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Fundamental Bounds on Performance of Periodic Electromagnetic Radiators and Scatterers
KTH, School of Electrical Engineering and Computer Science (EECS), Electrical Engineering, Electromagnetic Engineering.ORCID iD: 0000-0002-7057-6414
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, the optimal bandwidth performance of periodic electromagnetic radiators and scatterers is studied. The main focus is on the development and application of methods to obtain fundamental physical bounds, relating geometrical parameters, frequency bandwidth, efficiency and radiation characteristics of periodic electromagnetic structures.

Increasing demand on the performance of wireless electromagnetic systems in the modern world requires miniaturization, high data rates, high efficiency, and reliability in harsh electromagnetic environments. Attempts to improve all these design metrics at once confront the inevitable physical limitations. For example, an antenna’s size is fundamentally bounded with bandwidth performance, and attempts to decrease size result in reduced performance capabilities. Knowledge of such physical bounds is vital to achieve high performance: to gain an understanding of the trade-off between parameters and requirements, or to evaluate how optimal the realized design is.

Periodic structures are indispensable components in many wireless systems. As antenna arrays, they are in base stations of mobile phone networks, in radio astronomy, in navigation systems. As functional structures, they are used as frequency-selective filters, polarizers and metamaterials.

In this thesis, methods to construct fundamental bounds on Q-factor – a quantity inversely proportional to bandwidth – are presented for periodic structures. First, the Q-factor representation is derived in terms of the electric current density in a unit cell. Then, the bounds are obtained by minimizing the Q-factor over all current densities, that are supported in a specified spatial subset of a unit cell, with possibly additional constraints (e.g. on conductive losses, or on polarization) imposed.

Moreover, an alternative approach for obtaining fundamental bandwidth bounds is investigated – the sum rules, that are based on representing a physical phenomenon as a passive input-output system. Transmission of a plane wave through a periodically perforated metal screen is described by a passive system, and the sum rule bounds the transmission bandwidth with the static polarizability of the unit cell. Such a bound is shown to be tight for simulated and measured perforated screens.

Abstract [sv]

Den här avhandlingen undersöker den optimala prestandan av elektromagnetiska periodiska radiatorer och spridare. Huvudinriktningen är utveckling och tillämpning av metoder för att erhålla fundamentala fysikaliska begränsningar, som relaterar geometriska parametrar, bandbredd, verkningsgrad/effektivitet och strålningsegenskaper av periodiska elektromagnetiska strukturer.

Ökande krav på prestanda av trådlösa elektromagnetiska system driver fram miniatyrisering, hög datahastighet och hög tillförlitlighet i robusta elektromagnetiska miljöer. Försök att förbättra alla dessa designegenskaper på en och samma gång möter oundvikliga fysikaliska begränsningar. För antenner är deras bandbredd begränsad av antennens elektriska storlek, och försök att minska storleken resulterar i minskad prestanda. Kunskap om sådana fysikaliska relationer är avgörande för att uppnå hög prestanda: att öka förståelsen för kompromisser mellan olika parametrar, eller att avgöra hur optimal konstruktionen är.

Periodiska strukturer är viktiga komponenter i många trådlösa system. Till exempel gruppantenner, som finns i basstationer för mobiltelefonnätverk, i radioastronomi och i navigationssystem. Ytterligare exempel är funktionella strukturer som används som frekvensselektiva filter och metamaterial.

I denna avhandling presenteras metoder för att erhålla begränsningar av Q-faktorn, en storhet omvänt proportionell mot bandbredden för periodiska strukturer. Först bestäms Q-faktorn i termer av ytströmstätheten i en enhetscell. Sedan bestäms begränsningar genom att minimera Q-faktorn över alla möjliga strömstätheter i en delmängd av en enhetscell, med möjligtvis ytterligare restriktioner (t. ex. resistiva förluster).

I denna avhandling kommer även ett alternativt förhållningssätt för att uppnå fundamentala bandbredds begränsningar att undersökas – summaregler, baserade på att framställa ett fysikaliskt fenomen som ett passivt input-outputsystem. En överföring av en våg genom en periodiskt perforerad metallskärm beskrivs av ett passivt system, och summareglen begränsar bandbredden med enheltscellens statiska polariserbarhet. En sådan begränsning visar sig vara skarp för några simulerade och uppmätta perforerade skärmar.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2020. , p. 64
Series
TRITA-EECS-AVL ; 2020:8
Keywords [en]
Q-factor, bandwidth, antenna arrays, periodic structures, physical bounds, physical limitations
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-266703ISBN: 978-91-7873-413-9 (print)OAI: oai:DiVA.org:kth-266703DiVA, id: diva2:1386207
Public defence
2020-02-07, Kollegiesalen, Brinellvägen 8, Stockholm, 13:00 (English)
Opponent
Supervisors
Funder
Swedish Foundation for Strategic Research , AM13-0011Vinnova, ChaseOn/iAAAvailable from: 2020-01-17 Created: 2020-01-16 Last updated: 2020-01-17Bibliographically approved
List of papers
1. Stored energies and Q-factor of two-dimensionally periodic antenna arrays
Open this publication in new window or tab >>Stored energies and Q-factor of two-dimensionally periodic antenna arrays
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The Q-factor for lossless three-dimensional structures with two-dimensional periodicity is here derived in terms of the electric current density. The derivation in itself is shape-independent and based on the periodic free-space Green’s function. The expression for Q-factor takes into account the exact shape of a periodic element, and permits beam steering. The stored energies and the radiated power, both required to evaluate Q-factor, are coordinate independent and expressed in a similar manner to the periodic Electric Field Integral equation, and can thus be rapidly calculated. Numerical investigations, performed for several antenna arrays, indicate fine agreement, accurate enough to be predictive, between the proposed Q-factor and the tuned fractional bandwidth, when the arrays are not too wideband (i.e. when Q≥5). For completeness, the input impedance Q-factor, proposed by Yaghjian and Best in 2005, is included and agrees well numerically with the derived Q-factor expression. The main advantage of the proposed representation is its explicit connection to the current density, which allows the Q-factor to give bandwidth estimates based on the shape and current of the array element.

Keywords
electromagnetic theory, quality factor, periodic structures, scattering
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-266698 (URN)
Funder
Swedish Foundation for Strategic Research , SSF/AM13- 0011Vinnova, ChaseOn/iAA
Note

QC 20200117

Available from: 2020-01-16 Created: 2020-01-16 Last updated: 2020-01-17Bibliographically approved
2. Q-factor and bandwidth of periodic antenna arrays over ground plane
Open this publication in new window or tab >>Q-factor and bandwidth of periodic antenna arrays over ground plane
2020 (English)In: IEEE Antennas and Wireless Propagation Letters, ISSN 1536-1225, E-ISSN 1548-5757, Vol. 19, no 1, p. 158-162Article in journal (Refereed) Published
Abstract [en]

In this paper, the Q-factor expression for periodic arrays over a ground plane is determined in terms of the electric current density within the array's unit cell. The expression accounts for the exact shape of the array element. The Q-factor formula includes integration only over a volume of an element in a unit cell, and can thus be efficiently implemented numerically. The examples show good agreement between the proposed Q-factor, the full-wave-calculated tuned fractional bandwidth, and the input-impedance-based formula by Yaghjian and Best (2005) for the array of tilted dipoles and the loops array.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2020
Keywords
Periodic structures, electromagnetic theory, stored energies, antenna Q, quality factor
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-266699 (URN)10.1109/LAWP.2019.2956420 (DOI)000510939800033 ()2-s2.0-85078533560 (Scopus ID)
Funder
Swedish Foundation for Strategic Research , AM13-0011Vinnova, ChaseOn/iAA
Note

QC 20200117

Available from: 2020-01-16 Created: 2020-01-16 Last updated: 2020-02-26Bibliographically approved
3. Physical limitations of phased antenna arrays
Open this publication in new window or tab >>Physical limitations of phased antenna arrays
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper, the bounds on the Q-factor, a quantity inversely proportional to bandwidth, for phased antenna arrays are derived and investigated. Arrays in free space and above a ground plane are considered. The bounds are determined by optimizing the Q-factor represented in terms of electric current density on a unit-cell element. The optimization problem is formulated as a QCQP minimization of the Q-factor over all possible current densities on an enclosing element shape in a unit cell environment. The constraints can include conductive losses and polarization purity. We demonstrate how such bounds can be used to build Pareto-type trade-off relations between the Q-factor and other design specifications: element form-factor and size, efficiency and polarization purity.

Keywords
Q-factor, stored energy, fundamental bounds, optimization, QCQP
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-266700 (URN)
Funder
Swedish Foundation for Strategic Research , AM13-0011Vinnova, ChaseOn/iAA
Note

QC 20200117

Available from: 2020-01-16 Created: 2020-01-16 Last updated: 2020-01-17Bibliographically approved
4. Fundamental bounds on transmission through periodically perforated metal screens with experimental validation
Open this publication in new window or tab >>Fundamental bounds on transmission through periodically perforated metal screens with experimental validation
Show others...
2020 (English)In: IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, E-ISSN 1558-2221, Vol. 68, no 2, p. 773-782, article id 8852810Article in journal (Refereed) Published
Abstract [en]

This paper presents a study of transmission through arrays of periodic sub-wavelength apertures. Fundamental limitations for this phenomenon are formulated as a sum rule, relating the transmission coefficient over a bandwidth to the static polarizability. The sum rule is rigorously derived for arbitrary periodic apertures in thin screens. By this sum rule we establish a physical bound on the transmission bandwidth which is verified numerically for a number of aperture array designs. We utilize the sum rule to design and optimize sub-wavelength frequency selective surfaces with a bandwidth close to the physically attainable. Finally, we verify the sum rule and simulations by measurements of an array of horseshoe-shaped slots milled in aluminum foil.

Place, publisher, year, edition, pages
IEEE, 2020
Keywords
Electromagnetic scattering measurements, electromagnetic theory, frequency selective surfaces, periodic structures, scattering
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-266701 (URN)10.1109/TAP.2019.2943430 (DOI)000511198600017 ()2-s2.0-85079275936 (Scopus ID)
Funder
Vinnova, ChaseOn/iAASwedish Foundation for Strategic Research , AM13-0011
Note

QC 20200221

Available from: 2020-01-16 Created: 2020-01-16 Last updated: 2020-02-21Bibliographically approved
5. Evaluation of the Electric Polarizability for Planar Frequency-Selective Arrays
Open this publication in new window or tab >>Evaluation of the Electric Polarizability for Planar Frequency-Selective Arrays
2018 (English)In: IEEE Antennas and Wireless Propagation Letters, ISSN 1536-1225, E-ISSN 1548-5757, Vol. 17, no 7, p. 1158-1161Article in journal (Refereed) Published
Abstract [en]

This letter presents a method to evaluate the static electric polarizability of 2-D infinitely periodic metal patch arrays with dielectric substrate. Static polarizabilities are used in several design applications for periodic structures such as estimation of the bandwidth limitations for frequency-selective structures or prediction of the radiation properties for antenna arrays. The main features of the proposed method are its numerical efficiency and a deep insight into the physics of the fields interacting with the structure. We provide derivation and analysis of the method, and its verification against two another commercial solver-based approaches for various structure geometries. Additionally, we suggest the guidelines for applying the method to bandwidth optimization of frequency-selective structures and illustrate this with an example.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2018
Keywords
Frequency-selective surfaces, periodic structures, polarizability, scattering, sum rules
National Category
Telecommunications
Identifiers
urn:nbn:se:kth:diva-232396 (URN)10.1109/LAWP.2018.2836659 (DOI)000437873600008 ()2-s2.0-85047087751 (Scopus ID)
Funder
VinnovaSwedish Foundation for Strategic Research
Note

QC 20180726

Available from: 2018-07-26 Created: 2018-07-26 Last updated: 2020-01-17Bibliographically approved

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