Lecture Notes in Electrical Engineering 479 Mourad Fakhfakh Editors Marian Pierzchala Pathological Elements in Analog Circuit Design Lecture Notes in Electrical Engineering Volume 479 Board of Series editors Leopoldo Angrisani, Napoli, Italy Marco Arteaga, Coyoacán, México Bijaya Ketan Panigrahi, New Delhi, India Samarjit Chakraborty, München, Germany Jiming Chen, Hangzhou, P.R. 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Printedonacid-freepaper ThisSpringerimprintispublishedbytheregisteredcompanySpringerInternationalPublishingAG partofSpringerNature Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Foreword This book focuses on some kind of mystery circuit elements, namely norator, nullator, nullor, current mirror, and voltage mirror, all of them known as patho- logical elements. As you will see along the chapters of this book, the mystery of those pathological elements relies on its usefulness to perform circuit modeling, symbolic circuit analysis, circuit synthesis, circuit design and to develop applica- tions that involve modern active devices. The nullor concept was introduced to model the ideal behavior of the operational amplifier, and since the works of B. D. H. Tellegen and H. J. Carlin in the 60s, nowadays many researchers intro- duced contributions on analysis, synthesis, and design of active circuits. More recently,Prof. A.M.Soliman and co-authors have introduced contributions in this newmillenniumbyusingthecurrentmirrorandvoltagemirror,whichasapairthey form a universal element, as the nullor does, and they are useful to analyze and discover new designs of active devices. The editors are active researchers that have already published works on these topics,andtheyhaveincludedaPrefacethatlistsdetailedstatisticsonpublications and contributions associated with pathological elements. Personally, I met Prof. MouradattheSMACD conferenceheldatGammarth,Tunisia,in2012.From that time, I have followed his research not only on topics involving pathological ele- ments,butalsooncircuitoptimization.ProfessorMarianhasalsopublishedseveral worksusingpathologicalelementsinanalysisandsynthesisofanalogcircuits.Both editors have been organized eleven chapters in this book entitled: Pathological ElementsinAnalogCircuitDesign,whichisdividedintotwopartswhereyoucan finddetailstoinferthesignificanceofthepathologicalelementsandofthefixatorin analysis, synthesis, design and applications. The chapters highlight the use of the pathological elements to model transistors, voltage amplifiers, current amplifiers, impedance converters, current conveyors, inverting conveyors, operational transconductance amplifiers, operational transresistance amplifiers, and other modern active devices. v vi Foreword Without a doubt, this book will make your imagination to explore new chal- lenges in the application of pathological elements for the modeling, analysis, synthesis, and applications of analog circuits, and we will be happy reading your contributions in these topics. Puebla, México/Ciudad Esteban Tlelo-Cuautle de México, México Professor at Instituto Nacional de Astrofísica, Óptica y Electrónica Centro de Investigación y de Estudios Avanzados del IPN Preface Priorto1960,electroniccircuitsandsystemswereproducedbyconnectingdiscrete componenttodiscretedevices.Eachcomponentordevicewaspackagedseparately and connected by means of conducting wires. So, the procedures for analysis, synthesis, and design of electronic circuits were relatively simple. Some network theory and basic techniques were used for such purpose. Circuits were most often analyzed using a combination of Kirchhoff’s voltage and current laws. Models of active devices invariably involved resistors, capacitors, inductors, and dependent sources. In the 1960s, the integrated circuit was developed. This device created entire electronic circuits on or in a silicon wafer. The devices are interconnected through the silicon material or by very small conducting metal strips, deposited on the wafer. Since then, thousands of devices and components can be created on a very small wafer to produce very complex circuits. Although the integrated circuit is technically a circuit composed of thousands of components and devices, it is referred to as an electronic device. Many types of integrated circuits are available, forexample,operationalamplifiers,currentconveyors,transconductanceamplifiers, and so on. Due to their complexity, such new elements cannot be analyzed by the conventional simple laws of network theory. The development of new integrated circuits and the complexity of their constructions had stimulated the network the- orists to consider new basic elements which allow the circuit designer to analyze and synthesize integrated circuits in more simpler and effective ways. Among various basic elements proposed so far, nullors, which are the combinations of nullatorsandnorators,havebeenregardedtobeuniversalbuildingblockssinceall existing analog circuit building blocks can be represented using these elements. Althoughtheoriginofthenullorconceptitselfwasadvanced asearlyas1961– 1964,formanyyearsthiselementwaslargelyregardedastheoreticalconceptwith singular properties.Nowadays,this singularelement isconsidered asavery useful and powerful “tool-kit” as it can be argued by the increasing large number of publishedpapersdealingwiththeuseofsuchaparticularelementinanalogcircuit design (see Fig. 1). vii viii Preface 1400 1200 1000 800 600 400 200 0 65-69 70-74 75-79 80-84 85-89 90-94 95-99 00-04 05--09 10--14 Fig. 1 Quinquennal evolution (since 1965) of the number of papers on Google Scholar. (Key- words:Nulloranalogcircuit) Themirrorisanothersingularelementwhichprovidesaframeworknotonlyfor analysis, synthesis, and design of integrated circuits but also for interrelating betweendifferentnetworkelements.Itisarelativelynewlyknownsingularelement (when compared to the nullor). It was proposed in 1999. Nullorsandmirrorsarealsocalled“pathologicalelements”becausetheydonot possess the classical and the conventional obvious properties. Such pathological elements are used in a large spectrum of applications in the modern circuit and systemtheory,aswellasinthedesignpractice.Figure2showstheevolutionofthe useofthesepathologicalelementsinanalogcircuitdesignandsynthesis(thesource of these statistics is “Google Scholar” with the keywords “pathological elements”, “analog”, “circuit”). In view of the above, therefore, it clearly appears timely to propose a book on these pathological elements and their applications in analog circuit modeling, analysis, and synthesis. 4000 3500 3000 2500 2000 1500 1000 500 0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 Fig.2 Annual evolution (since2000)ofthenumberof papersonGoogleScholar.(Keywords: pathologicalelementsanalogcircuit)—updatedonDecember17,2017 Preface ix As far as is known, no book has so far been published on this topic yet. This book will fill this void. The editors have invited some experts from related disciplines involved in the synthesis and design of analog circuits using pathological elements to contribute and give a comprehensive overview of their particular field. In addition, an open call for chapters was launched. A large number of interesting proposals were submitted. Few of them were selected for inclusion in the book. The book is divided into two parts: Part I is entitled “Pathological Elements in the Analysis and the Synthesis of Analog Circuits.” It encompasses six chapters. PartIIhasthetitle“PathologicalElementsintheDesignofAnalogCircuits.”It contains five chapters. Hereafter, the eleven chapters are succinctly introduced. Chapter 1 is entitled “Symbolic Analysis and Synthesis of Analog Circuits Using Nullors and Pathological Mirror Elements” and is proposed by Miguel A. Duarte-Villaseñor, Esteban Tlelo-Cuautle, Luis Gerardo de la Fraga, and Carlos Sánchez-López. It reviews advantages of the (Modified) Nodal Analysis ((M)NA) theoryanddetailstheinclusionofpathologicalvoltagemirrors andcurrentmirrors into the NA formulation. It shows how to perform symbolic circuit analysis and then how to synthesize those circuit elements using MOS transistors. It is also highlighted that from such kind of circuit modeling, one can transform a voltage-mode circuit into a current-mode one and vice-versa. The authors show the design of both modes of operationatthetransistorlevelofdesign,forwhichtheyalsoprovidedetailsonthe synthesisapproachwhereeachnullator,norator,voltagemirror,andcurrentmirror can have multiple options to be implemented with MOS transistors. Several examples are provided to appreciate the advantages of the NA formulation from analog circuits modeled by nullors and mirrors, the symbolic circuit analysis, the transformation from voltage-mode to current-mode and vice-versa, and the syn- thesis of pathological circuits by using MOS transistors. Chapter2,“GeneralizedParameterExtractionMethodforSymbolicAnalysisof Analog Circuits Containing Pathological Elements”, authored by Vladimir Filare- tov, Konstantin Gorshkov, Sergey Kurganov, and Maxim Nedorezov deals with a description of the extension of Generalized Parameter Extraction Method (GPEM) for symbolic analysis of large-scale analog circuits containing pathological ele- ments. A brief overview of the parameter extraction approach is offered. An algorithm implementing the concept of Higher Order Summative Cofactors (HOSCs)for determinants computation of the pathological elements-based circuits isalsoproposed.Furthermore,thehierarchicaldecompositiontechniquesofupward and downward analysis of electronic circuits by GPEM are presented. Chapter3,entitled“Two-Graph-BasedSemi-topologicalAnalysisofElectronic Circuits with Nullors and Pathological Mirrors” and proposed by Marian Pierz- chala and Mourad Fakhfakh, deals with the abstraction level elements such as nullator,norator,currentmirrors,andvoltagemirrorsthathavebeenveryusefulin theanalysisoflinearcircuits. Inthis chapter, theauthorspropose amethodfor the