Pathological Element-Based Active Device Models and Their Application to Symbolic Analysis

This paper proposes new pathological element-based active device models which can be used in analysis tasks of linear(ized) analog circuits. Nullators and norators along with the voltage mirror-current mirror (VM-CM) pair (collectively known as pathological elements) are used to model the behavior of active devices in voltage-, current-, and mixed-mode, also considering parasitic elements. Since analog circuits are transformed to nullor-based equivalent circuits or VM-CM pairs or as a combination of both, standard nodal analysis can be used to formulate the admittance matrix. We present a formulation method in order to build the nodal admittance (NA) matrix of nullor-equivalent circuits, where the order of the matrix is given by the number of nodes minus the number of nullors. Since pathological elements are used to model the behavior of active devices, we introduce a more efficient formulation method in order to compute small-signal characteristics of pathological element-based equivalent circuits, where the order of the NA matrix is given by the number of nodes minus the number of pathological elements. Examples are discussed in order to illustrate the potential of the proposed pathological element-based active device models and the new formulation method in performing symbolic analysis of analog circuits. The improved formulation method is compared with traditional formulation methods, showing that the NA matrix is more compact and the generation of nonzero coefficients is reduced. As a consequence, the proposed formulation method is the most efficient one reported so far, since the CPU time and memory consumption is reduced when recursive determinant-expansion techniques are used to solve the NA matrix.