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

Abstract

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 elementbased 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 non-zero 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.

Binary Genetic Encoding for the Synthesis of Mixed-Mode Circuit Topologies

“…That way, this section introduces our proposed BGE representation for every kind of UGC. It is worthy to mention that the usefulness of the UGCs in analysis and design of analog circuits has been demonstrated in [4,5,18,20,22,23,27,29].…”

“…The BGE of the CFOA can be created from the cascade connection of a CCII+ with a VF [9,30], or equivalently the combination of three UGCs: VF-CM-VF. To synthesize first and third generation current conveyors [30], and other mixed-mode circuits [18], other combinations among three or four UGCs can be performed.…”

“…voltage and current, it is working in mixed-mode [5]. Examples of these mixed-mode circuits are the current conveyor [17,21,24,30], the operational transconductance amplifier (OTA) [34], the operational transresistance amplifier (OTRA) [16,19], the current-feedback operational amplifier (CFOA) [2,6,7,13,23,32], and other topologies described in [18] using pathological elements.…”

Behavioral modeling for synthesizing n-scroll attractors

“…Particularly on the generation of continuous time n-scroll attractors by using universal active devices [2,3], a piece-wise linear (PWL) approach is often used to model the nonlinear part of the third order chaotic system [4,5,6,7,8]. Despite of that PWL models are relatively easy to build and numerical simulations can be realized, in practice, the predicted performance of the chaotic system differs substantially from reality.…”

Derivation of Oscillators from Biquadratic Band Pass Filters Using Circuit Transformations

“…In recent times, the concepts of pathological elements have been proven to be very useful for circuit analysis, transformation and synthesis. Their applications have been presented in the literature [11][12][13][14]. By the use of nodal admittance matrix expansion method and pathological elements, the systematic synthesis of the current conveyor-based active RC canonic oscillators was reported in [15,16].…”