Analysis of inertance due to the higher order mode effects in a sudden area discontinuity

It is well known that an area discontinuity generates evanescent higher order modes even at low frequencies within the plane wave limit. The effect of these non-planar modes can be accounted for by their inertance effect in the form of a discontinuity inductance expressed as a function of the Karal correction factor. Earlier investigators have provided approximate expressions for this factor based on the analysis of coaxial discontinuities. In this paper, a 3-D finite element analysis is used to verify the results of earlier researchers for the coaxial discontinuities and to develop a simple, accurate and comprehensive expression for the Karal correction factor as a function of radius ratio, frequency and the offset distance for a generalized discontinuity.