Formulation of the power balance equation for a slot in a waveguide filled with a lossy dielectric

Thin slots in waveguide walls are used as antenna radiators or coupling elements. Waveguide filling with dielectric provides miniaturisation of devices. All dielectrics are more or less lossy. The theory of thin slots in empty waveguides or ones, homogeneously filled with ideal dielectric, is elaborated quite fully. In this work an attempt was made to consider some questions of slot theory in the case when dielectric filling of waveguide has a complex permitivity