Pathological equivalents of CMs and VMs with multi-outputs

New models based on pathological elements are introduced to describe the behavior of current- and voltage-mirrors with multi-outputs. To do so, simple element stamps for a current-controlled current source and a voltage controlled voltage source have been deduced. The difference of the new stamps with those reported in the literature is that herein, input---output impedances of the controlled sources are taken into account. As a consequence, not only the behavior of controlled sources can be directly introduced on the admittance matrix without extra variables, but also the new stamps have few nonzero elements. Relying on these stamps, the modeling of current- and voltage-mirrors with multi-outputs based on pathological elements is generated. Gain and parasitic elements associated to each input---output terminal of current- and voltage-mirrors are considered in the proposed models. Due to the simplicity of our models, a reduced and sparse system of equations is obtained for analog circuits containing current- and/or voltage-mirrors. As a consequence, the computational complexity used in the solution of the system of equations is diminished when recursive determinant-expansion techniques are applied. The usefulness of the models to realize symbolic analysis of analog circuits is demonstrated and compared with nullor-based models of current- and voltage-mirrors previously reported. Furthermore, these models can be used either at the transistor or circuit level of abstraction in order to compute fully-symbolic small-signal characteristics of analog circuits.