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Stored energies and Q-factor of two-dimensionally periodic antenna arrays
KTH, School of Electrical Engineering and Computer Science (EECS), Electrical Engineering, Electromagnetic Engineering.ORCID iD: 0000-0002-7057-6414
KTH, School of Electrical Engineering and Computer Science (EECS), Electrical Engineering, Electromagnetic Engineering.ORCID iD: 0000-0001-7269-5241
(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 [en]
electromagnetic theory, quality factor, periodic structures, scattering
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-266698OAI: oai:DiVA.org:kth-266698DiVA, id: diva2:1386176
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
In thesis
1. Fundamental Bounds on Performance of Periodic Electromagnetic Radiators and Scatterers
Open this publication in new window or tab >>Fundamental Bounds on Performance of Periodic Electromagnetic Radiators and Scatterers
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
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:nbn:se:kth:diva-266703 (URN)978-91-7873-413-9 (ISBN)
Public defence
2020-02-07, Kollegiesalen, Brinellvägen 8, Stockholm, 13:00 (English)
Opponent
Supervisors
Funder
Swedish Foundation for Strategic Research , AM13-0011Vinnova, ChaseOn/iAA
Available from: 2020-01-17 Created: 2020-01-16 Last updated: 2020-01-17Bibliographically approved

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Ludvig-Osipov, AndreiJonsson, B. Lars G.

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