Further non-series-parallel 3-terminal RC networks having no parallel equivalent

By the construction of an appropriate numerical example, Fialkow demonstrated the existence of a non-series-parallel 3-terminal RC network for which a series-parallel equivalent was intrinsically impossible. Starting from the set of short-circuit admittance functionscorresponding to this network and using computer synthesis methods, the authors obtained a number of realizations, or possibly near-realizations, for this set of functions. In view of the theoretical interest involved, it was decided to check whether any of these realizations did, in fact, correspond to exact solutions of the synthesis problem; a number of such exact solutions were found and are exhibited in this paper together with other sets of short-circuit admittance functions that can only be realized as 3-terminal RC networks in non-series-parallel form.