Some new results in the theory of normal distributed networks

The aim of this paper is to prove a partial converse of a representation theorem for normal distributed lossless two-port networks. The representation theorem states that the scattering matrix of a normal distributed lossless two-port network has a compact representation in terms of simple algebraic functions. In this paper it is shown that any2 \times 2matrix satisfying the conditions of the representation theorem is quasi-bounded-real (QBR). This result implies that the impedance and admittance matrices computed from the scattering matrix are reactance matrices in the rational case and quasi-reactance matrices in the nonrational case. These results have important applications in the synthesis of microwave filters and impedance transformers.