Modeling of Pyramidal Absorbers for an Anechoic Chamber

In this example, a microwave absorber is constructed from an infinite 2D array of pyramidal lossy structures. Pyramidal absorbers with radiation-absorbent material (RAM) are commonly used in anechoic chambers for electromagnetic wave measurements. Microwave absorption is modeled using a lossy material to imitate the electromagnetic properties of conductive carbon-loaded foam.

Figure 1: An infinite 2D array of pyramidal absorbers is modeled using periodic boundary conditions on the sides of one unit cell.

Model Definition

The infinite 2D array of pyramidal structures is modeled using one unit cell with Floquet-periodic boundary conditions on four sides, as shown in Figure 1. The geometry of one unit cell consists of one pyramid sitting on a block made of the same material. There are perfectly matched layers (PMLs) above the pyramid and the remaining space between the pyramid and the PMLs is filled with air.

The pyramidal absorber is made of a conductive material (σ = 0.5 S/m). At the interface of the conductive material and air, the incident field is partially reflected and partially transmitted into the pyramid. The transmitted field is attenuated inside of the lossy material. For angles within a particular range of normal incidence, the propagation direction of the reflected field is not back toward the source, but instead toward another surface of the conductive material. The process of partial reflection and partial transmission with subsequent attenuation is repeated until the field reaches the base of the pyramid. The amplitude of the field at the base of the pyramid is drastically reduced and so the reflection from the absorber at this point is marginal. The process is illustrated in Figure 2.

Figure 2: The incident wave is partially transmitted into the conductive foam where it is subsequently attenuated. For angles within a particular range of normal incidence, the reflected component of the field propagates toward another conducting surface where the process is repeated.

The bottom of the absorber has a thin highly conductive layer to block any noise from outside the anechoic chamber. Before mounting absorbers on the walls of the anechoic chamber, it is necessary to apply a conductive coating on the walls, which is modeled as a perfect electric conductor (PEC).

The model domain immediately outside of the conducting foam is filled with air. Perfectly matched layers (PMLs) above the air at the top of the unit cell absorb higher-order modes generated by the periodic structure — if there are any — as well as the upward traveling excited mode from the source port. The PMLs attenuate the field in the direction perpendicular to the PML boundary. Since the model is solved for a range of incident angles, the wavelength inside the PMLs is set to 2π/|k0cosθ|, which, in some sense, is the wavelength of the normal component of the wave vector.

A port boundary condition is placed on the interior boundary of the PMLs, adjacent to the air domain. The interior port boundaries with PML backing require the slit condition. The port orientation is specified to define the inward direction for the S-parameter calculation. Since higher order diffraction modes are not of particular interest in this example, the combination of a Domain-backed type slit port and PMLs is used instead of adding a Diffraction order port for each diffraction order and polarization.

The periodic boundary condition requires identical surface meshes on paired boundaries. An identical surface mesh can be created by using the Copy Face operation from one boundary to another boundary.

Results and Discussion

Figure 3 shows the norm of the electric field and power flow in the case where the elevation angle of incidence is 30 degrees and the azimuth angle is zero. The intensity of the illuminating wave is strong near the tip of the absorber. It decreases toward the base of the pyramid, where it is ultimately very weak.

The S-parameter for y-axis polarized incident waves is plotted in Figure 4. The plot shows quantitatively that the absorber performs well for a range of incident elevation angles less than 40 degrees.

Figure 3: The power flow and the default multislice plot of the electric field norm for the case where the elevation angle of incidence is 30 degrees and the azimuthal angle is zero.

Figure 4: The S-parameter is plotted as a function of incident angle.

RF_Module/EMI_EMC_Applications/pyramidal_absorber

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 5[GHz].

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
theta	0[deg]	0 rad	Elevation angle

Geometry 1

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 50.

In the text field, type 280.

Locate the section. In the text field, type -25.

In the text field, type -25.

In the text field, type -90.

Click

Click the

button in the toolbar.

Block 2 (blk2)

In the toolbar, click

In the window for , locate the section.

In the text field, type 50.

In the text field, type 180.

Locate the section. From the list, choose .

Block 3 (blk3)

In the toolbar, click

In the window for , locate the section.

In the text field, type 50.

In the text field, type 25.

Locate the section. From the list, choose .

In the text field, type -77.5.

Pyramid 1 (pyr1)

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type 50.

In the text field, type 120.

In the text field, type 0.

Locate the section. In the text field, type -65.

Click

The finished geometry should look like this.

Set up the physics based on the direction of propagation and the E-field polarization. Assume a TE-polarized wave which is equivalent to /[s/]-polarization and perpendicular polarization. Ex and Ez are zero while Ey is dominant.

Electromagnetic Waves, Frequency Domain (emw)

Periodic Condition 1

In the window, under right-click and choose .

Select Boundaries 1, 4, 18, and 19 only.

In the window for , locate the section.

From the list, choose .

Periodic Condition 2

In the toolbar, click

and choose .

Select Boundaries 9 and 20 only.

In the window for , locate the section.

From the list, choose .

Periodic Condition 3

In the toolbar, click

and choose .

Select Boundaries 2, 5, 13, and 14 only.

In the window for , locate the section.

From the list, choose .

Periodic Condition 4

In the toolbar, click

and choose .

Select Boundaries 10 and 16 only.

In the window for , locate the section.

From the list, choose .

Port 1

In the toolbar, click

and choose .

Select Boundary 11 only.

In the window for , locate the section.

From the list, choose .

For the first port, wave excitation is by default.

Select the check box.

From the list, choose .

Click .

Locate the section. Specify the E0 vector as


0	x
1	y
0	z

In the α1 text field, type theta.

The maximum frequency in the setting window will be used only when button is clicked to generate Diffraction Order features handling higher order mode individually. In this model, PML absorbs all higher order modes, so this setting is ineffective.

Scattering Boundary Condition 1

In the toolbar, click

and choose .

Select Boundary 12 only.

Definitions

Perfectly Matched Layer 1 (pml1)

In the toolbar, click

Select Domain 4 only.

In the window for , locate the section.

From the list, choose .

In the text field, type 2*pi/abs(emw.k0*cos(theta)).

Since the model is solved for a range of incident angles, the wavelength inside the PMLs is set to 2π/|k0cos(θ)|, which is the wavelength of the normal component of the wave vector.

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 1 and 3 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	1	1	Basic
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0.5	S/m	Basic