Symbolic formulation method for mixed-mode analog circuits using nullors

Abstract

A formulation method is introduced for the symbolic analysis of mixed-mode analog circuits consisting of opamps, current conveyors and/or current-feedback opamps. We show that by modeling all active devices using only nullors and grounded resistors, a reduced system of nodal equations can be formulated and solved by determinant decision diagrams. The nullor equivalents allow including parasitic elements as demonstrated in designing a universal filter.

Symbolic analysis of analog circuits containing voltage mirrors and current mirrors

“…As already shown in [22,37,39], the main advantage of transforming an analog circuit to a nullor network is to apply only NA in the formulation process, and to obtain a reduced system of equations for operational amplifier based circuits [7,37], and in general for circuits containing non-NA compatible elements.…”

“…The modeling process must include grounded admittances as much as possible, because they have only one entry in the NA formulation [37], while floating ones may have up to four entries requiring more computational work. The symbolic NA formulation method (i = Yv) can be summarized as follows:…”

“…6, the system of equations becomes order 6, because we need to introduce two stamps: one for the VM with a voltage-controlled voltage source and other for the independent voltage source. On the other hand, by applying the symbolic NA formulation, the order is reduced to 5, because the independent voltage source has been transformed to a current source [37], and the order becomes to be the number of nodes minus the number of nullator-norator pairs [7]. As a result, for large networks containing many VMs, the symbolic NA formulation is better than by applying the MNA method.…”

“…These representations are useful in circuit modeling [2,20,30,42], circuit transformation [28,29,41], and circuit synthesis [18,19]. However, these representations do not allow to include parasitics and they can not be used within the symbolic NA method, because their inverting characteristics do not allow to perform operations as it is done for networks containing nullators and norators [7,22,37,39]. In this manner, we introduce nullor-equivalents for the VM, CM and MO-CM to solve these problems.…”

“…there is not way to perform addition or deletion of columns or rows to preserve the inverting characteristics of either or both the VM and CM, as it is done in a nullor network [37]. In this manner, we are introducing nullorequivalents for the VM, CM and MO-CM to take advantage of the symbolic NA of nullor networks [7,37,39]. …”