Fundamentals of Electrical Engineering I

312 Pages·2008·2.37 MB·English

Fundamentals of Electrical Engineering I
By:
Don Johnson

Fundamentals of Electrical Engineering I
By:
Don Johnson
Online:
<http://cnx.org/content/col10040/1.9/ >
C O N N E X I O N S
RiceUniversity,Houston,Texas
'2008 Don Johnson
This selection and arrangement of content is licensed under the Creative Commons Attribution License:
http://creativecommons.org/licenses/by/1.0
Table of Contents
1 Introduction
1.1 Themes ......................................................................................1
1.2 Signals Represent Information ...............................................................2
1.3 Structure of Communication Systems ........................................................6
1.4 The Fundamental Signal .....................................................................7
1.5 Introduction Problems .......................................................................8
Solutions ........................................................................................11
2 Signals and Systems
2.1 Complex Numbers ..........................................................................13
2.2 Elemental Signals ...........................................................................17
2.3 Signal Decomposition .......................................................................20
2.4 Discrete-Time Signals .......................................................................21
2.5 Introduction to Systems ....................................................................24
2.6 Simple Systems .............................................................................26
2.7 Signals and Systems Problems ..............................................................29
Solutions ........................................................................................34
3 Analog Signal Processing
3.1 Voltage, Current, and Generic Circuit Elements .............................................35
3.2 Ideal Circuit Elements ......................................................................36
3.3 Ideal and Real-World Circuit Elements .....................................................39
3.4 Electric Circuits and Interconnection Laws ..................................................39
3.5 Power Dissipation in Resistor Circuits ......................................................43
3.6 Series and Parallel Circuits .................................................................44
3.7 Equivalent Circuits: Resistors and Sources ..................................................49
3.8 Circuits with Capacitors and Inductors .....................................................54
3.9 The Impedance Concept ....................................................................54
3.10 Time and Frequency Domains .............................................................56
3.11 Power in the Frequency Domain ...........................................................58
3.12 Equivalent Circuits: Impedances and Sources ..............................................59
3.13 Transfer Functions ........................................................................60
3.14 Designing Transfer Functions ..............................................................65
3.15 Formal Circuit Methods: Node Method ....................................................66
3.16 Power Conservation in Circuits ............................................................71
3.17 Electronics ................................................................................73
3.18 Dependent Sources ........................................................................73
3.19 Operational Ampli(cid:28)ers ....................................................................76
3.20 The Diode ................................................................................81
3.21 Analog Signal Processing Problems ........................................................84
Solutions .......................................................................................106
4 Frequency Domain
4.1 Introduction to the Frequency Domain .....................................................109
4.2 Complex Fourier Series ....................................................................109
4.3 Classic Fourier Series ......................................................................114
4.4 A Signal’s Spectrum .......................................................................116
4.5 Fourier Series Approximation of Signals ...................................................117
4.6 Encoding Information in the Frequency Domain ...........................................122
4.7 Filtering Periodic Signals ..................................................................124
iv
4.8 Derivation of the Fourier Transform .......................................................126
4.9 Linear Time Invariant Systems ............................................................131
4.10 Modeling the Speech Signal ..............................................................134
4.11 Frequency Domain Problems .............................................................140
Solutions .......................................................................................152
5 Digital Signal Processing
5.1 Introduction to Digital Signal Processing ..................................................155
5.2 Introduction to Computer Organization ...................................................155
5.3 The Sampling Theorem ....................................................................159
5.4 Amplitude Quantization ...................................................................162
5.5 Discrete-Time Signals and Systems ........................................................165
5.6 Discrete-Time Fourier Transform (DTFT) .................................................167
5.7 Discrete Fourier Transforms (DFT) ........................................................172
5.8 DFT: Computational Complexity ..........................................................174
5.9 Fast Fourier Transform (FFT) .............................................................174
5.10 Spectrograms ............................................................................177
5.11 Discrete-Time Systems ...................................................................180
5.12 Discrete-Time Systems in the Time-Domain ..............................................181
5.13 Discrete-Time Systems in the Frequency Domain .........................................185
5.14 Filtering in the Frequency Domain .......................................................186
5.15 E(cid:30)ciency of Frequency-Domain Filtering .................................................189
5.16 Discrete-Time Filtering of Analog Signals ................................................192
5.17 Digital Signal Processing Problems .......................................................193
Solutions .......................................................................................204
6 Information Communication
6.1 Information Communication ...............................................................209
6.2 Types of Communication Channels ........................................................210
6.3 Wireline Channels .........................................................................210
6.4 Wireless Channels .........................................................................215
6.5 Line-of-Sight Transmission .................................................................216
6.6 The Ionosphere and Communications ......................................................217
6.7 Communication with Satellites ............................................................217
6.8 Noise and Interference .....................................................................218
6.9 Channel Models ...........................................................................219
6.10 Baseband Communication ................................................................220
6.11 Modulated Communication ...............................................................221
6.12 Signal-to-Noise Ratio of an Amplitude-Modulated Signal .................................222
6.13 Digital Communication ...................................................................224
6.14 Binary Phase Shift Keying ...............................................................224
6.15 Frequency Shift Keying ..................................................................227
6.16 Digital Communication Receivers ........................................................228
6.17 Digital Communication in the Presence of Noise ..........................................230
6.18 Digital Communication System Properties ................................................231
6.19 Digital Channels .........................................................................233
6.20 Entropy ..................................................................................234
6.21 Source Coding Theorem ..................................................................235
6.22 Compression and the Hu(cid:27)man Code ......................................................236
6.23 Subtlies of Coding .......................................................................237
6.24 Channel Coding ..........................................................................238
6.25 Repetition Codes .........................................................................240
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6.26 Block Channel Coding ...................................................................241
6.27 Error-Correcting Codes: Hamming Distance ..............................................242
6.28 Error-Correcting Codes: Channel Decoding ...............................................245
6.29 Error-Correcting Codes: Hamming Codes ................................................246
6.30 Noisy Channel Coding Theorem ..........................................................248
6.31 Capacity of a Channel ...................................................................249
6.32 Comparison of Analog and Digital Communication .......................................250
6.33 Communication Networks ................................................................251
6.34 Message Routing .........................................................................252
6.35 Network architectures and interconnection ................................................253
6.36 Ethernet .................................................................................254
6.37 Communication Protocols ................................................................256
6.38 Information Communication Problems ....................................................258
Solutions .......................................................................................272
7 Appendix
7.1 Decibels ...................................................................................279
7.2 Permutations and Combinations ...........................................................280
7.3 Frequency Allocations .....................................................................281
Solutions .......................................................................................283
Index ...............................................................................................284
Attributions ........................................................................................290
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Chapter 1
Introduction
1.1 Themes1
From its beginnings in the late nineteenth century, electrical engineering has blossomed from focusing on
electrical circuits for power, telegraphy and telephony to focusing on a much broader range of disciplines.
However,theunderlyingthemesarerelevanttoday: Powercreationandtransmissionandinformationhave
been the underlying themes of electrical engineering for a century and a half. This course concentrates on
the latter theme: the representation, manipulation, transmission, and reception of information by electrical
means. This course describes what information is, how engineers quantify information, and how electrical
signals represent information.
Information can take a variety of forms. When you speak to a friend, your thoughts are translated by
yourbrainintomotorcommandsthatcausevariousvocaltractcomponents(cid:21)thejaw, thetongue, thelips(cid:21)to
moveinacoordinatedfashion. Informationarisesinyourthoughtsandisrepresentedbyspeech,whichmust
haveawellde(cid:28)ned, broadlyknownstructureso thatsomeone elsecan understandwhat yousay. Utterances
convey information in sound pressure waves, which propagate to your friend’s ear. There, sound energy is
converted back to neural activity, and, if what you say makes sense, she understands what you say. Your
words could have been recorded on a compact disc (CD), mailed to your friend and listened to by her on
her stereo. Information can take the form of a text (cid:28)le you type into your word processor. You might send
the (cid:28)le via e-mail to a friend, who reads it and understands it. From an information theoretic viewpoint, all
of these scenarios are equivalent, although the forms of the information representation(cid:21)sound waves, plastic
and computer (cid:28)les(cid:21)are very di(cid:27)erent.
Engineers, who don’t care about information content, categorize information into two di(cid:27)erent forms:
analog and digital. Analog information is continuous valued; examples are audio and video. Digital
information is discrete valued; examples are text (like what you are reading now) and DNA sequences.
The conversion of information-bearing signals from one energy form into another is known as energy
conversionortransduction. Allconversionsystemsareine(cid:30)cientsincesomeinputenergyislostasheat,but
thislossdoesnotnecessarilymeanthattheconveyedinformationislost. Conceptuallywecoulduseanyform
ofenergytorepresentinformation,butelectricsignalsareuniquelywell-suitedforinformationrepresentation,
transmission(signalscanbebroadcastfromantennasorsentthroughwires), andmanipulation(circuitscan
bebuilttoreducenoiseandcomputerscanbeusedtomodifyinformation). Thus,wewillbeconcernedwith
how to
• represent all forms of information with electrical signals,
• encode information as voltages, currents, and electromagnetic waves,
• manipulate information-bearing electric signals with circuits and computers, and
• receive electricsignalsandconverttheinformationexpressedbyelectricsignalsbackintoausefulform.
1Thiscontentisavailableonlineat<http://cnx.org/content/m0000/2.18/>.
1
2 CHAPTER 1. INTRODUCTION
Telegraphy represents the earliest electrical information system, and it dates from 1837. At that time,
electricalsciencewaslargelyempirical,andonlythosewithexperienceandintuitioncoulddeveloptelegraph
systems. Electrical science came of age when James Clerk Maxwell2 proclaimed in 1864 a set of equations
that he claimed governed all electrical phenomena. These equations predicted that light was an electro-
magnetic wave, and that energy could propagate. Because of the complexity of Maxwell’s presentation, the
development of the telephone in 1876 was due largely to empirical work. Once Heinrich Hertz con(cid:28)rmed
Maxwell’s prediction of what we now call radio waves in about 1882, Maxwell’s equations were simpli(cid:28)ed
by Oliver Heaviside and others, and were widely read. This understanding of fundamentals led to a quick
successionofinventions(cid:21)thewirelesstelegraph(1899),thevacuumtube(1905),andradiobroadcasting(cid:21)that
marked the true emergence of the communications age.
During the (cid:28)rst part of the twentieth century, circuit theory and electromagnetic theory were all an
electricalengineerneededtoknowtobequali(cid:28)edandproduce(cid:28)rst-ratedesigns. Consequently,circuittheory
served as the foundation and the framework of all of electrical engineering education. At mid-century, three
"inventions" changed the ground rules. These were the (cid:28)rst public demonstration of the (cid:28)rst electronic
computer (1946), the invention of the transistor (1947), and the publication of A Mathematical Theory of
Communication by Claude Shannon3 (1948). Although conceived separately, these creations gave birth to
the information age, in which digital and analog communication systems interact and compete for design
preferences. About twenty years later, the laser was invented, which opened even more design possibilities.
Thus, the primary focus shifted from how to build communication systems (the circuit theory era) to what
communications systems were intended to accomplish. Only once the intended system is speci(cid:28)ed can an
implementation be selected. Today’s electrical engineer must be mindful of the system’s ultimate goal,
and understand the tradeo(cid:27)s between digital and analog alternatives, and between hardware and software
con(cid:28)gurations in designing information systems.
Vision Impaired Access: Thanks to the translation e(cid:27)orts of Rice University’s Disability Sup-
port Services4 , this collection is now available in a Braille-printable version. Please click here5 to
download a .zip (cid:28)le containing all the necessary .dxb and image (cid:28)les.
1.2 Signals Represent Information6
Whether analog or digital, information is represented by the fundamental quantity in electrical engineering:
the signal. Stated in mathematical terms, a signal is merely a function. Analog signals are continuous-
valued; digital signals are discrete-valued. The independent variable of the signal could be time (speech, for
example), space (images), or the integers (denoting the sequencing of letters and numbers in the football
score).
1.2.1 Analog Signals
Analog signals are usually signals de(cid:28)ned over continuous independent variable(s). Speech (Section 4.10) is
produced by your vocal cords exciting acoustic resonances in your vocal tract. The result is pressure waves
propagating in the air, and the speech signal thus corresponds to a function having independent variables of
space and time and a value corresponding to air pressure: s(x,t) (Here we use vector notation x to denote
spatial coordinates). When you record someone talking, you are evaluating the speech signal at a particular
spatial location, x say. An example of the resulting waveform s(x ,t) is shown in this (cid:28)gure (Figure 1.1:
0 0
Speech Example).
2http://www-groups.dcs.st-andrews.ac.uk/∼history/Mathematicians/Maxwell.html
3http://www.lucent.com/minds/infotheory/
4http://www.dss.rice.edu/
5http://cnx.org/content/m0000/latest/FundElecEngBraille.zip
6Thiscontentisavailableonlineat<http://cnx.org/content/m0001/2.26/>.