Arbitrary filter design by using nonuniform transmission lines

We develop new formulations of reflection and transmission coefficients of nonuniform transmission lines having unequal reference impedances. By using the ABCD transmission matrix of a transmission line, we express the reflection and transmission coefficients of a nonuniform line as polynominal ratios in Z transforms. These formulations, in conjunction with digital signal processing (DSP) techniques and a reconstruction method, lead to the realization of nonuniform lines which satisfy prescribed scattering characteristics in frequency domain. Some examples are presented to illustrate the validity of this technique.