Dipole Antenna

The dipole antenna is one of the most straightforward antenna configurations. It can be realized with two thin metallic rods that have a sinusoidal voltage difference applied between them. The length of the rods is chosen such that they are quarter wavelength elements at the operating frequency. Such an antenna has a well-known torus-like radiation pattern.

Figure 1: A dipole antenna. The model consists of two cylindrical arms of conductive material with a voltage source in between. A region of free space bounded by a perfectly matched layer (PML) surrounds the antenna.

Model Definition

The model of the antenna consists of two cylinders representing each of the dipole arms. The free space wavelength at the antenna’s operating frequency is 4 m. Thus, each of the antenna arms is 1 m long and aligned with the z-axis. The arm radius is chosen to be 0.05 m. In the limit as the radius approaches zero, this antenna approaches the analytic solution for a thin linear half wave dipole antenna.

A small cylindrical gap of size 0.01 m between the antenna arms represents the voltage source. The power supply and feed structure are not modeled explicitly, and it is assumed that a uniform voltage difference is applied across these faces. This source induces electromagnetic fields and surface currents on the adjacent conductive faces.

The dipole arm surfaces are modeled using the Impedance Boundary Condition, which is appropriate for conductive surfaces that have dimensions much larger than the skin depth. This boundary condition introduces a finite conductivity at the surface as well as resistive losses.

The air domain around the antenna is modeled as sphere of free space of radius 2 m, which is approximately the boundary between the near-field and the far-field. This sphere of air is truncated with a perfectly matched layer (PML) that acts as an absorber of outgoing radiation. The far-field pattern is computed on the boundary between the air and the PML domains.

The mesh is manually adjusted such that there are five elements per free space wavelength and that the boundaries of the antenna are meshed more finely. The PML is swept with a total of five elements along the radial direction.

Results and Discussion

The magnitude of the electric field around the antenna is shown in Figure 2. The fields appear artificially high near the excitation, as well as at the ends of the arms. These peaks in the intensity are due to local singularities; the fields at sharp transitions in the model are locally artificially high, but they do not affect the results some distance (1~2 elements) away from these regions.

The polar plot in Figure 3 of the far-field pattern in the xy-plane shows the expected isotropic radiation pattern. The 3D visualization of the far-field intensity in Figure 4 shows the expected torus-shaped pattern.

The real part of the impedance as seen by the port is evaluated to be about 120 Ω, which agrees reasonably with expectations. With further tuning of the antenna length, radius and gap height to have the resonance at which the reactance is zero, the result approaches the well known value for a half-wave (0.48λ0) dipole antenna, which is 73 Ω.

Figure 2: A slice plot of the electric and magnetic field magnitude around the antenna.

Figure 3: The polar plot of the far field pattern in the xy-plane is isotropic.

Figure 4: A 3D visualization of the far-field pattern of the dipole shows the expected torus-shaped pattern.

RF_Module/Antennas/dipole_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

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
lda0	4[m]	4 m	Operating wavelength
arm_length	lda0/4	1 m	Dipole antenna arm length
r_antenna	arm_length/20	0.05 m	Dipole antenna arm radius
gap_size	arm_length/100	0.01 m	Gap between arms

Study 1

Step 1: Frequency Domain

In the window, under click .

In the window for , locate the section.

In the text field, type c_const/lda0.

Geometry 1

Create a sphere with a layer. The outer layer presents the PML.

Sphere 1 (sph1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 2.4*arm_length.

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


Layer name	Thickness (m)
Layer 1	0.5*arm_length

Click

Choose wireframe rendering to get a better view of the interior parts.

Click the

button in the toolbar.

Then, add a cylinder with layers. The top and bottom parts are the antenna radiators. A small gap between the antenna radiators is for the voltage source.

Cylinder 1 (cyl1)

In the toolbar, click

In the window for , locate the section.

In the text field, type r_antenna.

In the text field, type 2*arm_length+gap_size.

Locate the section. In the text field, type -(arm_length+gap_size/2).

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


Layer name	Thickness (m)
Layer 1	arm_length

Clear the check box.

Select the check box.

Click

The domain inside the antenna radiators is not part of the model analysis.

Difference 1 (dif1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

Find the subsection. Select the

toggle button.

Select the object only.

Click

Definitions

Create a set of selections to be used when setting up the physics. First, create a selection for the antenna radiator surface.

Antenna

In the toolbar, click

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

Locate the section. From the list, choose .

Click

In the dialog box, type 13-15, 18-20, 28, 30, 39, 41 in the text field.

Click .

Add a perfectly matched layer on the outermost domain of the sphere.

Perfectly Matched Layer 1 (pml1)

In the toolbar, click

Select Domains 1–4 and 6–9 only.

In the window for , locate the section.

From the list, choose .

Suppress some domains and boundaries. This helps to see the interior parts when setting up the physics and reviewing the mesh.

Hide for Physics 1

In the window, right-click and choose .

Select Domains 1 and 2 only.

Hide for Physics 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Select Boundaries 9 and 10 only.

Electromagnetic Waves, Frequency Domain (emw)

Set up the physics for the model. Add an Impedance Boundary Condition that overrides the default PEC boundary condition on the antenna radiator surface.

Impedance Boundary Condition 1

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

Lumped Port 1

In the toolbar, click

and choose .

Click the

button in the toolbar, a couple of times to see the small gap between antenna radiators clearly.

Select Boundaries 16, 17, 29, and 40 only.

In the window for , locate the section.

From the list, choose .

In the hport text field, type gap_size.

In the wport text field, type 2*pi*r_antenna.

Specify the ah vector as


0	x
0	y
1	z

For the first port, wave excitation is by default.

Click the

button in the toolbar.

Far-Field Domain 1

In the toolbar, click

and choose .

Materials

Assign air as the material for all domains and override the antenna radiator surface with copper.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Copper (mat2)

In the window for , locate the section.

From the list, choose .

Mesh 1

In the window, under right-click and choose .

Study 1

In the toolbar, click

Results

The default plot shows the E-field norm, 2D far-field polar plot, and 3D far-field radiation pattern.

Multislice

In the window, expand the node, then click .

In the window for , locate the section.

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

Click to expand the section. Select the check box.

In the text field, type 20.

Locate the section. From the list, choose .

In the toolbar, click

Click the

button in the toolbar.

Arrow Volume 1

In the window, right-click and choose .

In the window for , locate the section.

Find the subsection. In the text field, type 21.

Find the subsection. In the text field, type 1.

Find the subsection. In the text field, type 21.

Locate the section. From the list, choose .

From the list, choose .

Slice 1

Right-click and choose .

In the window for , locate the section.

In the text field, type 20*log10(emw.normH).

Locate the section. From the list, choose .

In the text field, type 1.

Locate the section. From the list, choose .

Select the check box.

Transparency 1

Right-click and choose .

In the window for , locate the section.

Set the value to .

Electric Field (emw)

In the window, click .

In the window for , click to expand the section.

From the list, choose .

Click

In the dialog box, type 5 in the text field.

Click .

In the toolbar, click

The results show the E-field norm and dB-scaled magnetic field norm distribution around the antenna radiators. It is plotted in Figure 2.

2D Far Field (emw)

Adjust the axis range.

In the window, click .

In the window for , locate the section.

Select the check box.

In the text field, type -20.

In the text field, type 0.

Radiation Pattern 1

In the window, expand the node, then click .

In the window for , locate the section.

In the text field, type emw.normdBEfar.

Click to expand the section. From the list, choose .

In the table, enter the following settings:


Legends
H-plane

In the toolbar, click

The plotted H-plane pattern is omnidirectional (isotropic) on the xy-plane as shown in Figure 3. The E- and H-plane of a linearly polarized antenna are defined by the antenna main polarization. The E-plane includes the main polarization that is Ez in this model while the H-plane is perpendicular to the main polarization.

Radiation Pattern 2

Right-click and choose .

In the window for , locate the section.

Find the subsection. In the text field, type 1.

In the text field, type 0.

Find the subsection. From the list, choose .

In the text field, type 3.

Locate the section. From the list, choose .

In the table, enter the following settings:


Legends
E-plane

In the toolbar, click

The calculates the beam width according to the given level down value. The computed half power beam width is about 75.5 degree. Note that the result is valid only when the main beam for calculation is at 0 degree in the plot. The beam orientation in the plot can be adjusted by setting the and .