EM.Libera Tutorial Lesson 2: Designing A Yagi-Uda Dipole Array

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Tutorial Project: Designing a Yagi-Uda Dipole Array
Libera L2 Fig title.png

Objective: In this project, you will build and analyze a Yagi-Uda dipole array using EM.Libera's Wire MoM solver.


  • CubeCAD
  • Array object
  • Gap Source
  • Mesh Density
  • Current Distribution
  • Radiation Pattern
  • S-Parameters
  • Adaptive sweep

Minimum Version Required: All versions

'Download2x.png Download Link: EMLibera_Lesson2

What You Will Learn

In this tutorial you will use a wizard to build and analyze a multi-element Yagi-Uda wire antenna array. You will learn how to perform a parametric sweep simulation using the project's design variables.

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Getting Started

Open the EM.Cube application and switch to EM.Libera. Start a new project with the following parameters:

Starting Parameters
Name EMLibera_Lesson2
Length Units Millimeters
Frequency Units GHz
Center Frequency 2.4GHz
Bandwidth 1GHz

The Yagi-Uda Array Design

A Yagi-Uda array is an end-fire array, which is typically made of an exciter element, a reflector element and several director elements. The lengths of all the elements vary around a half wavelength. The following table shows the electrical lengths and spacing of a typical design:

Element Length Distance from Exciter
Exciter 0.47λ0 0
Reflector 0.5λ0 0.25λ0
Director 0.406λ0 0.34λ0
The Yagi-Uda array schematic.

In the above design, the spacing between the director elements is uniform and equal to 0.34λ0. The radius of all wires is 0.003λ0. In this project, f0 = 2.4GHz, and the free-space wavelength is λ0 = 125mm.

Constructing the Array Geometry

Click on the Yagi-Uda Wizard YagiUdaWizardIcon.png button of the Wizard Toolbar or select the menu item Tools → Antenna Wizards → Yagi-Uda Array.

EM.Libera's wizard toolbar.

Keep the default settings for Array Direction, Dipole Polarization, and No. Elements as X, Y, and 5, respectibely, in the "Yagi Wizard Quick Settings" dialog window.

EM.Libera's Yagi Wizard Quick Settings dialog window.

The geometry of a 7-element Yagi-Uda dipole array appears at the center of the project workspace.

The dipole antenna geometry in the project workspace and the highlighted additions to the navigation tree.

Three items are added under a thin wire group called "YAGI" as follows:

  • Exciter: a line object
  • Reflector: a line object
  • Director_array: an array of line objects

The line array contains five equally spaced elements. Select "Director_array" in the navigation tree, right-click on its name and select Properties... from the contextual menu to open the array dialog.

The array object's property dialog.

As you can see from the array properties, Nx ≠ 1 and Ny = Nz = 1, representing an X-directed linear array. If you click the Primitive button of the array dialog, another property dialog opens up which belongs to the original geometric object the wizard used to create the array object.

The property dialog of the primitive line object.

Open the Variable Dialog and review all the variables used in the definition of the Yagi-Uda array.

The variables dialog showing the Yagi-Uda array parameters.

Examining the Source, Observables & Mesh Settings

The wizard placed a wire gap source at the center of the "Exciter" line object:

The property dialog of the exciter's gap source.

It also initiated a default current distribution observable called "CD_1" and a far-field radiation pattern observable called "FF_1" with 1° theta and phi angle increments. Open the radiation pattern dialog by right-clicking on "FF_1" in the navigation tree and selecting Properties... from the contextual menu. Check the boxes labeled Half Power Beam Width and Front-to-Back Ratio in the section titled "Additional Radiation Characteristics".

The radiation pattern dialog.

The wizard also set the mesh density equal to an unusually high value of 100 Cells per effective wavelength. Open the mesh settings dialog and verify this. The performance of the Yagi-Uda array greatly depends on the precision of the lengths and spacing of its elements. Considering the fact that these lengths and spacings are fairly close to each other, a high resolution mesh is naturally expected.

EM.Libera's mesh settings dialog.

Running a WMOM Analysis of the Yagi-Uda Array

Run a single-frequency Wire MoM analysis of the Yagi-Uda array. Note that even though you have a multi-element antenna array, your structure is indeed one-port. At the end of the simulation, the port characteristics of the array are reported as follows:

S11: -0.066842 + 0.022391j

S11(dB): -23.037127

Y11: 0.015227 - 0.000685j

Z11: 65.539975 + 2.949646j

Visualize the current distribution on the array structure. From the figure below, you can see that the exciter and reflector elements are much hotter than the director elements.

The current distribution on the Yagi-Uda antenna array.

Visualize the 3D radiation pattern of the Yagi-Uda array. The directivity of the antenna array is computed to be D0 = 7.461.

The 3D far-field radiation pattern of the Yagi-Uda antenna array with 5 directors.

Open the data manager and plot the data files "FF_1_PATTERN_Polar_XY.ANG" and "FF_1_PATTERN_Polar_ZX.ANG" as shown in the figures below. These are the polar graphs of the radiation patterns at the principal XY and ZX planes, respectively.

The 2D polar XY-plane radiation pattern of the Yagi-Uda antenna array with 5 directors.
The 2D polar ZX-plane radiation pattern of the Yagi-Uda antenna array with 5 directors.

You can also view the contents of any data file in the data manager by selecting its name and clicking the View button of this dialog. The table below shows some of the computed radiation characteristics of your Yagi-Uda array.

Data File Name Radiation Characteristic Value
HPBW_XY.DAT Half power beam width in XY palne 53.86°
HPBW_ZX.DAT Half power beam width in ZX palne 67.77°

Running a Parametric Sweep of the Number of Director Elements

In the last part of this tutorial lesson, you are going to increase the number of director elements and see its effect on the array characteristics. In a sweep simulation, one or more parameters are varied, and the simulation engine is run for each parameter set. Open the Simulation Run dialog and choose the Parametric Sweep option from the Simulation Mode drop-down list. Click on the Settings button next to this drop-down list to open the Parametric Sweep Settings dialog.

Selecting parametric sweep as the simulation mode in EM.Libera's run dialog.

The sweep variables list is initially empty. On the left side of this dialog, you see a list of all the available independent variables. Note that out of all the array-related variables you saw earlier in the variables dialog, only one called "n_direct" is listed here. This is the number of director elements in the Yagi-Uda array, and it is an independent variable. All the other array-related variables such as wire lengths, spacings, etc. are dependent variables whose definitions involve another variable called "lambda0_unit".

Parametric sweep settings dialog before designating a sweep variable.

Select "n_direct" from the left table and use the right arrow --> button to move it to the right table. Another dialog titled "Define Sweep Variable" opens up. You have to set the start, stop and step values of your sweep variable. By default, the sweep variable is of uniform type. Enter 5, 13, and 1 for the start, stop and step values, respectively. This will create a value list of {5, 6, 7, 8, 9, 10, 11, 12, 13}.

Sweep variable settings dialog.

Close the sweep variable dialog and return to the parametric sweep settings dialog.

Parametric sweep settings dialog after designating "n_direct" as the sweep variable.

Click on the OK button to close the parametric sweep settings dialog and return to the simulation run dialog. Run the sweep simulation. It may take a while as a total of nine individual WMOM simulations must be completed. At the end of the parametric sweep, you will see a total of nine 3D radiation pattern plots in the navigation tree. The figures below shows some of these plots.

The 3D radiation pattern of the Yagi-Uda array with 7 directors.
The 3D radiation pattern of the Yagi-Uda array with 10 directors.
The 3D radiation pattern of the Yagi-Uda array with 13 directors.

Analyzing the Array Directivity Data

Open the data manager and plot the data file "FF_D0_Sweep.DAT" in EM.Grid. You should see a graph like the figure below. It shows the variation of the directivity (D0) of the array as a function of the number of director elements. An almost linear variation is observed.

The graph of variation of the directivity of the Yagi-Uda array as a function of number of directors.

Next, while still in the data manager, view the contents of the data file "FF_D0_Sweep.DAT" in a spreadsheet using the View button of this dialog.

The data manager spreadsheet showing the directivity data.