Table Of ContentPaul J. Nahin
Transients for
Electrical Engineers
Elementary Switched-Circuit Analysis
in the Time and Laplace Transform
Domains (with a touch of MATLAB®)
Transients for Electrical Engineers
OliverHeaviside(1850–1925),thepatronsaint(amongelectricalengineers)of
transientanalysts.(Reproducedfromoneofseveralnegatives,dated1893,foundin
anoldcardboardboxwithanoteinHeaviside’shand:“Theonewithhandsinpockets
isperhapsthebest,thoughhismotherwouldhavepreferredasmile.”)
FrontispiecephotocourtesyoftheInstitutionofElectricalEngineers(London)
Paul J. Nahin
Transients for Electrical
Engineers
Elementary Switched-Circuit Analysis in the
Time and Laplace Transform Domains
®
(with a touch of MATLAB )
Foreword by John I. Molinder
PaulJ.Nahin
UniversityofNewHampshire
Durham,NewHampshire,USA
ISBN978-3-319-77597-5 ISBN978-3-319-77598-2 (eBook)
https://doi.org/10.1007/978-3-319-77598-2
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“An electrical transient is an outward
manifestation of a sudden change in circuit
conditions, as when a switch opens or closes
... The transient period is usually very short
... yet these transient periods are extremely
important, for it is at such times that the
circuit components are subjected to the
greatest stresses from excessive currents or
voltages ... it is unfortunate that many
electrical engineers have only the haziest
conception of what is happening in the circuit
atsuchtimes.Indeed,someappeartoviewthe
subject as bordering on the occult.”
and
“The study of electrical transients is an
investigationofoneofthelessobviousaspects
of Nature. They possess that fleeting quality
which appeals to the aesthetic sense. Their
study treats of the borderland between the
broad fields of uniformly flowing events ...
only to be sensed by those who are especially
attentive.”
—wordsfromtwoolderbooks1 on electrical
transients,expressingviewsthatarevalidtoday.
1The first quotation is from Allen Greenwood, Electrical Transients in Power Systems, Wiley-
Interscience 1971, and the second is from L. A. Ware and G. R. Town, Electrical Transients,
Macmillan1954.
In support of many of the theoretical calculations performed in this book,
software packages developed by The MathWorks, Inc. of Natick, MA, were
used (specifically, MATLAB® 8.1 Release 2013a and Symbolic Math
Toolbox 5.10), running on a Windows 7 PC. This software is now several
releases old, but all the commands used in this book work with the newer
versionsandarelikelytocontinuetoworkfornewerversionsforseveralyears
more.TheMathWorks,Inc.,doesnotwarranttheaccuracyofthetextofthis
book. This book’s use or discussions of MATLAB do not constitute an
endorsement or sponsorship by The MathWorks, Inc., of a particular
pedagogical approach or particular use of MATLAB, or of the Symbolic
MathToolboxsoftware.
To the Memory of
Sidney Darlington (1906–1997)
a pioneer in electrical/electronic circuit
analysis,2 who was a colleague and friend for
twenty years at the University of New
Hampshire. Sidney’s long and creative life
spanned the eras of slide rules to electronic
computers, and he was pretty darn good at
using both.
2Sidneyreceivedthe1945PresidentialMedalofFreedomforhiscontributionstomilitarytechnol-
ogyduringWorldWarII,andthe1981I.E.MedalofHonor.Oneofhisminorinventionsisthe
famous,nowubiquitousDarlingtonpair(theconnectionoftwo“ordinary”transistorstomakea
“super”transistor).WhenIonceaskedhimhowhecametodiscoverhiscircuit,hejustlaughedand
said,“Well,itwasn’tthathard—eachtransistorhasjustthreeleads,andsotherereallyaren’talotof
differentwaystohooktwotransistorstogether!”I’mstillnotsureifhewassimplyjoking.
Foreword
Day and night, year after year, all over the world electrical devices are being
switched “on” and “off” (either manually or automatically) or plugged in and
unplugged.Examplesincludehouselights,streetlights,kitchenappliances,refriger-
ators,fans,airconditioners,varioustypesofmotors,and(hopefullynotveryoften)
part of the electrical grid. Usually, we are only interested in whether these devices
areeither“on”or“off”andarenotconcernedwiththefactthatswitchingfromone
state to the other often results in the occurrence of an effect (called a transient)
betweenthetimetheswitchisthrownandthedesiredconditionof“on”or“off”(the
steady state) is reached. Unless the devices are designed to suppress or withstand
them,thesetransientscancausedamagetothedeviceorevendestroyit.
Takethecaseofanincandescentlightbulb.Thefilamentiscold(itsresistanceis
low)beforetheswitchisturnedonandbecomeshot(itsresistanceismuchhigher)a
shorttimeaftertheswitchisturnedon.Assumingthevoltageisconstantthefilament
current has an initial surge, called the inrush current, which can be more than ten
times the steady state current after the filament becomes hot. Significant inrush
current can also occur in LED bulbs depending on the design of the circuitry that
converts the alternating voltage and current from the building wiring to the much
lowerdirectvoltageandcurrentrequiredbytheLED.Duetothecompressormotor,
a refrigerator or air conditioner has an inrush current during startup that can be
severaltimesthesteadystatecurrentwhenthemotorisuptospeedandtherotating
armatureproducesthebackEMF.It’sveryimportanttotakethisintoaccountwhen
purchasing an emergency generator. The inrush current of the starter motor in an
automobile explains why it may run properly with a weak battery but requires
boostercablesfromanotherbatterytogetitstarted.
In this book, Paul Nahin focuses on electrical transients starting with circuits
consistingofresistors,capacitors,inductors,andtransformersandculminatingwith
transmission lines. He shows how to model and analyze them using differential
equations and how to solve these equations in the time domain or the Laplace
transform domain. Along the way, he identifies and resolves some interesting
apparentparadoxes.
ix
x Foreword
Readersareassumedtohavesomefamiliaritywithsolvingdifferentialequations
inthetimedomainbutthosewhodon’tcanlearnagooddealfromtheexamplesthat
areworkedoutindetail.Ontheotherhand,thebookcontainsacarefuldevelopment
oftheLaplacetransform,itsproperties,derivationsofanumberoftransformpairs,
anditsuseinsolvingbothordinaryandpartialdifferentialequations.The“touchof
Matlab” shows how modern computer software in conjunction with the Laplace
transform makes it easy to solve and visualize the solution of even complicated
equations.Ofcourse,aclearunderstandingofthefundamentalprinciplesisrequired
touseitcorrectly.
As in his other books, in addition to the technical material Nahin includes the
fascinatinghistoryofitsdevelopment,includingthekeypeopleinvolved.Inthecase
oftheTrans-Atlantictelegraphcable,youwillalsolearnhowtheywereabletosolve
thetransmissionlineequationswithoutthebenefitoftheLaplacetransform.
Whilethefocusofthebookisonelectricaltransientsandelectricalengineers,the
tools and techniques are useful in many other disciplines including signal
processing, mechanical and thermal systems, feedback control systems, and com-
municationsystems.Studentswillfindthatthisbookprovidesasolidfoundationfor
their further studies in these and other areas. Professionals will also learn some
things.Icertainlydid!
HarveyMuddCollege,Claremont, JohnI.Molinder
CA,USA
January2018
