Simultaneous canonic synthesis of two dual impedances

It is proved that two dual passive impedances Z and R 2 / Z (R real constant) each of degree m are simultaneously realizable by a lossless reciprocal 4‐port of degree 2 m closed on two constant resistances. Moreover, the lossless reciprocal 4‐port is itself realizable as a cascade of such 4‐ports of degrees 2 and 4. These are extensions of the Bott–Duffin and Fialkow‐Gerst bridges but generally contain ideal transformers. As in Fialkow‐Gerst synthesis, the only algebraic equation to be solved is Z(p) + Z(–p) = 0 but, in contrast with Fialkow‐Gerst, the realization is minimal.