Using Pathological Elements in Analog Circuit Analysis and Simulation

Abstract

Abstract This paper is focused on some kind of mystery circuit nullator, nullor, current mirror, and voltage mirror, all of them known as pathological elements. These pathological elements can be used to perform circuit modelling, symbolic circuit analysis, circuit synthesis, circuit design and to develop applications that involve modern active devices. It is described a new modeling of nullor-based active devices from the circuit abstraction level. In this paper it is presented the way all types of equations which describe the circuit containing nullors can be directly formulated from the diagrams of these circuits if we took into account that a nullator is an over-determined two-port circuit element (zero voltage, zero current) and the norator is an undetermined two-port circuit element (any voltage and any current). To simulate the nullors with ideal voltage controlled voltage sources, ec = Ac_c uc, with the control gate an ideal independent current source, jC = 0.0 A and with the amplification (transfer) factor Ac_C very big (theoretically ∞), the analog circuits with nullors can be analyzed by using any of the existing simulation software. By this way, it was possible the elaboration of efficient algorithms for an automatic formulation of Kirchhoff’s equations, of loop equations, of modified nodal equations and of state equations for circuits with pathological elements. These procedures can be easily implemented in dedicated programs for the simulations of the complex analog circuits with pathological elements. The example presented in this paper validates the presented models for nullors.