Minimum-gyrator synthesis of n-ports

The minimum number of gyrators needed for the synthesis of a general nonbilateral -port of prescribed scattering matrix has long been unknown although a lower bound is , where is the rank (necessarily even) of the skew part of , that is, rank . The synthesis procedure for lossless -ports, due to Belevitch, reaches the lower bound . For a general -port, however, the best known result is and is not related to . This paper shows that a general -port is synthesizable with gyrators. A numerical example is given in the Appendix.