Substrate Integrated Waveguide Leaky Wave Antenna

Substrate Integrated Waveguides (SIW) can be used in antenna applications. Leaky waves from a slot array on the top surface of the SIW in this example generate a beam in a certain direction that can be steered by choosing a different operating frequency.

Figure 1: A SIW is realized using 60 mil microwave substrate. The side walls are terminated with metalized via holes. The input and output microstrip lines are connected to the SIW via tapered lines.

Model Definition

Substrate integrated waveguides (SIWs) are widely used because they are easy to fabricate and slotted patterns of any shape can be drawn on the top surface. The leaky wave antenna in this example uses a SIW which is simply realized by using a microstrip line type structure. In the SIW, a 50 Ω microstrip line at the input and output is linearly tapered to a wider line in the middle of a 60 mil substrate with εr = 3.38 (Figure 1). The microstrip line and the ground plane work as the top and bottom walls of a waveguide and the side walls are built by adding metallic vias between the wider part of a microstrip line and the ground plane. All metallic parts are modeled using perfect electric conductor (PEC). There is a circular slot on each tapered line for the impedance matching to 50 Ω. Six slots are placed on the top surface of the microstrip line for a leaky wave radiation. The antenna is modeled in a spherical air domain. The air domain is truncated with Perfectly Matched Layers (PMLs) which absorb all outgoing radiation.

The cutoff frequency of the SIW is calculated using the equation from the rectangular waveguide which is defined by

where a and b are the dimension of a waveguide aperture. Here, a and b are replaced by the width of the wider line and thickness of the substrate, respecively.The calculated cutoff frequency of the SIW is 7.765 GHz with a = 10.5 mm at TE10 mode. The operating frequency of the leaky wave antenna should be higher than the SIW cutoff frequency.

All domains except the PMLs are meshed by a tetrahedral mesh with maximum element size of five elements per wavelength so that the wave is well-resolved. The PMLs are swept with a total of five elements along the absorbing direction.

Results and Discussion

Figure 2 shows the default electric field norm plot in the xy-plane. The intensity of the electric fields coupled to each slot is getting weaker from the inport to the outport direction. The phase of the electric fields coupled to each slot is arithmetically changing because the wave is traveling inside the SIW.

The combination of these two defines the magnitude and phase properties of the weight function for a slot array antenna. The direction of the maximum radiation of the SIW leaky wave antenna can be steered by controlling the operating frequency that changes the weight function.

The side view of the radiation pattern in a polar format is plotted in Figure 3. The 3D far-field radiation pattern is visualized in Figure 4. Though the slots are open to the upward direction, the radiation pattern is tilted toward the outport at 12.25 GHz because of the leaky wave coupling among the slots with different magnitudes and phases.

Figure 2: The electric field norm plot in the xy-plane shows the energy leaked via slots.

Figure 3: The x-axis cut polar plot of the far-field radiation pattern.

Figure 4: The 3D far-field radiation pattern is tilted toward the positive y-axis.

RF_Module/Antenna_Arrays/siw_leaky_wave_antenna

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Study 1

Step 1: Frequency Domain

In the window, under click .

In the window for , locate the section.

In the text field, type 12.25[GHz].

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Work Plane 1 (wp1)

In the toolbar, click

Work Plane 1 (wp1)>Plane Geometry

In the window, click .

Work Plane 1 (wp1)>Import 1 (imp1)

In the toolbar, click

In the window for , locate the section.

Click .

Browse to the model’s Application Libraries folder and double-click the file siw_leaky_wave_antenna.mphbin.

Click .

Block 1 (blk1)

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type 21.

In the text field, type 83.

In the text field, type 1.524.

Locate the section. From the list, choose .

In the text field, type -1.524/2.

Click

Click the

button in the toolbar.

Extrude 1 (ext1)

In the toolbar, click

In the window for , locate the section.

In the table, enter the following settings:


Distances (mm)
-1.524

Click

Sphere 1 (sph1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 65.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (mm)
Layer 1	20

Click

Click the

button in the toolbar.

Click the

button in the toolbar.

The finished geometry should look like this.

Definitions

Perfectly Matched Layer 1 (pml1)

In the toolbar, click

Select Domains 1–4 and 59–62 only.

In the window for , locate the section.

From the list, choose .

Electromagnetic Waves, Frequency Domain (emw)

Remove vias from the model domain. Then, PEC boundary condition is applied by default on the boundaries of vias.

In the window, under click .

In the window for , locate the section.

Click

Select Domains 1–7 and 51–63 only.

Perfect Electric Conductor 2

In the toolbar, click

and choose .

Select Boundaries 15, 20, 21, 283, 289, 295, 301, 307, 313, 332, 336, and 365 only.

Lumped Port 1

In the toolbar, click

and choose .

Select Boundary 340 only.

For the first port, wave excitation is by default.

Lumped Port 2

In the toolbar, click

and choose .

Select Boundary 342 only.

Far-Field Domain 1

In the toolbar, click

and choose .

Materials

Material 1 (mat1)

In the window, under right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1	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

Material 2 (mat2)

Right-click and choose .

Select Domains 6, 7, 51–58, and 63 only.

In the window for , locate the 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