Sum rules and constraints on passive systems
Bernland, Anders LU ; Luger, Annemarie LU and Gustafsson, Mats LU
(2011)
In Journal of Physics A: Mathematical and Theoretical
44(14).
- 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... (More) - 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1788854
- author
- Bernland, Anders
LU
; Luger, Annemarie
LU
and Gustafsson, Mats
LU
- organization
- publishing date
- 2011
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Physics A: Mathematical and Theoretical
- volume
- 44
- issue
- 14
- article number
- 145205
- publisher
- IOP Publishing
- external identifiers
-
- wos:000288597500008
- scopus:79953706646
- ISSN
- 1751-8113
- DOI
- 10.1088/1751-8113/44/14/145205
- project
- EIT_HSWC:Antenna MIMO antennas and channels
- language
- English
- LU publication?
- yes
- id
- deb9845a-25ea-4a2e-8aad-103b2a6fa466 (old id 1788854)
- date added to LUP
- 2016-04-04 09:16:16
- date last changed
- 2022-03-31 01:52:44
@article{deb9845a-25ea-4a2e-8aad-103b2a6fa466,
abstract = {{A passive system is one that cannot produce energy, a property that<br/><br>
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<br/><br>
functions mapping the open upper half plane to the closed upper half plane, is<br/><br>
closely related to the transfer functions of passive systems. Following a well-known<br/><br>
representation theorem, Herglotz functions can be represented by means of positive<br/><br>
measures on the real line. This fact is exploited in this paper in order to rigorously<br/><br>
prove a set of integral identities for Herglotz functions that relate weighted integrals<br/><br>
of the function to its asymptotic expansions at the origin and infinity.<br/><br>
The integral identities are the core of a general approach introduced here to derive<br/><br>
sum rules and physical limitations on various passive physical systems. Although<br/><br>
similar approaches have previously been applied to a wide range of specific applications,<br/><br>
this paper is the first to deliver a general procedure together with the necessary<br/><br>
proofs. This procedure is described thoroughly, and exemplified with examples from<br/><br>
electromagnetic theory.}},
author = {{Bernland, Anders and Luger, Annemarie and Gustafsson, Mats}},
issn = {{1751-8113}},
language = {{eng}},
number = {{14}},
publisher = {{IOP Publishing}},
series = {{Journal of Physics A: Mathematical and Theoretical}},
title = {{Sum rules and constraints on passive systems}},
url = {{http://dx.doi.org/10.1088/1751-8113/44/14/145205}},
doi = {{10.1088/1751-8113/44/14/145205}},
volume = {{44}},
year = {{2011}},
}