Pathological Equivalents of Fully-Differential Active Devices for Symbolic Nodal Analysis

The use of pathological elements (i.e., nullators, norators, and the voltage mirror-current mirror pair) as universal active elements opens up the possibility to model the behavior of active devices with either differential features or input-output multiples, in order to be used in analysis tasks of linear(ized) analog circuits. This brief tries on the modeling this class of active devices, which is carried out by considering the impedance characteristics along with the behavior equation of each active device, the kind of signal to be processed and by applying the pathological element properties. In order to obtain a more realistic model, not only parasitic elements associated to the input-output terminals of each active device are considered, but the tracking errors of voltage and current differential followers modeled with grounded pathological elements and admittances are also included. Due to that the gain and tracking errors are finites and of limited bandwidth, a two-pole model is used for each of them in order to include their contributions on the symbolic expressions computed. Because the behavior of fully-differential amplifiers is modeled with grounded pathological elements, a standard nodal analysis can be performed. This imply that not only the size of the admittance matrix is smaller than those generated by applying modified nodal analysis (MNA) method, for instance, but also the number of nonzero elements and the generation of cancellation-terms are both reduced. As a result, the computational complexity during the solution of the system of equations is reduced when recursive determinant-expansion techniques are applied. Examples are described and compared with the MNA method, in order to show the usefulness of the proposed models to compute fully-symbolic small-signal characteristics of analog circuits containing fully-differential active devices and/or with input-output multiples.