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array modeling

powerpoint presentation modeling antenna arrays with matching and decoupling

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array modeling

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  1. Optenni Lab – Antenna Array Analysis in Version 4.3 Optenni Ltd. 2019 www.optenni.com ©2019 Optenni Ltd. All rights reserved.

  2. Contents This tutorial shows how Optenni Lab can be used to assess antenna arrays and synthesize matching circuits for them The emphasis is on studying the effect of matching circuits and non-idealities on arrays, arising from mutual coupling (space limited designs), and varying environments (edge vs. center elements over a finite ground plane) The correction of excitation vectors due to matching circuits can be done in Optenni Lab Beamforming and active reflection coefficients will be introduced and studied Note: You need to have Optenni Lab Professional Edition to go through this tutorial example! It is assumed that you are familiar with the tutorial “1b – Optenni Lab basics” • • • • • • www.optenni.com 2 ©2019 Optenni Ltd. All rights reserved.

  3. Antenna Arrays: Theory An array is an antenna comprised of a number of radiating elements whose inputs are combined (IEEE definition) If the current distributions of the elements only vary by a constant phase and amplitude, the resulting radiation pattern can be analytically calculated as a product of the individual element pattern and array factor Many analytical formulations exist for beamforming of ideal arrays towards different goals – linear and equally spaced arrays for simplicity – binomial arrays for no side lobes – Dolph-Chebyschev arrays for optimum directivity – Schelkunoff polynomial array method for creating nulls etc. • • • www.optenni.com 3 ©2019 Optenni Ltd. All rights reserved.

  4. Example Array Let us study an array consisting of four identical dipoles spaced /2 from each other at 2.4 GHz Open a new Optenni Lab instance and read in the S-parameter data 4_element_dipole_array.s4p (File\Read Impedance File…) The elements are originally not well matched at the frequency of interest and the cross-terms are very small • • • 4 www.optenni.com ©2019 Optenni Ltd. All rights reserved.

  5. Bandwidth Potential Using Analyze\Bandwidth Potential we can quickly approximate how much bandwidth a port can provide at a certain matching level – Using conjugate match provides a quick result, but optimizing symmetric bandwidth gives a more realistic result with a 2-component matching circuit – Check leave other ports open to isolate the other ports for the moment – The dipoles should be easy to match for the WiFi band (2.4-2.483 GHz) at -20 dB matching! • www.optenni.com 5 ©2019 Optenni Ltd. All rights reserved.

  6. EM Isolation If we use Analyze\Electromagnetic Isolation… for the port pairs, we can find out the worst case coupling in the scenario that the selected port pair is perfectly matched – Again, we can choose to leave other ports open while considering a particular pair – In the S-parameters the strongest cross term (Sxy) was only some -27 dB whereas EM Isolation calculation gives about -15 dB – S-parameter cross terms of poorly matched array elements are in general not a good figure of merit for coupling analysis • www.optenni.com 6 ©2019 Optenni Ltd. All rights reserved.

  7. Importing Radiation Patterns • Read in the radiation patterns for all ports with File\Radiation Pattern Data • You can view the element patterns under Radiation patterns folder in project tree, choosing 90 degrees horizontal cut at 2.4 GHz. The array lies now along the radial axis at phi = 0° – Use manual scaling to better see for instance the -3 dB bandwidth, in the figure on the right the scale goes from -6 dB to -1 dB www.optenni.com 7 ©2019 Optenni Ltd. All rights reserved.

  8. Example Array: Radiation Patterns There are significant effects due to the reflections from the nearby elements – The minima at 0° and 180° are caused by the shadowing of the other elements for ports 2 and 3 (center elements) – For ports 1 and 4 (edge elements) only one of the minima is caused by the shadowing, whereas the other is caused by destructive interference – If you were to look at the patterns at any other frequency, the minima caused by the destructive interference would disappear or even become a maxima • Element 4 Element 3 Element 1 Element 2 www.optenni.com 8 ©2019 Optenni Ltd. All rights reserved.

  9. Example Array: Unmatched Performance To analyze the performance as an array, go to Multiport\Multiantenna Matching…, click a circuit, choose the “Manual topology creation” radio button and “Copy settings to other ports” checkbox + OK Under the frequencies tab, choose the WiFi/BT band at 2.4 GHz and Copy to other ports + OK x 2 • • www.optenni.com 9 ©2019 Optenni Ltd. All rights reserved.

  10. Unmatched Performance Right-click the plot > Select plot items…, and leave all S11, S22, S33… and Efficiency terms selected, and clear the rest The total efficiency is only some -7 dB – This is to be expected, as majority of the power is reflected, as illustrated by the Power Balance plot, which can be activated from the Plot Selection window The coupling is in practise negligible for the non-matched array • • • www.optenni.com 10 ©2019 Optenni Ltd. All rights reserved.

  11. Antenna Arrays: Beam Steering To study beam steering in Optenni Lab, port excitations must be defined by either activating the radiation pattern plot in the Plot Selection window, or going to Multiport\Enter Port Excitations – Use voltage input for this exercise Linear arrays become broadside arrays if they have a progressive phase shift of 0 and endfire arrays if the progressive phase shift is 180 Binomial arrays have the same phase shift requirements as linear arrays, but their amplitude coefficients are taken from Pascal’s triangle • • • www.optenni.com 11 ©2019 Optenni Ltd. All rights reserved.

  12. Steering the Beam of the Example Array As can be seen in the figures below, taken at 2.4 GHz horizontal cut, the array pattern can be steered exactly as the theory predicts! (plots scaled from -30 dB to 10 dB) – The binomial arrays do indeed have nearly zero side lobe level, which comes at the price of a lower directivity, i.e, broader main beam • Binomial: 1∠0°, 3∠180°, 3∠0°, 1∠180° Binomial: 1∠0°, 3∠0°, 3∠0°, 1∠0° Linear: 1∠0°, 1∠0°, 1∠0°, 1∠0° Linear: 1∠0°, 1∠180°, 1∠0°, 1∠180° www.optenni.com 12 ©2019 Optenni Ltd. All rights reserved.

  13. Steering the Beam of the Example Array It is interesting to see that the 4 element array can be used as a 2 or 3 element array as well We may notice that the attainable directivity of the array increases with the number of elements in the array • • 1∠0°, 1∠0°, 0, 0 1∠0°, 2∠0°,1∠0°,0 1∠0°, 3∠0°,3∠0°,1∠0° www.optenni.com 13 ©2019 Optenni Ltd. All rights reserved.

  14. Matching the Array Calculation of the total efficiency involves recombining the radiation patterns and integrating the radiation efficiencies from there – Therefore, to speed up optimization, it is wise to resample the data (use 5 points over 2.4 – 2.483 GHz, File\Resample Impedance Data) Choose Multiport\Multiantenna matching… Click on a circuit and choose Automatic topology creation: number of components = 2 – Remember to check “Copy settings to other ports” to save some labour! • • • www.optenni.com 14 ©2019 Optenni Ltd. All rights reserved.

  15. Example Array – Matched Performance The synthesis may take 5-10 min or so After the synthesis, one can resample back to the original frequency data Choose the first topology suggested by Optenni Lab to replicate the following results (P1:PLSC, P2:PCSL, P3:PCSL, P4:PCSL) The array performance has increased over 5 dB per element! – However, the coupled loss increases, i.e., now with well matched ports, the coupling terms are very close to the EM Isolation results • • • • www.optenni.com 15 ©2019 Optenni Ltd. All rights reserved.

  16. Steering the Beam of the Matched Array Something seems to be amiss, the patterns no longer are as theory predicts with the excitation vectors Could the increased coupling have ruined the operation? • • Linear: 1∠0°, 1∠0°, 1∠0°, 1∠0° Binomial: 1∠0°, 3∠0°, 3∠0°, 1∠0° Linear: 1∠0°, 1∠180°, 1∠0°, 1∠180° Binomial: 1∠0°, 3∠180°, 3∠0°, 1∠180° www.optenni.com 16 ©2019 Optenni Ltd. All rights reserved.

  17. Effect of the Matching Network If we have a look at the matching circuit and/or the smith chart, the problem becomes quite clear The ports have non-identical matching circuits (port 1 is different) and hence the antenna excitation phase and/or amplitude are no longer in sync with port excitation! Moreover, even with relatively small coupling, the coupled power also changes the amplitude and phase at each antenna input! • • • www.optenni.com 17 ©2019 Optenni Ltd. All rights reserved.

  18. Compensating for the Matching Circuit The port 1 topology is different Optenni Lab includes a tool to compensate for this: right-click on the circuit and choose Show excitation at antenna ports After some iterations correcting the feeds, one can recover the wanted voltages and phases at the antenna input • • • 0.59∠338°,1.4∠ − 105°, 1.5∠80°, 0.54∠302° 1∠0°, 3∠180°, 3∠0°, 1∠180° Iterations Not 3 times larger! Not 180 degrees phase shift 18 www.optenni.com ©2019 Optenni Ltd. All rights reserved.

  19. Poorly Isolated Array Example Sometimes the spatial requirements force to place the elements rather close to each other, resulting in mutual coupling between the array elements Also varying environments, arising e.g. from finite ground planes, change the radiation properties of the antennas Both of these factors change the current distributions on the array elements and hence deteriorate the array approximation! Let us next consider a four element monopole array over a small ground plane • • • • www.optenni.com 19 ©2019 Optenni Ltd. All rights reserved.

  20. Poorly Isolated Array: Initial Performance Open a new Optenni Lab instance and read in the S-parameter data 4_element_monopole_array.s4p as well as the corresponding radiation patterns All of the elements have a shift in resonance and the operation of edge elements varies significantly from those at the centre The EM Isolation is much poorer than with the dipole array, which will most likely affect the array performance • • • www.optenni.com 20 ©2019 Optenni Ltd. All rights reserved.

  21. Poorly Isolated Arrays: Beamforming Let us resample the data from 1.2 GHz to 3 GHz in 10 MHz steps • If we try to replicate the linear array results, we quickly realize that especially the endfire array does not operate as expected: the radiation intensity is rather small nor does its maxima locate in the expected directions! • The reason is rather simple: now excitation in any port causes significant currents in all other ports → the radiation patterns are no longer independent → the array approximation is ruined • Broadside: 1∠0°, 1∠0°, 1∠0°, 1∠0° Endfire:1∠0°, 1∠180°, 1∠0°, 1∠180° www.optenni.com 21 ©2019 Optenni Ltd. All rights reserved.

  22. Poorly Isolated Arrays: Correcting the Excitations In other words: the coupling between the elements is too high for the array approximation being useful This doesn’t mean that endfire pattern couldn’t be found – the process just becomes more involved • • Manully corrected endfire: 1∠0°, 1∠60°, 1∠ − 140°, 1∠200° www.optenni.com 22 ©2019 Optenni Ltd. All rights reserved.

  23. Total System Efficiencies If we compare per-port total efficiencies and the total system efficiency of broadside, endfire and corrected endfire excitations, we notice that the different excitations result in very different total system efficiencies – The broadside excitation has the highest efficiency, higher than any of the individual port efficiencies – The corrected endfire excitation has about the same efficiency as the individual ports – The endfire excitation has (by far) the poorest efficiency • www.optenni.com 23 ©2019 Optenni Ltd. All rights reserved.

  24. Total Efficiency vs. Total System Efficiency There is a major difference between total efficiency and total system efficiency – Total efficiency is calculated for each port when a single port is excited at a time and the other ports are terminated by their matching circuits – Total system efficiency is calculated for a given excitation vector as the ratio of radiated power from the array and the sum of available powers from the ports As the power propagates from one port to another upon the simultaneous excitation, the classical definition of reflection and transmission coefficients no longer properly describe the impedance of the port ➢ Active reflection coefficients (ARCs) are needed • • www.optenni.com 24 ©2019 Optenni Ltd. All rights reserved.

  25. Active Reflection Coefficients If both ports of a 2-port system are excited simultaneously, the wave traveling backwards at port one can be expressed as ??= ?????+ ????? The active reflection coefficient of port one is defined as ????=?? • • ??=?????+????? ?? – Part of the forward traveling wave of port 2 becomes part of the backward traveling wave in port 1 and visa versa! If the mutual coupling term ???is very small, the equation for active reflection coefficient reduces to the classical one, yielding ????≈????? ?? • = ??? www.optenni.com 25 ©2019 Optenni Ltd. All rights reserved.

  26. Active Reflection Coefficients - Effect of Phase ARCs determine the load impedance seen by the beam steering amplifier – PA does not distinguish reflected and coupled waves If the mutual coupling between array elements is high, ARC may vary from the reflection coefficient significantly, and it may improve or deteriorate the element matching The graphs below illustrate this: “reflected” represents the ?????term, while “coupled” is the ?????term with a few phase shifts As can be seen, some phase shifts improve the matching while some others deteriorate it, compared to S11 • • • • www.optenni.com 26 ©2019 Optenni Ltd. All rights reserved.

  27. ARCs for the Poorly Isolated Array Beams Coming back to the poorly isolated array example, upon inspecting the ARCs it is rather clear, why the broadside array performs better than the endfire – The endfire edge elements’ ARC falls outside of the Smith chart With low isolation arrays it is always necessary to check the operation for each excitation vector to ensure that the total system efficiency and ARCs remain good! • • www.optenni.com 27 ©2019 Optenni Ltd. All rights reserved.

  28. Matching the Poorly Isolated Array Matching is done the same way as with the well isolated array Even with a relatively simple 2 component matching circuit, one can improve the performance quite significantly An upper limit for the efficiency is set by the coupling between the ports • • • www.optenni.com 28 ©2019 Optenni Ltd. All rights reserved.

  29. ARCs and Efficiencies for the Matched Array If identical matching circuits are used, there is no need to correct the excitation vectors – This can be enforced in Optenni Lab through the manual topology creation and copy/paste of circuits Even if the total system efficiencies were almost identical for different topologies, the phases of ARCs may vary significantly, which can have significant implications depending on the driving PA load-pull contours! • • Topology 1 Topology 2 www.optenni.com 29 ©2019 Optenni Ltd. All rights reserved.

  30. Loading and saving excitation vectors Since 4.3 SP1 it has been possible to save and load pre-determined excitations vectors This allows the user to use in-house scripts to generate the analytical excitation vectors for large arrays to certain directions, nulls and side lobe levels and then quickly evaluate with the realistic system behaviour the resulting radiation pattern, system efficiency and ARCs The format accepted is space separated values • • • www.optenni.com 30 ©2019 Optenni Ltd. All rights reserved.

  31. Antenna Arrays: Conclusions Optenni Lab provides diagnostics tools to asses antenna array performance Matching circuits can be synthesized to improve array total system efficiency For weakly coupled array, the excitation vectors can be adjusted to account for the presence of the (possibly asymmetric) matching circuits For highly coupled arrays it is crucial to study the attainable system efficiencies with desired beam directions – The feed vectors can no longer be analytically calculated, only approximated, and they have to be corrected by inspecting the total radiation pattern – High directivity beam may correspond to worse ARC than lower directivity beam, and eventually cause lower gain for the array Different matching circuits may result in identical total system efficiencies, but quite different ARCs, so from PA perspective one or the other may be preferred • • • • • www.optenni.com 31 ©2019 Optenni Ltd. All rights reserved.

  32. For more info visit www.optenni.com www.optenni.com ©2019 Optenni Ltd. All rights reserved.

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