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dc.contributor.advisorSkaar, Johannesnb_NO
dc.contributor.authorBondevik, Tarjeinb_NO
dc.date.accessioned2014-12-19T13:28:09Z
dc.date.available2014-12-19T13:28:09Z
dc.date.created2014-02-28nb_NO
dc.date.issued2014nb_NO
dc.identifier699800nb_NO
dc.identifierntnudaim:10448nb_NO
dc.identifier.urihttp://hdl.handle.net/11250/249466
dc.description.abstractThe Kramers-Kronig (KK) relations provide a mathematical relation between the real and imaginary part of a complex function that is analytic in the upper half plane and tends to zero as the argument tends to infinity. The magnetic susceptibility may satisfy the KK relations, but not in all cases. In cases where the susceptibility does not satisfy the usual KK relations, the analogous Modified Kramers-Kronig (MKK) relations were defined. The MKK relations provided a connection between the real and imaginary part of the magnetic permeability. It is the behavior of the permeability for low and high frequencies that determines if the MKK relations are satisfied.The behavior of the magnetic permeability as a function of the frequency was studied, for a general metamaterial. From causality, the permeability was found to behave only as unity, 1/frequency or 1/frequency^2 when the frequency approached zero. The same result were obtained when the frequency approached infinity. This lead to 3^2=9 different possibilities of how the permeability could behave. The nine different possibilities show that the permeability may behave in ways not characterized by the usual KK relations. Thus, causality was found to be less restrictive than the KK relations.Some of the nine possibilities would satisfy the MKK relations directly. However, for other possibilities, a slight modification of the input function was needed. These modifications were found, and based on the nine different possibilities, six different functions of the permeability were found to satisfy the MKK relations.Passive transmission line metamaterials were also studied specifically. Their magnetic permeability permeability were found to generally satisfy the MKK relations, given that their circuit topology consisted of solely serial and parallel circuits with loss.nb_NO
dc.languageengnb_NO
dc.publisherInstitutt for elektronikk og telekommunikasjonnb_NO
dc.titleModifications of the Kramers-Kronig Relations for the Magnetic Permeabilitynb_NO
dc.typeMaster thesisnb_NO
dc.source.pagenumber65nb_NO
dc.contributor.departmentNorges teknisk-naturvitenskapelige universitet, Fakultet for naturvitenskap og teknologi, Institutt for materialteknologinb_NO


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