Log-Periodic Antenna

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Log-Periodic Antenna

A log-periodic antenna is known to be a wideband or frequency-independent antenna. One of the most popular forms is a coplanar dipole array type, which is commonly used for UHF-range antenna measurements in an anechoic chamber. This example computes the voltage-standing-wave-ratio (VSWR) and far-field radiation pattern between 250 MHz and 750 MHz.

Figure 1: A log-periodic antenna is realized by fitting a coplanar dipole array through a couple of metallic body frames. The surrounding air domain and perfectly matched layers, which are required for the simulation, are not included in this figure.

Model Definition

The shape of a log-periodic antenna resembles that of a Yagi-Uda antenna. While the Yagi-Uda consists of a driven element and multiple passive elements such as a reflector and a few directors to obtain a higher gain, the log periodic antenna is composed of a coplanar array to achieve a wider bandwidth. In this log-periodic antenna model, all metallic parts are modeled using perfect electric conductor (PEC) boundary conditions since the surface loss is negligible in the given simulation frequency range. The modeling domain excludes the interior part of the antenna body, including frames and dipole rods in which wave propagation is not expected. The antenna is excited by a lumped port that is placed at one end of the gap between two body frames at the location of a pair of the shortest rods. A lumped element with a 300 Ω resistor is used to terminate the other end of the gap at the location of a pair of the longest rods. The antenna is modeled in a spherical air domain, which is enclosed by perfectly matched layers (PML) that absorb all outgoing radiation from the antenna.

The length of dipole rods is gradually decreasing with a constant ratio toward the lumped port. The repeated pattern of a radiating structure is easily built by using parameterized geometry parts.

Results and Discussion

Figure 2 shows the impedance matching properties on a Smith plot. All frequency swept complex impedance normalized by 50 Ω is plotted around the spot shifted from the center of the Smith plot, that is, approximately 68 Ω. The 2D far-field polar plot is visualized in Figure 3. The directionality of the radiation pattern is slightly varying as the frequency increases. The 3D far-field radiation pattern in Figure 4 shows the same tendency. Figure 5 presents the voltage-standing-wave-ratio (VSWR) of the antenna, which is better than 2:1.

Figure 2: Smith plot of the seven-element log-periodic antenna. Each color represents a different frequency.

Figure 3: Far-field radiation pattern in a polar plot. It is directed toward the lumped port.

Figure 4: 3D far-field radiation pattern. Sidelobes can be visualized accurately by applying a finer angular resolution.

Figure 5: The computed VSWR shows the antenna impedance is close to 50 Ω for all simulated frequencies

RF_Module/Antennas/log_periodic_antenna

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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In the tree, select .

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Step 1: Frequency Domain

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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 range(250[MHz],25[MHz],750[MHz]).

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
f_min	250[MHz]	2.5E8 Hz	Minimum frequency
f_max	750[MHz]	7.5E8 Hz	Maximum frequency
l_min	c_const/f_max	0.39972 m	Minimum wavelength
l_max	c_const/f_min	1.1992 m	Maximum wavelength
l0	l_max/4	0.29979 m	Longest rod length
r0	5[mm]	0.005 m	Rod radius
d0	l_max/8	0.1499 m	Distance between first two elements
ratio	1.27	1.27	Rod scale ratio
gap	1[cm]	0.01 m	Mounting frame gap size
zstub	300[ohm]	300 Ω	Terminating stub impedance

Here, c_const is a predefined COMSOL constant for the speed of light in vacuum.

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In the toolbar, click

and choose .

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

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


Name	Default expression	Value	Description
n	0	0	Number of antenna rods pair

Cylinder 1 (cyl1)

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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 r0.

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In the text field, type l0.

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Locate the section. In the text field, type gap/2+r0.

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Locate the section. From the list, choose .

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Rotate 1 (rot1)

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In the toolbar, click

and choose .

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Select the object only.

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In the window for , locate the section.

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In the text field, type 0 180.

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From the list, choose .

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button in the toolbar.

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In the toolbar, click

and choose .

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Click in the window and then press Ctrl+A to select both objects.

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In the toolbar, click

and choose .

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Select the object 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 text field, type 1/ratio^n.

Rotate 2 (rot2)

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In the toolbar, click

and choose .

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Select the object only.

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In the window for , locate the section.

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In the text field, type 180*mod(n,2).

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In the toolbar, click

and choose .

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Select the object only.

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In the window for , locate the section.

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In the text field, type d0*((n>0)*1+(n>1)*1/ratio+(n>2)*1/ratio^2+(n>3)*1/ratio^3+(n>4)*1/ratio^4+(n>5)*1/ratio^5).

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In the toolbar, click

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In the toolbar, click

and choose .

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In the window for , type Rods 0 in the text field.

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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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In the table, enter the following settings:


Name	Expression	Value	Description
n	1	1	Number of antenna rods pair

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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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In the table, enter the following settings:


Name	Expression	Value	Description
n	2	2	Number of antenna rods pair

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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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In the table, enter the following settings:


Name	Expression	Value	Description
n	3	3	Number of antenna rods pair

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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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In the table, enter the following settings:


Name	Expression	Value	Description
n	4	4	Number of antenna rods pair

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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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In the table, enter the following settings:


Name	Expression	Value	Description
n	5	5	Number of antenna rods pair

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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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In the table, enter the following settings:


Name	Expression	Value	Description
n	6	6	Number of antenna rods pair

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button in the toolbar.

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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 d0*(1+1/ratio+1/ratio^2+1/ratio^3+1/ratio^4+1/ratio^5)+r0*2+0.02.

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In the text field, type 0.02.

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In the text field, type 0.01.

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Locate the section. In the text field, type -r0.

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In the text field, type -0.01.

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In the text field, type -gap/2-0.01.

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type gap/2.

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type gap.

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

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In the toolbar, click

and choose .

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Select the objects , , , , , , , , and only.

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In the window for , click

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In the toolbar, click

and choose .

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Click in the window and then press Ctrl+A to select both objects.

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In the window for , locate the section.

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In the text field, type -d0*(1+1/ratio).

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button in the toolbar.

Sphere 1 (sph1)

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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 l_max/1.8.

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


Layer name	Thickness (m)
Layer 1	l_max*0.1

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button in the toolbar.

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button in the toolbar.

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button in the toolbar.

Difference 1 (dif1)

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In the toolbar, click

and choose .

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Select the object only.

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In the window for , locate the section.

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Find the subsection. Click to select the

toggle button.

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Select the object only.

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Perfectly Matched Layer 1 (pml1)

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In the toolbar, click

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Select Domains 1–4 and 7–10 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 in the window toolbar.

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In the toolbar, click

to close the window.

Electromagnetic Waves, Frequency Domain (emw)

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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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In the dialog box, type 129 in the text field.

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For the first port, wave excitation is by default.

Lumped Element 1

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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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In the dialog box, type 20 in the text field.

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In the window for , locate the section.

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In the Zelement text field, type zstub.

Far-Field Domain 1

In the toolbar, click

and choose .

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

We will now exclude the PML regions from the results visualization. For this purpose, create an explicit selection containing only that only contains domains 5 and 6 and store result values only in this selection.

Results visualization

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In the toolbar, click

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In the window for , type Results visualization in the text field.

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Locate the section. Click

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In the dialog box, type 5 6 in the text field.

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Step 1: Frequency Domain

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In the window, under click .

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In the window for , click to expand the section.

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Find the subsection. From the list, choose .

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Under , click

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In the dialog box, select in the list.

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In the toolbar, click

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Replace the default expression for the electric field norm by a logarithmic expression. This gives better insights to the electric field distribution of the antenna.

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In the window, expand the node, then click .

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In the window for , locate the section.

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

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

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

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Find the subsection. From the list, choose .

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In the text field, type 0.

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Locate the section. Click

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In the dialog box, select in the tree.

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In the toolbar, click

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S-parameter (emw)

Smith Plot (emw)

Smith plot of the seven-element log-periodic antenna is shown in Figure 2.

2D Far Field (emw)

Check Figure 3 for far-field radiation patterns in a polar plot.

Radiation Pattern 1

Figure 4 shows 3D far-field radiation pattern.

1D Plot Group 6

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In the window, expand the node.

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Right-click and choose .

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In the window, right-click and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Expression	Unit	Description
emw.VSWR_1	1	Voltage Standing Wave Ratio

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In the toolbar, click

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All computed VSWR values should be better than 2:1 (Figure 5).

3D Plot Group 7

In the toolbar, click

and choose .

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Right-click and choose .

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In the window for , locate the section.

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In the text field, type 20*log(emw.normE+0.01).

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Locate the section. In the text field, type 15.

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Right-click and choose .

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Select Domain 5 only.

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In the window, right-click and choose .

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In the window for , locate the section.

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In the text field, type z<0.

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In the window, click .

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In the window for , locate the section.

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In the dialog box, select in the tree.

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In the toolbar, click

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