Transmission Lines in Digital and Analog Electronic Systems: Signal Integrity and Crosstalk

306 Pages·2010·12.46 MB·English

by  Clayton R. Paul

TRANSMISSION LINES IN
DIGITAL AND ANALOG
ELECTRONIC SYSTEMS
TRANSMISSION LINES IN
DIGITAL AND ANALOG
ELECTRONIC SYSTEMS
Signal Integrity and Crosstalk
CLAYTON R. PAUL
Department ofElectrical and Computer Engineering
Mercer University
Macon, Georgia
and
EmeritusProfessor of Electrical Engineering
Universityof Kentucky
Lexington, Kentucky
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LibraryofCongressCataloging-in-PublicationData:
Paul,ClaytonR.
Transmissionlinesindigitalandanalogelectronicsystems:signalintegrityand
crosstalk/ClaytonR.Paul.
p.cm.
ISBN978-0-470-59230-4
1. Multiconductortransmissionlines. 2. Telecommunicationlines. 3. Crosstalk.
4. Signalintegrity(Electronics) 5. Electroniccircuits. I. Title.
TK872.T74P38242010
621.382’3–dc22
2010006495
PrintedintheUnitedStatesofAmerica
10987654321
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CONTENTS
Preface xi
1 Basic Skills and Concepts Having Application
to Transmission Lines 1
1.1 Units and Unit Conversion 3
1.2 Waves, Time Delay, Phase Shift, Wavelength, and
Electrical Dimensions 6
1.3 The Time Domainvs. the Frequency Domain 11
1.3.1 Spectra of Digital Signals 12
1.3.2 Bandwidth of Digital Signals 17
1.3.3 Computing the Time-Domain Response
of Transmission Lines Having Linear
Terminations Using Fourier Methods and
Superposition 27
1.4 The Basic Transmission-Line Problem 31
1.4.1 Two-Conductor Transmission Lines and Signal
Integrity 32
1.4.2 Multiconductor Transmission Lines and
Crosstalk 41
Problems 46
vii
viii CONTENTS
PART I TWO-CONDUCTOR LINES AND
SIGNAL INTEGRITY 49
2 Time-Domain Analysis of Two-Conductor Lines 51
2.1 The Transverse Electromagnetic (TEM) Mode
of Propagation and the Transmission-Line Equations 52
2.2 The Per-Unit-Length Parameters 56
2.2.1 Wire-Type Lines 57
2.2.2 Lines of Rectangular Cross Section 68
2.3 The General Solutions for the Line Voltage and Current 71
2.4 Wave Tracing and Reflection Coefficients 74
2.5 The SPICE (PSPICE) Exact Transmission-Line Model 84
2.6 Lumped-Circuit Approximate Models of the Line 91
2.7 Effects of Reactive Terminations on Terminal
Waveforms 92
2.7.1 Effect of Capacitive Terminations 92
2.7.2 Effect of Inductive Terminations 94
2.8 Matching Schemes for Signal Integrity 96
2.9 Bandwidth and Signal Integrity: When Does
the Line Not Matter? 104
2.10 Effect of Line Discontinuities 105
2.11 Driving Multiple Lines 111
Problems 113
3 Frequency-Domain Analysis of Two-Conductor Lines 121
3.1 The Transmission-Line Equations for Sinusoidal
Steady-State Excitation of the Line 122
3.2 The General Solution for the Terminal Voltages
and Currents 123
3.3 The Voltage Reflection Coefficient and Input Impedance
to the Line 123
3.4 The Solution for the Terminal Voltages and Currents 125
3.5 The SPICE Solution 128
3.6 Voltage and Current as a Function of Position
on the Line 130
3.7 Matching and VSWR 133
3.8 Power Flow on the Line 134
3.9 Alternative Forms of the Results 137
3.10 The Smith Chart 138
3.11 Effects of Line Losses 147
CONTENTS ix
3.12 Lumped-Circuit Approximations for Electrically
Short Lines 161
3.13 Construction of Microwave Circuit Components Using
Transmission Lines 167
Problems 170
PART II THREE-CONDUCTOR LINES AND CROSSTALK 175
4 The Transmission-Line Equations for Three-Conductor Lines 177
4.1 The Transmission-Line Equations for Three-Conductor Lines 177
4.2 The Per-Unit-Length Parameters 184
4.2.1 Wide-Separation Approximations for Wires 185
4.2.2 Numerical Methods 196
Problems 205
5 Solution of the Transmission-Line Equations
for Three-Conductor Lossless Lines 207
5.1 Decoupling the Transmission-Line Equations with Mode
Transformations 208
5.2 The SPICE Subcircuit Model 210
5.3 Lumped-Circuit Approximate Models of the Line 227
5.4 The Inductive-Capacitive Coupling Approximate Model 232
Problems 236
6 Solution of the Transmission-Line Equations
for Three-Conductor Lossy Lines 239
6.1 The Transmission-Line Equations for Three-Conductor
Lossy Lines 240
6.2 Characterization of Conductor and Dielectric Losses 244
6.2.1 Conductor Losses and Skin Effect 244
6.2.2 Dielectric Losses 248
6.3 Solution of the Phasor (Frequency-Domain)
Transmission-Line Equations for a
Three-Conductor Lossy Line 251
6.4 Common-Impedance Coupling 260
6.5 The Time-Domain to Frequency-Domain Method 261
Problems 270
Appendix A Brief Tutorial on Using PSPICE 273
Index 295
PREFACE
This book is intended as a textbook for a senior/first-year graduate-level
course in transmission lines in electrical engineering (EE) and computer
engineering(CpE)curricula.Ithasbeenclasstestedattheauthor’sinstitution,
MercerUniversity,andcontainsvirtuallyallthematerialneededforastudent
to become competent in all aspects of transmission lines in today’s high-
frequencyanalogandhigh-speeddigitalworld.Thebookisalsoessentialfor
industryprofessionalsasacompactreviewoftransmission-linefundamentals.
Untilasrecentlyasadecadeago,digitalsystemclockspeedsanddatarates
were in the hundreds of megahertz range. Prior to that time, the ‘‘lands’’ on
printed circuit boards (PCBs) that interconnect the electronic modules had
littleornoimpactontheproperfunctioningofthoseelectroniccircuits.Today,
the clock and data speeds have moved into the low gigahertz range. As the
demandforfasterdataprocessingcontinuestoescalate,thesespeedswillno
doubt continue to increase into the gigahertz frequency range. In addition,
analog communication frequencies have also moved steadily into the giga-
hertz range and will no doubt continue to increase. Although the physical
dimensions of these lands and the PCBs supporting them have not changed
significantlyover theseinterveningyears, thespectralcontentofthesignals
they carry has increased significantly. Because of this the electrical dimen-
sions (in wavelengths) of the lands have increased to the point where these
interconnectshaveasignificanteffectonthesignalstheyarecarrying,sothat
justgettingthesystemstoworkproperlyhasbecomeamajordesignproblem.
Thishasgeneratedanewdesignproblem,referredtoassignalintegrity.Good
signalintegritymeansthattheinterconnectconductorsshouldnotadversely
xi
xii PREFACE
affecttheoperationofthemodulesthattheconductorsinterconnect.Priorto
some 10 years ago, these interconnects could be modeled reliably with
lumped-circuit models that are easily analyzed using Kirchhoff’s voltage
and current laws and other lumped-circuit analysis methods. Because these
interconnectsarebecoming‘‘electricallylong,’’lumped-circuitmodelingof
themisbecominginadequateandgiveserroneousanswers.Mostinterconnect
conductors must now be treated as distributed-circuit transmission lines.
In the last 30 years there have been dramatic changes in electrical
technology, yet the length of the undergraduate curriculum has remained
four years. Since the undergraduate curriculum is a ‘‘zero-sum game’’, the
introduction of courses necessitated by the advancements in technology, in
particular digital technology, has caused many of the standard topics to
disappear from the curriculum or be moved to senior technical electives
whichnotallgraduatestake.Thesubjectoftransmissionlinesisanimportant
exampleofthis.Untiladecadeago,theanalysisoftransmissionlineswasa
standardtopicintheEEandCpEundergraduatecurricula.Todaymostofthe
undergraduate curricula contain a rather brief study of the analysis of
transmissionlinesinaone-semesterjunior-levelcourseonelectromagnetics
(often the only course on electromagnetics in the required curriculum). In
someschools,thisstudyoftransmissionlinesisrelegatedtoaseniortechnical
elective or has disappeared from the curriculum altogether. This raises a
serious problem in the preparation of EE and CpE undergraduates to be
competentinthemodernindustrialworld.Forthereasonsmentionedabove,
today’sundergraduateslackthebasicskillstodesignhigh-speeddigitaland
high-frequency analog systems. It does little good to write sophisticated
software if the hardware is unable to process the instructions. This problem
will increase as the speeds and frequencies of these systems continue to
increase, seemingly without bound. This book is meant to repair that basic
deficiency.
InChapter1,thefundamentalconceptsofwaves,wavelength,timedelay,
andelectricaldimensionsarediscussed.Inaddition,thebandwidthofdigital
signals and its relation to pulse rise and fall times is discussed. Preliminary
discussions of signal integrity and crosstalk are also given.
PartIcontainstwochapterscoveringtwo-conductortransmissionlinesand
designingforsignalintegrity.Chapter2coversthetime-domainanalysisof
those transmission lines. The transmission-line equations are derived and
solved,andtheimportantconceptofcharacteristicimpedanceiscovered.The
important per-unit-length parameters of inductance and capacitance that
distinguishonelinefromanotherareobtainedfortypicallines.Theterminal
voltages and currents of lines with various source waveforms and resistive
terminationsarecomputedbyhandviawavetracing.Thisgivesconsiderable
insightintothegeneralbehavioroftransmissionlinesintermsofforward-and
PREFACE xiii
backward-traveling waves and their reflections. The SPICE computer pro-
gramanditspersonalcomputerversion,PSPICE,containanexactmodelfora
two-conductorlosslesslineandisdiscussedasacomputationalaidinsolving
for transmission-line terminal voltages and currents. SPICE is an important
computationaltoolsinceitprovidesadeterminationoftheterminalvoltages
andcurrentsforpracticallinearandnonlinearterminationssuchasCMOSand
bipolar devices, for which hand analysis is very formidable. Matching
schemes for achieving signal integrity are covered, as are the effects of line
discontinuities.Chapter3coversthecorrespondinganalysisinthefrequency
domain.Theimportantanalogconceptsofinputimpedancetotheline,VSWR
andtheSmithchart(whichprovidesconsiderableinsight),arealsodiscussed.
The effect of line losses, including skin effect in the line conductors and
dielectric losses in the surrounding dielectric, are becoming increasingly
critical, and their detrimental effects are discussed.
Part II repeats these topics for three-conductor lines in terms of the
importantdetrimentaleffectsofcrosstalkbetweentransmissionlines.Cross-
talkisbecomingofparamountconcerninthedesignoftoday’shigh-speedand
high-frequencyelectronicsystems.Thetransmission-lineequationsforthree-
conductor lossless lines are derived, and the important per-unit-length
matrices of the inductance and capacitance of the lines are covered in
Chapter 4. Numerical methods for computing the per-unit-length parameter
matricesofinductanceandcapacitance arestudied,andcomputerprograms
are given that compute these numerically for ribbon cables and various
structures commonly found on PCBs. Chapter 5 covers the solution of
three-conductor lossless lines via mode decoupling. A SPICE subcircuit
model is determined via this decoupling and implemented in the computer
program SPICEMTL.EXE. This program performs the tedious diagonaliza-
tion of the per-unit-length parameter matrices and gives as output a SPICE
subcircuitformodelinglosslesscoupledlines.Asinthecaseoftwo-conductor
lines,this allowsthe study of line responsesnot onlyfor resistiveloadsbut,
more important, nonlinear and/or reactive loads such as CMOS and bipolar
devicesthatarecommonlineterminationsintoday’sdigitalsystems.Howto
incorporate the frequency-dependent losses of the line conductors and the
surroundingdielectricintoasolutionforthecrosstalkvoltagesisdiscussedin
Chapter 6. The frequency-domain solution of the MTL equations is again
given in terms of similarity transformations in the frequency domain. The
time-domain solution for the crosstalk voltages is obtained in terms of the
frequency-domaintransferfunction,whichisobtainedbysuperimposingthe
responses to the Fourier components of V ðtÞ.
S
The appendix gives a brief tutorial of SPICE (PSPICE), which is used
extensively throughout the book. Several computer programs used and
describedinthisbookforcomputingtheper-unit-lengthparametermatrices