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)
- 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.
... (More) - 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1581316
- author
- Bernland, Anders
LU
; Luger, Annemarie
LU
and Gustafsson, Mats
LU
- organization
- publishing date
- 2010
- type
- Book/Report
- publication status
- published
- subject
- in
- Technical Report LUTEDX/(TEAT-7193)/1-31/(2010)
- pages
- 31 pages
- publisher
- [Publisher information missing]
- report number
- TEAT-7193
- external identifiers
-
- scopus:78650368838
- project
- EIT_HSWC:Antenna MIMO antennas and channels
- language
- English
- LU publication?
- yes
- additional info
- Published version: Journal of Physics A: Mathematical and Theoretical, Vol. 44, No. 14, pp. 145205, 2011.
- id
- 82891f1a-1ee6-42d6-989d-7b071f6233eb (old id 1581316)
- date added to LUP
- 2016-04-04 13:28:37
- date last changed
- 2022-01-30 00:19:05
@techreport{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}},
institution = {{[Publisher information missing]}},
language = {{eng}},
number = {{TEAT-7193}},
series = {{Technical Report LUTEDX/(TEAT-7193)/1-31/(2010)}},
title = {{Sum rules and constraints on passive systems}},
url = {{https://lup.lub.lu.se/search/files/6129287/1581317.pdf}},
year = {{2010}},
}