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ADVANCED TECHNIQUES FOR THE SYNTHESIS OF WIDEBAND ARRAY ANTENNAS

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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

______________________

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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.

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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

B

for an aperture lying over

an infinitely long PEC cylinder ... 55

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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

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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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advantage of deterministic aperiodic arrays is that, due to the fact that their element positions can be described by simple equations their synthesis to achieve a desired pattern can be performed in a more straightforward manner having to deal with a reduced number of parameters. A further major advantage of self-similar spiral arrays compared to completely randomised ones, is the reduced construction costs as a result of the minimisation of conduits, power cables, optic fibres, etc., obtained by following the spiral path.

Therefore in chapter 1, after describing the flow-chart of the synthesis algorithm, the constrained multi-objective algorithm has been employed for optimizing aperiodic arrays whose elements are arranged in concentric rings or spirals. Several optimized designs, including some constraints of both electromagnetic and geometric nature, are presented and commented.

Next, in the following chapter 2, the interest is focused on designing a wideband miniaturized loaded single-element antenna that can be employed as the basic radiating element for wideband antenna arrays. As a matter of fact, especially when dealing with lower frequencies, making the antenna resonating would imply an antenna comparable in size with the considered wavelength, usually resulting in a very large structure. In order to miniaturize the antenna as well improve both the voltage standing wave ratio (VSWR) and the gain performance, loading the antenna with lumped RF components can improve its broad-band characteristics considerably. Hence an efficient novel technique for miniaturizing broadband loaded antennas has been developed. The procedure relies on the application of a two-level evolutionary genetic algorithm (GA), accounting for either the design geometric variables or the position, the connection type (series / parallel circuits) and the values of each loading circuit component. Furthermore, in order to include the mutual coupling effects in the optimization process, the surrounding operating environment has been introduced in the evaluation of the antenna performance.

In the final chapter 3 conformal antenna arrays, i.e. several aperture antennas lying over

a infinitely long perfectly electric conducting cylinder, have been investigated. Particularly, a

full wave Mode Matching (MM)/ Finite Element (FE) / Method of Moments (MoM) hybrid

approach has been jointly employed with the spectral rotation technique for the analysis of

arbitrarily shaped single element and array aperture antennas with radiating apertures on an

infinitely long perfectly electric conducting cylinder. In addition two synthesis techniques of

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such an aperture antenna array, either narrowband or wideband, including mutual coupling

effects have been developed.

Riferimenti

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