In this example a broad-bandwidth band-pass filter is simulated using XF7. The filter geometry employs a substrate integrated waveguide (SIW) with etched complementary split ring resonators (CSRRS). Simulated S-Parameters are compared to measured results. The filter design and measured data are taken from [1].

The SIW portion of the filter is comprised of a RT/Duroid 5880 substrate sandwiched between two copper plates. Metallic vias rows are located along the top and bottom edges of the top plate creating a waveguide structure. Etched out of the top plate are three CSSR structures sized to create a stop band from 9.5 GHz to 11 GHz. Microstrips are connected to the SIW transitioning with a planar taper. The geometry is shown in Figure 1.

This example uses a plugin from XFdtd’s XTend Library to perform a Particle Swarm Optimization (PSO) of an Inverted-F Antenna (IFA). The IFA is a popular antenna for use in mobile devices due to its small size. In this instance, the antenna will be optimized to operate over the GSM-1900 band (1.85 - 1.99 GHz).

PSO is a global optimization technique inspired by swarm behavior found naturally in schools of fish, flocks of birds, and swarms of insects. A number of particles comprising a swarm are distributed throughout the N-dimensional solution space. An evolutionary process ensues where each particle evaluates the fitness of its current location and moves on to a new location based on the best result seen by that particular particle and the best result seen by the overall swarm. Over a number of generations, the solution space is explored and an optimal solution is reached.

The fitness function for this particular optimization simply evaluates the linear return loss of the antenna over the band of interest and sets the fitness level to be the worst return loss encountered. One advantage of this approach is that the minimum in-band performance is known at every generation. The user can monitor the current fitness value and terminate if a desired target level is reached.

The IFA is a bent monopole antenna that employs a shunt stub for impedance matching. Four variables control the behavior of the structure as detailed in Figure 1. These parameters are permitted to vary according to Table 1. Since some of the variables are dependent on one another, XTend’s PSO plugin uses a dynamic constraint system to update parameter bounds throughout the optimization. Table 2 details the dynamic constraints.

Figure 3 demonstrates the progression of the optimization by examining the return loss achieved at several milestone points including the final optimal solution. The parameters of this solution are listed in Table 3.

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This example uses a macro script from Remcom's XTend library to design a mobile base station using an array of half wavelength dipoles. The procedure could be the first step in designing a new base station, or the technique might be used to match a commercially-available product and the resulting far-zone pattern used for cell site analysis within Remcom's Wireless Insite. As with other design-oriented offerings in XTend, this script does more than simply automate the design process for the array. It sets up the entire project -- materials, waveforms, feeds, grid, sensors, and even parameters. A user can be ready to run their simulation in just a few seconds.

After installing XTend, the Mobile Base Station Designer is available on XF7's integrated Macros menu along with a number of other helpful extensions to XF as seen in Figure 1. Launching the script presents the user with the customized GUI in Figure 2 which allows the user to specify appropriate design criteria. Portions of the interface update dynamically as the user makes changes in order to offer suggestions on how many elements to use, warn if sidelobe suppression goals conflict with steering goals, and provide feedback on the resulting design.

The specifications for a commercially available base station antenna were used for this demonstration:

• Center frequency: 893 MHz
• Horizontal beamwidth: 65 degrees
• Vertical beamwidth: 15 degrees
• Beam tilt: 0 degrees
• Sidelobe suppression: 15 dB

Although this product is not electrically steerable, the example assumes the new array will be. The dialog warns that the number of elements is insufficient to achieve the maximum electrical downtilt and simultaneously meet the sidelobe suppression goals. The warning is ignored for this purpose. Pressing OK prompts the script to generate the project.

The script employs the Fourier transform technique to generate the array and a modified Taylor distribution to control sidelobes. The resulting antenna geometry with its feeds and materials can be seen in Figure 3. A number of parameters are generated to allow the user to control the dipole lengths, electrical downtilt, scan angle, component amplitudes and component phasing. Far-zone sensors are automatically added to capture the horizontal and vertical patterns in addition to the full 3D pattern. The script even prompts the user for a project name and location, so they can be ready to run their simulation immediately. This project requires approximately 150 MB of RAM, and each downtilt angle can be completed in about 45 - 60 seconds on four CPUs or six to seven seconds using XStream on a single C2070.

Figures 4 and 5 contain the horizontal and vertical patterns calculated by XF7. Steering of the pattern is demonstrated through a sweep of the automatically-parameterized electrical downtilt. The vertical patterns for several angles is shown in Figure 6. The full 3D patterns for 0 and 15 degree tilts is displayed in Figure 7.

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In this example a multiband frequency selective surface (FSS) is simulated with XF7. Simulated results are compared to measured results. The filter design and measured data are taken from [1].

The frequency selective surface consists of a pattern of tripoles surrounded by ternary tree loops made of perfect electric conductor, Figure 1. Beneath the conductor layer is 76.2 μm thick polyethylene terephthalate resin with εr = 3.3. A simulation using the full dimensions of the physical device is too computationally complex to simulate. Instead, periodic boundary conditions are used to pattern the structure infinitely in all directions reducing the required resources to a manageable size. Energy was introduced into the space using a plane wave excitation. A near field sensor point was added to capture the electric field in order to compute the transmission.

In this example a cavity-backed slot/strip antenna is simulated in XF7 using the XACT meshing feature. The simulated results for return loss, axial ratio, and gain are compared to measured results. The antenna design and measured results are taken from [1].

A CAD representation of the antenna structure is shown in Figure 1. The cavity is air-filled with perfectly conducting walls. The slots and ground plane are also perfectly conducting. Under the slots lies a very thin dielectric substrate which adds a challenging aspect to this otherwise fairly simple geometry. With a standard staircased mesh, the thickness of the dielectic layer will need to be defined by several FDTD cells. This would require either using a very small mesh size or some other technique such as a variable gridding. With XACT, the mesh size can be larger, but it is important to still make sure each layer of the geometry with distinct features is defined. In this geometry, fixed points are added to the Z plane of the slots and of the feed stub (top and bottom of the substrate) to ensure that each plane is defined. The base cell size is chosen as a much larger 0.8 mm cube, with a ratio allowing the smaller Z thickness to be defined. To aid in the simulation results, the outer surfaces of the dielectric substrate are covered by a thin averaging layer that has the dielectric value halfway between free space and the full dielectric value. Fixed points are also added to the end points of the feed to ensure they are properly connected between the feed line and the cavity wall. A view of the top layer of the antenna is shown in Figure 2 while the feed structure is shown in Figure 3.

Figure 3
A two-dimensional view of the feed line shows the sub-cellular size of the microstrip line and the XACT mapping used to define the shape exactly.

A frequency range of interest for the simulation is defined from 4 to 8 GHz. This automatically adjusts the waveform to cover this range of interest. The excitation for the actual antenna is provided by a coaxial line that attaches to the side of cavity and feeds the microstrip line on the bottom of the dielectric layer. A port is defined at the feed location, which is defined between the microstrip line and the cavity wall, much like the coaxial feed for the real antenna. Near zone fields are saved at this location for the computation of S-parameter results. Additionally, far zone sensors are defined to save the axial ratio and gain as a function of frequency directly above the antenna, and the gain in two principal planes through the center of the antenna. Simulation is performed on a GPU cluster of four NVidia Telsa C870 GPU cards and takes 23 minutes. With a base cell size of 0.8 mm, the project required 611 thousand cells and 63 MB of memory. The S-parameter result for return loss at the feed compares well with the measured results defined in the paper (Figure 4). The axial ratio and gain results versus frequency also show good agreement when compared to the measured results (Figures 5 and 6). The circularly-polarized gain in the two principal planes is plotted for two different frequencies in Figures 7-10. The results are similar to those described in the paper.

Figure 10
Here the right and left-hand circularly polarized gains are plotted in the Phi=90 plane (along the longer dimension of the antenna) at 6.7 GHz.

References

1. R. Li, B. Pan, A. N. Traille, J. Papapolymerou, J. Laskar, and M. M. Tentzeris, “Development of a Cavity-Based Broadband Circularly Polarized Slot/Strip Loop Antenna With a Simple Feeding Structure,” IEEE Trans. Antenna Propag., Vol. 56, No. 2, Feb. 2008, pp. 312-318.

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The crystal geometry is an array of rods, each 0.18125 microns on a side and spaced at a period of 0.58 microns with a curved waveguide line defect introduced by removing several rows of rods as shown in Figure 1. The dielectric properties of gallium arsenide are assigned to the rods. Also, in Figure 1, note the three red field sample points used to determine the frequency characteristics of this structure.

Figure 1
The two-dimensional array of rods.
Two simulations are run with this geometry. The first simulation determines the frequency characteristics using a broadband excitation. The second simulation shows the time domain progression of electric fields through the waveguide at a single frequency.

A waveform containing frequency content from 50 THz to 250 THz is applied to the structure at the center of the waveguide. Electric fields are collected at three points throughout the simulation. Figure 2 shows the normalized frequency response at each of the points and it can be seen that the waveguide supports frequencies between 150 THz and 200 THz.

Figure 2
The supported frequencies in the waveguide.
The broadband waveform was changed to a 160 THz sinusoid and time domain fields were collected as they traveled through the waveguide. Figures 3 - 5 show the propagation of the applied signal through the curve in the waveguide. The containment of the fields within the waveguide is clearly visible as the signal turns the corner and continues.

Figure 5
Fields continuing on as they are contained to the waveguide.

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The four targets consist of small bodies of revolution that were measured at several frequencies for monostatic RCS around the azimuthal axis. The targets were developed by NASA and published in [1]. The measured results used in this example were extracted from the later publication [2].

The target shapes were chosen to highlight challenging situations for simulation software such as smoothly curved surfaces. The four bodies of revolution simulated here include a symmetrical single ogive, a double ogive, a half-cone, half-sphere shape, and a similar cone sphere shape with a small gap encircling the connection point between the cone and the sphere. The four targets are shown in Figures 1-4.

• Figure 1 shows the Single Ogive geometry with a total length of 10 inches (254 mm) with a maximum radius of 1 inch (25.4 mm).
• Figure 2 shows the Double Ogive with a maximum length of 7.5 inches (190.5 mm) and a maximum radius of 1 inch (25.4 mm). The +X side of the Double Ogive matches the Single Ogive structure while the –X side has a larger angle.
• Figure 3 shows the Cone-Sphere geometry with an overall length of 26.768 inches (679.9072 mm) and the cone section having a length of 23.821 inches (605.0534 mm) with a base of radius of 2.947 inches (74.8538 mm). The radius of the sphere section matches the base of the cone section.
• Figure 4 shows the Cone-Sphere with Gap geometry, which matches the Cone-Sphere shown in Figure 3, but with a small gap included in the half-sphere section at the intersection with the cone. The gap is 0.25 inch (6.35 mm) wide and deep.

The simulations were performed using XFdtd 7 with the XACT Accurate Cell Technology meshing feature used for all targets. The software used a mesh size equivalent to 20 cells per wavelength at the frequency of the simulation. The fixed points feature was employed for all geometries and manual fixed points were added at the vertices of the ogives and cones. In some cases good results were possible with a lower resolution, but for consistency all results are shown in the same resolution. To better illustrate the fidelity of the simulation, a view of the XACT mesh is shown in Figure 5 for the Single Ogive geometry at 20 cells per wavelength resolution for a frequency of 1.18 GHz.

Figure 5
A view of the XACT mesh of the Single Ogive geometry.

The simulations used an incident plane wave with a sinusoidal source and data was collected using a steady-state far zone transform. This combination was shown to give the most rapid results for this single-frequency analysis. Due to the results required in a backscatter RCS situation, each simulation produced a single data point for the file output graph.

The XStream GPU solution was used to perform all simulations to provide the quickest results. A single value parameter sweep was performed with the incident phi direction (azimuth angle) used as the parameter in increments of one degree. The output was processed with a custom script written to extract the backscatter RCS at each incident angle and plot the results in a single graph. The simulation execution times varied with the frequency geometry, but generally required less than 20 seconds per angle for the lower frequencies and less than 5 minutes per angle for the higher frequencies on an NVIDIA Tesla C1060 GPU card.

The Single Ogive geometry is aligned with the X axis, so an incident angle of zero degrees strikes the point of the ogive while an angle of 90 degrees hits the side. The Single Ogive was simulated at two frequencies: 1.18 GHz where the ogive is approximately one wavelength long, and 9 GHz where the ogive is about 8 wavelengths long. The simulated results compared to measured results from the referenced publications at 1.18 GHz are shown in Figures 6 and 7 for the vertical and horizontal polarizations, respectively. The results show generally good agreement over all incident angles. Similarly, the results for 9 GHz are shown in Figures 8 and 9.

The Double Ogive is aligned along the X axis like the Single Ogive. The blunter end of the ogive is towards the –X direction while the end that matches the Single Ogive curvature is pointing in the +X direction. The Double Ogive was simulated at 1.57 GHz and 9 GHz. The RCS results for both frequencies and both polarizations are shown in Figures 10 through 13. The agreement with the measurements is generally good, although there are some points, such as near broadside for the low frequency horizontal polarization, that show several decibels of variation. In the original published work, the author’s simulations showed very similar results to those obtained with XFdtd.

The Cone-Sphere geometry lies along the X axis and has a conical point facing in the –X direction and a spherical end in the +X direction. The Cone-Sphere was simulated at 0.869 GHz and 9 GHz. The RCS results for both frequencies and polarizations are shown in Figures 14 through 17. At the lower frequency there is some variation between the simulated and measured results when the incident angle nears the point of the cone. Very similar variation was observed in the published results with the author’s simulations. Also, the geometry is completely symmetrical at 0 and 180 degrees for both polarizations and the XFdtd results match at the end points while the measurements show several decibels of difference, making it seem likely there is some error in the measured results at those angles.

Finally, the Cone-Sphere with Gap geometry is aligned like the Cone-Sphere geometry. The structure was simulated at the same frequencies of 0.869 GHz and 9 GHz as well. The results are shown in Figures 18 through 21 and have similar characteristics to the Cone-Sphere results.

References

1. H. T. G. Wang, M. L. Sanders, A. C. Woo, and M. J. Schuh. “Radar Cross Section Measurement Data, Electromagnetic Code Consortium Benchmark Targets.” NWC TM 6985, May 1991.
2. A. C. Woo, H. T.G. Wang, M. J. Schuh, and M. L. Sanders. “Benchmark Plate Radar Targets for the Validation of Computational Electromagnetics Programs.” IEEE Antennas and Propagation Magazine, vol. 35, no. 1, February 1993.

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The four targets consist of small flat plates that were measured at 5.9 GHz for monostatic RCS at an elevation angle of 10 degrees (above the surface of the plate) and varying azimuth angles. The targets were developed by NASA and published in [1]. The measured results used in this example were extracted from the later publication [2].

The shapes were chosen based on various factors considered difficult for simulation software. The shapes are a “business card” which is a 2 x 3.5 wavelength rectangular plate; a “wedge cylinder” which has a triangular edge and a semi-circular edge joined together; a “plate cylinder” which is a combination of the business card with the semi-circular edge of the wedge cylinder; and a “wedge plate cylinder” which is a combination of the various shapes. Figures of the four shapes are shown in Figures 1 – 4. [Note: more detailed explanations of each of the figures used in this example can be found below.] For the sake of the simulations, the plates were considered to have a thickness of 41 mils and were perfectly conducting.

The simulations were performed using XF7 with the XACT meshing feature used for all targets except the “business card.” The software used a mesh size equivalent to 20 cells per wavelength at the target frequency (5.9 GHz) for all simulations and the fixed points feature was employed for all geometries. In some cases good results were possible with a lower resolution, but for consistency all results are shown in the same resolution. To better illustrate the fidelity of the simulation, a view of the mesh is shown in Figure 5 for the Wedge Plate Cylinder geometry.

Figure 5
A three dimensional view of the Wedge Plate Cylinder geometry mesh.

The simulations used an incident plane wave with a sinusoidal source and data was collected using a steady-state far zone transform. This combination was shown to give the most rapid results for this single-frequency analysis. Due to the results required in a backscatter RCS situation, each simulation produced a single data point for the file output graph.

The XStream GPU solution was used to perform all simulations to provide the quickest results. A single value parameter sweep was performed with the incident phi direction (azimuth angle) used as the parameter in increments of one degree. The output was processed with a custom script written to extract the backscatter RCS at each incident angle and plot the results in a single graph. Each incident angle required less than 20 seconds of execution time on an NVIDIA Quadro FX 1600M graphics card.

The Business Card geometry is already aligned with the rectangular FDTD grid, so the use of the XACT meshing capabilities was not required. The geometry is aligned so that 0 degrees azimuth is normally incident on one of the shorter sides of the plate. The simulated results compared to measured results from the referenced publications are shown in Figures 6 and 7 for the vertical and horizontal polarizations, respectively. The results show generally good agreement over all incident angles. The slightly lower simulated RCS values for the middle of the vertical polarization graph mirrored the simulated results presented by the authors of the referenced publications as well.

The Wedge Cylinder presents a more challenging structure for the FDTD simulation due to the curved surfaces and the sharp point. In the XFdtd simulation, a fixed point was added at the vertex of the wedge to ensure a balanced mesh was created. The RCS results for both polarizations are shown in Figures 8 and 9 with generally good agreement to the published measurements.

The Plate Cylinder geometry builds off the business card shape but adds a semi-circular portion on one of the short sides. The simulated results again agree well with the measured results, as can be seen in Figures 10 and 11.

Finally, the Wedge Plate Cylinder geometry combines the three structures with the vertex of the wedge at the 0 degree point and the center of the semi-circle at 180 degrees. The simulated and measured results show good agreement once again as is shown in Figures 12 and 13.

Explanations of Figures

• Figure 1: The Business Card geometry: The X length is 3 wavelengths while the Y length is 2 wavelengths (at 5.9 GHz). The thickness is 41 mils.
• Figure 2: The Wedge Cylinder geometry: The radius of the semi-circle is 1 wavelength while the length of one wedge side is 2 wavelengths (at 5.9 GHz). The angle of the wedge is 60 degrees while the thickness of the plate is 41 mils.
• Figure 3: The Plate Cylinder geometry: The radius of the semi-circle portion is 1 wavelength while the plate section is 2.5 x 2 wavelengths (at 5.9 GHz). The thickness of the plate is 41 mils.
• Figure 4: The Wedge Plate Cylinder geometry: The radius of the semi-circle portion is 1 wavelength. The center section is a 1 x 2 wavelength rectangular plate while the wedge section has a side length of 2 wavelengths (at 5.9 GHz). The angle of the wedge is 60 degrees while the plate thickness is 41 mils.
• Figure 5: A three dimensional view of the Wedge Plate Cylinder geometry mesh shown to illustrate the cell size used for the simulations, the plate thickness, and the XACT meshing capabilities.
• Figure 6: Simulated and Measured backscatter RCS results for the Business Card at 5.9 GHz, vertical polarization. The elevation angle was 10 degrees above the plane of the plate and the azimuth angle was varied. Zero degrees represents normal incidence on one of the shorter sides of the plate while 90 degrees is normal incidence on a longer side.
• Figure 7: Simulated and Measured backscatter RCS results for the Business Card at 5.9 GHz, horizontal polarization. The elevation angle was 10 degrees above the plane of the plate and the azimuth angle was varied. Zero degrees represents normal incidence on one of the shorter sides of the plate while 90 degrees is normal incidence on a longer side.
• Figure 8: Simulated and Measured backscatter RCS results for the Wedge Cylinder at 5.9 GHz, vertical polarization. The elevation angle was 10 degrees above the plane of the plate and the azimuth angle was varied. Zero degrees represents normal incidence on vertex of the wedge.
• Figure 9: Simulated and Measured backscatter RCS results for the Wedge Cylinder at 5.9 GHz, horizontal polarization. The elevation angle was 10 degrees above the plane of the plate and the azimuth angle was varied. Zero degrees represents normal incidence on vertex of the wedge.
• Figure 10: Simulated and Measured backscatter RCS results for the Plate Cylinder at 5.9 GHz, vertical polarization. The elevation angle was 10 degrees above the plane of the plate and the azimuth angle was varied. Zero degrees represents normal incidence on the short straight side of the plate, while 180 degrees represents the center of the circular edge.
• Figure 11: Simulated and Measured backscatter RCS results for the Plate Cylinder at 5.9 GHz, horizontal polarization. The elevation angle was 10 degrees above the plane of the plate and the azimuth angle was varied. Zero degrees represents normal incidence on the short straight side of the plate, while 180 degrees represents the center of the circular edge.
• Figure 12: Simulated and Measured backscatter RCS results for the Wedge Plate Cylinder at 5.9 GHz, vertical polarization. The elevation angle was 10 degrees above the plane of the plate and the azimuth angle was varied. Zero degrees represents normal incidence on the vertex of the wedge, while 180 degrees represents the center of the circular edge.
• Figure 13: Simulated and Measured backscatter RCS results for the Wedge Plate Cylinder at 5.9 GHz, horizontal polarization. The elevation angle was 10 degrees above the plane of the plate and the azimuth angle was varied. Zero degrees represents normal incidence on the vertex of the wedge, while 180 degrees represents the center of the circular edge.

References

1. H. T. G. Wang, M. L. Sanders, A. C. Woo, and M. J. Schuh. “Radar Cross Section Measurement Data, Electromagnetic Code Consortium Benchmark Targets.” NWC TM 6985, May 1991.
2. A. C. Woo, H. T.G. Wang, M. J. Schuh, and M. L. Sanders. “Benchmark Plate Radar Targets for the Validation of Computational Electromagnetics Programs.” IEEE Antennas and Propagation Magazine, vol. 34, no. 6, December 1992.

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