CAD Benchmark

In this second part of the 2000 CAD Benchmark, we continue the presentation of the solutions provided by the CAD vendors to the free space electromagnetic problem detailed in our October issue. The problem is based on a balanced antipodal Vivaldi antenna. The measured results on the original hardware, along with the solution from the originator of the problem, will be given in the February issue.

Model geometry printout

The "Build" tool performs Micro-Stripes geometry entry and problem setup. This tool is based on the industry standard ACIS kernel and offers all the necessary primitives to create very complex models.

For the antipodal Vivaldi antenna, the geometry input took less than 10 minutes as all the primitives needed to define the geometry were available.

The top ground plane was defined first as a set of points following the outline of the copper etching using line and ellipse primitives. This edge is then turned into a surface, which is given a thickness to represent a solid object. This object is then copied and translated by the total thickness of the substrate to become the bottom ground plane. The centre conductor was also generated from a rotated copy of the ground plane, which has in turn been translated by half the total thickness of the dielectric.

The next step is assigning material properties for the different entities of the model. The model contains three solid objects.

Figure 1: shows the 3D metallic entities in the of the Vivaldi antenna modelled by KCC Micro-Stripes. Yellow represents the ground plane, and blue the central strip line

Figure 2: 3D representation of antenna showing the dielectric extent in red. The dielectric has a thickness 50.8 x 1.57mm 2 (2 x 0.062")

• The ground plane (Top and bottom), shown in yellow in both Figure 1 and Figure 2, is defined as a single body because it is joined at the input end by a plate with an aperture. The aperture is the opening for connecting a SMA coaxial connector.
• Central strip shown in blue in Figure 1.
• Dielectric, shown in red in Figure 2.

The electrical properties of metals, dielectrics and microwave substrates are contained in a database, which is made accessible to the user through the build tool. The wanted metal or dielectric is easily attached to a geometrical entity via a mouse click. In this case both materials copper and the Rogers Duroid 5870 are in the database. The Duroid material has a permittivity of 2.32 and also a loss tangent defined at 10GHz. The loss tangent has been included in our model.

Figure 3: Shows the Vivaldi antenna enclosed by a box just big enough to surround the model and defines a volume where the meshing is done finely within it and a bigger work space volume where the grid size can be increased substantially without loss of accuracy in the model

The "Build" model requests the user for the upper frequency limit of the model to compute the maximum grid size. In this case an upper limit of 18GHz is chosen giving a maximum grid size of 1.6 mm in air.

The meshing of the model is performed automatically by the auto-mesh function to ensure that:

• The correct grid size is chosen in-side the dielectrics
• The major features and planes are snapped to the grid so their size is correctly mapped in to the discretised model.

Figure 4: S 11 response of Vivaldi antenna (a) referred to 43 line impedance and (b) normalised to 50 impedance

The use of multi-gridding in the auto-mesh function allows selective gridding of the model by allowing areas where detail requires to be meshed more finely than other parts of the model. This ability results in optimal grid size distribution and gives a substantial reduction in the problem size.

The model symmetry along the plane y=0 mm is exploited to reduce the problem size by half and is enforced by a magnetic wall boundary condition at this plane.

The excitation of the model is performed using the "Ports" module, which attaches a TEM port at the input of the device. Other ports are also available to excite different microwave devices such as coaxial lines and waveguides.

The last step to perform is to write out a discretised file to input the solver. The total work space defining the geometry without symmetry is 152 x 90 x 120mm ² . In our model half of this was eliminated by symmetry.

Figure 5(a): Three-dimensional radiation pattern from antipodal Vivaldi antenna at 10GHz. The peak computed directivity is 5.2dBi, and is not coincident with boresight for this particular antenna

Figure 5(b) shows the field plot at 10GHz

S-Parameters and input impedance

Figure 4(a) shows the return loss (S ₁₁ ) response of the antenna referred to the line impedance at the input port of the model, which is 43 , and Figure 4(b) shows the return loss when the port impedance is normalised to 50 .

Pattern data output at 10GHz

The radiation patterns were computed for the Vivaldi antenna at 10GHz, and are shown in full in Figure 5(a). The bold line represents the outline of the 3dB beam. The fine lines mark the 10ý intervals from boresight. The radial scale covers 30dB.

Figure 6(a): Principal plane cuts for Vivaldi antenna at 10GHz

Figure 6(b): Expanded co-polar E plane cut, giving a 3dB beamwidth of 130ý

Figure 6(c): Expanded co-polar H plane cut giving a 3dB beamwidth of 110ý

Figure 6(a) shows the principal plane cuts for the Vivaldi antenna at 10GHz. For clarity, the 3dB beamwidth has been evaluated from the expanded plots for both E and H plane cuts, shown in Figures 6(b) and (c) respectively. The E plane cut shows two distinct peaks disposed on either side of boresight. The total 3dB beamwidth given by this cut is 130ý.

The definition of the 3dB beamwidth is not clear, because the beam shape does not exhibit a main lobe on boresight. If we assume that the beam peak is located off boresight and off the H plane cut, a level 3dB down from the peak intersects this pattern at 2.2dBi. The beamwidth would then be ý8.5ý. Note that should the phase distribution across the aperture at this frequency changes slightly, this might cause the first shoulder in the pattern to dip below -0.6dBi (-3dB below the peak for the H plane cut). This will give a significantly narrower beamwidth, which can be extrapolated to be around 80ý.

Hardware information

The computer used is a Hewlett Packard Omnibook 6000 laptop, with a 650MHz Pentium III processor, a single CPU, and 128Mb of RAM. The operating system was Windows NT, Service Pack 6.

Software information

The software used was Micro-Stripes Version 5.5. The RAM required was 50Mb (negligible disk space). The number of cells was 400,000.

The time to compute the response over the 500MHz to 18GHz is 42 minutes. When the band is reduced to 500MHz to 10GHz, the run time is only 15 minutes.

Model geometry printout

This was an easy model to define in CONCERTO and took an experienced user about 1 hour to set up. The software is based on the FDTD method with conforming material boundaries. The curved nature of the metallic layers is ideally suited to CONCERTO's conforming elements, and the time domain nature of the software is highly appropriate for this wideband problem. The full 0.5GHz to 20GHz band was modelled.

Figure 1: Antenna model with upper dielectric layer removed

Figure 2: Line view of CONCERTO model

The modelling process was as follows:

1. The lower ground plane layer was created using the thin sheets available in the software. This means that the layer thickness does not need to be meshed. The shape of the metal was created using the editor's Boolean operations to 'cut' and 'glue' simple shapes into the more complex shape required.

2. The lower ground plane was duplicated to create the top-most metallisation layer.

3. The central microstrip line was created as in (1).

4. The dielectric layers with the appropriate properties and the metal end- plates were added.

5. A TEM port excitation was set up with a pulse excitation where the pulse was created with the frequency content required.

6. A mesh was created and "mesh planes" were used to allow some grading between a fine mesh around the antenna and a slightly coarser mesh out-side. CONCERTO demands at least 10 cells per shortest wavelength (1.5mm at 20GHz). For high accuracy close to the antenna, some cell separations of 0.25mm and 0.5mm were used.

7. An absorbing box and a "near- to far-field" transform box were added. The boundaries in CONCERTO should be at least 1/4 of the longest wavelength from the radiating device (0.15m at 0.5GHz).

8. Due to cell size and boundary distance requirements, it was found that the run times and memory requirements could be optimised by splitting the problem into two runs. Model 1 was from 0.5GHz to 5GHz and Model 2 was from 5GHz to 20GHz. The only difference between the models was the proximity of the outer boundary, which was brought much closer for Model 2. The radiation results were taken at 10GHz from Model 2.

The antenna modelled in Concerto is shown in Figures 1 and 2. The upper dielectric layer has been removed for display purposes only. The top metallization and central microstrip layers can be seen.

Figure 2 shows the line view of the model. The absorbing boundary box is shown by the outer blue box. The inner green box is the surface for the near to far field transform. The excitation port can be seen at the lower left of the antenna. The blue rectangle beyond is the "reference plane" for the port where the S-parameters are calculated

S-Parameters and input impedance

Figure 3: Return loss (S 11 ) vs. angle

The input impedance of the device was calculated as 43.7 . The S ₁₁ results are shown in Figure 3. The results from Models 1 and 2 were combined to give the complete 0.5GHz to 20GHz characteristic. A Touchstone file was also supplied.

Pattern data output at 10GHz

Figure 4: H plane results

Figure 5: E plane results

The H plane radiation pattern at 10GHz is shown plotted on a Cartesian scale in Figure 4. It should be noted that the feed for the antenna is in the negative x direction. Good cross-polar performance was observed.

The E plane radiation pattern at 10GHz is shown plotted on a Cartesian scale in Figure 5. Figure 6 shows a view of the 3D radiation pattern. This is in ACIS SAT file format and can be manipulated on screen.

Figure 6: 3D view of radiation pattern

Hardware information

A single Pentium III Dell PC running at 600MHz with 384Mb of memory was used to run the problem, although 256Mb of memory would have been sufficient.

Software information

CONCERTO version 1.9 was used for this benchmark, running under Windows NT4 (service pack 4). The total number of cells was approximately 2.5 million for each of the two models. Converged S ₁₁ results were achieved after about 4000 time steps, where each time step ( t) was 0.5ns. Each step took about 1.5 seconds of CPU time (Model 2). The total run time was approximately 2 hours.

Disk space requirements are minimal, but depend entirely upon how much information is saved. For example a run can be frozen at any time on disk. This model occupied about 50Mb in frozen form.

Figure 1: The top view and the 3D view of the structure

Model geometry printout

The Vivaldi antenna was simulated and benchmarked with the IE3D Electromagnetic Simulation and Optimization Package and the FIDELITY Electromagnetic Simulation Package from Zeland Software, Inc.

The IE3D is based upon a method of moment based full wave electromagnetic simulator for 3D and planar metallic structures in layered dielectrics. The FIDELITY is a non-uniform FDTD simulator for general 3D dielectric structures.

The antenna is printed on the substrate. The finite size substrate will not have much effect to the s-parameters and input impedance antenna. The IE3D is expected to yield accurate results on the s-parameters and the input impedance. However, the IE3D's calculated pattern should be affected by the assumption of infinite extended substrate. The effect of finite substrate size is included in the FIDELITY simulation.

Figure 2: The 3D view of the structure on FIDELITY

S-Parameters and input impedance

The structure was built with exact dimensions as supplied. The top view and 3D view on the IE3D are shown in Figure 1. They are described in the following:

There are 3 types, 6 elliptical quarters in the geometry:

• No.1 type elliptical quarter: short axis length = L2, long axis length = L4
• No.2 type elliptical quarter: both axis length = L2
• No.3 type elliptical quarter: short axis length = W4, long axis length = L1

The feed line width is W1. The SMA outer conductor contact width is W2. The width of the structure is W3. The ground-plane separation or the substrate thickness is 1.5748mm. The permittivity of the substrate is 2.32. The length parameters are labelled in Figure 1.

The geometry entry on the structure is quite straightforward on the IE3D. We first build the tri-plate portion close to the feed. It is rectangular and can be created easily. The smooth curvature on each elliptical quarter is created as 8-straight lines for good approximation.

The elliptical quarters are created using the CIRCLE entity on the MGRID (IE3D's layout editor). The circle is stretched to the elliptical shape by using the Change Dimensional Scales menu item in the Adv. Edit menu of the MGRID. The appropriate elliptical quarter is then moved and snapped to the rectangular portion of the structure. The Copy and Reflect command in the Edit menu is used to create the symmetrical portion of the structure. The SMA outer conductor is modelled as some vertical polygons connecting the two ground planes. The coaxial pin is modelled as a horizontal localised port on the IE3D with some horizontal strip feeding the centre plate. The whole process takes about 10 to 20 minutes for experienced users.

Figure 3: The s-parameters on Smith Chart obtained from IE3D and FIDELITY

Figure 4: The s-parameter results from IE3D and FIDELITY

IE3D's layout editor MGRID is offered to FIDELITY users. On the FIDELITY, the user can describe the ground planes and the centre plate as multiple vertex polygons. However, the fastest way to build the structure is to export it from the IE3D layout editor. It is suggested that the user should merge all the polygons into three large polygons, and delete the vertical polygons before the merging. From the FIDELITY layout editor, the user can add the SMA contact, the pin from the centre conductor of the SMA to the feed line. Finally, the user can define a localised coaxial port to model the SMA connector rigorously.

The S-parameters on both the IE3D and FIDELITY simulators are displayed and compared in Smith Chart in Figure 3, and in Cartesian co-ordinates in Figure 4. The input impedance is displayed and compared in Figure 7. Good agreement is observed in the s-parameters and input impedance between the IE3D and FIDELITY.

Pattern data output at 10GHz

The current distribution on the structure is available at specified frequency on the IE3D. The plot at 10GHz is created in Figure 5. The near field distribution (E, H and Poynting vectors) can be visualised on the FIDELITY. The near field created on the FIDELITY is shown in Figure 6.

Figure 5: The current distribution on the centre strip and the bottom ground on IE3D

Figure 6: The near E-field distribution on the layer where the centre strip is located

The IE3D calculated 3D radiation pattern is shown in Figure 7(a). The FIDELITY calculated 3D radiation pattern is shown in Figure 7(b). They are different, although the general shapes do look alike. The main difference is at the elevation angle = 90ý. IE3D's radiation pattern is affected by the assumption of infinitely extended substrate. On the other hand, the effect of finite size substrate is included precisely in the FIDELITY simulation.

Figure 7: The calculated 3D radiation pattern at 10GHz using (a) IE3D with infinite substrate and (b) FIDELITY with finite substrate

The IE3D patterns and the FIDELITY patterns are also compared in Cartesian co-ordinates in Figures 8(a) and 8(b). Again, the finite substrate in this antenna has a significant effect on the antenna radiation pattern. IE3D's infinite substrate assumption can not capture the radiation patterns of this antenna close to elevation angle = 90ý precisely. Due to the above fact, we use the pattern at elevation angle = 80ý for the azimuth pattern for the IE3D in Figure 8(b).

Figure 8: The comparison of the IE3D and FIDELITY patterns (a) in elevation at azimuth angle Φ = 90ý, and (b) in azimuth with elevation angle = 80ý for IE3D and = 90ý for FIDELITY

Hardware and software information

The IE3D simulation is performed on the IE3D 7.12 on a Pentium II 450 machine with 256Mb RAM. Total 2724 cells and 4534 unknowns are created. The advanced symmetric matrix solver is used to solve the matrix. Total 170Mb RAM is required to solve the problem. Each frequency point takes about 2734 seconds. The complete frequency response from 0.5GHz to 10GHz of 195 frequency points is obtained in 25.8 hours using the Adaptive Intelli-Fit scheme on the IE3D. Radiation pattern is obtained with an extra simulation at 10GHz.

The FIDELITY simulation is performed on the FIDELITY 3.0 on a Pentium II 450 machine with 256 Mb RAM. Total grids are 80 by 96 by 28 = 215040. It requires about 28 Mb RAM to solve the problem. The total simulation time for the complete frequency response is 4244 second (total 7777 time steps).

This is a relatively large structure for the IE3D. However, it is a relatively small structure on the FIDELITY. The FIDELITY takes much less RAM and time to simulate this structure.

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