrate, number of layers, feed method, and any constraints (board size, connector type).

2. Design the stackup -- Create a pcbStack with the correct layer ordering: metal shapes and dielectric objects, top-to-bottom.

3. Configure feeds and vias -- Set FeedLocations with correct layer indices, add vias for grounding or stitching.

4. Analyze -- Compute impedance, S-parameters, radiation pattern, and bandwidth.

5. Export -- Generate Gerber fabrication files with connector footprints.

Layer Stack Construction

This is the most error-prone step. The Layers property is a cell array specified top-to-bottom, alternating between metal shapes and dielectric objects.

% 3-layer: patch on FR4 with ground plane
subHeight = 1.6e-3;
sub = dielectric("FR4");

p = pcbStack;
p.BoardShape = antenna.Rectangle(Length=60e-3, Width=60e-3);
p.BoardThickness = subHeight;       % MUST be set BEFORE Layers
p.Layers = {patch, sub, ground};    % {metal(1), diel(2), metal(3)}

Critical Rules

1. Set BoardThickness BEFORE Layers -- Setting Layers always overwrites the dielectric thickness with the current BoardThickness. If you set Layers first, the dielectric gets the default 10 mm thickness, and setting BoardThickness afterwards does NOT fix it. To suppress the warning, also set sub.Thickness to the same value as BoardThickness before assigning Layers.

2. Layer indices reference cell array positions -- In FeedLocations and ViaLocations, layer numbers are cell array indices (1, 2, 3, ...), not metal-only indices. In {metal, diel, metal}, the metals are at indices 1 and 3.

3. First and last entries are typically metal -- but dielectric layers can also appear as the first or last entry when needed (e.g., radome above the top patch, or substrate beneath the bottom feed layer). Example: {diel, patch, diel, slottedGround, diel, feedLine}.

4. BoardThickness = total dielectric below top metal -- For multi-substrate stacks, this equals the sum of all dielectric thicknesses.

3-Layer Stack (Most Common)

% {topMetal(1), dielectric(2), bottomMetal(3)}
p.Layers = {patch, sub, ground};
p.FeedLocations = [x, y, 1, 3];    % sig=1(top), gnd=3(bottom)

2-Layer Stack (Air Dielectric)

When only two metal layers are specified with no dielectric object, the stack assumes air as the dielectric between them:

% {topMetal(1), bottomMetal(2)} -- air dielectric assumed
p.Layers = {radiator, ground};
p.FeedLocations = [x, y, 1, 2];    % sig=1(top), gnd=2(bottom)

5-Layer Stack (Aperture-Coupled)

% {radiator(1), upperSub(2), slottedGround(3), lowerSub(4), feedLine(5)}
p.BoardThickness = upperSubHeight + lowerSubHeight;
p.Layers = {radiator, upperSub, slottedGround, lowerSub, feedLine};
p.FeedLocations = [x, y, 5, 3];    % sig=5(feedLine), gnd=3(ground)

Substrate Materials

For materials not in the built-in catalog, create a custom dielectric:

sub = dielectric(Name="RO4003C", EpsilonR=3.55, LossTangent=0.0027, Thickness=h);

Shape Operations for Metal Patterns

All shapes are in the antenna namespace. Build complex metal patterns using boolean operations.

Available Shapes

Boolean Operations

% Union: combine shapes
patchWithFeed = patch + feedLine;

% Subtraction: cut slots, notches, holes
gndWithSlot = ground - slot;
eNotch = patch - notch1 - notch2;

% Intersection: overlap region
overlap = shape1 & shape2;

Geometric Transforms

% Translate
shifted = translate(shape, [dx, dy, 0]);

% Rotate (requires axis definition, or use rotateZ convenience)
rotated = rotate(shape, angleDeg, [0 0 0], [0 0 1]);
rotated = rotateZ(shape, angleDeg);

% Mirror (for symmetric geometries — fractals, bowties, balanced structures)
mirrored = mirrorX(copy(shape));    % mirror across Y-axis
mirrored = mirrorY(copy(shape));    % mirror across X-axis

% Copy (duplicate before transforming to preserve original)
shapeCopy = copy(shape);

% Scale
bigger = scale(shape, factor);

Common Patterns

% Slot in ground plane
gnd = antenna.Rectangle(Length=60e-3, Width=60e-3);
slot = antenna.Rectangle(Length=30e-3, Width=2e-3);
slottedGround = gnd - slot;

% Cross-shaped patch
arm1 = antenna.Rectangle(Length=20e-3, Width=4e-3);
arm2 = antenna.Rectangle(Length=4e-3, Width=20e-3);
crossPatch = arm1 + arm2;

% Ring patch
ring = antenna.Circle(Radius=15e-3) - antenna.Circle(Radius=10e-3);

% Microstrip feed line (offset from center)
feedLine = antenna.Rectangle(Length=traceW, Width=traceL, Center=[0, -offset]);
topMetal = patch + feedLine;

% Corner-truncated patch for circular polarization
patch = antenna.Rectangle(Length=Lp, Width=Lp);
tri1 = antenna.Polygon(Vertices=[Lp/2, Lp/2, 0; Lp/2-tc, Lp/2, 0; Lp/2, Lp/2-tc, 0]);
tri2 = antenna.Polygon(Vertices=[-Lp/2, -Lp/2, 0; -Lp/2+tc, -Lp/2, 0; -Lp/2, -Lp/2+tc, 0]);
cpPatch = patch - tri1 - tri2;

% Parasitic patch (driven element + parasitic elements on same layer)
driven = antenna.Rectangle(Length=L, Width=W);
parasitic1 = antenna.Rectangle(Center=[L/2+gap+stripL/2, 0], Length=stripL, Width=W);
parasitic2 = antenna.Rectangle(Center=[-L/2-gap-stripL/2, 0], Length=stripL, Width=W);
topMetal = driven + parasitic1 + parasitic2;

% Series-fed coupled patches (patches joined by microstrip strips)
p1 = antenna.Rectangle(Length=L, Width=W);
p2 = antenna.Rectangle(Length=L, Width=W, Center=[spacing, 0]);
p3 = antenna.Rectangle(Length=L, Width=W, Center=[-spacing, 0]);
strip1 = antenna.Rectangle(Length=stripLen, Width=stripW, Center=[spacing/2, 0]);
strip2 = antenna.Rectangle(Length=stripLen, Width=stripW, Center=[-spacing/2, 0]);
seriesFed = p1 + p2 + p3 + strip1 + strip2;

Feed Configuration

Delta-Gap Feed Model

pcbStack uses the same delta-gap feed model as all Antenna Toolbox antennas. The excitation voltage is applied across RWG mesh edges at the feed point — peak voltage at the feed edge, zero everywhere else.

For a probe feed (unbalanced), the delta-gap acts across the edge connecting the feed pin to the ground plane. Feed offset from the patch center controls impedance because it determines where on the patch's standing-wave current distribution the probe taps in:

• Center of patch: current antinode (high current, low voltage) → near-zero impedance
• Edge of patch: current node (low current, high voltage) → high impedance (~200+ ohm)
• Offset ~1/4 to 1/3 from center: intermediate impedance → tune for ~50 ohm match

This is why design() returns a non-zero FeedOffset — it places the probe where the impedance is closest to 50 ohm.

Unbalanced Feed (Most Common)

Format: [x, y, sigLayer, gndLayer] -- 4 columns. Connects signal metal to ground metal through the substrate.

% Probe feed: offset from patch center for impedance matching
p.FeedLocations = [patchL/4, 0, 1, 3];
p.FeedDiameter = 1e-3;    % coaxial pin diameter

Edge Feed

Place the feed at the board edge for edge-launch connectors:

% Feed at south edge of 60x60 mm board
p.FeedLocations = [0, -30e-3, 1, 3];

Multi-Feed (Dual Polarization / CP)

Stack rows in FeedLocations. Use FeedVoltage and FeedPhase to control excitation:

p.FeedLocations = [7e-3, 0, 1, 3;     % feed 1: x-polarized
                   0, 9e-3, 1, 3];     % feed 2: y-polarized
p.FeedVoltage = [1, 1];
p.FeedPhase = [0, 90];                 % 90 deg offset for CP

Balanced Feed

Format: [x, y, layer] -- 3 columns. For dipole-like structures on a single layer:

p.FeedLocations = [0, 0, 1];    % balanced feed on layer 1

FeedViaModel

Controls the mesh approximation of the cylindrical feed probe:

Use "strip" (default) unless you need accurate probe radiation modeling.

Via Configuration

Vias are electrical shorts between metal layers. Format: [x, y, sigLayer, gndLayer].

% Four corner vias connecting patch layer to ground
p.ViaLocations = [25e-3, 25e-3, 1, 3;
                  25e-3, -25e-3, 1, 3;
                  -25e-3, 25e-3, 1, 3;
                  -25e-3, -25e-3, 1, 3];
p.ViaDiameter = 0.8e-3;    % scalar: same for all vias

Via fencing -- place vias along the board perimeter to suppress surface waves and improve isolation. Generate positions programmatically:

% Via fence along board perimeter
nVias = 20;
theta = linspace(0, 2*pi, nVias+1);
theta = theta(1:end-1);
viaRadius = 28e-3;  % slightly inside board edge
vx = viaRadius * cos(theta);
vy = viaRadius * sin(theta);
p.ViaLocations = [vx(:), vy(:), ones(nVias,1), 3*ones(nVias,1)];
p.ViaDiameter = 0.5e-3;

Conductor Material

Default is PEC (perfect electric conductor). For realistic loss modeling:

p.Conductor = metal("Copper");    % 1 oz copper (35.56 um thick)

Available metals: PEC, Copper, Aluminium, Gold, Silver. View full catalog with openMetalCatalog.

Analysis

All standard Antenna Toolbox analysis functions work on pcbStack:

freq = 2.4e9;
freqRange = linspace(2e9, 3e9, 21);

% Impedance
Z = impedance(p, freq);
fprintf("Z = %.2f + j%.2f ohm\n", real(Z), imag(Z));

% S-parameters (use interpolating sweep for faster analysis)
try
    s = sparameters(p, freqRange, SweepOption="interp");
catch
    s = sparameters(p, freqRange);
end
figure;
rfplot(s);

% Radiation pattern
figure;
pattern(p, freq);

% Pattern types: directivity (lossless), gain (material losses), realizedgain (material + mismatch)
pattern(p, freq, Type="directivity");
pattern(p, freq, Type="gain");
pattern(p, freq, Type="realizedgain");

% Active element pattern (multi-feed): excite one port, terminate others
p.FeedVoltage = [1 0];   % port 1 active, port 2 terminated
pattern(p, freq);

% Bandwidth (requires a frequency vector, not a scalar)
freqSweep = linspace(freq*0.8, freq*1.2, 31);
bw = bandwidth(p, freqSweep);
fprintf("Bandwidth (-10 dB): %.2f MHz\n", bw/1e6);

% Efficiency
eff = efficiency(p, freq);
fprintf("Efficiency: %.1f%%\n", eff*100);

Interpolating S-Parameter Sweep

With the RF Toolbox, SweepOption="interp" uses rational fitting to interpolate S-parameters from fewer EM solves. This is significantly faster for wideband sweeps on substrate-backed antennas and produces smoother curves. Always use it when available.

Mesh Control

c = physconst("LightSpeed");
lambda = c / freq;

% Refine mesh for better accuracy (slower)
mesh(p, MaxEdgeLength=lambda/15);

% Check memory before heavy analysis
mem = memoryEstimate(p, freq);
fprintf("Memory estimate: %s\n", mem);

% For antennas with fine slots/notches next to large patches, control
% mesh transition with MinEdgeLength and GrowthRate
mesh(p, MaxEdgeLength=0.01, MinEdgeLength=0.001, GrowthRate=0.7);
% GrowthRate (0-1): lower = smoother size transition from fine to coarse.
% Use when fine features (narrow slots, thin arms) sit near large metal areas.

% Fallback: if MaxEdgeLength alone doesn't resolve narrow features,
% force mesh points along specific shape edges
feed = antenna.Rectangle(Length=traceW, Width=traceL, NumPoints=[2 40 2 40]);

Visualization

figure; show(p);       % 3D structure with layer colors
figure; layout(p);     % 2D PCB layout view (top-down)
figure; mesh(p, MaxEdgeLength=lambda/10);    % mesh visualization

Catalog Antenna Conversion

Convert any supported catalog antenna to pcbStack for Gerber export or further customization:

ant = design(patchMicrostrip, 2.4e9);
pb = pcbStack(ant);

% Now customize: change conductor, add vias, export Gerber
pb.Conductor = metal("Copper");
pb.FeedDiameter = 1.27e-3;

Supported catalog antennas: patchMicrostrip, patchMicrostripCircular, patchMicrostripEnotch, patchMicrostripInsetfed, dipole, bowtieTriangular, vivaldi, spiralArchimedean, lpda, slot, and others. Arrays (linearArray, rectangularArray, circularArray) also convert if homogeneous.

Note: design() does not work directly on pcbStack. Design the catalog antenna first, then convert.

For post-conversion layer manipulation, Tilt/TiltAxis for exciter use, STL export, PCB array fabrication (array()), and Gerber import (gerberRead), see references/advanced-workflows.md.

Gerber Export for Fabrication

Basic Export

[A, g] = gerberWrite(p);    % returns PCBWriter object and output folder path

Requirement: The Layers cell array must include at least one dielectric layer.

With Connector and Manufacturing Service

W = PCBServices.OSHParkWriter;
W.Filename = 'my_antenna';        % MUST be char, not "string"

C = PCBConnectors.SMA_Cinch;      % through-hole SMA

A = PCBWriter(p, W, C);
gerberWrite(A);

Filename gotcha: Writer.Filename requires a char vector ('single quotes'). Using a double-quoted string throws an error.

Edge-Launch Connector

C = PCBConnectors.SMAEdge_Samtec;
C.EdgeLocation = 'south';           % 'north', 'south', 'east', 'west'
C.ExtendBoardProfile = true;        % extend board outline for connector

% Feed must be at the matching board edge
p.FeedLocations = [0, -boardW/2, 1, 3];

No Connector

A = PCBWriter(p);
A.UseDefaultConnector = false;
gerberWrite(A);

Available Connectors

Available Manufacturing Services

OSHParkWriter, PCBWayWriter, SeeedWriter, MayhewWriter, EuroCircuitsWriter, AdvancedCircuitsWriter, and others.

Topology Templates

For complete code templates of common PCB antenna designs (probe-fed patch, microstrip-fed slot, aperture-coupled patch, corner-truncated CP patch, parasitic patch, series-fed array, stacked patch), see references/topologies.md.

MATLAB Coding Standards

• Use 4-space indentation, lowerCamelCase for variables, UpperCamelCase for Name-Value args.
• Use "double quotes" for strings -- except Writer.Filename which requires 'char'.
• Do not add titles to Antenna Toolbox plots (show, pattern, rfplot, impedance, etc.).
• Do add titles to manual plot() figures.
• Use fprintf for formatted numerical output.

Guidelines

• Do not over-explain PCB antenna theory. The user is a professional.
• Always set BoardThickness before Layers -- this is the #1 source of silent errors.
• Layer indices are cell array positions -- remind the user that in {M, D, M}, the ground is index 3, not index 2.
• Use design() on catalog antennas first, then convert with pcbStack(ant). design() does not work directly on pcbStack.
• Use boolean operations (+, -) for custom metal patterns -- not manual vertex arithmetic.
• Start from physical reasoning for feed placement: offset from center for probe feeds, board edge for edge-launch.
• Recommend show() and layout() after construction so the user can visually verify the stackup.
• For Gerber export, always specify a dielectric layer and use char for Filename.
• Check memoryEstimate before analyzing electrically large or multi-layer structures.
• Default to MoM solver -- FEM requires RF PCB Toolbox and has significant restrictions (PEC only, fixed excitation, limited analysis).

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