Numerical Modeling of Antenna Systems for the Square Kilometre Array SKA

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Numerical Modeling of Antenna Systems for the
Square Kilometre Array (SKA)
Rob Maaskant maaskant_at_astron.nl
The LOFAR High Band Antenna
Tile of densely packed Vivaldi elements
In collaboration with - Eindhoven University of
Technology (Prof. Anton Tijhuis) - Penn State
University (Prof. Raj Mittra)
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The array modeling problem

• Any wideband densely packed array has significant
  mutual coupling
• Coupling is a positive thing (gives you
  bandwidth) but it should be properly taken into
  account
• Mutual interaction between elements
• Array truncation effects
• Under some conditions, for example in large
  aperture arrays, this can be simplified. However
  dense FPAs do not allow these simplifications.
• We need a full model for the array receiving
  system

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Modeling of large antenna arrays

• ASTRON concentrates on three activities to
  address the problem
• 1. Efficient methods
• Use the periodic nature of the structure to speed
  up computation
• Suitable for design
• In-house software development in collaboration
  with Eindhoven and Penn State University
• 2. Brute force
• Use the massive power of supercomputers (LOFAR
  BlueGene/L)
• Application final simulations and validation
• Penn State (GEMS)
• University of Manchester (FDTD)
• 3. System simulation

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CAESAR 2.0 (Computationally Advanced and
Efficient Simulator for ARrays)

• Efficient ElectroMagnetic (EM) Solver for
  Large Antenna Arrays
• MicroWave (MW) circuit simulator for signal
  and noise analysis
• The CAESAR software has been tailored to analyze
  receiver sensitivities of large antenna arrays
  efficiently

Technical report Getting Started written (124
pages)
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Solving antenna array problems using CBFM
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4557 unknowns (RWGs)
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Solving antenna array problems using CBFM
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4557 unknowns (RWGs)
Allocation of 3 Generating Sub-Arrays
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Solving antenna array problems using CBFM
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4557 unknowns (RWGs)
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1/2
Apply Windowing Technique
2 CBFs
3 CBFs
2 CBFs
Primary CBFs
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Solving antenna array problems using CBFM
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4557 unknowns (RWGs)
Use MoM to Determine CBF Expansion Coefficients
19 unknowns (primary CBFs)
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Results for disconnected arrays (LOFAR HBA)

• IE3D 8186 unknowns, 2665 sec. (Brute Force)
• CBFM 8160 unknowns, 180 sec. (All in MATLAB)
• We gain a speed advantage of 15 times without
  compromising the accuracy

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Results for disconnected arrays (LOFAR HBA)
Mutual impedance Z1x between the corner and other
array elements
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Results for disconnected arrays (cont.)
CAESAR 2.0 A 20x20x2 array of Bow-Tie elements

• Using translation symmetry, only 761 moment
  sub-matrix blocks had to be constructed instead
  of all 400400 sub-matrices
• Initial number of unknowns 47200 RWGs
• Total simulation time 24 min. and 45 sec.

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Results for connected single-polarized arrays
?5?
RWGs 93924 CBFs 1080 Meshing time
40 sec. CBF Generation time 4 min. 43
sec. Matrix Construction Time 17 min. 46
sec. Total CPU time 26 min. 41
sec. (including pattern calculations)
Edge truncation effects
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Combining electromagnetic models with microwave
circuits models
System Modeling

High S/N
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Study of the noise coupling mechanism
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R. Maaskant, B. Woestenburg, Applying the Active
Antenna Impedance to Achieve Noise Match in
Receiving Array Antennas, IEEE AP-S
International Symposium, Honolulu, Hawaii, June
2007.
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Combining antenna EM-models with MW-circuit models
Prototype Array
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In progress validation for small and very large
arrays
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In progress modeling of a 8x7x2 Vivaldi Array
Measurements
Simulations
114.667 unknowns reduced to 2968 unknowns
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In progress a multi-scale antenna problem
arrays of subarrays

• Number of RWGs 375192
• Number of CBFs 4320
• Meshing Time 40 min.
• Total Solve Time 5hr. 50 min. (Single CPU
  1.73 GHz, 2.0 GB RAM)

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Summarizing

• The CAESAR software is being developed to analyze
  the receiver sensitivity of large antenna array
  systems

• More research is needed to deal with increasingly
  larger and complex problems (computational
  efficiency, accuracy, robustness, etc.)