Electrical Measurements in the Laboratory Practice

296 Pages·2016·7.92 MB·English

by  Rosario Bartiromo

Undergraduate Lecture Notes in Physics
Rosario Bartiromo
Mario De Vincenzi
Electrical
Measurements
in the
Laboratory
Practice
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Rosario Bartiromo Mario De Vincenzi
(cid:129)
Electrical Measurements
in the Laboratory Practice
123
RosarioBartiromo Mario DeVincenzi
UniversitàRoma Tre UniversitàRoma Tre
Rome Rome
Italy Italy
ISSN 2192-4791 ISSN 2192-4805 (electronic)
Undergraduate Lecture Notesin Physics
ISBN978-3-319-31100-5 ISBN978-3-319-31102-9 (eBook)
DOI 10.1007/978-3-319-31102-9
LibraryofCongressControlNumber:2016934203
©SpringerInternationalPublishingSwitzerland2016
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Foreword
This book is intended for students in physics or engineering attending laboratory
classes in electrical measurements. It covers the basic theory of electrical circuits,
describes analog and digital instrumentation, and applies modern methods to
evaluate uncertainties in electrical measurements. Its structure and content are the
result of a specific teaching experience lasted for more than 5 years.
Indeedwhenwefirstfacedthetaskofofferinglaboratoryclassesinelectricityto
physics students, we soon realized that available textbooks had two major short-
comings. First, the evaluation of measurement uncertainties they propose is often
inconsistent with modern methodology, as elaborated in the review of the expert
panel appointed by the Bureau International des Poids et Measures (BIPM).
Second, digital measuring devices, now ubiquitous in class and research labora-
tories,arenotdescribedormarginallymentioned.Moreover,textbooksavailablein
the published literature are often very specialized and do not pay enough attention
tothelinksthatthematterdealtwithhaswiththegeneralframeworkandmethods
of physics and engineering.
The material presented inthese pages can be taught during the second semester
of the second year of the course of studies. At this stage, students should have
completed their basic physics studies and achieved a level of maturity enabling
them to generalize to other subjects the concepts they learn in the study of a
particular topic. Therefore, we were encouraged to use the matter subject of the
course, which is electrical circuits with the relevant instrumentation and experi-
ments, as an opportunity for students to:
(cid:129) Consolidate the understanding of the concepts needed for the evaluation of the
uncertainties in experimental measurements and complete the learning of nec-
essary formal tools
(cid:129) Illustratewithexamplesthemethodstoconstructmodelsofphysicalsystems,a
veryimportant task intheprofessionallife,emphasizingtheirpotentialities and
limitations
v
vi Foreword
(cid:129) Familiarizewithamodernelectronicequipmentwheretheunderstandingofthe
functional relationships between different parts of the measuring device allows
for an effective exploitation even without the knowledge of the construction
details
(cid:129) Learn to use the tools of linear system analysis, such as harmonic decomposi-
tion,symbolicmethod,thedualitybetweenfrequencyandtimedomain,andthe
concept of normal modes
(cid:129) Learn to design and perform simple laboratory experiments to verify physical
laws and to measure parameters used to characterize components and materials
(cid:129) Take advantage of the availability of data in digital form to learn how to write
simple software for their analysis
(cid:129) Learnhowtoreportonlaboratoryactivitiesinamannersuitableforascientific
presentation of experimental results.
We are convinced that the availability of a valuable written text is a necessary
condition for students to learn and internalize the arguments dealt with during the
lecturesandthelaboratorysessionsandtoreachalevelofknowledgesignificantat
the professional level. Since we did not find in the available literature a book, or a
reasonablecombinationofbooks,thatwassuitabletosupportthetypeofcoursewe
had in mind to offer, we decided the writing of these notes.
This book consists of ten chapters, each followed by an adequate number of
exercises, which are briefly outlined below. In addition, in the first of its three
appendices we propose a series of nine experiments to carry out in the laboratory,
with an illustration mainly intended for the use of student tutors.
Inlinewiththeexperimentalapproachwehavechosen,westartinChap.1with
the definition of electrical circuits and the description of components required for
theirconstruction.Wethenintroducethediscretecomponentmodelanddiscussits
validity limits. Next, we discuss the characteristics of ideal components by intro-
ducing the concepts of impedance and admittance. Construction methods of
resistors, inductors, and capacitors are then briefly outlined. A discussion of the
skin effect is presented at this stage, and completed in a separate appendix, to
illustratethelimitationsofthediscretecomponent modelwithaconcreteexample.
This chapter assumes a certain degree of familiarity with the content of General
Physics courses, but where we deem it useful, or necessary, the relevant concepts
are recalled in special notes.
InChap.2,weintroducethetwoKirchhofflawsandweillustratethetopological
properties of electric networks. The principal methods used under steady-state
conditionstocomputethedistributionofvoltagesandcurrentsinacircuitarethen
presented. After a brief description of problems posed by the possible nonlinearity
in the characteristics of components, we discuss the properties of linear networks:
superposition and reciprocity theorems and the concept of equivalent circuit with
related theorems (Norton and Thévenin).
Foreword vii
Chapter 3 examines the uncertainties associated with electrical measurements
adopting as a reference the guide developed by the International Organization for
Standardization (ISO) [1] that has standardized the treatment of measurement
uncertainties in science and industry. We first discuss the different types of
uncertainties and their causes, and introduce the concept of standard uncertainty.
Then we show how to evaluate the combined effect of various sources of uncer-
tainty. Particular emphasis is given to the possibility of correlation between the
measurements, a concept that can be usefully introduced at this stage of under-
graduate studies program. All these concepts are applied in a number of examples
in order to achieve an appropriate level of clarity.
In Chap. 4, we first discuss methods to measure steady-state currents and
voltages.Afterrecallingtheimportantfeaturesofmeasuringinstruments,theuseof
a current meter is illustrated and the principles of operation of the moving coil
galvanometer are presented in detail. This is followed by a discussion of voltage
measurements and an illustration of the different types of voltmeter and their
characteristics. Throughout this chapter, a special attention is given to explain to
students the influence of the instrument used to perform the measurement on its
result and the importance of systematic uncertainties that may come with it. The
chapter ends with a detailed discussion of methods for measuring the resistance
of the circuit components.
Chapter 5 begins with the definition and characterization of time-dependent
signals. We recall again the properties of the inductors and capacitors and then
proceed to the derivation of the differential equation that governs the evolution of
currentandvoltageinaseriesRLCcircuit.Thisequationissolvedforasinusoidal
signalafterillustratingthespecificityandtheimportanceofthistypeofsignal.Itis
then explained how the generalization to the space of complex numbers allows a
more easy solution of linear circuits under sinusoidal excitation by reducing the
differential equations into algebraic equations. This result is finally formalized in
the symbolic method with the introduction of the complex representation of volt-
ages and currents and the concept of complex impedance of circuit components.
In Chap. 6, the frequency response of important alternating current circuits is
obtained.Itbeginswithresonantcircuits,seriesandparallel,andthenitdealswith
bridge circuits that allow the measurement of unknown impedances. The series–
parallel transformation is used for the assessment of the effect due to nonideal
components in resonant circuits. We then introduce the notion of two-port circuits
and discuss Bode diagrams for their amplitude and phase response. The chapter
continueswithadetailedsolutionoftheRCandRLcircuitsinbothofthehigh-pass
and low-pass filter configuration and a discussion of their possible use as differ-
entiators and integrators of waveforms. Then we recall the phenomenon of mutual
inductionanditsuseinelectricaltransformerswhoseidealbehaviorisevaluatedin
detail. The chapter ends with a discussion of the problem of impedance matching
and a presentation of the main methods used in this regard.
viii Foreword
Chapter 7 is devoted to the illustration of alternating signals other than sinu-
soidalandtotheexperimentalmethodsusefultocharacterizethem.Theconceptof
effective value of an electrical quantity is introduced and methods for its mea-
surement are presented. Finally, phase measurements are briefly discussed.
In Chap. 8, both analog and digital oscilloscopes are introduced and their
operation is analyzed in detail. We first illustrate the principles of operation of a
cathoderaytubeandtheblockdiagramofananalogoscilloscope.Wedealindetail
with the need to synchronize this instrument with the phenomena whose time
evolution we want to study and we discuss the methods to achieve it. The modern
version of the instrument, the digital oscilloscope, is then introduced and its
functionalstructureisdescribed.Thebenefitsobtainedareillustrated,andemphasis
is given to the possibility of reading the instrument memory with a personal
computer to process the data numerically in a personalized way. Finally, we
describe the methods for measuring the phase shift between two electrical signals
with an oscilloscope.
Chapter9isdevotedtotheanalysisofthebehaviorofnon-sinusoidalwaveforms
withparticularregardtocircuitexcitationbypulses.Wefirstdiscussthetechniques
forsolvingelectrical circuits in thetime domain and thespecialrole played bythe
step function.Then we proceed toobtainthe step response ofthe two-portcircuits
already studied in Chap. 6 in the frequency domain, with a particular emphasis on
the initial conditions to be imposed to the solution of the relevant differential
equations.Again,wefindtheconditionsunderwhichtheybehaveasintegratorsor
differentiatorsofinputsignals.TheresponseofRLCcircuitsisthenstudiedindetail
anditisused,asanexample,toevaluatetheparasiticinductanceinaRChigh-pass
filter. The chapter ends with an exhaustive evaluation of the properties of a com-
pensated voltage divider that we analyze in both the time and the frequency
domains. In this chapter we did not use Laplace methods to be consistent with the
undergraduate level of the book and to avoid the risk of hiding behind a formal
approach, the basic physics of circuit operation.
Finally, Chap. 10 addresses the problem of the behavior of components that
cannot be treated as discrete and in particular discusses the properties of trans-
mission lines. After introducing an appropriate representation, we derive the
so-called telegrapher equation. Its solution in the time domain shows that, in the
absence of losses, signals are transmitted without distortion with a propagation
speed given by line parameters. The general solution in the frequency domain is
worked out to introduce the concept of line impedance. Then, the issue of the
terminationoftheline isaddressedandtheexpressionforthereflectioncoefficient
isobtained.Afterdiscussingtheattenuationduetoresistivelosses,wedescribethe
electrical behavior of terminated transmission lines and obtain the expression for
their apparent impedance. The chapter ends with some practical considerations on
the cables used for connections in laboratory experiments.
Thebookcontainsthreeappendices.AppendixAisanimportantcomplementto
the main text. There we illustrate a series of nine experiments that we have used
extensivelyinourlaboratoryclasses.Foreachofthemwegiveaplanofactionthat
studentsshouldfollowandanotethatcanbeusefultotutorsbothinthepreparation
Foreword ix
and in the illustration of the experiment to students. Appendix B and C deal,
respectively, with the skin effect and the Fourier analysis. They are meant to give
more information on their subject to the interested readers.
Mostchaptersinthisbookareequippedwithanumberofproblemsthatstudents
can solve using concepts and methods discussed therein. For these problems, we
tried to maintain a level of difficulty in line with the preparation of students in the
second semester of undergraduate course of studies. Problems that require much
effort are marked with an asterisk.
Reference
1.BIPM,IEC,IFCC,ILAC,ISO,IUPAC,IUPAPandOIML,Evaluationofmeasurementdata-
Guidetoexpressionofuncertaintyinmeasurement.JCGM100:2008(2008)