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Sum rules and constraints on passive systems

Bernland, Anders LU ; Luger, Annemarie LU and Gustafsson, Mats LU (2010) In Technical Report LUTEDX/(TEAT-7193)/1-31/(2010) TEAT-7193.
Abstract
A passive system is one that cannot produce energy, a property that naturally poses constraints on the system. A system on 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.



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A passive system is one that cannot produce energy, a property that naturally poses constraints on the system. A system on 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. (Less)
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author
organization
publishing date
type
Book/Report
publication status
published
subject
in
Technical Report LUTEDX/(TEAT-7193)/1-31/(2010)
volume
TEAT-7193
pages
31 pages
publisher
[Publisher information missing]
external identifiers
  • Scopus:78650368838
project
EIT_HSWC:Antenna MIMO antennas and channels
language
English
LU publication?
yes
id
82891f1a-1ee6-42d6-989d-7b071f6233eb (old id 1581316)
date added to LUP
2010-04-06 09:39:38
date last changed
2016-10-13 04:55:19
@misc{82891f1a-1ee6-42d6-989d-7b071f6233eb,
  abstract     = {A passive system is one that cannot produce energy, a property that naturally poses constraints on the system. A system on 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.<br/><br>
<br/><br>
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.},
  author       = {Bernland, Anders and Luger, Annemarie and Gustafsson, Mats},
  language     = {eng},
  pages        = {31},
  publisher    = {ARRAY(0x86e6928)},
  series       = {Technical Report LUTEDX/(TEAT-7193)/1-31/(2010)},
  title        = {Sum rules and constraints on passive systems},
  volume       = {TEAT-7193},
  year         = {2010},
}