An extension of Vratsanos' theorem to nonreciprocal networks

An extension of Vratsanos' theorem to nonreciprocal networks is considered. It is shown that for an impedance
Z_{0}
carrying a current
I_{0}, \partial Z_{0} / \partial Z^{(n)} = I^{(n)}I^{(n)}' / I_{0}^{2}
; where
I^{(n)}
and
I^{(n)}'
are branch currents through an element
Z^{(n)}
in conjugate networks obtained from each other by gyrator coupling reversals.