CAD Benchmark

In the October 2000 issue we outlined the details of our latest CAD Benchmark - a free space electromagnetic problem based on a balanced antipodal Vivaldi antenna. The response from CAD vendors has produced so much information that we are running the results over two issues. The December/January issue will also contain the measured results on the original hardware.

In the briefing provided to the participating CAD vendors, which was reproduced in the October issue of Microwave Engineering Europe, the following outputs were specified. For consistency they will be used as section headings throughout the presentation of the solutions from each of the vendors.

Model geometry printout
The printout should be supplied with annotation that would confirm dimensions/ approximations used, boundary regions/definitions (e.g. air volumes, excitations, radiation boundaries etc), as well as feedback on ease of definition etc.

S-Parameters and input impedance
A minimum analysis range of 0.5 - 10GHz is required, but optionally higher (the original device was characterised up to 18/20GHz). Plots (in dB vs. frequency format), and Touchstone format files for return loss are needed (to make re-plotting and comparisons easier).

Pattern data output at 10GHz
For E and H Plane cuts, Co and Cross Polar, Gain, Beamwidth. Plots should be in Cartesian format in dB vs Degrees. Optionally 3D colourful plots/animations may be submitted electronically to illustrate features. As this is principally an antenna benchmark, emphasis will be on these results.

Comments: For example on problem entry/setup, solution process etc, discussion of results

Setup information: solution setup parameters for meshing, frequency sweep etc Hardware information: make/model, operating system, clock speed, RAM fitted, number of CPUs.

Software information: Name, Version, elapsed run times, RAM/disk space needed, number of elements used (or cells/unknowns).

Vendor information (name, dept, address/contact details etc in case of queries) was also requested.

Participants

The following companies were invited to participate in the 2000 CAD Benchmark: Agilent EEsof; Ansoft; APLAC; Applied Wave Research; Computer Simulation Technology (CST); EM Software and Systems (EMSS); ESTEC; IMST; KCC; Vector Fields; Zeland. Five of these eleven vendors declined to take part.

Taking the respondents in alphabetical order, the solutions from Ansoft, CST and IMST are presented here. Those from KCC, Vector Fields and Zeland will be included in the December/January issue, along with practical and simulated results from the Microwave Technology Group at BAE Systems Advanced Technology Centres, Great Baddow, who kindly set the problem for us.

Model geometry printout

Figure 1. 3D geometry simulated in Ansoft HFSS (a) top view with absorber removed to show ground plane, and (b) bottom view showing trace layer

Figure 1 shows the device that was constructed and simulated in Ansoft HFSS. The system has a built in 3D CAD system in which the geometry was constructed. The geometry construction process took about 15 minutes to create. This time would be shortened if the structure had been supplied in electronic format. The dimensions of the circular and elliptical arcs (except the elliptical flare arc, which is specified in the benchmark document) were taken from the graphics provided.

The elliptical shape of the flare is considered critical to this device performance. The flares were modelled with 12 segment elliptical arcs to provide an accurate edge to apply a tetrahedral mesh. The use of a tetrahedral mesh allows Ansoft HFSS to model a curved surface with arbitrary accuracy. In this case, the 12-segment arc was chosen to keep the accuracy of the curve to within 1% of a true ellipse.

The geometry used in this simulation is half symmetry geometry where the device was cut in half in the plane of the stripline. This approach simplifies the structure and allows for greater mesh density and solution accuracy. The symmetry plane imposed is H Plane Symmetry. Ansoft HFSS allows for the calculation of the full radiation pattern when a geometry has been modelled using symmetry planes.

The trace and ground planes were modelled as infinitely thin conductor for this simulation, as allowed in the benchmark specification document. The thickness of the metallisation layers was also treated as insignificant compared to the overall dimensions of the device.

The air region surrounding the antenna was terminated using a Perfectly Matched Layer (PML) type of absorbing boundary. This type of boundary condition was chosen because of its excellent properties close to a radiating source. The distance from the antenna to the absorber at 10GHz is 1/2 wave-length (15mm). Normally the absorber placement would be between 1/10 and 1/4 wave-length, however, the larger dimension was chosen so that the distance at 0.5GHz was 1/40 wavelength. In any computational system, the boundary can have an impact on the solution if the boundary is placed too close to the radiator. The choice of location was a compromise between being too close at the low end of the frequency band and being too far away at the high end of the band. This was done to accomplish a single simulation across the entire specified frequency range.

S-Parameters and input impedance

The frequency sweep data was generated using Ansoft's proprietary ALPS algorithm. This allows the user to calculate the response curve across a broad bandwidth and maintain a complete solution at each frequency in the band. This is a significant feature as it allows the user to switch to any frequency within the solution range and recover the full field solution without additional solution time. Once the field solution is recovered at a frequency of interest, the full post processing capability of the system is available including field plotting, antenna pattern calculation, field quantity manipulation such as SAR calculation, and file data output.

Figure 2. S-Parameters for balanced antipodal Vivaldi antenna from 0.5 to 10GHz with (a) matched input impedance and (b) after renormalisation to 50 input impedance.

Figures 2(a) and (b) show the S ¹¹ characteristic obtained using Ansoft HFSS. The characteristic ranges from 0.5 to 10GHz with a sharp resonance at approximately 4.32GHz representing an area where the device is well matched. Below 2GHz, the device performance degrades as the taper becomes too narrow and the metallisation becomes resonant. At higher frequencies (between 8 and 10GHz) the performance also suffers as a result of energy coupled to the backside of the flared metallisation.

Pattern data output at 10GHz

Figure 3. Ansoft HFSS field solutions at 10GHz.

Figure 3 illustrates the co-ordinate system used for the antenna pattern plots. The substrate lies in the y-z plane with the nominal direction of propagation in the positive z direction. The slot is oriented along the y-axis for these plots. Figure 4 shows the 10GHz electric field plots in the plane of the flare. Figures 5(a) and (b) illustrate the computed antenna pattern in the E and H-Planes for the device. As expected the H-Plane antenna pattern is broader than the pattern in the E-Plane cut.

Figure 4: The 10GHz electric field plots in the plane of the flare.

Figures 5(a) and (b) show the computed antenna pattern in the E and H-Planes.

Finally, Figures 6(a) and 6(b) show the gain patterns normalised to the peak field in the cut so that the 3dB beamwidth may be determined. The markers on the plots illustrate the approximate 3dB points and the calculated beamwidth. The values are 70ý for the E-Plane cut and 125ý for the H-Plane cut.

Figures 6(a) and (b) show the gain patterns normalised to the peak field in the cut so that the 3dB beamwidth may be determined.

Comments

The performance of the antenna was characterised over a very broad bandwidth using a single adaptive simulation at 10GHz and a frequency sweep over the full 0.5 - 10GHz specified range. The simulation took approximately 20 minutes total time to set up and less than 3 hours to perform the full simulation. Post processing of the results to get plots and figures in real time took another hour to complete, as the specifications required for this benchmark.

Numerous other types of plots and data analyses are possible with Ansoft HFSS. Since the field data is maintained over the full sweep range, it is possible to do analysis at multiple frequencies without need for further solutions.

Setup information

No additional information was supplied.

Hardware information

The Ansoft simulation was performed on a 450MHz Sun Ultra II machine with 4 processors and 2GB of installed memory.

The amount of time required performing the simulation at 10GHz was 20 minutes 10 seconds. The starting mesh was 24,071 (156k unknowns), and the final mesh after three adaptive passes was 33,914 (218k unknowns). The sweep from 0.5GHz to 10GHz took 2 hours, 23 minutes and 21 seconds for 950 frequency points. The maximum memory required was 821Mb, and the maximum disk space required was115Mb.

Software information

The software version used was Ansoft HFSS V8 Alpha.

Model geometry printout

The structure was built as a fully parametric model. The real thickness of the metallic layers (17ým) was taken into account. By using a few primitives (elliptical objects etc.), relative construction and easy Boolean operations and transformations, the whole setup can be completed in less than 2 hours by an experienced user.

The boundaries of the calculation domain were defined as PML boundaries. The appropriate distance to the object is automatically determined by CST MICROWAVESTUDIO (MWS). An adapted waveguide port was used to model the excitation of the antenna. The whole definition of boundaries, materials and frequency range is straightforward, and does not take longer than 1-2 minutes.

Figure 1: Vivaldi Antenna modelled with CST MICROWAVESTUDIO.

Figure 1 shows the Vivaldi Antenna modelled with CST MICROWAVESTUDIO.

S-Parameters and input impedance

Figure 2: Amplitude of the S-Parameters over the range 0 - 20GHz, at a reference impedance of 41.88 without normalisation.

Figure 2 shows the amplitude of the S-Parameters over the range 0 - 20GHz, at a reference impedance of 41.88 without normalisation.

Pattern data output at 10GHz

Figure 3(a) E-Plane co-polar and H-Plane cross-polar, and (b) E-Plane cross-polar and H-Plane co-polar directivity at 10GHz

The E-plane and H-plane co-polar and cross-polar directivity plots are shown in Figures 3(a) and 3(b).

The gain at 10GHz is 3.24 (= 5.11dBi). The beamwidth at 10GHz in E-plane amounts to 69.7ý, and in H-plane amounts to 128.1ý.

Figure 4(a) Phi and 4(b) theta components of gain at 10GHz.

The phi and theta components of gain are represented in 3D in Figures 4(a) and 4(b) respectively. Figures 5(a) and (b) show respectively a contour plot of the electric near field and a vector plot of current distribution on the antenna, both at 10GHz.

Figure 5(a) Contour plot of electric near field, and (b) vector plot of current distribution on the antenna, both at 10GHz.

Comments

The program automatically delivers S-parameter curves. The impedance of the exciting waveguide was adapted to the microstrip of the antenna. A normalisation to 50 was not applied as it was not requested in the specification of the benchmark.

Setup information

No additional information was supplied.

Hardware information

A fast calculation of the S-parameters for the desired frequency range 0 -10GHz can be performed within 15 minutes on a 800MHz PIII. The results of this quick calculation are in excellent agreement with a second simulation, which was made for the whole frequency band (0 - 20GHz) using a refined mesh. This high accuracy solution for the whole frequency range from 0 -20GHz was obtained in 64 minutes on the same PC.

For both simulations an automatic mesh generation was used which is based on an expert system approach. Alternatively a fully automatic mesh adaptation can be used which requires 4 passes and around 78 minutes for the broadband solution (0-20GHz).

Both calculations were performed on a single processor machine. The usage of a dual processor would reduce this time additionally.

The required memory for this calculation was about 100MB.

Software information

The Benchmark's simulation was performed with the new version 2.1 of CST MICROWAVE STUDIO (CST MWS). This 3D solver is based on the FI method in combination with the Perfect Boundary Approximation (PBA) which allows the partial filling of mesh cells.

Model geometry printout

The proposed Vivaldi antenna mainly consists of metallic circular and elliptical arcs, which are separated by dielectric substrates. A bitmap drawing was supplied which could be imported into the AutoCAD editor to be used as a drawing model since at least one of the geometry parameter was missing in the initial benchmark description. The model was built very easily by using extruded polygons.

Figure 1. Wire frame model of simulated Vivaldi antenna.

A 3D wire frame model printout is depicted in Figure 1, which shows metallisation, substrate and near field box. The distances to the open boundaries were chosen to 16, which is enough to ensure low reflections from the walls applying PML boundary conditions, resulting in a 40mm distance for the lowest frequency of 0.5GHz.

Further the typical staircase approximation for FDTD schemes is visible in the area of curved structures. Applying a non-equidistant meshing the number of grid cells is kept low.

S-Parameters and input

Figure 2(a) Return loss S 11 in dB, and (b) real (red) and imaginary (blue) parts of the input impedance in .

S-parameters and input impedance have been simulated for the frequency range 0 to 20GHz by exciting the structure with a Gaussian pulse. Due to the impedance of the stripline, all values correspond to approximately 43 . Plots are given in Figures 2(a) and 2(b), and a Touchstone format file for the return loss (not reproduced here) was also supplied with the reference impedance of 43 .

Pattern data output at 10GHz

Figure 3(a) E-plane and (b) H-plane radiation patterns: co-polar patterns are shown in red and cross-polar in blue.

Figures 3(a) and (b) show the radiation patterns of the E- and H- plane cuts for both co- and cross-polarization. They have been calculated by a near to far field transformation of the recorded near field on a rectangular box surrounding the antenna which is shown as a white box in Figure 1. The values are normalised to the radiated power thus giving the directivity. The calculated directivity is 2.9 dB in z direction. In main radiation direction
=38ýand =0, the directivity is 5.2dB. Because losses have been neglected, the gain is equal to the directivity, reduced by 0.46dB at 10GHz due to the reflected power. The 3dB beamwidth angles are found to be ^E = 110ý and ^H = 75ý. Figure 4 illustrates the electric field at 10GHz.

Figure 4: Electric field in plane where y = constant.

Comments

The problem set-up (structure definition, meshing, port and boundary definition) is straightforward, and can be handled within half an hour for an experienced software user. Care has to be taken for choosing the right port impedance, which is necessary to separate incident and reflected time signals. Since this antenna has a low quality factor the time signals decay fast and therefore the required number of time steps is low.

The results show a poor impedance match at 10GHz and the radiation patterns exhibit significant side lobes. A small parasitic capacitance that can be introduced by a feeding connector can significantly change the simulated parameters. In our experience, the connector should be included into the simulation for a comparison of the simulated results with measurements. Further, it is well known that a small misalignment or asymmetry of the two substrates can lead to substantial higher cross-polarization in the E-plane.

Setup information

The structure was resolved using a non-equidistant Cartesian grid using 103 x 28 x 149 cells in x, y, and z directions respectively, where distances from 0.2mm to 6mm have been used. A 4-layer PML has been used to simulate free space condition. The structure is excited by a Gaussian pulse with a dura-tion of 1.8*10 -10 s. The optimum time step was found to be t = 4.8*10-13s.

Hardware information

Windows NT 4.0; 600MHz single Athlon processor; 256 MB RAM Software information EMPIRE v2.20; run time 14 min (13 min without near field recording); number of cells: 430,000; including near field recording the needed RAM space was 36 MB.

Software information

EMPIRE v2.20; run time 14 min (13 min without near field recording); number of cells: 430,000; including near field recording the needed RAM space was 36 MB.

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