EM Software & Systems GmbH

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1 EM Software & Systems GmbH Otto-Lilienthal-Straße 36 D Böblingen GERMANY Telefon Telefax Web FEKO Benchmark to handle big antenna arrays Edited by Dr. Niels Berger, Tel / Benchmark problem The benchmark problem is a simplified example to show how big antenna arrays can be handled in the computer code FEKO. The point of interest is a e.g. 25 x 40 antenna array made with the patch antennas shown in Figure 1 with the patch size lambda/4 in square and the ground plane size of lambda/2 in square. The distance between patch and ground plane is lambda/20 and the offset of the feeding pin is lambda/3 from the centre shifted in x-direction. The problem is scalable but a frequency of 2.5 GHz was chosen. The array is extended in x- direction with 25 elements and in y-direction with 40 elements so there are in total 1000 Elements (as shown in Figure 2). The shifting distance in x- and y- direction is each time lambda. Figure 1: Single patch antenna element as base of a big array shown in the CADFEKO-window.

2 Figure 2: 25 x 40 antenna array based on the single patches. FEKO-Model of the single element The single element patch antenna was shown in Figure 1 already in the FEKO model its farfield pattern is given in Figure 3 with the meshed model. Figure 3: Meshed FEKO model of the single patch antenna with farfield pattern (gain in db). The radiation is mainly to top perpendicular to the patch but also to the bottom and the sides

3 FEKO-Model of a 3 x 3 array The idea to handle big arrays in FEKO is based on the calculation of a 3x3 array with switching each of the 9 elements on and all other elements off to derive its farfield pattern and to replace later each one element by the pattern of one of these 9 elements regarding its relative position. The 3x3 array considers the most important cases. The lower left element is in one corner and has the 8 neighbours considered in the simulation with the coupling and the losses in their loads. So the calculation will lead to 9 solutions for the farfield pattern, where all can be different to each other due to the different coupling and constellation (relative position in this neighbourhood). Lower left element number Upper right element number 9 Figure 4: 3x3 array FEKO model in CADFEKO. At the moment there is no automation to handle this switching on/off of the different elements and calculating the pattern each time. Especially the pattern must be calculated each time in respect of the correct phase centre within an offset coordinate system. This can be done in FEKO, but it has to be done in EDITFEKO. Figure 5 shows such an EDITFEKO window with the according PRE-file open. First the model is imported with all elements and labels. To have a better access to the label names, the feeding pin labels are renamed and the phase centre of each element is specified in an array variable. The calculation then is based on a FOR-NEXT loop over all 9 element sources and switching this on and a 50 Ohm load to all other elements before calculating for this element the full 3D farfield pattern from the given phase centre and with exporting the pattern to ASCII-file (FFE) for later usage

4 Figure 5: EDITFEKO-window to perform the 3x3 array calculation. This calculation is now based on 1877 triangular metallic elements and 9 feeding segments. This results in 2656 unknowns and a matrix size of about 55 MByte. The FEKO calculation requires for the 9 solutions and farfield calculations (5 resolution in theta and phi) about 9 min on an INTEL Xeon CPU with 2.4 GHz clock rate. The result is shown in Figure

5 Figure 6: Meshed FEKO model of the 3x3 array with the 9 patches and their farfield pattern (gain in db). Decomposed FEKO-Model of a M x N array The MxN array is realized in FEKO then with importing selectively one of the 9 patterns which has the same relative position as before (decomposed solution). So the pattern of the corner elements 1,3,7 and 9 are imported only once the pattern of the side elements 2,4,6 and 8 are imported for all side elements and the centre element 5 is imported for all elements which is not at a side or in a corner. FEKO can reuse already loaded patterns effectively, so there is a bigger advantage of this approach. Only this corner is based on element 1 Inner elements are based on former element 5 This side is based on element 6 Figure 7: FEKO-model of a 25 x 40 array based on the imported radiation patterns

6 This approach can be performed with EDITFEKO effectively in the PRE-file as shown in Figure 8, where such a parametric setup is shown. The number of elements is chosen here with 25 elements in x-direction and 40 elements in y-direction. Two FOR NEXT loops are required to specify the according position (shifted each time the same way as in the 3x3 array before!) and to select the correct pattern (e.g. former element number 5 for the inner part). This then allows deriving the correct entry point into the pattern file to be read. This information is stored as last solution to be able to refer to this in the next iteration. It is possible to specify for each of these 1000 elements an individual magnitude and phase, but for this test all elements are fed with the same amplitude 1 and phase 0. Figure 8: EDITFEKO window to perform the 25x40 array with pattern import. The big advantage of this approach here is that there is no mesh, no unknown, no matrix to be filled and solved. All array elements are impressed sources and the total pattern can be derived very fast and nearly no memory is required. In this example the FEKO calculation with same CPU as before requires now 10 MByte of memory and about 4 minutes to derive the full 3D farfield pattern but now with 1 DEG resolution to consider also the higher gain of this array

7 Figure 9: FEKO result of the decomposed solution for the 3D farfield pattern (gain in db) with 1 resolution together with the 1000 impressed farfield sources. This example was kept simple to be able to also calculate also exactly this situation with the Multi Level Fast Multipole Method (MLFMM). Reference FEKO-solution of this 25x40 array using MLFMM The meshed FEKO model of the 25x40 array is shown in Figure 2 and consists of triangular elements and 1000 feeding segments resulting in unknowns and would require about 1 TByte using classical MoM solver. FEK has also a very efficient exact solver for electrically large scale problems as given here (about 40 wavelength x 25 wavelength in size) which is called the MLFMM. It is an iterative solver, which avoids the setup of the full coupling matrix but only sets up matrices for the nearfield environment coupling but replaces the farfield coupling by efficient grouping and transformation algorithms, where initial approximate inaccuracies are removed iteratively, so that finally an exact solution can be found. For this given example FEKO requires on an AMD OPTERON CPU with also 2.4 GHZ clock rate about 2.1 GByte of memory (that s why a 64 bit machine was required) and - 7 -

8 115 minutes (less than 2 hours) to solve the current distribution and calculate the 3D farfield again with 1 resolution. Figure 10: FEKO result of the full MLFMM reference solution for the 3D farfield pattern (now directivity in db) with 1 resolution together with the 1000 meshed patch antenna elements. This is still some very good performance but as soon as e.g x 1000 elements shall be investigated FEKO still offers the efficient decomposed solution with the impressed patterns. If one now compares these two results for the 25 x 40 array, one first find an offset in the absolute gain/directivity value due to the influence of the presence/absence of losses (loads) in the reference/decomposed solution. If one the compares the shape of the vertical patterns and horizontal patterns one can find very well a good agreement between both as can be seen in Figure

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10 Figure 11: Two vertical patterns (phi=0 and phi=90 ) and the horizontal pattern (theta =90 ) to compare the reference solution (red) with the decomposed solution (blue). Summary FEKO is very well able to also handle more complex antenna arrays, but this simplified example shows the performance, features and methods/approaches to cope with such types of problems