512 element vivaldi array

32x16 Element UWB Vivaldi ArrayArray

30dB Taylor Weighted Array

Simulation Using CST Studio Suite 2011Microwave Studio at Sonnet Software Inc

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2011 Sonnet Software, Inc. (315)453-3096 [email protected]

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Microwave Studio at Sonnet Software, Inc.Dr. James R Willhite

32x16 Element Array

A 512 element wideband array was built and simulated in CST Microwave Studio. The elements are on /2 centers at 10 GHz. The array ground plane is 48x24 cm 18 9x9 45


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The array ground plane is 48x24 cm, 18.9x9.45 .

Vivaldi Unit Cell

The unit cell of the array is a Vivaldi radiator based on work reported by researchers at the University of Mass; H. Holter, T. Chio, and D. Schaubert Experimental Results of 144 Element Dual PolarizedSchaubert, Experimental Results of 144-Element Dual-Polarized Endfire Tapered-Slot Phased Arrays, IEEE Trans. Ant. Prop., 48, pp 1707-1718, Nov. 2000. The element is shown here with a cut plane to reveal the stripline feed The element was scaled to the UWB range


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reveal the stripline feed. The element was scaled to the UWB range.

Unit Cell Return

The return for the Vivaldi element simulated with periodic boundaries shows a broad band good match from 2 to 11 GHz. This was aimed


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at the UWB range, 3.1 to 10.6 GHz.

CST Array Wizard

After the unit cell was designed, it was used in a macro to construct an array. The array wizard could be used to set an excitation for a beam


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y ydirected to a particular direction with a particular amplitude taper.

Simultaneous Excitation

Using the T-solver the default source type is one port at a time. However a Selection can be done to define an Excitation List. In this list particular ports can be selected for excitation. A Simultaneous excitation could be activated and an amplitude/phase table defined to gi e a beam shape This co ld be a tomaticall placed b the arra


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give a beam shape. This could be automatically placed by the array wizard or done manually.

Port Signals at Central Elementexcitation

array simulation

element simulation

Four separate simulations were done with the T-solver: an array simulation with all elements excited uniformly (all), the array with a 30dB Taylor y ( ), y yweighting, and element simulations of the array with only a central element (272) or the corner element (1) excited. In the element simulation all ports were terminated but only one excited. The array simulations gives the


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active returns and beams and the element simulation gives standard wideband S-parameters including couplings and element factors.

Active and Standard Returns

The returns differ with location of the element (S1,all and S272,all) and between single element excitations and array simulations (S272,272 and S272,all). The element had been designed as if in


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an infinite array with all elements excited and the single element match is not good because of coupling between elements.

Return & Coupling

This figure shows some of the S-parameters with the central element (272) excited. The return (S272,272) is shown as well as coupling to the first 2 elements to the side (S273,272 & S274,272) and above


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( , , )(S304,272) & S336,272). Coupling is stronger above than to the side.

Near Fields for Uniform Excitation of 32x16 Arrayof 32x16 Array

The field is at 4 GHz and the elements are on /2 centers at 10 GHz


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The field is at 4 GHz and the elements are on /2 centers at 10 GHz.

Near Field for Excitation of Central Element in 32x16 ArrayCentral Element in 32x16 Array


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Phi=0 Polar Cuts Thru Directivity

arraycentral element

Taylor weighted array

array

Far field monitors were defined for multiple frequencies over the band This figure shows thethe band. This figure shows the directivity at 6.6 GHz for the full array simulations and for excitation of only a central element (element factor). The side lobe level was -30.3dB for the Taylor weighted array.


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Broadside Un-Weighted Directivity for 512 Element ArrayDirectivity for 512 Element Array

at 6.6 GHz


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Directivity vs. Frequency: 512 element array and elementelement array and element

A set of far field monitors had been defined using a macro

d i t i ftand in post processing after one simulation far field properties could be obtained vs frequencyvs. frequency.This figure shows the peak directivity vs. frequency from simulations of the array withsimulations of the array with uniform and Taylor weighted elements and simulation of the central element alone


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central element alone.

Element & Array Beam WidthsTh 3dB b idth f th l tThe 3dB beam width for the element factor is near 115 from 3 to 10.6 GHz and similar for both phi=0 and phi=90 cuts For the 32x16 element array thecuts. For the 32x16 element array, the beam width drops with frequency and differs by approximately 2dB between the uniform and weighted arrays.the uniform and weighted arrays.


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Field Energy

Simulations in the time domain are normally terminated when the energy in the model has dropped to a set level. For MWS the default is -30dB but this was changed to 35dB for this study The full array simulationthis was changed to -35dB for this study. The full array simulation damped out much faster than that for the central element.


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Solver Log for Array SimulationSteady state energy criterion met, solver stopped. The simulation was done----------------------------------------------------------------------------

Peak memory used (kB) Free physical memory (kB) Physical Virtual At begin Minimum

----------------------------------------------------------------------------Matrices calc. 18701218 24396952 40922856 18544296 Solver run total 5844420 73338924 41078692 18453256

The simulation was done on a dual hex core desktop with a C2070 GPU accelerator. It

----------------------------------------------------------------------------Solver Statistics:

Computer name: BETH GPU info: 1 GPU solver(s) used, type Tesla 2050 / 2070

GPU memory usage approx. 40 %LP support activated

GPU accelerator. It required 18.7 Gb of RAM and 1.5 hours. This would be near the requirements LP support activated

Number of threads used: 12

Number of mesh cells: 37781312Excitation duration: 7.898997e-001 ns Calculation time for excitation: 291 sNumber of calculated pulse widths: 3.27567 St d t t li it 35 dB

qto simulate any given beam by adjusting the excitation list.

Steady state accuracy limit: -35 dB Simulated number of time steps: 5628 Maximum number of time steps: 34362 Time step width:

without subcycles: 4.597467e-004 nsused: 4.597467e-004 ns

Note that 0.9 hours were used in meshing the model. If other simulation

Matrix calculation time: 3299 sSolver setup time: 694 sSolver loop time: 1048 sSolver post processing time: 219 s

------------Total time: 5260 s ( = 1 h, 27 m, 40 s )

were then run without modifying the geometry much less time would be

t i hi--------------------------------------------------------------------------------Total simulation time: 5261 s ( = 1 h, 27 m, 41 s )


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spent in meshing.

Solver Log for Central ElementSteady state energy criterion met, solver stopped.

---------------------------------------------------------------------------- The simulation of thePeak memory used (kB) Free physical memory (kB) Physical Virtual At begin Minimum

----------------------------------------------------------------------------Matrices calc. 18701218 24396952 40922856 18544296 Solver run total 5738704 73052940 41063356 34385612 ----------------------------------------------------------------------------

The simulation of the single central element in the 512 element array required 1 hours and 57

--------------------------------------------------------------------------------Solver Statistics:

Computer name: BETH GPU info: 1 GPU solver(s) used, type Tesla 2050 / 2070

GPU memory usage approx. 40 %

required 1 hours and 57 minutes, 7002 seconds.However other elements require less time. ElementLP support activated

Number of threads used: 12

Number of mesh cells: 37781312Excitation duration: 7.898997e-001 ns Calculation time for excitation: 278 sNumber of calculated pulse widths: 19.5761

require less time. Element 1, lower corner of the array, required 4039 seconds to simulate.

Steady state accuracy limit: -35 dB Simulated number of time steps: 33634 Maximum number of time steps: 34362 Time step width:

without subcycles: 4.597467e-004 nsused: 4.597467e-004 ns

Matrix calculation time: 27 sSolver setup time: 595 sSolver loop time: 6164 sSolver post processing time: 216 s

------------Total time: 7002 s ( = 1 h, 56 m, 42 s )


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Array Simulation in Design Studio

CST li i i itCST supplies a companion circuit simulator (Design Studio) with MWS. In that package you can add additional blocks to the MWS


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add additional blocks to the MWS model and do circuit simulation.

S-Parameter Task in DS

External ports can be automatically added to all open pins in the DS model p pand a task such as an S-Parameter simulation defined. If the matrix for the MWS model is not available that model would be first simulated. If all S-parameters are available, only a quick circuit simulation will be done not an EM sim lation


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EM simulation.

DS Combine Results Simulation

I th DS S P t i l ti th it ti f th i it b d fi dIn the DS S-Parameter simulation, the excitation of the circuit can be defined and the amplitude and phase of each port could be set as parameterized values. If the Combine results box is checked, an array beam will be generated Any given array could be defined to give active returns and


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generated. Any given array could be defined to give active returns, and optimization could be done to define a beam shape.

Summary for Array Simulations If all 512 elements of the array needed to be excited

individually to a -35 dB accuracy this would require between 1000 and 575 hours (41.5 and 24 days) on a single computer similar to the one used in this study.

If only the S-matrix were needed, the symmetry of the array could be used to reduce the time by a factor of 4.

A significant improvement in speed would happen if distributed computing were used to spread the simulations for different ports over a cluster of computers. N computers would reduce the time by nearly a factor of N.

If an 8-node cluster were available each with one or 2 GPUs, the time would be reduced to between 3 and 5 days for obtaining full element factors.

In 5 days approximately 82 beam patterns with associated broadband active return sets could be obtained on one computer similar to that used in this study.


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512 element vivaldi array

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