| 1. |
- Bernland, Anders
(författare)
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Bandwidth Limitations for Scattering of Higher Order Electromagnetic Spherical Waves with Implications for the Antenna Scattering Matrix
- 2012
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Ingår i: IEEE Transactions on Antennas and Propagation. - 0018-926X. ; 60:9, s. 4345-4353
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Tidskriftsartikel (refereegranskat)abstract
- Various physical limitations in electromagnetic theory and antenna theory have received considerable attention recently. However, there are no previous limitations on the scattering of higher order electromagnetic vector spherical waves, despite the widespread use of spherical wave decompositions. In the present paper, bandwidth limitations on the scattering matrix are derived for a wide class of heterogeneous objects, in terms of their electrical size, shape and static material properties. In particular, it is seen that the order of the dominating term in the Rayleigh limit increases with the order of the spherical wave. Furthermore, it is shown how the limitations place bounds on the antenna scattering matrix, thus introducing a new approach to physical limitations on antennas. Comparisons to other types of antenna limitations are given, and numerical simulations for two folded spherical helix antennas and a directive Yagi-Uda antenna are included to illuminate and validate the theory. The results in this paper are derived using a general approach to derive limitations for passive systems: First, the low-frequency asymptotic expansion of the scattering matrix of a general scatterer is derived. This gives a set of sum rules, from which the limitations follow.
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| 2. |
- Bernland, Anders
(författare)
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Bandwidth limitations for scattering of higher order electromagnetic spherical waves with implications for the antenna scattering matrix
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Various physical limitations in electromagnetic theory and antenna theory have received considerable attention recently. However, there are no previous limitations on the scattering of higher order electromagnetic vector spherical waves, despite the widespread use of spherical wave decompositions. In the present paper, bandwidth limitations on the scattering matrix are derived for a wide class of heterogeneous objects, in terms of their electrical size, shape and static material properties. In particular, it is seen that the order of the dominating term in the Rayleigh limit increases with the order of the spherical wave. Furthermore, it is shown how the limitations place bounds on the antenna scattering matrix, thus introducing a new approach to physical limitations on antennas. Comparisons to other types of antenna limitations are given, and numerical simulations for two folded spherical helix antennas and a directive Yagi-Uda antenna are included to illuminate and validate the theory. The results in this paper are derived using a general approach to derive limitations for passive systems: First, the low-frequency asymptotic expansion of the scattering matrix of a general scatterer is derived. This gives a set of sum rules, from which the limitations follow.
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| 3. |
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| 4. |
- Bernland, Anders, et al.
(författare)
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Estimation of Spherical Wave Coefficients from 3D Positioner Channel Measurements
- 2012
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Ingår i: IEEE Antennas and Wireless Propagation Letters. - 1548-5757. ; 11, s. 608-611
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Tidskriftsartikel (refereegranskat)abstract
- Electromagnetic vector spherical waves have been used recently to model antenna-channel interaction and the available degrees of freedom in MIMO systems. However, there are no previous accounts of a method to estimate spherical wave coefficients from channel measurements. One approach for this, using a 3D positioner, is presented and analyzed in this letter. Measurement results are presented and discussed. It is concluded that estimates based on randomly positioned measurements within a volume are less sensitive to noise than those based only on measurements on the surface.
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| 5. |
- Bernland, Anders, et al.
(författare)
-
Estimation of Spherical Wave Coefficients from 3D Positioner Channel Measurements
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Electromagnetic vector spherical waves have been used recently to model antenna channel interaction and the available degrees of freedom in MIMO systems. However, there are no previous accounts of a method to estimate spherical wave coefficients from channel measurements. One approach, using a 3D positioner, is presented in this letter, both in theory and practice. Measurement results are presented and discussed. One conclusion is that using randomly positioned measurements within a volume is less sensitive to noise than using only measurements on the surface.
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| 6. |
- Bernland, Anders
(författare)
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Integral Identities for Passive Systems and Spherical Waves in Scattering and Antenna Problems
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Sum rules and physical limitations within electromagnetic theory and antenna theory have received significant attention in the last few years. However, the derivations are often relying on application specific and sometimes unsupported assumptions, and therefore a mathematically rigorous and generally applicable approach seems timely. Such an approach is presented in this thesis, along with examples and all the necessary proofs. The approach is also applied in the thesis to derive sum rules and physical limitations on electromagnetic spherical wave scattering. This has not been done before, despite the widespread use of spherical wave decompositions. For example, spherical waves and the antenna scattering matrix provide a complete and compact description of all the important properties of an antenna, are crucial parts in spherical near-field antenna measurements, and have been used recently to model antenna-channel interaction and multiple-input multiple-output (MIMO) communication systems. This thesis is also the first to present a method to estimate spherical wave coefficients from propagation channel measurements. The results of this thesis can roughly be divided into three categories: Firstly, a general approach to derive sum rules and physical limitations on input-output systems based on the assumptions of causality and passivity is presented (Paper I). Secondly, sum rules and physical limitations on the scattering and matching of electromagnetic spherical waves are derived, and the implications for antennas are explored (Papers II-IV). Thirdly, a method to estimate spherical wave coefficients from channel measurements, and the results of a measurement campaign, are presented and analysed (Paper V). The thesis consists of a General Introduction and five appended papers.
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| 7. |
- Bernland, Anders
(författare)
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On physical limitations for broadband electromagnetic scattering --- high order spherical waves
- 2011
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Ingår i: [Host publication title missing]. ; , s. 619-622
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Konferensbidrag (refereegranskat)abstract
- Limitations on the scattering matrix are derived for a wide class of objects, restricting their broadband interaction with electromagnetic vector spherical waves in terms of their size, shape and static material properties. In particular, it is seen that the order of the dominating term for electrically small objects increases with the order of the spherical wave. The results are applicable to many areas concerned with electromagnetic waves interacting with matter. For instance, they open up a new approach to derive bounds on antenna performance. They can also be generalized to acoustic and elastodynamic scattering. Two intermediate results presented are a set of sum rules for and the low-frequency asymptotic expansions of the scattering and transition matrices of a general scatterer.
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| 8. |
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| 9. |
- Bernland, Anders, et al.
(författare)
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Physical limitations on the scattering of electromagnetic vector spherical waves
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Understanding the interaction between electromagnetic waves and matter is vital in applications ranging from classical optics to antenna theory. This paper derives physical limitations on the scattering of electromagnetic vector spherical waves. The assumptions made are that the heterogeneous scatterer is passive, and has constitutive relations which are on convolution form in the time domain and anisotropic in the static limit. The resulting bounds limit the reflection coefficient of the modes over a frequency interval, and can thus be interpreted as limitations on the absorption of power from a single mode. They can be used within a wide range of applications, and are particularly useful for electrically small scatterers. The derivation follows a general approach to derive sum rules and physical limitations on passive systems on convolution form. The time domain versions of the vector spherical waves are used to describe the passivity of the scatterer, and a set of integral identities for Herglotz functions are applied to derive sum rules from which the physical limitations follow.
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| 10. |
- Bernland, Anders, et al.
(författare)
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Sum rules and constraints on passive systems
- 2011
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 44:14
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Tidskriftsartikel (refereegranskat)abstract
- A passive system is one that cannot produce energy, a property that naturally poses constraints on the system. A system in convolution form is fully described by its transfer function, and the class of Herglotz functions, holomorphic functions mapping the open upper half plane to the closed upper half plane, is closely related to the transfer functions of passive systems. Following a well-known representation theorem, Herglotz functions can be represented by means of positive measures on the real line. This fact is exploited in this paper in order to rigorously prove a set of integral identities for Herglotz functions that relate weighted integrals of the function to its asymptotic expansions at the origin and infinity. The integral identities are the core of a general approach introduced here to derive sum rules and physical limitations on various passive physical systems. Although similar approaches have previously been applied to a wide range of specific applications, this paper is the first to deliver a general procedure together with the necessary proofs. This procedure is described thoroughly, and exemplified with examples from electromagnetic theory.
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