On Circuit Analysis and Simulation of Networks with Nullors

This paper describes the new modeling of nullor-based active devices from the circuit abstraction level. After a brief overview of the nullor concept and its properties, follows a detailed description regarding the modeling of active devices in the voltage-mode, current-mode, respectively in the mixed mode of operation. This modeling description reflects the two-port and four-terminal network point of view. Simulation of the four nullor-controlled types of sources, as well as modeling of the multiport circuit elements, requires the development of suitable equivalent circuits constructed using bipolar circuit elements and the nullor. Studying the behavior of such a circuit, voltage and current wise, require its association with two graphs: one current graph namely Gi, for the systematic formulation of the 1st Kirchhoff's Theorem, and one voltage graph called Gv, for the systematic formulation of the 2nd Kirchhoff's Theorem. The use of the two graphs in the analog analysis applied to circuits with nullors implies the elaboration of efficient algorithms, implemented in specialized software, capable of generating voltage and current graphs automatically. Considering the nullator an over-determined two-port circuit element (zero voltage, zero current) whereas the norator is an undetermined two-port circuit element (any voltage and any current), this paper presents the way of formulating equations of all kinds, straight from the diagrams of the functional circuits containing nullors. Existing simulation software may be applied to simulate the nullor having an ideal voltage-controlled voltage source, ec = Ac_c uc, with an ideal independent current source, jC=0.0 A used for gate control and possessing a substantial amplification (transfer) factor Ac_C. Therefore, all types of equations, which describe functional circuits have a simple formulation, no matter the presence of nullors. In this way, it becomes possible to elaborate efficient algorithms applicable for the automatic formulation of Kirchhoff's equations, loop equations, modified nodal equations and state equations for circuits with nullors as well. The example presented here pleaded for the validity of the nullor modeling.