On Complete Versions of Thevenin–Norton and Maximum Power Transfer Theorems

Abstract

In this paper, we state and prove complete versions of two basic theorems of linear circuit theory, viz. Thevenin–Norton and Maximum power transfer theorems. We show how to compute port behavior of multiports which have port equations of the general form $Bv_P-Qi_{P}=s,$ which cannot even be put into the hybrid form, indeed may have number of equations ranging from 0 to 2n,  where n is the number of ports. The method works for linear multiports which are consistent for arbitrary internal source values and further have the property that the port conditions uniquely determine internal conditions. We present the most general version of maximum power transfer theorem possible. This version of the theorem states that ‘stationarity’ (derivative zero condition) of power transfer occurs when the multiport is terminated by its adjoint, provided the resulting network has a solution. If this network does not have a solution, there is no port condition for which stationarity holds. This theorem does not require that the multiport has a hybrid immittance matrix.