EM.Tempo Tutorial Lesson 1: Analyzing a Center-Fed Resonant Dipole Antenna
Contents
Objective:
To construct a center‐fed resonant dipole antenna in EM.Cube’s FDTD Module, analyze it and visualize its near and far field characteristics.
What You Will Learn:
A simple half‐wave dipole antenna in free space will be analyzed in the first tutorial. This tutorial will guide you through all necessary steps required to set up and perform a basic FDTD simulation and visualize and graph the simulation results.
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We strongly recommend that you read through the first few tutorials and study them carefully before setting up your own projects. |
Getting Started
Open the EM.Cube application by double-clicking on its icon on your desktop. By default, EM.Cube opens a blank project with the name “UntitledProj1” in its CubeCAD Module. You can start drawing objects and build up your physical structure right away. Or you can initiate a new project by selecting the New 
button of the System Toolbar or using the keyboard shortcut Ctrl+N. This opens up the New Project Dialog, where you can enter a title for your new project and set its path on your hard drive. From the same dialog, you can also set the project’s Length Units, Frequency Units, Center Frequency and Bandwidth.
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For this tutorial lesson, set the following parameters in the new project dialog:
Click the Create button of the dialog to accept the settings. A new project folder with your given name is immediately created at your specified path.
To navigate to EM.Tempo (EM.Cube's FDTD Module), simply select its icon from the Module Toolbar on the left side of the screen. Any module may be selected this way. Selecting the module icon changes the contents of the navigation tree to reflect the types of objects supported by the current module.
Creating a Wire Object
Select the Line Tool from the Object Toolbar (or use the keyboard shortcut F3, or the menu Object → Curve → Line).
With the line tool selected, click the origin (0,0,0), and drag the mouse to start drawing a line. While still in “Draw Mode”, press and hold the Alt button of the keyboard. This forces the drawn line to be constrained along the alternate Z-axis (normal to the default XY plane on which the mouse pointer moves). Observe the changing Length value in the dialog box as you drag the mouse back and forth. When the length reaches a value of 150 units, left-click to “lock-in” the value. You may also left-click at any point and adjust the length by typing in a value of 150 in the object’s property dialog.
Since the center frequency of the project is 1GHz, the operating wavelength is:
[math] \lambda_0 = \frac{c}{f} = \frac{3e+8}{1e+9} = 0.3m = 300mm [/math]
For your resonant dipole to be half-wave, it can be approximated at 150mm.
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If you have a mouse with a scroll wheel, you can use the scroll wheel to zoom in or zoom out while you draw the line. You can also rotate the view using the right mouse button, or pan the view using the right mouse button while holding the keyboard’s Shift Key down. |
button of View Toolbar. After you have rotated or panned the view, you can always restore EM.Cube’s standard perspective view using the keyboard’s Home Key or by clicking the Perspective View 
button of View Toolbar.
In EM.Cube’s FDTD Module, objects are grouped together and organized by material under the “Physical Structure” node of the Navigation Tree. Since you selected no material for your line object, the first drawn object is automatically assigned a PEC_1 material group. The default perfect electric conductor (PEC) group is set as the active material. When a material group is set as active, its name appears in bold letters, and all subsequently drawn objects will be placed under that material node. Any material group can be set as the active material by right-clicking on its name in the Navigation Tree and selecting Activate from the contextual menu.
Computational Domain & Boundary Conditions
button of Simulate Toolbar (or select the menu item Compute → Computational Domain → Domain Settings… or use the keyboard shortcut Ctrl+A) to bring up the domain dialog box. For the default domain type, the domain size is specified in terms of offsets along the ±X, ±Y, and ±Z directions, i.e., the distances between the largest bounding box of the geometry and all the six domain boundaries. The offsets are expressed in free space wavelengths calculated at the highest frequency of the project, which is fmax = f0 + Δf/2, where f0 is the center frequency of the project and Δf is the bandwidth.
The boundary Conditions at the six faces of the computational domain can be set by selecting the menu item Simulate → Computational Domain → Boundary Conditions… or by right clicking on the “Boundary Conditions” item in the “Computational Domain” section of the Navigation Tree. By default, EM.Cube’s FDTD Module assumes an open-boundary physical structure. All the six boundaries default to PML, or Perfectly Matched Layer, which you are going to maintain for this tutorial lesson. But the dropdown lists allow you to also choose PEC, or a Perfect Electric Conducting boundary, or PMC, a Perfect Magnetic Conducting boundary.
Source Definition
A dipole antenna can be excited using a lumped source, which is one of the simplest source types in FDTD Module. A lumped source is a voltage source in series with an internal resistance that is placed between two adjacent nodes of the FDTD mesh. To define a lumped source, right-click on the Lumped Source item in the “Sources” section of the Navigation Tree, and select Insert New Source… The Lumped Source Dialog opens up.
A lumped source can only be placed on a line object. Additionally, the line must be parallel to one of the principal axes. The dropdown list labeled Line Object displays all the eligible lines in the project workspace. In this project, there is only one object, which is selected by default. A new lumped source is placed at the center of the host line object by default. The location of the source can be changed via the Offset parameter of the dialog. We will leave this at 75 for this tutorial, as we want to test a center-fed dipole. You can also change the direction of the lumped source.
Your lumped source will have an Amplitude of 1V and a zero Phase. This means that the voltage source will excite the dipole with a modulated Gaussian pulse waveform centered at 1GHz with a frequency bandwidth of 1GHz, where the envelope of the signal reaches a maximum voltage of 1V. You will see the lumped source in the middle of the dipole, represented by an arrow pointing in the +Z direction.
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Grid Settings & Mesh Generation
EM.Cube’s FDTD Module generates a Yee mesh of your physical structure. The mesh properties can be accessed by clicking the Mesh Settings 
button of the Simulate Toolbar (or using the keyboard shortcut Ctrl+G or via the menu Simulate → Discretization → Mesh Settings). For this tutorial, accept the default value of 20 Cells/λeff for Minimum Mesh Density.
To view the mesh, click the Show/Generate Mesh 
button of the Simulate Toolbar (or alternatively use the keyboard shortcut Ctrl+M). For this particular project, the mesh view does not reveal much because the mesh of a vertical line object conforms to the grid. In general, the mesh view shows how the simulation engine sees your physical structure. You can also display the three mesh grid planes by right clicking on one of the three items XY Grid Plane, YZ Grid Plane, or ZX Grid Plane in the “Discretization” section of the Navigation Tree and selecting Show from the contextual menu. To remove the grid planes from the project workspace, open the same contextual menu and select Hide.
Defining Project Observables
Project observables are output quantities that you would like to compute at the end of an FDTD simulation. By default, an FDTD time marching scheme does not generate any output data unless you define one or more project observables before you start a simulation.
Field Probes
The simplest observable is a Field Probe, which is used to record the field values as a function of time at a specific point inside the computational domain. To define a field probe, right click on the Field Probes item in the “Observables” section of the navigation Tree and selec Insert New Observable… In the Field Probe Dialog, select X from the dropdown list labeled Direction. This means that your probe will record the X component of electric and magnetic fields. Enter the point (5, 5, 75) as the Coordinates of the field probe. Click the OK button of the dialog to accept the changes
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Field Sensors
Field sensors are used to visualize the near fields of your structure on a plane parallel to one of the three principal planes. The field sensor planes extend across the entire computational domain. To define a field sensor, right click on the Field Sensors item in the “Observables” section of the Navigation Tree and select Insert New Observable… In the Field Sensor Dialog, enter the point (0, 0, 0) for Coordinates and select X from the dropdown list labeled Direction. This means that your field sensor plane will be the YZ plane, which passes through the dipole antenna. We would like to display the fields in the frequency domain at 1GHz. Accept the other default settings in the dialog box, and select OK to continue. A new entry Sensor_1 is added to the Navigation Tree, and the field sensor is now represented in the project workspace by a purple plane across the computational domain.
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Radiation Patterns
To plot the radiation patterns of a radiating structure, you need to define a far field observable. A radiation box has to be established that encloses all the radiating objects. The electric and magnetic fields on the surface of this box are used to calculate the far field. By default, the radiation box is defined 0.1 free-space wavelength away from the bounding box of the geometry. To define a far field observable, right click on the Far Fields item in the Observables section of the Navigation Tree, and select Insert New Radiation Pattern… In general, you can accept the default values, unless a special case is being analyzed. The radiation box appears as a cyan or light blue box around your physical structure.
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Port Definition
For calculating the port characteristics of the dipole antenna such as S parameters and input impedance, you need to set up a port. To do so, right click on Port Definitions under the Observables section of the Navigation Tree, and select Insert New Port Definition… By default, since you have only one source, it is assigned as Port 1. Accept the default values for PORT_1 and click OK to accept these values.
Running the FDTD Simulation
Button of the Simulate Toolbar to open up the Simultion Run Dialog. Or alternatively, use the keyboard shortcut Ctrl+R, or the menu Simulate → Run… The simplest simulation mode in EM.Cube is “Analysis”. In this mode, your physical structure is taken “As Is” and its mesh is passed to the FDTD simulation engine, along with the necessary information regarding the sources and observables. An FDTD “Analysis” is a wideband analysis by nature depending on your project’s specified bandwidth. At the end of an FDTD analysis, the port characteristics are calculated over the entire bandwidth of your project. However, some frequency-domain observables like field sensors or radiation patterns are calculated only at the specified frequencies.
Before you run your first FDTD simulation in EM.Cube, let’s take a closer look at the FDTD simulation engine’s settings. Click the Settings button next to the “Select Engine” dropdown list to bring up the FDTD Engine Settings Dialog box. The “Convergence” section of this dialog offers three criteria for terminating the FDTD time marching scheme. The first one is a Power Threshold of -30dB. The second one is a Maximum Number of Time Steps equal to 10,000. The third option is labeled “Both”, which means that both of the above termination criteria will be considered until one of is met. If your computer has a CUDA-enabled Nvidia GPU, you can use EM.Cube’s accelerated GPU FDTD solver. The default setting is to use the Multi-Core CPU solver.
To run the simulation, click the Run button of the Simulation Run Dialog. A separate window pops up displaying messages from the simulation engine. In four separate fields, the engine reports the current time step, elapsed time, performance in MCells/second, and convergence status. Once the simulation has been completed, you can close the message window and return to the project workspace. The Navigation Tree is now populated with simulation results, most notably under Field Sensors and Far Fields nodes.
Viewing the Results
A list of all the 2D output data files generated at the end of a simulation can be viewed in EM.Cube’s Data Manager. To open this dialog, click the Data Manager 
button of Simulate Toolbar, or use the keyboard shortcut Ctrl+D, or access the menu Simulate → Data Manager, or right click on the Data Manager item in the “Observables” section of the Navigation Tree and select Open Data Manager…
Select the two data files “Probe_1_E_Time” and “Probe_1_H_Time” and click the Plot button of Data Manager to open EM.Grid. For multiple file selection, use the keyboard’s Ctrl Key, or use the Shift Key to select a range of rows in the list. The Ex and Hx field components are plotted as functions of time on two Cartesian graphs in EM.Grid.
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Next, you will visualize the electric and magnetic field distributions on the near field sensor plane. The field sensor section of the Navigation Tree has a list of twelve amplitude and phase plots for all the six field components: Ex, Ey, Ez, and Hx, Hy, Hz. There are also two additional plots for the magnitude of total electric field and total magnetic field. Click on any of these plots to display them in the project workspace. You can use the standard view operations such as dynamic zoom, rotate view, pan view, etc. to better examine these plots.
The Far Fields section of the Navigation Tree contains three different 3D radiation pattern plots: the Theta component of the far‐zone electric field, the Phi component of the far‐zone electric field, and the Total far field. You will notice that the Far Field plots are all centered at the origin of coordinates. This is due to the fact that the radiation patterns are calculated in a standard spherical coordinate system center at (0, 0 , 0). Once you are in a near field or far field visualization view, you can always go back to the Normal view mode of the project workspace using the keyboard’s Esc Key.
Besides 3D visualization of the radiation patterns, you can plot 2D graphs of the patterns at certain plane cuts. The 2D radiation patterns can be plotted as both Cartesian and polar graphs. Open up the Data Manager dialog and spot Cartesian pattern data files with a “.DAT” file extension as well as the polar (angular) data files with a “.ANG” file extension. The figure below shows the Cartesian and polar radiation pattern plots in the YZ plane cut. Besides the three principal XY, YZ and ZX plane cuts, there are also data files for one additional user defined Phi‐plane cut, which by default is calculated at φ = 45o.
To examine the port characteristics of the dipole antenna, open up the Data Manager again. The S/Z/Y parameters are written into complex data files with a “.CPX” file extension. To graph the S11 and Z11 parameters, select the files “DP_S11.CPX” and “DP_Z11.CPX”. You can view the contents of the two files using the View button of Data Manager. To plot them in EM.Grid, click the Plot button of the dialog. By default, the S parameters are plotted on magnitude/phase Cartesian graphs, while the Z and Y parameters are plotted on real/imaginary Cartesian graphs.
From the above graphs, it appears that the resonance occurs somewhere around 900MHz. This is the frequency at which the imaginary part of the Z11 parameter (input reactance) crosses zero. But, how does that make sense? There are several reasons to justify this result. First, a resonant dipole is not exactly half‐wave, and its resonant length is usually slightly less than λ0/2. Second, the input impedance of a dipole antenna is a function of the wire radius. In this FDTD simulation, you did not model the wire thickness. In other words, you assumed that the dipole has a “zero radius”. Third, the lumped source is connected between two adjacent mesh nodes. Therefore, its field strength depends on the mesh density. If you increase the mesh density to 30 or 40 Cells/λeff, you will observe that resonant frequency of the dipole antenna will change and get closer to 1GHz.
