Frequency dependent dielectric constants and its numerical computation through Kramers-Kronig relations and Hilbert transform.

Date of Award


Degree Type


Degree Name



Electrical and Computer Engineering

First Advisor

Raju, Govinda,


Engineering, Electronics and Electrical.




The dielectric constant and loss are important (real and imaginary components) properties of interest to electrical engineers because these two parameters, among others, decide the suitability of a material for a given application. The nature of some physical important parameters is such that frequency dependent real and imaginary components cannot be specified independently from each other. The Kramers-Kronig relations provide the coupling between real and imaginary components. Occasions arise when only one of the components can be readily obtained from theoretical or experimental procedures. The mathematical technique used by Kramers-Kronig relations, which allows one component to be defined in terms of the other is Hilbert transform since &egr;'(o) and &egr;″(o) can be shown to be Hilbert transform pairs. The particle formation of this Hilbert transform pair is not an easy task in most instances. One cannot produce an analytical function in order to obtain its Hilbert transformation over a large frequency range. An efficient algorithm is developed to obtain the complex dielectric permittivity of materials over a large frequency range. In this thesis, the algorithm has been verified for both theoretically generated data (Debye equation) and measured data for various high temperature dielectric materials. This procedure calculates the one component of the dielectric constant from its other component by use of the Hilbert transform properties of Kramers-Kronig relation and FFT techniques. Different laboratory equipments and measuring techniques were used in this project and described in detail.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .W44. Source: Masters Abstracts International, Volume: 43-01, page: 0287. Adviser: Govinda Raju. Thesis (M.A.Sc.)--University of Windsor (Canada), 2004.