A new approach for using the pathological mirror elements in the ideal representation of active devices

Abstract

SUMMARYThis paper is adopting a new approach to investigate the capabilities of pathological mirror elements in the ideal representation of active building-blocks and shows that the voltage mirror (VM) and current mirror (CM) are the basic pathological elements. The descriptions for the floating mirror elements in the nodal admittance matrix (NAM), using infinity-variables, are derived. The descriptions for nullator and norator using infinity-variables in the NAM are shown to represent special cases from the derived descriptions of the floating VM and the CM, respectively. Hence, new representations for the nullator and norator in terms of the floating VM and CM, respectively, are obtained. A systematic procedure for the derivation of pathological configurations to ideally represent various analog signal-processing properties featured by active building-blocks is presented. This systematic approach became plausible by virtue of the versatility offered by the NAM descriptions of floating mirror elements. Novel pathological configurations ideally describing most popular signal-processing properties that involve differential or multiple single-ended signals; like conversion between differential and single-ended voltages, differential voltage conveying, current differencing, differential current conveying, and inverting current replication; are derived systematically using this procedure. The resulting pathological configurations are shown to be constructed mainly using mirror elements and hence the capabilities of the mirrors as basic pathological elements are further demonstrated. Pathological representations for some active building-blocks, using the derived pathological sections, are presented as application examples.

Behavioral Modeling of Mixed-Mode Integrated Circuits

“…All kinds of current conveyors work in mixed-mode and basically they are composed of unity gain cells (Soliman, 2009;Tlelo-Cuautle, Duarte-Villaseñor & Guerra-Gómez, 2008), which can be superimposed (Tlelo-Cuautle, Moro-Frias & Duarte-Villaseñor, 2008) to generate different kinds of active devices (Biolek et al, 2008), all of them useful for analog signal processing applications. Among the unity gain cells, the voltage mirror (Tlelo-Cuautle, Duarte-Villaseñor & Guerra-Gómez, 2008) and current mirror can be modeled by using nullators and norators (Tlelo-Cuautle, Sánchez-López, , but also they have the pathological representation introduced in (Saad & Soliman, 2010), and they can be used to model the behavior of active devices with inverting characteristics. Although the current conveyor is a mixed-mode device, it can be used to implement voltage-mode circuits such as active filters (Chen, 2010;Maheshwari et al, 2010).…”

“…From the advantages infered above, we present the symbolic behavioral modeling of analog circuits using the pathological elements: nullators and norators. The other two pathological elements: voltage mirrors and current mirrors can be described as already shown in (Saad & Soliman, 2010;. Some examples for the generation of behavioral models for mixed-mode devices and circuits are introduced in (Fakhfakh et al, 2010;Sánchez-López, Fernández & Tlelo-Cuautle, 2010;Tlelo-Cuautle, Sánchez-López & Moro-Frias, 2010).…”

Symbolic analysis of analog circuits containing voltage mirrors and current mirrors

“…1 [2]. 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].…”

“…The modeling of active devices possessing inverting characteristics can be done by using the VM and CM, as pathological elements [2,20,30,42]. An important thing is that an analog circuit containing VMs and CMs also allows to transform circuit topologies or voltage-mode to currentmode circuits and vice-versa [5,8,10,15,28,29,41].…”

Active filter synthesis based on nodal admittance matrix expansion

“…During matrix manipulating, terms in columns j and k connected between a nullator (a) (b) (c) (a) (b) Fig. 2 a Nullor equivalence of OPA [13] . …”