Variational bound analysis of a discontinuity in nonradiative dielectric waveguide

The application of the variational bound method to nonradiative dielectric waveguide is described for the analysis of scattering by a dielectric obstacle, in this case a rectangular, air-filled discontinuity (hole) in the dielectric center strip. A variational bound is obtained on the phase shift, which measures the amount by which the asymptotic solution for the fields in the guide in the presence of the discontinuity is displaced relative to the guide without a discontinuity. A major advantage of the procedure is that a closed-form expression for the equivalent network is obtained that can be used directly in the design of networks using reactive components, such as filters. Measured data agree well with the theoretical calculations