# Vivaldi Antenna

Microwave Engineering Europe's (MWEE) EM simulation benchmark has become quite a tradition over the last few years, enticing some of the best known software providers to put their diverse simulation methods to the test. The results are always eagerly awaited as they represent the current status of simulation technology and permit revealing comparisons between individual methods and software packets.

Figure 1: Geometry of a vivaldi antenna

For the first time in MWEE benchmark's history an antenna problem was set. The balanced Vivaldi antenna posed a worthy challenge to the benchmark participants due to its complex form and size (Fig.1). The CAD benchmark was presented in the October 2000 edition of MWEE and results from six contributors were published in the subsequent editions with the measured results ending the series in February 2001.

The comparison between the published measured and simulated results from all software producers revealed significant differences. No possible reason for this striking discrepancy was put forward by MWEE. CST calculated the Vivaldi structure with great diligence and, having carried out a detailed convergence study, consider our results to be highly accurate.

We would therefore like to share our thoughts with you, commenting on some of the results.

Over the next few pages you will find a discussion of performance and accuracy, commentary on the differences between measured and simulation results, remarks on model input time, and the benchmark results achieved with CST MICROWAVE STUDIO® illustrated with a wide range of plots and animations.

Figure 2: Benchmark results

Figure 1 illustrates the results published in the February 2001 edition of MWEE submitted by six benchmark participants. At first glance all curves - at least in the frequency range from 0-5 GHz - are similar. But when you take a closer look they demonstrate clear differences. The importance of these differences is shown by the following convergence study performed with the help of CST MWS®'s automatic mesh adaptor.

Figure 3: Final solution in a rough mesh with 10.000 mesh nodes

Figure 2 illustrates large variations with the final solution in a rough mesh with 10.000 mesh nodes (Pass 1). After the fifth run (with 53.000 mesh nodes, 12 min. calculation time) hardly any deviation is present in the results and strong convergence can be seen. It has been mathematically proven that our method must always converge and so is absolutely reliable.

Figure 4: Frequency band section

We will now take a closer look at one section of the frequency band (Figure 3). The resonance peak around 3 GHz decreases in intensity and the resonance frequency shifts until a mesh density of 330.000 nodes is used where an extremely high accuracy is attained (pass 9). The difference between the absolute minimum of these peaks for runs 1 and 9 is, nevertheless, 25 dB, the frequency shift 330 MHz. A renewed look at the results submitted by the benchmark participants, clearly reflects the time spent and reliability of the various methods. The difference between the individual resonance peaks amounts to 12dB / 250 MHz for this frequency range. This enormous difference impressively clarifies the importance of a carefully carried out convergence study. It should be noted that the 9 runs made here, were only carried out in order to clearly illustrate the convergence process. In practice, substantially fewer runs are sufficient to reach a reliable result.

As an optional extra, MWEE had challenged the participants to calculate results for the 10 to 20 GHz range. Unfortunately MWEE neither presented the measured results for this range, nor published a comparison between the submitted simulation results. It is precisely in this frequency range that the widely differing abilities of the methods would have appeared most clearly, due to the problem size in wave lengths and the resulting increase in the number of mesh nodes points.

Figure 5: Measurement

Figure 1 illustrates the reflection for the same frequency range (0.5 – 10 Ghz) as measured by BAE Systems, Great Baddow. The variation with the common trend present in all simulation results is so large, that it has to be asked whether the layout of the measured antenna completely corresponds with the structural information made available. It seems very unlikely that all published simulation results should be so full of errors. We would like you to bear in mind that the published simulation results represent state of the art 3D EM simulation and their accuracy and agreement with measurements have been verified over the years by thousands of users of these methods. A possible explanation for the deviation would be the confirmed presence of an SMA launcher in the real antenna model, which was additionally given as the explanation for the enormous ripple (see MWEE Feb. 2001 edition).

Figure 6: Geometry of a vivaldi antenna

User friendliness, along with the accuracy and speed of calculations, is an important criterion of modern CAE packages. Often a large part of the time available for design and analysis will be used for the inputting of data. The input times submitted by the competitors vary greatly. They range from 10 to <120 minutes. Many customers have already certified that CST MICROWAVE STUDIO® has the most easy to use interface of all EM simulation programs. Ironically, the makers of this software submitted the longest input time.

We leave it up to you and your experience of interpreting technical drawings, inputting structures, setting up simulation boundary conditions and the parametrisation of models, to determine how realistic a complete input time of 15 minutes is for such a structure. CST believes that only realistic input times are of any use to readers of this Benchmark. We therefore stand by our statement of <120 minutes, which implies that an experienced user, with a CAD interface as user-friendly as present in CST MICROWAVE STUDIO®, could also achieve substantially shorter times.

**Microwave Engineering Europe** have unveiled their CAD Benchmark
2000 - a free space electromagnetic problem based on a balanced antipodal Vivaldi
antenna. The results achieved using CST MICROWAVE STUDIO can be viewed here or
alternatively on the MEE website.

The Vivaldi Antenna was modelled with CST MICROWAVE STUDIO. The structure was built as a fully parametric model and the real thickness of the metallic layers (17µm) was taken into account.

Figure 7: Model geometry

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

Figure 8: S-Parameter

This plot shows E-Plane co-polar and H-Plane cross-polar directivity at 10GHz. For this far field plot the coordinate system was oriented so that the z-axis was parallel to the main lobe.

Figure 9: E-Plane co-polar and H-Plane cross-polar plots

This plot shows the E-Plane cross-polar and H-Plane co-polar directivity at 10GHz. For this far field plot the coordinate system was oriented so that the z-axis was parallel to the main lobe.

Figure 10: E-Plane cross-polar and H-Plane co-polar plots

This plot shows a contour plot of the electric near field at 10 GHz.

Figure 11: Contour plot

This plot shows a vector plot of current distribution on the antenna at 10 GHz.

Figure 12: Current distribution

A fast calculation of the S-parameters for the desired frequency range 0 - 10GHz was performed within 15 minutes on a 800MHz PIII. The results of this quick calculation are in excellent agreement with a second simulation made for the whole frequency band (0 - 20GHz) using a refined mesh. This high accuracy solution for the whole frequency range 0 - 20GHz was obtained in 64 minutes on the same PC and required about 100MB memory .

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

The Benchmark's simulation was performed with version 2.1 of CST MICROWAVE STUDIO®. 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.

As an optional extra, MWEE had challenged the participants to calculate results for the 10 - 20 GHz range. Unfortunately MWEE neither presented the measured results for this range, nor published a comparison of the submitted simulation results. It is precisely in this frequency range that the widely differing abilities of the methods would have appeared most clearly, due to the problem size in wave lengths and the resulting increase in the number of mesh node points.

A comparison of the data provided by the individual competitors revealed the clear superiority of the Time Domain with regards computation time and memory requirements.

### The Finite Element program, Ansoft’s "HFSS", needed 143 minutes for the frequency range 0 - 10 GHz, whereas CST MICROWAVE STUDIO™ only needed 15 minutes and with a memory requirement eight times smaller.

No results from HFSS were published for the frequency range 10 - 20 GHz.

CST MICROWAVE STUDIO® produced results for this frequency range within 15 minutes, but as it turned out, to achieve our desired high levels of accuracy at 20 GHz, a finer discretisation and therefore a longer computation time (up to 64 minutes) was necessary.

CST Article "Vivaldi Antenna"

last modified 19. Jan 2009 3:14

printed 2. Jul 2015 7:14, Article ID 15

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