Physical limitations of phased array antennas

In this paper, the bounds on the Q-factor, a quantity inversely proportional to bandwidth, are derived and investigated for narrow-band phased array antennas. Arrays in free space and above a ground plane are considered. The Q-factor bound is determined by solving a minimization problem over the electric current density. The support of these current densities is on an element-enclosing region, and the bound holds for lossless antenna elements enclosed in this region. The Q-factor minimization problem is formulated as a quadratically constrained quadratic optimization problem that is solved either by a semi-definite relaxation or an eigenvalue-based method. We illustrate numerically how these bounds can be used to determine trade-off relations between the Q-factor and other design specifications: element form-factor, size, efficiency, scanning capabilities, and polarization purity.Comment: 12 pages, 11 figure

Fundamental bounds on transmission through periodically perforated metal screens with experimental validation

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.Comment: 10 pages, 11 figures. Updated Introduction and Conclusion

Herglotz functions and applications in electromagnetics

Herglotz functions inevitably appear in pure mathematics, mathematical physics, and engineering with a wide range of applications. In particular, they are the pertinent functions to model passive systems, and thus appear in modeling of electromagnetic phenomena in circuits, antennas, materials, and scattering. In this chapter, we review the basic theory of Herglotz functions and its applications to determine sum rules and physical bounds for passive systems.Peer reviewe

Fundamental Bounds on Performance of Periodic Electromagnetic Radiators and Scatterers

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.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

Fundamental bounds on extraordinary transmission with experimental validation

This paper presents a study of extraordinary transmission (EoT) through arrays of 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 bandwidth of EoT 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

Herglotz functions and applications in electromagnetics

Herglotz functions inevitably appear in pure mathematics, mathematical physics, and engineering with a wide range of applications. In particular, they are the pertinent functions to model passive systems, and thus appear in modeling of electromagnetic phenomena in circuits, antennas, materials, and scattering. In this chapter, we review the basic theory of Herglotz functions and its applications to determine sum rules and physical bounds for passive systems.Peer reviewe