Design of Analog Circuits through Symbolic Analysis

Fakhfakh, Mourad; Tlelo‐Cuautle, Esteban; Fernández, Francisco V.; Asenova, Irina; Biolek, Dalibor; Biolková, Viera; Broz, Jochen; Castro-López, R.; Coito, Fernando V.; Dumitriu, Lucia; Fino, M. Helena; Gielen, Georges; Grasso, Francesco; Hennig, Eckhard; Horta, Nuno; Iordache, Mihai; Krauße, Dominik; Loulou, Mourad; Luchetta, Antonio; Manetti, S.; McConaghy, Trent; Nitsche, Gregor; Piccirilli, Maria Cristina; Pierzchala, Marian; Reatti, Alberto; Roca-Moreno, Elisenda; Rodanski, Benedykt; Sánchez–López, C.; Santos, Mauro; Schafer, Eric; Schwarz, Peter; Sommer, Ralf; Tan, Sheldon X.-D.

doi:10.2174/97816080509561120101

Cited by 54 publications

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“…The remaining connections have equivalents according to the nullator and norator i-v characteristics. https://www.degruyter.com/view/j/cjece Carpathian Journal of Electronic and Computer Engineering 13/2 (2020) 1-6 Another approach, the nullor along with grounded resistors can be manipulated in order to obtain inverting properties, features that the nullator and the norator cannot model by themselves [22,23]. The main purpose of the introduction of inverting properties is that the behavior of some active devices involves inverting the voltage and current input-signals.…”

Section: Nullor Equivalencesmentioning

confidence: 99%

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Using Pathological Elements in Analog Circuit Analysis and Simulation

Grib

Erdei

Turcu

et al. 2020

Carpathian Journal of Electronic and Computer Engineering

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This paper is focused on some kind of mystery circuit nullator, nullor, current mirror, and voltage mirror, all of them known as pathological elements. These pathological elements can be used to perform circuit modelling, symbolic circuit analysis, circuit synthesis, circuit design and to develop applications that involve modern active devices. It is described a new modeling of nullor-based active devices from the circuit abstraction level. In this paper it is presented the way all types of equations which describe the circuit containing nullors can be directly formulated from the diagrams of these circuits if we took into account that a nullator is an over-determined two-port circuit element (zero voltage, zero current) and the norator is an undetermined two-port circuit element (any voltage and any current). To simulate the nullors with ideal voltage controlled voltage sources, ec = Ac_c uc, with the control gate an ideal independent current source, jC = 0.0 A and with the amplification (transfer) factor Ac_C very big (theoretically ∞), the analog circuits with nullors can be analyzed by using any of the existing simulation software. By this way, it was possible the elaboration of efficient algorithms for an automatic formulation of Kirchhoff’s equations, of loop equations, of modified nodal equations and of state equations for circuits with pathological elements. These procedures can be easily implemented in dedicated programs for the simulations of the complex analog circuits with pathological elements. The example presented in this paper validates the presented models for nullors.

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Section: Nullor Equivalencesmentioning

confidence: 99%

“…The nullor is a two-port element and it is known as universal active element [13,22,23]. This concept means that the nullor along with capacitors and resistors can be used to design a maximum number of functions with the minimum number of active devices.…”

Section: Introductionmentioning

confidence: 99%

Using Pathological Elements in Analog Circuit Analysis and Simulation

Grib

Erdei

Turcu

et al. 2020

Carpathian Journal of Electronic and Computer Engineering

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Symbolic analysis of electric networks with higher order summative cofactors and parameter decision diagrams

Lasota

2018

Circuit Theory & Apps

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SummaryThe paper introduces the concept of higher order summative cofactors (HOSCs) to the circuit analysis. Although the concept is not new, it is not well known. In the paper, some mathematical background of HOSCs is presented. The further development of the concept of HOSC will yield computer implementation arithmetic of HOSC. A cancellation‐free symbolic analysis technique, which is based on HOSC arithmetic, is presented. This technique allows results to be created directly from a netlist in the form of a binary decision diagram, which is called a parameter decision diagram. Additionally, HOSC arithmetic allows the calculation to be started in many places (sometimes distant) simultaneously. The techniques of rolling up the already analyzed parts of a circuit, which is built into HOSC arithmetic, result in a novel multilevel hierarchical analysis method that is called hierarchical parameter decision diagram (HPDD). Unlike in most hierarchical methods, the results that are obtained based on the subcircuit representation in HPDD always maintain a cancellation‐free form. The HPDD always represents the sum of the product form, which is heavily compressed due to the self‐similarities of the actual circuit. The time that is required for any recalculation of the transfer functions is greatly reduced. Analysis of models that are based on pathological components is also a natural consequence of using HOSC arithmetic.

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Efficient generation of compact symbolic network functions in a nested rational form

Filaretov

Gorshkov

2020

Circuit Theory & Apps

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SummaryThis paper presents the extension of generalized parameter extraction method for direct circuit function generation in a fully symbolic form of rational expressions or a nested s‐expanded polynomial. The new formula for implicit extraction of parameters that allows effective factoring by grouping of determinants of circuits containing any linear models of active elements, such as controlled sources, nullors, and pathological mirrors, is proposed. The concept of nullor with parameter is used for implicit extraction. The rules of optimal selection of parameters for extraction are presented. The proposed algorithm of symbolic analysis is implemented in the CirSym program, which is available online. The paper discusses the results of automatic analysis of several large active circuits, as well as determinants of matrixes and passive topologies, in terms of compact size and minimization of the number of arithmetic operations. Experimental results demonstrate that the expressions of determinants derived by CirSym are more compact than the results of the factorization algorithms of commercial computer algebra systems. The comparison with several other symbolic analysis algorithms shows that CirSym is the only available program that provides the exact calculation of the symbolic function of large circuits in the s‐expanded form with every coefficient being a compact‐nested expression.

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Design of Analog Circuits through Symbolic Analysis

Cited by 54 publications

References 0 publications

Using Pathological Elements in Analog Circuit Analysis and Simulation

Using Pathological Elements in Analog Circuit Analysis and Simulation

Symbolic analysis of electric networks with higher order summative cofactors and parameter decision diagrams

Efficient generation of compact symbolic network functions in a nested rational form

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