A novel formulation of the nodal admittance matrix for linear active circuits with nullors via the component stamps method

The nullor, as a network element, is very popular in the areas of modeling, synthesis and analysis of analog circuits. Nullors are pathological or singular elements that posses ideal characteristics and are specified according to the constraints they impose on their terminal voltages and currents. Therefore, in order to compute symbolic expressions of pathological element-base equivalent analog circuits, the nullor properties should be taken into account in the formulation process. Nodal analysis (NA) of these circuits is very popular. However, the recently proposed methods of formulation the nodal admittance (NA) matrix, require many operations on the rows and columns of an initial node admittance matrix (INAM), which has the order (nxn), for the (n+1) node network or a laborious procedure of computation of norator and nullator indexes. This paper presents a new method of formulation of the nodal admittance matrix for linear active circuits with nullors that performs direct construction of the final nodal admittance matrix (FNAM), which has the order (n-k)x(n-k), and uses only classical methods of element stamps. (k is the number of nullators and norators pairs). The viability and the potentiality of the proposed method (of the FNAM) is showcased via application examples. The improved formulation method is compared with other formulation methods, showing that it is simpler.