COMSOL 6.4 - Substrate Integrated Waveguide

A waveguide-type structure can be fabricated on a substrate by adding vias between the microstrip line and the ground plane. Such a device behaves as a high-pass filter and is attractive because it is easy to fabricate. This example computes the S-parameters as a function of frequency and a sharp cutoff is shown at the expected frequency.

Figure 1: Substrate integrated waveguide fed by lumped ports. The side walls are terminated with PEC vias.

Model Definition

The substrate integrated waveguide (SIW) also known as laminated waveguide is realized from a microstrip line. The microstrip line is modeled as a perfect electric conductor (PEC) surface on a 0.060 inch thick dielectric substrate, with another PEC surface below that acts as the ground plane. The width of the microstrip line is initially set to that of 50 ohm line, linearly tapered to a much wider line, and finished symmetrically shown in Figure 1. The entire modeling domain is bounded by scattering boundaries that represent an open space except the ground plane. Each side of the wide part of the microstrip line is terminated with the PEC vias. The width of the line defines the operating frequency of the SIW.

The cutoff frequency of a rectangular waveguide can be calculated using

where a and b are the dimension of the waveguide aperture. The calculated cutoff frequency of the SIW model is 8.582 GHz with a = 9.5 mm, TE10 mode. Because the height of the substrate is much smaller than the dimension of a conventional rectangular waveguide, the higher order modes generated in the direction of the height of the substrate can be ignored.

Results and Discussion

The computed S-parameters are plotted in Figure 2. The frequency response behaves as that of a high-pass filter and the cutoff is observed at the expected frequency. The SIW can replace a conventional rectangular waveguide with limited TE modes and there is no TM mode due to the boundary condition on the side walls which are realized with metallic via holes.

Figure 2: Frequency response of the substrate integrated waveguide resembles that of a conventional rectangular waveguide.

References

1. D.M. Pozar, Microwave Engineering, John Wiley & Sons, 1998.

2. H. Uchimura, T. Takenoshita, and M. Fujii, “Development of the laminated waveguide,” IEEE Microw. Theory Tech. International Symposium Digest, vol. 3, no. 12, pp. 2438–2443, 1999.

3. Y. Dong, Y. Tao, and T. Itoh, “Substrate Integrated Waveguide Loaded by Complementary Split-Ring Resonators and Its Applications to Miniaturized Waveguide Filters,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 9, 2211–2223, 2009.

RF_Module/Transmission_Lines_and_Waveguides/substrate_integrated_waveguide

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

Define the study frequency ahead of performing any frequency-dependent operation such as building mesh. The physics-controlled mesh uses the highest frequency value in the specified range.

In the window, under click .

In the window for , locate the section.

Click

In the dialog, type 6[GHz] in the text field.

In the text field, type 11[GHz].

In the text field, type 250[MHz].

Click .

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file substrate_integrated_waveguide_parameters.txt.

Here, mil refers to milliinch.

Geometry 1

First, created a block for the simulation domain.

Air

In the toolbar, click

In the window for , type Air in the text field.

Locate the section. In the text field, type l_line/1.5.

In the text field, type l_line*1.25.

In the text field, type thickness*5.

Locate the section. From the list, choose .

In the text field, type thickness*2.5.

Click

Click the

button in the toolbar.

Add a work plane to create the waveguide and microstrip line layout.

Work Plane 1 (wp1)

In the toolbar, click

In the window for , click

Work Plane 1 (wp1) > Plane Geometry

In the window, click .

Add a rectangle for the substrate.

Substrate

In the toolbar, click

In the window for , type Substrate in the text field.

Click the

button in the toolbar.

Locate the section. In the text field, type l_line/1.5.

In the text field, type l_line.

Locate the section. From the list, choose .

Add a rectangle for the microstrip feed line.

Feed line

In the toolbar, click

In the window for , type Feed line in the text field.

Locate the section. In the text field, type w_line.

In the text field, type l_line.

Locate the section. From the list, choose .

Add a polygon for the tapered feed line working as a transition part between the feed line and waveguide.

Taper

In the toolbar, click

In the window for , type Taper in the text field.

Locate the section. In the table, enter the following settings:


xw (m)	yw (m)
-0.0016	0.012
-0.00475	0.00975
0.00475	0.00975
0.0016	0.012

Click

Work Plane 1 (wp1) > Rotate 1 (rot1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

Select the checkbox.

Locate the section. In the text field, type 180.

Topper

In the toolbar, click

In the window for , type Topper in the text field.

Locate the section. In the text field, type w_topper.

In the text field, type l_topper.

Locate the section. From the list, choose .

Work Plane 1 (wp1) > Union 1 (uni1)

In the toolbar, click

and choose .

Select the objects , , , and only.

In the window for , locate the section.

Clear the checkbox.

In the toolbar, click

Via

In the toolbar, click

In the window for , type Via in the text field.

Locate the section. In the text field, type r_via.

Locate the section. In the text field, type -(w_topper/2-1[mm]).

In the text field, type -l_topper/2.

Work Plane 1 (wp1) > Array 1 (arr1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

In the text field, type 2.

In the text field, type 14.

Locate the section. In the text field, type (w_topper/2-1[mm])*2.

In the text field, type r_via*3.

In the toolbar, click

Extrude 1 (ext1)

In the window, under > right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Distances (m)
thickness

Click

Definitions

Create a set of selections for use before setting up the physics. First, create a selection for the substrate.

Substrate

In the toolbar, click

In the window for , type Substrate in the text field.

Select Domains 2, 3, and 20 only.

Add a selection for the air domain.

Air

In the toolbar, click

In the window for , type Air in the text field.

Select Domain 1 only.

Next, combine the two selections to define the modeling domain.

Model domains

In the toolbar, click

In the window for , type Model domains in the text field.

Locate the section. Under , click

In the dialog, select in the list.

Click .

In the window for , locate the section.

Under , click

In the dialog, select in the list.

Click .

Add a selection for the microstrip line and the top part of the waveguide.

Metal

In the toolbar, click

In the window for , type Metal in the text field.

Locate the section. From the list, choose .

Select Boundary 15 only.

Add a selection for the scattering boundaries. These are the outermost boundaries of the modeling domain except for the ground plane.

Scattering boundaries

In the toolbar, click

In the window for , type Scattering boundaries in the text field.

Locate the section. From the list, choose .

Select Boundaries 1–5, 10, 11, 214, and 215 only.

To get a better view, suppress some of the boundaries.

Hide for Physics 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Select Boundaries 1, 2, and 4 only.

Electromagnetic Waves, Frequency Domain (emw)

In the window, under click .

In the window for , locate the section.

From the list, choose .

The default boundary condition is Perfect electric conductor, which applies to all exterior boundaries. Assign perfect electric conductor on the interior boundary on the microstrip line and the top part of the waveguide.

Perfect Electric Conductor 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Scattering Boundary Condition 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Lumped Port 1

In the toolbar, click

and choose .

Select Boundary 110 only.

For the first port, wave excitation is by default.

Lumped Port 2

In the toolbar, click

and choose .

Select Boundary 112 only.

Materials

Next, assign material properties on the model. Begin by specifying air for all domains.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Materials

Override the substrate with the dielectric material of εr = 3.38.

Substrate

In the window, under right-click and choose .

In the window for , type Substrate in the text field.

Locate the section. From the list, choose .

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
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0	S/m	Basic

Mesh 1

In the window, under right-click and choose .

Study 1

In the toolbar, click

Results

Electric Field (emw)

Begin the results analysis and visualization by modifying the first default plot to show the E-field norm on the bottom of the substrate.

Multislice 1

In the window, expand the node, then click .

In the window for , locate the section.

Find the subsection. In the text field, type 0.

Find the subsection. From the list, choose .

In the text field, type 0.

In the toolbar, click

S-Parameter (emw)

Modify the automatically generated S-parameter plot.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Compare the resulting plot with that shown in Figure 2.

Smith Plot (emw)

In the window, click .

Electric Field, Logarithmic (emw)

In the window, click .

Analyze the same model with a much finer frequency resolution using based on asymptotic waveform evaluation (AWE). When a device presents a slowly varying frequency response, the AWE method provides a faster solution time when running the simulation on many frequency points. The following example with the Adaptive Frequency Sweep can be computed five times faster than regular Frequency Domain sweeps with a same finer frequency resolution.

Electromagnetic Waves, Frequency Domain (emw)

Lumped Port 1

In the window, under > click .

In the window for , locate the section.

Click

In the dialog, type Lumped port 1 in the text field.

Click .

Lumped Port 2

In the window, click .

In the window for , locate the section.

Click

In the dialog, type Lumped port 2 in the text field.

Click .

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Study 2

Step 1: Adaptive Frequency Sweep

In the window for , locate the section.

In the text field, type range(6[GHz],25[MHz],11[GHz]).

Use a five times finer frequency resolution.

A slowly varying scalar value curve works well for AWE expressions. When is set to in the study settings, abs(comp1.emw.S21) is used automatically for two-port devices.

Because such a fine frequency step generates a memory-intensive solution, the model file size will increase tremendously when it is saved. When only the frequency response of port related variables are of interest, it is not necessary to store all of the field solutions. By selecting the checkbox in the section, we can control the part of the model on which the computed solution is saved. We only add the selection containing these boundaries where the port variables are calculated. The lumped port size is typically very small compared to the entire modeling domain, and the saved file size with the fine frequency step is more or less that of the regular discrete frequency sweep model when only the solutions on the port boundaries are stored.

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