Table Of ContentLecture Notes in Electrical Engineering 441
Mauro Parodi
Marco Storace
Linear and
Nonlinear Circuits:
Basic & Advanced
Concepts
Volume 1
Lecture Notes in Electrical Engineering
Volume 441
Board of Series editors
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Samarjit Chakraborty, München, Germany
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Tan Kay Chen, Singapore, Singapore
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About this Series
“Lecture Notes in Electrical Engineering (LNEE)” is a book series which reports
the latest research and developments in Electrical Engineering, namely:
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Mauro Parodi Marco Storace
(cid:129)
Linear and Nonlinear
Circuits: Basic & Advanced
Concepts
Volume 1
123
MauroParodi MarcoStorace
Department ofElectrical, Electronic, Department ofElectrical, Electronic,
Telecommunications Engineering Telecommunications Engineering
andNavalArchitecture (DITEN) andNavalArchitecture (DITEN)
University of Genoa University of Genoa
Genoa Genoa
Italy Italy
ISSN 1876-1100 ISSN 1876-1119 (electronic)
Lecture Notesin Electrical Engineering
ISBN978-3-319-61233-1 ISBN978-3-319-61234-8 (eBook)
DOI 10.1007/978-3-319-61234-8
LibraryofCongressControlNumber:2017944207
©SpringerInternationalPublishingAG2018
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To our past, present, and the future students.
Foreword
Circuit Theory is the bedrock of Electrical and Electronic Engineering.
Traditionally, the didactic treatment of the subject has been restricted to linear
framework.Whilelinearmethodsareextremelypowerfulanduniversallyappliedin
Engineering practice, they miss the richness of nonlinear phenomena.
This book takes a unified approach to both Linear and Nonlinear Circuits,
emphasizingfromtheoutset,thatCircuitTheoryprovidesapowerfulparadigmfor
modelling and analysing a range of physical systems, not just the electrical and
electronic ones. The laws of Circuit Theory are rooted in fundamental physical
principles, and the methods rely on profound mathematics. The circuits paradigm
provide accessible insight and intuition into the operation of a wide range of
physical systems, from neural networks to coupled pendula.
Parodi and Storace have done an excellent job in presenting foundational
material that every undergraduate student should know, followed by advanced
concepts which will enrich the learning experience for more advanced undergrad-
uatesandgraduatestudents.Bycombiningthismaterial,theirbookwillalsobean
invaluable resourcefor practising researchers who will, for the first time, findboth
classical linear circuits concepts and advanced results in the one place.
Michael Peter Kennedy
vii
Preface
Circuit theory is a discipline at the crossroad between physics, mathematics and
system theory and providesbasic knowledge in various fields of engineering, such
as electronic devices and circuits, signal processing, control systems. The circuit
theory core is the concept of model, i.e., a mathematical description of a physical
system. Circuit theory treats circuits with a field-less approach and, contrary to
general electromagnetic theory, neglects the electromagnetic propagation.
Circuit theory was developed later than electrical circuits, whose origin (ne-
glecting the Greek discover of static electricity) dates back to the end of XVIII
century. The first circuit theory laws were provided in the middle of XIX century
and, up to the middle of XX century, the development of circuit theory was basi-
cally related to electrical circuits. During World War II, circuit theory received a
strong boost due to the influence and growth of disciplines such as system theory,
automatic controls and electronics. With the development of transistors and com-
puters, the realization criteria and the potentialities of circuits underwent deep
changes, concerned with both design (the semiconductor miniaturization made it
possible to conceive ever more ambitious, complex and low-cost circuits) and the
growing corpus of knowledge that circuit theory was called to provide and to
rationalize. The devices made available by technology were described by models,
first of elementary devices, such as transistors, and subsequently of circuit parts to
be used as building blocks in broader architectures. The detailed behavior of the
devices inside these blocks became unessential for the user and, as such, usually
ignored.
Overtheyears,theneedofbothdesigningincreasinglycomplexcircuits(largely
containing nonlinear devices) and checking their behaviors before concretely
realizethemrequiredmoreandmoretheuseofcomputernumericalsimulations.In
this perspective, the use of models is essential to provide to the computer a sys-
tematicdescriptionofthecircuitstructure,togetherwiththeelectricalpropertiesof
its components; furthermore, models contributed to the formalization of methods
suitabletobemappedintomathematicalalgorithms,inparticular,forthetreatment
of large-size systems of algebraic equations and of systems of ordinary differential
equations. The numerical solutions provided by computers in shorter and shorter
ix
x Preface
timesmadeitpossibletostudycomplexcircuitsalsointheabsenceofananalytical
solution.
The circuit theory development had repercussions also outside the circuit field,
inareasseeminglyfarfromcircuits,butwhereexperimentalobservationsdisplayed
astrongsimilaritytophysicalbehaviorsobservableincircuits.Thisledtoformulate
equivalentcircuitmodelsmimickingtheobservedphenomena.WhenWorldWarII
was still in full swing, for example, Hodgkin and Huxley formulated their circuit
model for neurons, now head of a family of models.
In our vision, a circuit theory course must systematically show ideas and
methodssuitabletostudybothlinearandnonlinearcircuits,eitherpassiveoractive.
The presentation of concepts and fundamental methods of analysis must aim not
only to allow their application in today’s problems, but also to highlight their
meaning and potential as tools to understand and address future developments.
These needs were clearly expressed during the ’60s of the last century, when
CharlesDesoerandErnestKuhadoptedthemasguidelinesfortheirtreatise“Basic
Circuit Theory”, which became a classic for university education. In 1969, at
University of Genoa, Giuseppe Biorci adopted this text (in the original English
version)forhiscourse,andin1972hewastheEditorofitsItalianversion.Among
theuniversitytextswrittenwithsimilarmotivationsinthefollowingyears,itshould
be definitely mentioned “Linear and Nonlinear Circuits”, written by the previous
authorsandbyLeonChuaabouttwentyyearslater.Morerecentbooksfocusedon
circuits have downsized, in our opinion, this character. Even if the university
programsstronglychangedinthelastdecades,givinginsomecasesalargerspace
toinformation attheexpensesofknowledge,thereisstillneedofbooksproviding
not only a solid background to all students, but also a broader view to the most
motivated among them. We strongly believe that circuit theory is a highly educa-
tional discipline, not only for Engineers. Indeed, students learn a quite large set of
toolsand,whendealingwithaspecificproblem,theyhavetodecidewhatsubsetof
tools can be (or hasto be) usedto solve it. Inour opinion,this capacity of solving
non-trivial problems should remain one of the main elements of the scientific
cultural baggage. It can certainly be aided and made more powerful by many
practical skills, but cannot be replaced by them.
Withtheseguidelinesinmind,thisbookisstructuredinmultiplereadinglevels:
each part is split into two chapters (basic level and advanced level), with two
independent levels of reading. Moreover, in the advanced level some suggested
shortcuts provide simplified reading paths, left to the reader’s choice. The basic
chaptersareaimedatnewcomerstocircuittheory,especiallystudentstakingafirst
courseinthesubject.Theirorganizationislargelybasedontheexperienceripened
through a one-semester course, taught for several years, first at the Polytechnic
UniversityofMilanandthenattheUniversityofGenoa.Ourgoalwiththeseparts
is to explain the mathematics needed to handle circuits as clearly and simply as
possible, and to show how it can be used to analyze/understand how a circuit
works, also through many worked examples. A peculiar feature of this book is its
emphasis on examples, showing how the proposed methods can be applied. The
advanced chapters are aimed at both basic-level university students driven by
Preface xi
curiosity—inthebeliefthatcuriosityisthemaindriverforstudyingandlearning—
and higher-level students, up to Ph.D. students and young researchers that want to
find a complete treatment of many mathematical aspects related to circuits. The
theory is developed systematically, starting with the simplest circuits (linear,
time-invariant and resistive) and providing food for thought on nonlinear circuits,
potentialfunctions,linearalgebra,geometricalinterpretationsofsomeresults.This
is the subject of this volume. Circuits characterized by time-evolution/dynamics
willbetreatedwiththesamespiritinasecondvolume.Inouropinion,themultiple
reading levels help teachers to adapt their course to best meet students’ needs and
background.Inallcases,studentsshouldbeassignedhomeworkfromtheproblems
at the end of each chapter. They could also do computer projects based on circuit
simulators and/or build real circuits during lab activities, e.g., to reproduce and
check the results of some of the proposed examples. These aspects are left to the
teacher experience and availability.
We are indebted to our friend Lorenzo Repetto, who carefully revised the pre-
liminary version of this book reporting bugs and providing detailed comments,
manyofwhichwereincludedinthepresentvolume.Wealsowanttorememberour
colleague and friend Amedeo Premoli, who passed away in 2014 and who shared
ourvisionofcircuittheory.Thestructureofthisbookreflectsatleastinpartmany
discussions had in the past with him.
Genoa, Italy Mauro Parodi
February 2017 Marco Storace
