CICLO XXVI – ANNO 2012 SSD ING-INF/02
C ORSO DI D OTTORATO DI R ICERCA IN
TELERILEVAMENTO
PhD Thesis
ADVANCED TECHNIQUES FOR THE SYNTHESIS OF WIDEBAND ARRAY ANTENNAS
Tutors:
Prof. Ing. Agostino MONORCHIO
____________________________
Prof. Ing. Guido BIFFI GENTILI
____________________________
Candidate:
Davide BIANCHI
______________________
A BSTRACT
Antenna arrays are the most effective solution for radiating systems that need high
directivity and low sidelobe level, such as radio astronomy, remote sensing, and radar
applications. Typically, antenna arrays are only designed for narrowband applications, thus
several radiating systems are to be employed, one per each operating bandwidth. Recently,
with the aim of reducing the number of antenna system onboard a vehicle, such as aircrafts,
satellites or terrestrial vehicles, a great interest has been focused on techniques for designing
wideband antenna arrays. Therefore most of the dissertation deals with novel techniques for
the synthesis of both narrowband and wideband planar antenna array, aiming to provide a
pretty good wide-angle scanning while imposing several constraints to meet imposed by the
designer. In addition, an advanced technique for the synthesis of a wideband miniaturized
single-element antenna placed in realistic environments has been developed. Furthermore an
hybrid technique for the analysis of conformal arrays of antennas as well several synthesis
procedures have been developed. Mutual coupling has been also taken into account.
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To my parents, my relatives and everyone close to me.
A CKNOWLEDGMENTS
First, I would like to thank my parents for allowing me to realize my own potential. All the support they have provided me over the years was the greatest gift anyone has ever given me. Also, I need to thank Prof. Monorchio for encouraging me to pursue my Ph.D., for reading this thesis and sharing his knowledge on electromagnetics. Next, I need to thank all the people who create such a good atmosphere in the lab, particularly Dr. Simone Genovesi, who spent countless hours in the lab explaining and showing me how to do everything and for sacrificing his time to help me. I would also like to thank Prof. Guido Biffi Gentili for giving me important feedbacks for all the 3 years of my Ph. D.. Finally, I would like to thank Dr. D.
H. Werner for allowing me to join the Computational Electromagnetics and Antennas
Research Lab (CEARL) at the Pennsylvania State University, University Park, PA (USA).
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I NDEX
Abstract ... 2
Acknowledgments ... 4
Index ... 5
List of Acronyms ... 7
Introduction ... 8
1 Constrained Pareto Optimization of Wide Band and Steerable Concentric Ring Arrays ... 11
1.1 Constrained Pareto Optimization ... 12
1.2 Concentric Ring Arrays Optimization ... 17
1.3 Concentric Ring Array Design as a Benchmark for Multi-objective Constrained Optimization ... 18
1.4 Optimization Results: Concentric Ring Array synthesis ... 21
1.4.1 Constrained optimization of PSLL and HPBW ... 22
1.4.2 Constrained optimization of SLL for broadside and steered direction ... 26
1.4.3 Constrained Optimization of wideband CRAs ... 29
1.5 Wideband Spiral Array synthesis ... 33
2 Broadband Antenna Miniaturization ... 36
2.1 Broadband antenna ... 36
2.1.1 Scattering matrix of a partially loaded n-port network ... 38
2.1.2 Fitness function Definition ... 40
2.1.3 Numerical resuls: Optimization of a wideband loaded multiple-arm monopole ... 41
3 Conformal Antenna Arrays ... 48
3.1 MM/ FEM / MoM Hybrid Approach for the Analysis of Arbitrary Shaped Single Element and Array Aperture Antennas Radiating on an Infinitely long PEC cylinder ... 49
3.1.1 Computation of the GSM for the Inner Part of the Horn Antenna... 49
3.1.2 Computation of the GSM for the Radiating Aperture by MoM ... 50
3.1.3 Evaluation of the source matrix I ... 52
3.1.4 Evaluation of the admittance matrix for the region A Y
A... 53
3.1.5 Evaluation of the admittance matrix for the region B Y
Bfor an aperture lying over
an infinitely long PEC cylinder ... 55
3.1.6 Evaluation of the Generalized Scattering Matrix for the Aperture ... 57
3.1.7 Coupling of GSM and evaluation of the outputs ... 57
3.1.8 Array Analysis: Computation of the GSM for the inner problem ... 59
3.1.9 Computation of the GSM for the Outer Problem and Coupling with the internal one 60 3.1.10 5-by-5 open-ended rectangular waveguide antenna array ... 69
3.2 Conformal array synthesis: single-frequency optimization ... 73
3.2.1 Least-Mean-Squares method including mutual coupling effects ... 73
3.2.2 The Method of alternating projections ... 75
3.2.3 Numerical results: design of a conformal 19-aperture antenna array ... 76
3.3 The Pareto Optimization of Wide-Band Conformal Antenna Arrays ... 79
3.3.1 Array Configuration and Basic Conformal Rps Array Performance ... 80
3.3.2 Numerical results: design of a conformal 2-stage rps array ... 83
Conclusions ... 86
References ... 88
Publications ... 94
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L IST OF A CRONYMS
AP: Alternating Projections CRA: Concentric Ring Array DFT: Discrete Fourier Transform E.M., e.m.: Electromagnetic FBW: Fractional Bandwidth FEM: Finite Element Method FFT: Fast Fourier Transform GA: Genetic Algorithm HF: High Frequency
HPBW: Half-Power Beamwidth
IEEE: Institute of Electrical and Electronic Engineering LMS: Least-Mean-Squares
MM: Mode Matching
MM/MoM/SD: Mode Matching / Method of Moment / Spectral Domain MOEA: Multi-Objective Evolutionary Algorithm
MoM: Method of Moment
NSGA-II: Non-dominated Sorting Genetic Algorithm version II PEC: Perfect Electric Conductor
PF: Pareto Front
PSLL: Peak Sidelobe Level
PSO: Particle Swarm Optimization RPS: Raised Power Series
RF: Radio Frequency
UTD: Uniform Theory of Diffraction VHF: Very High Frequency
VSWR: Voltage Standing Wave Ratio
I NTRODUCTION
A challenging task in array design is to synthesize an array working at multiple frequencies within a large frequency band, with constraints imposed to the radiation pattern in terms of side lobe level (SLL). This kind of array synthesis requires a multi-objective approach since there is no single solution which can be considered the best at the multiple investigated frequencies for all the compulsory requirements.
Generally, for the design of wideband large transmitting arrays is much more effective to use unequally spaced arrays than more traditional periodic array arrangements. One of the main advantages of aperiodic arrays is the possibility to reduce the number of elements in a given aperture and achieve the desired resolution by more widely spacing apart the radiating elements without major impact on the beamwidth and SLL, allowing also the realization of a more efficient and less costly system. In particular, contrarily to uniform arrays, aperiodic arrays can effectively be employed for spreading out the energy that would accumulate in grating lobes due to the wide inter-element spacing. Aperiodic arrays are also much more robust with respect to the correct placement of antenna elements.
A straightforward approach to design an aperiodic array is to randomly disperse the radiating elements over a given aperture with a suitable spatial density. Random arrays have demonstrated to suppress grating lobes, improving the SLL, and to provide good radiation performance over large bandwidths. However, random structures, while providing localization, are irreproducible and lack predictive and synthesis theoretical models.
Moreover, a completely random array configuration impede the use of generic building blocks and involve a more complex array infrastructure.
A more attractive strategy to the design of non-uniform arrays is to consider
deterministic aperiodic structures generated through some mathematical rule and number
theory, that manifest unique element localization and properties. Such a kind of structures
represents an intermediate situation between random and periodic ones, and can combine the
advantages of both of them. To this class of configurations belong, for example, aperiodic
planar arrays organized in concentric rings. Another interesting option to generate an aperiodic
configuration yet described by a deterministic law, is by sampling a self-similar geometry like
a spiral, whose scalable structure can have intrinsically wideband properties. A main
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