Dual topological theorems of linear active networks

It is shown that in a network with current-controlled voltage sources the sum of the products of the impedances of the tree branches and their driving-point admittances plus the sum of the products of the controlling parameters of the current-controlled voltage sources and their associated transfer admittances equals the sum of the products of the admittances of the co-tree links and their driving-point impedances. In a network with voltage-controlled current sources (VCCS), the sum of the products of the admittances of co-tree links and their driving-point impedances plus the sum of the products of the controlling parameters of the VCCS and their associated transfer impedances equals the sum of the products of the impedances of tree branches and their driving-point admittances.