How to add a substrate to an antenna pattern

I am a bleeding newbie to Matlab and found the example below to simulate RFID tag antennas, BUT do not see in the description how to add the influence of the substrate below the metallic atenna pattern ( In the case of the example PET approx. 90µm thick - Dielectricity constant between 3 and 4).

Can anybody help me with pointing the right way ?

Thanks in advance !!

RFID Antenna Design

This example uses:

• Antenna Toolbox
• Partial Differential Equation Toolbox

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This example creates a commercially available RFID tag operating at 915 MHz. The planar antenna is drawn and meshed using PDE Toolbox™. The meshed structure is then imported into Antenna Toolbox and solved for its EM properties.

This example requires the following product:

• Partial Differential Equation Toolbox™

Answer 1

[Chandra Amma Palanisamy]

The RFID example uses customAntennaMesh to create the antenna. To include a PET substrate (90 µm thick, εr ≈ 3.5), you can recreate the geometry as a pcbStack and add a dielectric layer beneath the conductor.

The workflow is:

1. Import the RFID tag geometry(RFIDtag.mat) from the example RFID Antenna Design
2. Extract the antenna boundary from the triangulation.
3. Create the conducting top layer using the antenna boundary.
4. Define the feed region and feed location.
5. Create a dielectric substrate.
6. Build a pcbStack object with the conductor and substrate layers.
7. Visualize the geometry and compute the radiation pattern.

load RFIDtag.mat

% Create a triangulation object from the imported mesh data
tr = triangulation(t(1:3,:)', p.');

% Extract the outer boundary vertices of the antenna geometry
[~, vert] = freeBoundary(tr);

% Create the metal pattern for the top conducting layer
topLayer = antenna.Polygon("Vertices", vert);

% Vertex indices corresponding to the feed region
feedIDs = [41 42 212 213];

% Create a rectangular feed polygon using the feed vertices
feedRectangle = antenna.Polygon("Vertices", vert(feedIDs,:));

% Add the feed polygon to the antenna metal pattern
topLayer = topLayer + feedRectangle;

% Define a square board shape that encloses the antenna geometry
lw = max(vert(:,1));
bShape = antenna.Rectangle( ...
    "Length", lw, ...
    "Width",  lw, ...
    "Center", [lw/2 lw/2]);

% Compute feed location from the feed rectangle vertices
xs = (vert(feedIDs(1),1) + vert(feedIDs(2),1))/2;
ys = vert(feedIDs(1),2);

% Feed width used to determine feed diameter
ws = vert(feedIDs(1),1) - vert(feedIDs(2),1);

% Create a PET dielectric substrate
substrate = dielectric( ...
    "Name", "PET", ...
    "EpsilonR", 3.5, ...
    "LossTangent", 0.0002, ...
    "Thickness", 90e-6);

% Create the pcbStack model
ant = pcbStack;

% Assign board dimensions
ant.BoardShape = bShape;

% Set substrate thickness
ant.BoardThickness = substrate.Thickness;

% Define stack-up:
% Layer 1 -> Conducting RFID tag pattern
% Layer 2 -> PET dielectric substrate
ant.Layers = {topLayer, substrate};

% Define feed location on layer 1
ant.FeedLocations = [xs ys 1];

% Set feed diameter
ant.FeedDiameter = ws/2;

% Visualize the antenna structure
figure;
show(ant)

% Plot radiation pattern at 915 MHz
figure;
pattern(ant, 915e6)