Two‐graph analysis of pathological equivalent networks

Abstract

Recently, abstract current mirror and voltage mirror elements have been proposed for behavioral modeling of active analog blocks. Such artificial elements and the traditionally used nullor element together are called pathological elements in the literature. Pathological elements are very useful in modeling and analysis of active network. Hence, researchers have been motivated to study symbolic analysis methods for networks containing pathological elements. However, so far, only nodal admittance matrix analysis has been formulated. In this work, an alternative two-graph method is formulated, which has the advantage of providing a compact intermediate form for subsequent symbolic term generation. With a compact two-graph representation, either a matrix method or a tree enumeration method can be employed. For completeness, the classical two-graph theory has been extended in this paper to encompass all four types of dependent sources and all pathological elements. Illustrative examples are presented to demonstrate the principle of compact symbolic term generation by the presented two-graph method.The classical two-graph method developed in the 1960s was only applicable to networks containing RCL-g m elements, that is, elements of R (resistor), C (capacitor), L (inductor), and g m (voltage-controlled current 1128 G. SHI

Revisited generalized substitution theorem and its consequences for circuit analysis

“…4. As will be shown in the next paragraph, an alternative ST based on Source Set may be obtained by resorting to the concept of nullator-norator pair or nullor that has been successfully employed for several purposes in circuit theory (see, e.g., [29][30][31] for recent applications). Such an element may be regarded as a peculiar two-port and different symbols are employed for it in the literature.…”

“…Such theorems are naturally extended to the generic N-port case whenfor k = 1, 2, 4. An alternative solution for implementing stems straightforwardly from the very definition of M. Indeed, recalling (29) one is soon convinced that, among all the possible N-ports fulfilling (27), one surely finds Q off , that is, the N-port obtained from Q itself by simply killing its independent sources. It is important to emphasize that, as clearly seen from the foregoing reasoning, the previously mentioned possibility is completely independent of the nature of x (q) .…”