EM.Libera Tutorial Lesson 5: Modeling Radiation from Open-Ended Waveguides and Horn Antennas
Contents
- 1 Objective:
- 2 What You Will Learn:
- 3 Getting Started
- 4 Creating a Hollow Rectangular Waveguide
- 5 Defining a Short Dipole Source and Observables
- 6 Running an Surface MOM Analysis of the Rectangular Waveguide
- 7 Adding an Finite-Sized Aperture Ground Plane
- 8 Building the Pyramidal Horn
- 9 Running a Surface MOM Analysis of the Waveguide-Fed Horn Antenna
Objective:
To construct waveguide structures in EM.Cube’s MoM3D Module, illuminate them with a short dipole source and compute their radiation patterns.
What You Will Learn:
In the first part of this tutorial lesson, you will build a hollow rectangular waveguide and excite it with a short dipole source. In the second part, you will add a hollow pyramid to the waveguide feed to build a pyramidal horn antenna.
Getting Started
Open the EM.Cube application and switch to MoM3D Module. Start a new project with the following attributes:
- Name: SMOMLesson2
- Length Units: cm
- Frequency Units: GHz
- Center Frequency: 1.2
- Bandwidth: 1.0
A hollow rectangular waveguide supports a set of discrete propagating modes that have nonzero cutoff frequencies. The first few modes of the standard WR-650 rectangular waveguide of dimensions a = 16.51cm × b = 8.255cm are given by:
[math] f_{c,TE10} = \frac{c}{2\pi} k_{c,TE10} = \frac{c}{2\pi} \frac{\pi}{a} = \frac{3e+8}{2(0.1651)} \approx 0.908GHz [/math]
[math] f_{c,TE01} = \frac{c}{2\pi} k_{c,TE01} = \frac{c}{2\pi} \frac{\pi}{b} = \frac{3e+8}{2(0.08255)} \approx 1.817GHz [/math]
[math] f_{c,TE11} = \frac{c}{2\pi} k_{c,TE11} = \frac{c}{2\pi} \sqrt{ \left( \frac{\pi}{a} \right)^2 + \left( \frac{\pi}{b} \right)^2 } = \frac{3e+8}{2} \sqrt{ \left( \frac{1}{0.1651} \right)^2 + \left( \frac{1}{0.08255} \right)^2 } \approx 2.032GHz [/math]
In the first part of this tutorial lesson, you will excite a WR-650 rectangular waveguide using a short dipole source. As you can see from the cutoff frequency of the waveguide modes, at an operation al frequency of 1.2GHz, the WR-650 waveguide supports only the dominant TE10 mode.
Creating a Hollow Rectangular Waveguide
Position the mouse cursor at the origin of coordinates (0, 0, 0) and draw a box object of dimensions 16.51cm × 8.255cm × 100cm. While the property dialog of the box object is still open, remove the check mark from the box labeled “Cap Ends: Top”. This turns the box into a hollow object with a closed bottom end. At an operating frequency of 1.2GHz, the free-space wavelength is λ0 = 250mm. Therefore, the height of your open-ended waveguide is 4.4λ0.
Defining a Short Dipole Source and Observables
You are going to excite your hollow waveguide using a short dipole source placed close to its closed bottom end. The short dipole source provides a good representation of a probe that is used to feed a practical waveguide. The short dipole must be oriented parallel to the Y-axis to excite the dominant TE10 mode.
To define a short dipole source, right click on the Short Dipoles item of the Sources section in the Navigation Tree and select Insert New Source… from the contextual menu. The Short Dipole Source Dialog opens up with a number of default settings. Set the coordinates of the dipole source to (0, 0, 6.25cm). This is a quarter free-space wavelength above the bottom end wall. Set the components of the dipole's unit vector to uX = 0, uY = 1, and uZ = 0 to make it +Y-directed. Click the OK button of the dialog to make your changes effective and close the dialog.
As for the observables of your project, first define a default "Current Distribution" observable. Then, define a "Far Fields" observable for radiation pattern. Right-click on the Far Fields item of the "Observables" section of the Navigation Tree and select Insert New Radiation Pattern... from the contextual menu. In the Radiation Pattern Dialog, change the value of "Angle Increment" for both "Theta" and "Phi" angles from their default value of 5° to 3° to have a finer resolution.
Running an Surface MOM Analysis of the Rectangular Waveguide
Before running the simulation, let's first examine the Surface MoM mesh of your rectangular waveguide. Click the Mesh Settings button of the Simulate Toolbar or use the keyboard shortcut Ctrl+G to open the Mesh Setting dialog. Change the mesh type to "Surface MoM" and keep the default mesh density of 10 cells per wavelength. To view the mesh, click the Show/Generate Mesh button of the Simulate Toolbar or alternatively use the keyboard shortcut Ctrl+M.
At this time, your project is ready for the Surface MoM simulation of your metal plate structure. Click the Run Button of the Simulate Toolbar to open up the Simulation Run Dialog. Change the simulation engine type to "Surface MoM" and open the Engine Settings dialog. Due to the large size of the problem, this time you will choose the "TFQMR" option for the "Solver Settings". This is an iterative linear solver. On the right side of the dialog, check the options "Use Matrix Preconditioner", "Use MPI Solver" and "Use AIM Acceleration". Set the number of CPUs to 4 or higher depending on the number of cores of your CPU.
EM.Cube's Surface MoM solver is highly parallelized for multicore CPU architectures. Surface MoM simulations can greatly speed up if you choose the MPI solver. |
This project involves a total of 2,138 triangular cells and results in a linear system of size N = 3,197. After the completion of the Surface MoM simulation, visualization the current distribution. You can clearly see the TE10 modal pattern of the surface electric current on the waveguide walls. Note that this is related to the tangential magnetic field distribution on the sidewalls.
You can change some aspects of the current distribution plots. Double-click on the legend box to open the Output Plot Settings dialog. At the top of this dialog, you can set the limits of your intensity plots. Choose the radio button labeled "95% Conf." and see how its changes the colors of your plot. This option thresholds the plot values from the lowest and highest ends to exclude the outliers.
Next, visualize the total 3D far field radiation pattern plot. Also, plot the 2D Cartesian graphs of the radiation pattern in the YZ and ZX planes in EM.Grid. You can see that the open-ended waveguide radiator has a directivity of 3.716 or 5.7dB.
Adding an Finite-Sized Aperture Ground Plane
Next, let's examine the effect of adding a finite-size PEC ground plane at the radiating aperture of your open-ended waveguide. For this purpose, draw a rectangle strip object and make it hollow so that it accommodates the mouth of your waveguide. The dimensions of the rectangle are 106.51cm × 98.255cm and its local coordinate system (LCS) is located at (0, 0, 110cm). In the property dialog of the rectangle strip object, check the box labeled "Hollow" and set the value of the "Border Thickness" parameter to 45cm.
Run a new Surface MoM analysis of the modified waveguide structure with the aperture ground plane. In this case, the mesh involves 5,998 triangular cells with a linear system size of N = 8,915. After the completion of the simulation, visualize the current distribution and 3D radiation pattern. Also, plot the 2D Cartesian graphs of the radiation patterns in the YZ and ZX planes in EM.Grid. Note how the presence of the relative large PEC ground plane at the waveguide aperture, has made its radiation pattern unidirectional, with very little radiation into the lower half-space.
Building the Pyramidal Horn
In this part of the tutorial lesson, you will build a pyramidal horn object and attach it to the open-end of your hollow rectangular waveguide. The horn provides a gradual transition from the open end of the waveguide to the free space. It will also increase the effective aperture size of your radiating structure. You will use a shorter version of the WR-650 waveguide you built earlier in the beginning of this tutorial lesson as the feed of the horn antenna.
Before drawing the pyramid, first delete the rectangle strip object you created in the previous part for the aperture ground plane. Then, open the property dialog of your hollow box object and reduce its height from 110cm to 20cm. Keep the bottom end cap, while the top end of the box is open. The new dimensions of the hollow box should be: 16.51cm × 8.255cm × 20cm.
In EM.Cube, a pyramid is drawn bottom-up by default with a pointed apex at the top. This means that its "Top Dimensions" along X and Y are initially zero. For a pyramidal horn antenna, you need an upside-down, chopped-top, pyramid object with both end caps removed. In this case, the top dimensions of the pyramid are larger than its base dimensions. On a blank space in the project workspace, draw an upside-down pyramid object with smaller "Base Dimensions" 16.51cm × 8.255cm and larger "Top Dimensions" 80cm × 60cm and a height of 90cm. Remove the end caps from both top and bottom of the pyramid. Place the local coordinate system (LCS) of the pyramid object at (0, 0, 20cm). This moves the pyramid to the top of your shortened hollow waveguide. Generate and view the mesh of the horn structure with the default mesh density of 10 cells per wavelength.
Running a Surface MOM Analysis of the Waveguide-Fed Horn Antenna
Keep the short dipole source and all the project observables from the previous part. Run a Surface MoM analysis of your waveguide-fed horn antenna. In this case, the mesh involves 6,310 triangular cells with a linear system size of N = 9,409. After the completion of the simulation, visualize the current distribution and 3D radiation pattern. Also, plot the 2D Cartesian graphs of the radiation patterns in the YZ and ZX planes in EM.Grid. As you can see from the figures below, the horn antenna has a very high directivity of 61.82 or 17.9dB.