An extension of a dual theorem on the summation of return differences [electrical networks]

The authors extend a previous result on return differences for a planar network to any network, planar or nonplanar. It is shown that based on the indefinite-impedance matrix formulation, the sum of the reciprocals of the return differences with respect to all network elements of a planar or nonplanar network equals the rank of the network. Some consequences of this theorem in relation to the summation of driving-point and transfer admittances are discussed