COMSOL 6.4 - Magnetic Frill

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Feeding antennas with proper signals can be difficult. The signal is often described as a voltage, and voltages are not well defined in electromagnetic wave formulations. There are several tricks to model voltage generators in such situations, and one is the magnetic frill. This example shows the basic steps of defining a magnetic frill voltage generator for a dipole antenna, and it also compares the resulting antenna impedance with known results.

Model Definition

Magnetic frills can only be defined using Electromagnetic Waves interface, which is based on the time-harmonic Faraday’s law.

Although there are no magnetic charges, it is possible to mathematically define a current of magnetic charges, called a magnetic current. This current enters the right-hand side of Faraday’s law in the same manner as the ordinary current enters the right-hand side of Ampère’s law. Similar to the ordinary current density that has the unit A/m2, the magnetic current density has the unit V/m2.

A closed loop of magnetic current therefore has the unit V and represents a voltage generator for the surface closed by the loop. In this example, the loop is located around a thin straight wire and acts as a voltage source at the center of the wire. This is a dipole antenna fed by a voltage signal in the center.

The current through the wire is measured with another loop, along which a line integral of the H-field is specified.

Note that this loop and the magnetic current loop must be two different loops.

The antenna is placed in a spherical air domain surrounded by a perfectly matched layer (PML) serving to absorb the radiation from the antenna with a minimum of reflection.

Results and Discussion

The dipole antenna is fed with a voltage signal of 1 V, and from the measured current it is possible to extract the impedance. Taken from Ref. 1, the impedance and dimensions of a typical dipole antenna are shown in the table below. The dimensions are given in terms of the wavelength, λ.


Wavelength	Length	Radius
0.3	0.47λ	0.005λ

The impedance from the COMSOL Multiphysics model is 76.00 + 15.98i, which agrees well with the results from Ref. 1.

1. C.A. Balanis, Advanced Engineering Electromagnetics, John Wiley & Sons, 1989.

RF_Module/Antennas/magnetic_frill

Modeling Instructions

From the menu, choose .

In the window, click

.

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In the window, click

.

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In the tree, select > .

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4

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In the tree, select > .

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Global Definitions

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In the window, under click .

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In the window for , locate the section.

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In the table, enter the following settings:


Name	Expression	Value	Description
lda0	0.3[m]	0.3 m	Wavelength
l	0.47	0.47	Scale factor
k	0.005	0.005	Scale factor
L	l*lda0	0.141 m	Dipole length
r_wire	k*lda0	0.0015 m	Wire radius
f0	1/lda0/sqrt(epsilon0_const*mu0_const)	9.9931E8 1/s	Frequency

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 specified frequency value.

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In the window, under click .

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In the window for , locate the section.

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In the text field, type f0.

Work Plane 1 (wp1)

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In the toolbar, click

.

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In the window for , locate the section.

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From the list, choose .

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Work Plane 1 (wp1) > Rectangle 1 (r1)

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In the toolbar, click

.

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In the window for , locate the section.

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In the text field, type r_wire.

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In the text field, type L.

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Locate the section. In the text field, type -L/2.

Work Plane 1 (wp1) > Rectangle 2 (r2)

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 0.3.

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In the text field, type 0.6.

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Locate the section. In the text field, type -0.3.

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In the text field, type -0.3.

Work Plane 1 (wp1) > Circle 1 (c1)

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 0.3.

Work Plane 1 (wp1) > Circle 2 (c2)

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In the toolbar, click

.

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In the window for , locate the section.

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In the text field, type 0.2.

Work Plane 1 (wp1) > Difference 1 (dif1)

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In the toolbar, click

and choose .

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Select the objects and only.

Alternatively, you can select all objects and remove r1 and r2 from the selection list.

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In the window for , locate the section.

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Click to select the

toggle button for .

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Select the objects and only.

Work Plane 1 (wp1) > Line Segment 1 (ls1)

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

4

Locate the section. From the list, choose .

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Locate the section. In the text field, type 0.2.

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Locate the section. In the text field, type 0.3.

This line segment simplifies meshing.

Work Plane 1 (wp1) > Point 1 (pt1)

1

In the toolbar, click

.

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In the window for , locate the section.

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In the text field, type r_wire+0.001.

Work Plane 1 (wp1) > Point 2 (pt2)

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In the toolbar, click

.

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In the window for , locate the section.

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In the text field, type 0.01.

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In the toolbar, click

.

Revolve 1 (rev1)

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

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In the window for , locate the section.

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Click the button.

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In the text field, type -90.

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6

button in the toolbar.

Form Union (fin)

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In the window, click .

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In the window for , click

.

3

button in the toolbar.

Integration 1 (intop1)

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Select Edge 20 only.

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In the toolbar, click

.

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In the window for , locate the section.

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From the list, choose .

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Select Edge 20 only.

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


Name	Expression	Unit	Description
intcpl_source_I	4(emw.Hxt1x+emw.Hy*t1y)	A/m

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In the toolbar, click

.

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In the window for , locate the section.

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In the table, enter the following settings:


Name	Expression	Unit	Description
I	intop1(intcpl_source_I)	A	Current
Z	1/I	1/A	Impedance

Perfectly Matched Layer 1 (pml1)

1

In the toolbar, click

.

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Select Domains 1 and 3 only.

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

to open the window.

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Go to the window.

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In the tree, select > .

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Click the button in the window toolbar.

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In the toolbar, click

to close the window.

Electromagnetic Waves, Frequency Domain (emw)

Perfect Magnetic Conductor 1

1

In the toolbar, click

and choose .

2

Select Boundaries 1, 2, 4, 5, 9, and 10 only.

Magnetic Current 1

1

In the toolbar, click

and choose .

2

Select Edge 21 only.

3

In the window for , locate the section.

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In the Im text field, type 1.

1

In the window, under click .

2

In the window for , locate the section.

3

From the list, choose .

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In the toolbar, click

.

Electric Field (emw)

The default plot shows the electric field on slices through the geometry.

Visualize the electric field around the antenna by modifying this plot as follows:

Delete the Multislice plot.

1

In the window, expand the node.

2

Right-click and choose .

Electric Field (emw)

Add two Slice plots.

1

Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

4

From the list, choose .

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Click to expand the section. Select the checkbox.

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In the text field, type 20.

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Select the checkbox.

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In the text field, type 20.

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Right-click and choose .

2

In the window for , locate the section.

3

From the list, choose .

4

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

Right-click and choose .

Electric Field (emw)

1

In the window for , click to expand the section.

2

From the list, choose .

3

In the text area, type Electric field norm (V/m).

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In the toolbar, click

.

Global Evaluation 1

1

In the toolbar, click

.

2

In the window for , locate the section.

3

In the table, enter the following settings:


Expression	Unit	Description
Z	1/A	Impedance

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