512 Element Vivaldi Array

32x 16 El em en t UWB Vi v al d i

30dB Taylor Weighted Array

Simulati im ulation on Using si ng CST Stu Studi dio o Suite uit e 201 2011 1 ® , . Dr. James R Wil Willh lhit ite e 1

©2011 Sonnet S oftware, oftware, Inc. (315)453-309 (315)453-3096 6 [email protected]

32x16 Element Array

A 512 element wideband array was built and simulated in CST Microw Microwave ave S tudio. udio. The element elements s are on /2 centers at 10 GHz. , . . ”. 2

©2011 Sonnet S oftware, oftware, Inc. (315)453-309 (315)453-3096 6 [email protected]

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. ,“ 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 . . 3

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

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 at the UWB range, 3.1 to 10.6 GHz. 4


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 directed to a particular direction with a particular amplitude taper. 5


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 g ve a eam s ape. s cou e au oma ca y p ace y e array wizard or done manually. 6


Port Signals at Central Element excitation

array simulation

element simulation

Four separate simulations were done with the T-solver: an array simulation with all elements excited uniforml (all), the arra with a 30dB Ta lor weighting, 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 active returns and beams and the element simulation gives standard wideband S-parameters including couplings and element factors. 7


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 an infinite array with all elements excited and the single element match is not good because of coupling between elements. 8


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 (S304,272) & S336,272). Coupling is stronger above than to the side. 9


Near Fields for Uniform Excitation

. 10


Near Field for Excitation of

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Phi=0 Polar Cuts Thru Directivity Taylor weighted array

central element

arra

Far field monitors were defined for multiple frequencies over . 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 at 6.6 GHz

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Directivity vs. Frequency: 512

A set of far field monitors had been defined using a macro an n post process ng a ter one simulation far field properties could be obtained . . This figure shows the peak directivity vs. frequency from uniform and Taylor weighted elements and simulation of the . 14


Element & Array Beam Widths e eam w or e e emen factor is near 115° from 3 to 10.6 GHz and similar for both phi=0 and phi=90 . , beam width drops with frequency and differs by approximately 2dB between

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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 . damped out much faster than that for the central element.

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Solver Log for Array Simulation Steady state energy criterion met, solver stopped. ---------------------------------------------------------------------------Peak memory used (kB)

Free physical memory (kB)

Physical

At begin

Virtual

Minimum

---------------------------------------------------------------------------Matrices calc.

18701218

24396952

40922856

18544296

Solver run total

5844420

73338924

41078692

18453256

---------------------------------------------------------------------------Solver Statistics: Computer name:

BETH

GPU info:

1 GPU solver(s) used, type Tesla 2050 / 2070 GPU memory usage approx. 40 %

Number of threads used:

12

Number of mesh cells:

37781312

Excitation duration:

7.898997e-001 ns

Calculation time for excitation:

291

Number of calculated pulse widths:

3.27567

ea y s a e accuracy

m

:

s

-

Simulated number of time steps:

5628

Maximum number of time steps:

34362

Time step width: without subcycles: used:

4.597467e-004 ns 4.597467e-004 ns

Matrix calculation time:

3299

s

Solver setup time:

694

s

Solver loop time:

1048

s

Solver post processing time:

219

s

Total time:

5260

-----------s

( = 1 h, 27 m, 40 s )

-------------------------------------------------------------------------------Total simulation time:

17

5261

s

on a dual hex core desktop with a C2070 required 18.7 Gb of RAM and 1.5 hours. This would be near the requirements to simulate any given beam by adjusting the excitation list. Note that 0.9 hours were used in meshing the model. If other simulation were then run without modifying the geometry much less time would be spen n mes ng.

( = 1 h, 27 m, 41 s )


Solver Log for Central Element Steady state energy criterion met, solver stopped. ---------------------------------------------------------------------------Peak memory used (kB)

Free physical memory (kB)

Physical

At begin

Virtual

Minimum

---------------------------------------------------------------------------Matrices calc.

18701218

24396952

40922856

18544296

Solver run total

5738704

73052940

41063356

34385612

----------------------------------------------------------------------------------------------------------------------------------------------------------Solver Statistics: Computer name: GPU info:

BETH 1 GPU solver(s) used, type Tesla 2050 / 2070

single central element in the 512 element array re uired 1 hours and 57 minutes, 7002 seconds. However other elements

GPU memory usage approx. 40 % LP support activated Number of threads used:

1, lower corner of the array, required 4039 seconds to simulate.

12

Number of mesh cells:

37781312

Excitation duration:

7.898997e-001 ns

Calculation time for excitation:

278

Number of calculated pulse widths:

19.5761

Steady state accuracy limit:

-35

Simulated number of time steps:

33634

Maximum number of time steps:

34362

s dB

Time step width: without subcycles: used:

4.597467e-004 ns 4.597467e-004 ns

Matrix calculation time:

27

s

Solver setup time:

595

s

Solver loop time:

6164

s

Solver post processing time:

216

s

Total time:

7002

------------

18

s

( = 1 h, 56 m, 42 s )


Array Simulation in Design Studio

supp es a compan on c rcu simulator (Design Studio) with MWS. In that package you can model and do circuit simulation. 19


S-Parameter Task in DS

External ports can be automatically added to all open pins in the DS model and 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 Sparameters are available, only a quick circuit simulation will be done not an s mu a on. 20


DS Combine Results Simulation

n e - arame er s mu a on, e exc a on o e c rcu can e e ne 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 . , optimization could be done to define a beam shape. 21


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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