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Spiral Slot Antenna
Introduction
Spiral slot antennas provide a conformal design and can be used for communication, sensing, tracking, positioning, and many applications in different microwave frequency bands due to their wideband frequency response. This example shows how to build a spiral geometry using parametric curves, and computes S-parameters and far-field patterns.
Figure 1: A spiral slot antenna patterned on a single-sided metal substrate is excited by a lumped port.
Model Definition
The spiral slot antenna is built with a two-arm Archimedean spiral slot, which is patterned on a thin single-sided metal substrate using parametric curves. The metal surface is modeled as a perfect electric conductor (PEC) assuming the conductivity is very high and the loss on the surface is negligible. A lumped port is placed at the center of the spiral slot to excite the antenna. The antenna structure and air region are enclosed by a perfectly matched layer (PML). All domains except the PML are meshed by a tetrahedral mesh with approximately five elements per wavelength and the slot boundary is meshed more finely. The PML is swept with a total of five elements along the radial direction.
Results and Discussion
Figure 2 shows the electric field norm on the top surface of the spiral slot antenna. The intensity of the fields along the slot is stronger than at the rest of the surface. The polar plot and 3D far-field visualization in Figure 3 and Figure 4 show bidirectional radiation pattern and maximum radiation along the z-axis. Figure 5 shows the calculated S-parameters. In particular, S11 over the simulated frequency range is better than −10 dB.
Figure 2: The log-scaled electric field norm on the xy-plane describes how the electric fields are confined on a slotted substrate.
Figure 3: 2D polar plot on the yz-plane showing bidirectional radiation patterns.
Figure 4: 3D far-field radiation pattern at 3 GHz. The direction of the maximum radiation is along the z-axis.
Figure 5: The S-parameter plot shows better than -10 dB S11 over the simulated frequency range.
Application Library path: RF_Module/Antennas/spiral_slot_antenna
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Radio Frequency>Electromagnetic Waves, Frequency Domain (emw).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Frequency Domain.
6
Click  Done.
Study 1
Step 1: Frequency Domain
1
In the Model Builder window, under Study 1 click Step 1: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
In the Frequencies text field, type range(1.5[GHz],0.5[GHz],4[GHz]).
Geometry 1
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, locate the Units section.
3
From the Length unit list, choose mm.
First, create a cylinder for the substrate.
Cylinder 1 (cyl1)
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Radius text field, type 40.
4
In the Height text field, type 1.524.
5
Click  Build Selected.
Add a work plane on the top surface of the substrate.
Work Plane 1 (wp1)
1
In the Geometry toolbar, click  Work Plane.
2
In the Settings window for Work Plane, locate the Plane Definition section.
3
From the Plane type list, choose Face parallel.
4
On the object cyl1, select Boundary 4 only.
5
Click  Show Work Plane.
Work Plane 1 (wp1)>Plane Geometry
Add a parametric curve to start building a spiral slot.
Work Plane 1 (wp1)>Parametric Curve 1 (pc1)
1
In the Work Plane toolbar, click  More Primitives and choose Parametric Curve.
2
In the Settings window for Parametric Curve, locate the Parameter section.
3
In the Maximum text field, type 7*pi.
4
Locate the Expressions section. In the xw text field, type 1.5*s*cos(s).
5
In the yw text field, type 1.5*s*sin(s).
6
Click  Build Selected.
7
Click the  Zoom Extents button in the Graphics toolbar.
Work Plane 1 (wp1)>Parametric Curve 2 (pc2)
1
In the Work Plane toolbar, click  More Primitives and choose Parametric Curve.
2
In the Settings window for Parametric Curve, locate the Parameter section.
3
In the Maximum text field, type 7*pi.
4
Locate the Expressions section. In the xw text field, type (1.5+1.5*s)*cos(s).
5
In the yw text field, type (1.5+1.5*s)*sin(s).
Work Plane 1 (wp1)>Polygon 1 (pol1)
1
In the Work Plane toolbar, click  Polygon.
2
In the Settings window for Polygon, locate the Coordinates section.
3
In the table, enter the following settings:
xw (mm)
yw (mm)
-35
0
-32
0
Work Plane 1 (wp1)>Rotate 1 (rot1)
1
In the Work Plane toolbar, click  Transforms and choose Rotate.
2
Click in the Graphics window and then press Ctrl+A to select all objects.
3
In the Settings window for Rotate, locate the Input section.
4
Select the Keep input objects check box.
5
Locate the Rotation section. In the Angle text field, type 180.
Work Plane 1 (wp1)>Rectangle 1 (r1)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type sqrt(8).
4
Locate the Position section. From the Base list, choose Center.
5
Locate the Rotation Angle section. In the Rotation text field, type atan2(1,sqrt(8))/pi*180.
6
Click  Build Selected.
All parts to form a spiral slot are added.
Remove unnecessary geometry entities by converting the added parts to solid.
Work Plane 1 (wp1)>Convert to Solid 1 (csol1)
1
In the Work Plane toolbar, click  Conversions and choose Convert to Solid.
2
Click in the Graphics window and then press Ctrl+A to select all objects.
Remove interior boundaries.
Work Plane 1 (wp1)>Union 1 (uni1)
1
In the Work Plane toolbar, click  Booleans and Partitions and choose Union.
2
Select the object csol1 only.
3
In the Settings window for Union, locate the Union section.
4
Clear the Keep interior boundaries check box.
This is the boundary where the excitation port will be assigned.
Work Plane 1 (wp1)>Square 1 (sq1)
1
In the Work Plane toolbar, click  Square.
2
In the Settings window for Square, locate the Position section.
3
From the Base list, choose Center.
4
Locate the Rotation Angle section. In the Rotation text field, type atan2(1,sqrt(8))/pi*180.
5
In the Work Plane toolbar, click  Build All.
The layout of the antenna is a two-arm Archimedean spiral.
Add a sphere with a layer definition for the PML.
Sphere 1 (sph1)
1
In the Model Builder window, right-click Geometry 1 and choose Sphere.
2
In the Settings window for Sphere, locate the Size section.
3
In the Radius text field, type 90.
4
Click to expand the Layers section. In the table, enter the following settings:
Layer name
Thickness (mm)
Layer 1
30
5
Click  Build All Objects.
6
Click the  Wireframe Rendering button in the Graphics toolbar.
The antenna structure is enclosed by the spherical shell.
Definitions
Add a perfectly matched layer.
Perfectly Matched Layer 1 (pml1)
1
In the Definitions toolbar, click  Perfectly Matched Layer.
2
Select Domains 1–4 and 7–10 only.
3
In the Settings window for Perfectly Matched Layer, locate the Geometry section.
4
From the Type list, choose Spherical.
View 1
Suppress some domains and boundaries to get a better view of the interior parts when setting up the physics and reviewing the mesh.
Hide for Physics 1
1
In the Model Builder window, right-click View 1 and choose Hide for Physics.
2
Select Domains 1, 2, 7, and 8 only.
Hide for Physics 2
1
Right-click View 1 and choose Hide for Physics.
2
In the Settings window for Hide for Physics, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
Select Boundaries 9, 10, 25, and 26 only.
Electromagnetic Waves, Frequency Domain (emw)
Set up the physics. Start by assigning an additional PEC boundary on the metal surface.
Perfect Electric Conductor 2
1
In the Model Builder window, under Component 1 (comp1) right-click Electromagnetic Waves, Frequency Domain (emw) and choose Perfect Electric Conductor.
2
Select Boundary 16 only.
Lumped Port 1
1
In the Physics toolbar, click  Boundaries and choose Lumped Port.
2
Select Boundary 19 only.
For the first port, wave excitation is on by default.
Far-Field Domain 1
In the Physics toolbar, click  Domains and choose Far-Field Domain.
Materials
Now assign material properties. Use air for all domains and override the substrate with a dielectric material.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in>Air.
4
Click Add to Component in the window toolbar.
5
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Dielectric material
1
In the Model Builder window, under Component 1 (comp1) right-click Materials and choose Blank Material.
2
In the Settings window for Material, type Dielectric material in the Label text field.
3
Select Domain 6 only.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
3.38
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electrical conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0
S/m
Basic
Mesh 1
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Build All.
Study 1
In the Home toolbar, click  Compute.
Results
The default plot shows the E-field norm, a 2D far-field polar plot, and the 3D far-field radiation pattern. Adjust plot settings to reproduce the result figures.
Electric Field (emw)
1
In the Model Builder window, under Results click Electric Field (emw).
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Parameter value (freq (GHz)) list, choose 3.
Multislice
1
In the Model Builder window, expand the Electric Field (emw) node, then click Multislice.
2
In the Settings window for Multislice, locate the Expression section.
3
In the Expression text field, type 20*log10(emw.normE).
4
Locate the Multiplane Data section. Find the X-planes subsection. In the Planes text field, type 0.
5
Find the Y-planes subsection. In the Planes text field, type 0.
6
Find the Z-planes subsection. From the Entry method list, choose Coordinates.
7
In the Coordinates text field, type 1.524.
Selection 1
1
Right-click Multislice and choose Selection.
2
Select Domains 5 and 6 only.
Deformation 1
1
Right-click Multislice and choose Deformation.
2
In the Settings window for Deformation, locate the Expression section.
3
In the Z component text field, type 20*log10(emw.normE).
4
In the X component text field, type 0.
5
In the Y component text field, type 0.
6
In the Electric Field (emw) toolbar, click  Plot.
Compare the reproduced plot with that in Figure 2.
S-parameter (emw)
The calculated S-parameter plot should look like that shown in Figure 5.
Smith Plot (emw)
Radiation Pattern 1
1
In the Model Builder window, expand the Results>2D Far Field (emw) node, then click Radiation Pattern 1.
2
In the Settings window for Radiation Pattern, locate the Evaluation section.
3
Find the Angles subsection. In the Number of angles text field, type 100.
4
Find the Reference direction subsection. In the x text field, type 0.
5
In the y text field, type 1.
6
Find the Normal vector subsection. In the x text field, type 1.
7
In the z text field, type 0.
8
In the 2D Far Field (emw) toolbar, click  Plot.
The 2D far-field pattern shows bidirectional characteristics as plotted in Figure 3.
3D Far Field, Gain (emw)
1
In the Model Builder window, under Results click 3D Far Field, Gain (emw).
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Parameter value (freq (GHz)) list, choose 3.
4
In the 3D Far Field, Gain (emw) toolbar, click  Plot.
Compare the 3D far-field pattern with the plot in Figure 4.