Transmission Lines in Digital Systems for EMC Practitioners

275 Pages·2011·13.692 MB·English

by  Clayton R. Paul(auth.)

TRANSMISSION LINES
IN DIGITAL SYSTEMS
FOR EMC PRACTITIONERS
TRANSMISSION LINES
IN DIGITAL SYSTEMS
FOR EMC PRACTITIONERS
CLAYTON R. PAUL
Department ofElectrical and Computer Engineering
Mercer University
Macon, Georgia
and
Emeritus Professor of Electrical Engineering
Universityof Kentucky
Lexington, Kentucky
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LibraryofCongressCataloging-in-PublicationData:
Paul,ClaytonR.
TransmissionlinesindigitalsystemsforEMCpractitioners/ClaytonR.Paul.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-1-118-14399-5(hardback)
1. Electromagneticcompatibility. 2. Telecommunicationlines. I. Title.
TK7867.2.P383.2012
621.382024–dc23
2011021000
PrintedintheUnitedStatesofAmerica
oBookISBN:9781118145579
ePDFISBN:9781118145548
ePubISBN:9781118145562
MOBI ISBN:9781118145555
10 9 8 7 6 5 4 3 2 1
This book is dedicated to the humane and compassionate treatment
of animals
and my beloved pets:
Patsy, Dusty, Megan, Tinker, Bunny, Winston, Sweetheart, Lady, Tigger,
Beaver,Ditso,Buru,OldDog,Zip,Tara,Timothy,Kiko,Valerie,Red,Sunny,
Johnny, Millie, Molly, Angel, Autumn, and Shabby.
Those readers who are interested in the humane and compassionate
treatment of animals are encouraged to donate to
The Clayton and Carol Paul Fund for Animal Welfare
c/o the Community Foundation of Central Georgia
277 MLK, Jr. Blvd.
Suite 303
Macon, GA 31202
TheprimaryandonlyobjectiveofthisFundistoprovidemonetarygrantsto
(1) animal humane societies
(2) animal shelters
(3) animal adoption agencies
(4) low-cost spay-neuter clinics
(5) individual wildlife rehabilitators
(6) as well as other organizations devoted to animal welfare
in order to allow these volunteer organizations to use their enormous
enthusiasm, drive and willingness to reduce animal suffering and home-
lessness through the monetary maintenance of their organizations where
little or no monetary funds existed previously.
CONTENTS
Preface xi
1 Transmission Lines: Physical Dimensions vs.
Electric Dimensions 1
1.1 Waves, Time Delay, Phase Shift, Wavelength,
and Electrical Dimensions, 4
1.2 Spectral (Frequency) Content of Digital
Waveforms and Their Bandwidths, 10
1.3 The Basic Transmission-Line Problem, 22
2 Time-Domain Analysis of Two-Conductor Lines 31
2.1 The Transverse Electromagnetic Mode
of Propagation and the Transmission-Line Equations, 32
2.2 The Per-Unit-Length Parameters, 37
2.2.1 Wire-Type Lines, 37
2.2.2 Lines of Rectangular Cross Section, 47
2.3 The General Solutions for the Line Voltage
and Current, 50
2.4 Wave Tracing and Reflection Coefficients, 54
2.5 A Simple Alternative to Wave Tracing
in the Solution of Transmission Lines, 60
2.6 The SPICE (PSPICE) Exact Transmission-Line
Model, 70
vii
viii CONTENTS
2.7 Lumped-Circuit Approximate Models
of the Line, 75
2.8 Effects of Reactive Terminations on
Terminal Waveforms, 84
2.8.1 Effect of Capacitive Terminations, 85
2.8.2 Effect of Inductive Terminations, 87
2.9 Matching Schemes for Signal Integrity, 89
2.10 Effect of Line Discontinuities, 96
2.11 Driving Multiple Lines, 101
3 Frequency-Domain Analysis of Two-Conductor Lines 103
3.1 The Transmission-Line Equations for Sinusoidal
Steady-State (Phasor) Excitation of the Line, 104
3.2 The General Solution for the Line Voltages
and Currents, 105
3.3 The Voltage Reflection Coefficient and Input
Impedance of the Line, 106
3.4 The Solution for the Terminal Voltages
and Currents, 108
3.5 The SPICE Solution, 111
3.6 Voltage and Current as a Function of Position
on the Line, 112
3.7 Matching and VSWR, 115
3.8 Power Flow on the Line, 117
3.9 Alternative Forms of the Results, 120
3.10 Construction of Microwave Circuit Components
Using Transmission Lines, 120
4 Crosstalk in Three-Conductor Lines 125
4.1 The Multiconductor Transmission-Line
Equations, 125
4.2 The MTL Per-Unit-Length Parameters
of Inductance and Capacitance, 131
4.2.1 Wide-Separation Approximations
for Wires, 135
4.2.2 Numerical Methods, 145
5 The Approximate Inductive–Capacitive Crosstalk Model 155
5.1 The Inductive–Capacitive Coupling
Approximate Model, 159
CONTENTS ix
5.2 Separation of the Crosstalk into Inductive
and Capacitive Coupling Components, 166
5.3 Common-Impedance Coupling, 172
5.4 Effect of Shielded Wires in Reducing
Crosstalk, 173
5.4.1 Experimental Results, 182
5.5 Effect of Shield Pigtails, 183
5.5.1 Experimental Results, 187
5.6 Effect of Multiple Shields, 188
5.6.1 Experimental Results, 188
5.7 Effect of Twisted Pairs of Wires in Reducing
Crosstalk, 197
5.7.1 Experimental Results, 203
5.8 The Shielded Twisted-Pair Wire:
The Best of Both Worlds, 209
6 The Exact Crosstalk Prediction Model 211
6.1 Decoupling the Transmission-Line Equations
with Mode Transformations, 212
6.2 The SPICE Subcircuit Model, 215
6.3 Lumped-Circuit Approximate Models
of the Line, 231
6.4 A Practical Crosstalk Problem, 237
Appendix A Brief Tutorial on Using PSPICE 245
Index 267
PREFACE
Most of the numerous textbooks I have published were intended for class
instructionalbooksforelectricalengineering(EE)andcomputerengineering
(CpE)coursesinauniversityenvironment.Idecidedtowritethisbookforthe
industrial professional. My work has been in the field of electromagnetic
compatibility (EMC), known more commonly as interference in electronic
systems.Inthecourseofmyteaching,Ihavealsohadthepleasureofworking
withmanyEMCprofessionals.ItistothisgroupofprofessionalsthatIhave
focused the book.
I have written a brief but comprehensive book covering the set of
transmission-line skills that EMC practitioners today require in order to
besuccessfulinhigh-speeddigitalelectronics.Thebasicskillsinthebook
weren’tstudiedinmostcurriculasometenyearsago.Therapidlychanging
digitaltechnologyhascreatedthisdemandforadiscussionofnewanalysis
skills, particularly for the analysis of transmission lines where the con-
ductorsthatinterconnecttheelectronicmoduleshavebecome“electrically
large,”longerthanatenthofawavelength,whicharebecomingincreasingly
important.Crosstalkbetweenthelinesisalsorapidlybecomingasignificant
problemingettingmodernelectronicsystemstoworksatisfactorily.Hence
this small volume is concentrated on modeling “electrically long”connec-
tionconductorswherepreviouslyusedKirchhoff’svoltageandcurrentlaws
andlumped-circuitmodelinghavebecomeobsoletebecauseoftheincreas-
ingspeedsofmoderndigitalsystems.OneimportantexceptionisChapter5,
whereelectricallyshortlinesareconsideredexclusivelywhenweconsider
xi
xii PREFACE
the use of shielded lines and twisted pairs of wires to eliminate or reduce
crosstalk for electrically short lines.
Untilasrecentlyassometenyearsago,digitalsystemclockspeedsanddata
rateswereinthelowmegahertzrange.The“lands”onprintedcircuitboards
(PCBs)thatinterconnecttheelectronicmoduleshadlittleornoimpactonthe
proper functioning of those electronic circuits. Today, the clock and data
speedshavemovedintothelowgigahertzrange.Asthedemandforfasterdata
processing continues to escalate, these speeds will no doubt continue to
increaseintothegigahertzfrequencyrange.Inaddition,analogcommunica-
tionfrequencieshavealsomovedsteadilyintothegigahertzrangeandwillno
doubtcontinuetoincrease.Althoughthe“physicaldimensions”oftheselands
and the PCBs supporting them have not changed significantly over the
interveningyears,thespectralcontentofthesignalstheycarryhasincreased
significantly.Becauseofthis,the“electricaldimensions”(inwavelengths)of
the lands have increased to the point where these “interconnects” have a
significant effect on the signals they are carrying, so that just getting the
systemstoworkproperlyhasbecomeamajordesignproblem.Priortosome
ten years ago, these interconnects could be reliably modeled with lumped-
circuitmodelsthatareeasilyanalyzedusingKirchhoff’svoltageandcurrent
lawsandotherlumped-circuitanalysismethods.Becausetheseinterconnects
arebecoming“electricallylong,”lumped-circuitmodelingofthemisbecom-
ing inadequate and gives erroneous answers. Most of the interconnect con-
ductors must now be treated as distributed-circuit transmission lines.
In Chapter 1, the increasingly important fundamental concepts of waves,
wavelength,timedelay,andelectricaldimensionsarediscussed.Inaddition,
thebandwidthofdigitalsignalsanditsrelationtopulseriseandfalltimesare
discussed. The effect of electrically long conductors on signal integrity is
discussed.
Chapter2coversthetime-domainanalysisoftwo-conductortransmission
lines. The transmission-line equations are derived and solved, and the im-
portant concept of characteristic impedance is covered. The important per-
unit-lengthparametersofinductanceandcapacitancethatdistinguishoneline
fromanotherareobtainedfortypicallines.Theterminalvoltagesandcurrents
of lines with various source waveforms and resistive terminations are com-
puted by hand via wave tracing. This gives considerable insight into the
general behavior of transmission lines in terms of forward- and backward-
traveling waves and their reflection. The SPICE computer program and its
personal computer version, PSPICE, contains an exact model for a two-
conductorlosslesslineandisdiscussedasacomputationalaidinsolvingfor
the transmission-line terminal voltages and currents. SPICE is an important
computationaltool,sinceitprovidesadeterminationoftheterminalvoltages
andcurrentsforpracticallinearandnonlinearterminationssuchasCMOSand
PREFACE xiii
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. The important analog concepts of input impedance to the line and
high-frequency modeling of electronic circuits are also discussed.
The remaining chapters, Chapters 4, 5, and 6, cover crosstalk between
adjacent transmission lines. Chapter 4 covers the derivation of the multi-
conductortransmissionline(MTL)equations,consistingoflineshavingthree
conductors and the crosstalk between these lines. The derivation of the per-
unit-length parameters in the 2(cid:1)2 inductance and capacitance matrices,
L and C, for three-conductor lines are discussed either in an approximation
fashionforwidelyspacedlinesorintermsofcomputerprogramsforhandling
these difficult calculations. These computer programs can be downloaded
from the John Wiley ftp site:
ftp://ftp.wiley.com/public/sci_tech_med/multiconductor_transmission/
Their use is discussed for various cross-sectional geometries.
Chapter 5 discusses an approximate solution of the MTL equations for
electrically short lines. This model is not only easy to use to compute the
crosstalkinanapproximatefashionbutalsoillustratestheuseof(1)shielded
wires and (2) twisted pairs of wires for eliminating crosstalk. Numerous
experimentalresultsareshownthatverifythemodel.Theeffectofpigtailsin
degrading the effect of shielded wires is shown along with experimental
results.
Finally,Chapter6discussesanexactPSPICEsubcircuitforthesolutionof
anylosslessMTL.Severalexperimentalresultsthatverifytheaccuracyofthis
modelareshown.Acomputerprogram,SPICEMTL,thatgeneratesaPSPICE
subcircuitmodelthatcanreadilybeembeddedinaSPICEprogramtoprovide
the exact solution can be downloaded from the ftp site.
Severalimportantfeatures ofthis textbookare (1)thebasicsof transmis-
sion-linefundamentals,(2)thenumerousexperimentalresults thatillustrate
and verify the mathematical results, and (3) the availability of computer
programs that facilitate the solution of transmission lines for determining
signal integrity as well as crosstalk.
The appendix gives a brief tutorial of SPICE (PSPICE), which is used
extensively throughout the book.
CLAYTON R. PAUL
Macon,Georgia