Table Of ContentUndergraduate Lecture Notes in Physics
Bryan H. Suits
Electronics
for Physicists
An Introduction
Undergraduate Lecture Notes in Physics
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Bryan H. Suits
Electronics for Physicists
An Introduction
123
BryanH.Suits
Physics Department
Michigan Technological University
Houghton,MI,USA
ISSN 2192-4791 ISSN 2192-4805 (electronic)
Undergraduate Lecture Notesin Physics
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Preface
Physicists rely heavily on electrical instrumentation to measure physical phenom-
ena.Therewasatime,notlongagoinhistory,whenitwasnormalforaphysicistto
routinelydesignandconstructtheirownelectricalinstrumentation.Whilethereare
exceptions, in general this is no longer the case; design and construction of most
electronicinstrumentationislefttospecialistsandengineers.However,aphysicist,
whether an experimentalist or theorist, will need some understanding of the basics
of electronics and how the equipment works in order to fully understand and
evaluate the results of measurements, and possibly in order to troubleshoot and
makesimplerepairs.Muchofthisunderstandingmustfirstcomefromaknowledge
of the language of electronics—the lexicon as well as the symbolic representation
of circuits using schematic diagrams. This book was written for use as an under-
graduatephysicstextwithsuchfutureuseinmind.Thedetailsnecessaryforquality
engineering design are generally excluded here in favor of a basic and practical
understanding of what is going on.
A second utility of electronics in the physics curriculum is that many ideas and
problem-solving strategies show up that are also used in other areas of science.
Indeed,electricalanalogiesareoftenusedasanexplanationforsituationsthathave
little to do with electronics. One prime example of cross-use is the appearance of
imaginary numbers. Imaginary numbers show up in all areas of science and engi-
neeringthatincludeperiodic signals.Inaddition toelectronics,thoseareasinclude
studies of vibration, including seismometry, acoustics, optics, radio and radar, and
even “brain waves.” It is important to understand how to use and interpret imagi-
narynumberssince,afterall,bydefinitionnorealmeasurementwillevergiveyou
animaginaryresult.Otheroverlappingtopicsincluderesonance,solutionsoflinear
equations, and the use of linearized models.
Each electronics instructor will have their own idea about what is most impor-
tant.Thatcannotbehelped.Whatispresentedhererepresentsmypriorities.Based
onmyperspectiveandexperienceasaphysicistandteacherofelectronics,Ichose
introductorytopicsandproblemsthatIfindmostinterestingandpotentiallyuseful.
There is, however, more in this book than can possibly be covered in a single
v
vi Preface
semester course. Anyone using the book as a course textbook, in whole or in part,
should feel free to skip those topics that do not match their interests.
Anyelectronicscoursewouldbeexpectedtoincludealaboratorycomponent.In
fact, some of the material here originated as background material for such a lab-
oratory experience. It is recognized that each instructor has their own laboratory
priorities, and possibly a limited or specialized supply of laboratory equipment for
suchapurpose.Itishopedthatthepresentationhereiswritteninamannersuitable
for use in either the laboratory or classroom. The first obvious examples of labo-
ratories that appear here are the sections related to the Wheatstone and Kelvin
bridges, both of which originated primarily as laboratory exercises. Along with
material in the last chapter, some practical experience using an embedded micro-
controller—that is, some programming—is definitely useful. Programming varies
fromdevicetodeviceandisnotreally“electronics,”andsoitisonlyincludedhere
in a very general way.
The book includes three broad categories of electronics. Chapters 1–5 cover
passive linear electronics, Chaps. 6–11 look at nonlinear and active devices
includingdiodes,transistors,andop-amps,andChaps. 12–14considerthebasicsof
digital electronics and simplified computers.
This text originated as weekly handouts and laboratory write-ups for a course
designed primarily for second-year university physics students. The level of the
materialhereisappropriateforstudentswhohavesuccessfullylearnedthematerial
in introductory electricity and magnetism as well as mathematics up to the first
course in integral calculus. As the extent of the material in the handouts expanded
overtheyears,itgottothepointthatsomestudentsstartedreferringtothehandouts
as “the book.” That reference served as one motivating factor to formalize those
coursenotesintoafullvolume.Ithankthosestudentsforprovidingthatinspiration,
and I hope this proves to be a useful exercise for both of us.
Houghton, MI, USA Bryan H. Suits
Contents
1 The Basics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Voltage and Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Simple Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Kirchhoff’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Resistors in Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Resistors in Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Effective Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Resistors in Parallel–Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Solving Circuits with Circuit Reduction. . . . . . . . . . . . . . . . . . . . . . . 11
Solving Circuits with Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Branch and Mesh Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Example—Using Kirchhoff’s Laws . . . . . . . . . . . . . . . . . . . . . . . . 15
Nodal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
The Ideal Current Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
The Ground and Common Connections . . . . . . . . . . . . . . . . . . . . . . . 21
Multiple Sources—The Superposition Theorem . . . . . . . . . . . . . . . . . 22
Electrical Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Additional Application—The Kelvin-Varley Divider. . . . . . . . . . . . . . 24
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2 Additional Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Thevenin and Norton Equivalents . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Determining the Thevenin and/or Norton Parameters. . . . . . . . . . . . 32
How Is This Used for Circuit Reduction?. . . . . . . . . . . . . . . . . . . . 34
Equivalent for an Infinite Array of Resistors. . . . . . . . . . . . . . . . . . 35
The Wheatstone Bridge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Wheatstone Bridge “Hieroglyphics” . . . . . . . . . . . . . . . . . . . . . . . . 38
The Reciprocity Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Example—R-2R Ladder with Sources . . . . . . . . . . . . . . . . . . . . . . 40
vii
viii Contents
Delta-Y Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
The Kelvin Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Additional Application—Resistivity of Lamellae. . . . . . . . . . . . . . . 47
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3 Complex Impedances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
What Is a Linear Device? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Some Vocabulary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Passive Linear Circuit Elements with Two Leads . . . . . . . . . . . . . . . . 55
Idealized Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
RC and L/R Time Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
RC Time Constant Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Capacitors and Inductors with Sinusoidal Sources . . . . . . . . . . . . . . . 60
Superposition and Complex Impedances . . . . . . . . . . . . . . . . . . . . . . 62
Series and Parallel Capacitors and Inductors. . . . . . . . . . . . . . . . . . . . 66
Comments About Complex Arithmetic. . . . . . . . . . . . . . . . . . . . . . . . 67
Solving Circuits Using Complex Impedances. . . . . . . . . . . . . . . . . . . 68
A.C. Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Condenser Microphones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4 More on Capacitors and Inductors. . . . . . . . . . . . . . . . . . . . . . . . . 79
Real Capacitors and Inductors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Measuring Capacitors and Inductors . . . . . . . . . . . . . . . . . . . . . . . . . 80
Capacitive Position Sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
A Simple Circuit for Measuring Inductors . . . . . . . . . . . . . . . . . . . . . 82
Switched Capacitor Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Charging a Capacitor Efficiently . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Mutual Inductance and Transformers . . . . . . . . . . . . . . . . . . . . . . . . . 86
The Dot Convention for Transformers . . . . . . . . . . . . . . . . . . . . . . . . 89
Inductive Position Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
RLC Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Cable Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Cable Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Signal Speed in a Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Impedance of Finite Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Capacitor and Inductor Labels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Duality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Contents ix
5 The Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
The Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Laplace Transform Example 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Method I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Method II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Laplace Transform Example 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Laplace Transform Example 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Comment on Partial Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Poles and Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6 Diodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Semiconductor Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Diode Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Piece-Wise Linear Diode Models. . . . . . . . . . . . . . . . . . . . . . . . . . 125
An Analytic Model for the Semiconductor Diode . . . . . . . . . . . . . . 126
Solving Circuits with Diodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
The Ideal Diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Graphical Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Diode Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Diode Capacitance and Response Time . . . . . . . . . . . . . . . . . . . . . . . 136
Specialty and Other Diodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7 FETs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Junction Field Effect Transistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Circuit Analysis with a JFET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Example 1—Determine Circuit Components. . . . . . . . . . . . . . . . . . 146
Example 2—Determine Operating Point. . . . . . . . . . . . . . . . . . . . . 147
The FET A.C. Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
FET Amplifier Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
The Ohmic Region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
MOSFETs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Additional Application—Dynamic Memory . . . . . . . . . . . . . . . . . . . . 158
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
8 Bipolar Junction Transistors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
BJT D.C. Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
BJT A.C. Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
BJT Large Signal Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Graphical Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Single Supply Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Solutions from Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
