Critical analysis of cut-insertion theorem

Abstract

The paper gives a critical analysis of recently proposed cut-insertion theorem. It is shown that all cut-insertion equivalent networks can be obtained using a simple extension of the substitution theorem. For example, using two voltage sources connected in parallel between a chosen and reference node, then cutting the wire between the voltage sources one concludes that a wire with a known voltage and known current can be substituted by a two port where one input is connected to the impedance seen by the voltage source operating at the second port. The calculation of this impedance is difficult; in the general case one have to solve an algebraic equation of the fifth degree. Hence, when the network with cut-inserted two-port is represented as a feedback system the parameters of this system may be defined for very simple networks only, when the degree of the defining equation is lessened. An example shows these difficulties.