Synthesis of a Class of Reciprocal -Ports and a Highly Singular Construction

We give a canonical synthesis of those reciprocal <inline-formula> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula>-ports which are at the same time antireciprocal as well, using only as many components as the number of independent nonzero entries in the describing hybrid matrix, and using series-parallel topology. Examining the smallest non-series-parallel topology we obtain a 2-port which behaves as two nullators or two norators at some extreme values. Mathematically its level of singularity is the same as that of the classical example of Carlin and Youla but they used a 3-port circulator while we use reciprocal devices only.