Sum rules and constraints on passive systems
(2010) In Technical Report LUTEDX/(TEAT7193)/131/(2010) TEAT7193. 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 wellknown 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 wellknown 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:
http://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/(TEAT7193)/131/(2010)
 volume
 TEAT7193
 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
 82891f1a1ee642d6989d7b071f6233eb (old id 1581316)
 date added to LUP
 20100406 09:39:38
 date last changed
 20170101 08:12:10
@techreport{82891f1a1ee642d6989d7b071f6233eb, 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 wellknown 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}, pages = {31}, series = {Technical Report LUTEDX/(TEAT7193)/131/(2010)}, title = {Sum rules and constraints on passive systems}, volume = {TEAT7193}, year = {2010}, }