Design of inhomogeneous slabs for filtering applications via closed form solutions of the reflection coefficient

A novel efficient design technique for microwave inhomogeneous media components (filters and matching lines) is developed in this paper. The inhomogeneity here considered can be modeled via a continuous spatial variation of the permittivity along the power flow direction and can be taken into account in the transmission line equivalent circuit representation in terms of a longitudinal line impedance and a transverse line admittance varying along the same direction. In order to design a filter or a matching line layout with such a material, new analytical expressions of the reflection and transmission coefficients for nonuniform transmission lines are found. Some examples are also presented in order to illustrate the validity of this technique for an efficient realization of proper layouts involving inhomogeneous layers which satisfy prescribed filtering characteristics in the frequency domain.