A recent definition of genericity for resistor-inductor-capacitor (RLC) networks is that the realisability set of the network has
dimension one more than the number of elements in the network. We prove that such networks are minimal in the sense that it is
not possible to realise a set of dimension n with fewer than n − 1 elements. ...
A recent definition of genericity for resistor-inductor-capacitor (RLC) networks is that the realisability set of the network has
dimension one more than the number of elements in the network. We prove that such networks are minimal in the sense that it is
not possible to realise a set of dimension n with fewer than n − 1 elements. We provide an easily testable necessary and sufficient
condition for genericity in terms of the derivative of the mapping from element values to impedance parameters, which is illustrated
by several examples. We show that the number of resistors in a generic RLC network cannot exceed k + 1 where k is the order
of the impedance. With an example, we show that an impedance function of lower order than the number of reactive elements
in the network need not imply that the network is non-generic. We prove that a network with a non-generic subnetwork is itself
non-generic. Finally we show that any positive-real impedance can be realised by a generic n
