In this paper, by using two-variable network functions, the explicit characterizations of lossless ladder networks with lumped and distributed elements are aimed. The explicit two-variable descriptions of some special classes of lossless ladders networks of low-pass, high-pass, band-pass and band-reject types are presented. The explicit formulas define the mixed elements networks under consideration are obtained up to a certain complexity. At the end of this study, the application of the proposed method in the design of two-stage microwave FET amplifier is illustrated with an example.