Feedback in Analog Circuits

174 Pages·2016·5.05 MB·English

by  Agustin Ochoa (auth.)

Agustin Ochoa
Feedback
in Analog
Circuits
Feedback in Analog Circuits

Agustin Ochoa
Feedback in Analog Circuits
AgustinOchoa
XACT
Vista,CA,USA
ISBN978-3-319-26250-5 ISBN978-3-319-26252-9 (eBook)
DOI10.1007/978-3-319-26252-9
LibraryofCongressControlNumber:2015955840
SpringerChamHeidelbergNewYorkDordrechtLondon
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To Dad, Jess, and Basilio, I miss you
To Buck
To Mom
To Sonia, Diane, and David
And always, to Norma

Preface
Thepathtobecomingananalogdesignerislong,winding,andnarrow.Itisnotwell
marked and has many exits to other specialties and lines of work. Mostly it is a
lonelyexperiencepunctuatedwithperiodsofintensescrutinywhenthedesignfails
to meet a specification. Experience is the key. But where do we get it? We are
taught basic tools, such as the Kirchhoff nodal and loop analysis, device models,
matrix resolutions, and lots of tricks. What can we simplify, ignore, and approxi-
mate? Then we simulate over all imagined conditions and environments. But this
processisnotsatisfying.Weusetrickseveryoneelseknowsanduses,attributedto
someone else, that usually work. Mostly. Matrix analysis produces a jumble of
literals that do not easily reveal design trade-offs, and simulation results are even
worse with everything done in the background. Developing design insight is
difficult.
Thisbookpresentsatooltobeusedinthiseffort—theDrivingPointImpedance/
SignalFlowGraphmethod(DPI/SFG).Thistool,aswithalltools,issharpenedwith
use,anditsapplicationbecomessecondaryallowingthecircuittomaintaincentral
focus. With this tool, a circuit is mapped onto a flow graph, a pictorial schematic
showingcircuitcouplingsandcircuittopology.Loopsshowfeedback,andsummers
show where and how signals combine. The mapping process with use will not
necessitatetheintermediatestepofdrawingthesmallsignalequivalentcircuit;and
the transfer functions obtained will be in factored form associating pole-zero
information with particular nodes and elements–Low Entropy solutions. Such
resultswillaidinthedesignprocessandinthedevelopmentofexperiencequickly
andeffectively.
While thisbookiswrittenfor thepracticinganalog designer struggling togain
insight into a design handed to him from a previous project and asked to fix a
particularproblem,itisprobablyofmostvaluetothestudent,bothundergraduate
and graduate, before they generate bad habits. It is a tool that once mastered will
become a primary approach to their work facilitating the design process as it
exposes design dependencies and limitations. It is a book that I wish I had had at
anearlystageinmycareer.
vii
viii Preface
Howwillthisbookaidinthedevelopmentofananalogdesigner?TheDPI/SFG
process is based on fundamentals. It is grounded in basics and, as such, any
conclusion will have a direct path to these fundamentals providing confidence
that results are valid. Analysis based on insight lacks this tractability, especially
if the insight was not ours. What elements were ignored in the “insight” approxi-
mation to your problem? While that simplification may have been appropriate
before, is it valid here? And what happens to that approximation when the loop
gain goes below unity and we operate in open loop conditions? The DPI/SFG
approach provides a basis for examining simplifications systematically to insure
thatanyapproximationwemakeremainsvalidthroughouttherangeofoperationof
thedesign.Forexample,weusethedifferentialamplifierhalf-cellequivalentswith
little concern as to their origin and validity. But what were the assumptions
embedded in these equivalents? Primarily symmetry. Does our design have that
symmetry? And at what frequency will that high-frequency pole, ignored in this
equivalent,becomeactive?WecananswerthesequestionsdirectlyusingDPI/SFG.
And very quickly alongour analogpath,we cometofeedback which seems to
change everything. We soon realize that it is everywhere—an inverter shows the
effects of feedback as a kickback transient response when the output switches,
causing the inputsignaltospike,andasingletransistorLNA stage has output-to-
inputcapacitivecouplingandsharesapowerlinewithapoweroutputstage.These
examples are parasitic and sometimes may be handled by layout corrections and
isolation. Internal device feedback however cannot be corrected and we need to
live with it. What about intentional feedback? Now we need to address loading
effects and bidirectional signal propagations through circuit elements. Complicat-
ing the analysis of feedback is the language, language borrowed from the ideal
blocks where life is simple, applied to real circuits where everything mixes. We
cannotsimplyopenthelooptofindtheloopgainorisolatetheamplifiertofindits
openloopgain,Aol.Insteadwefindthattheseparameterscontaineffectsofloading,
of source impedance, and of reverse loop transmission. This book will show the
readerhowtohandlethesepropertiesdirectlyandefficiently.
Thepathtoanalogdesign,whilelongandwinding,hasbeenamostinteresting
one.MythankstoDonPatterson,HowardTang,andRogerGillforwalkingmuch
ofthispathwithme,toDr.JimEarlywhotoldmetoalwayssharpenmytools,to
Dr.WilliamShockleywhoremindedmetocountmyequationsandmyunknowns
early in problem solving, to Dr. Ruben Kelly who introduced me to DPI, and to
Dr. Doug Hamilton, Dr. Gabor Temes, and Bob Baker - excellent teachers and
gentlemen.
This work is filled with Pride, Elliot, and Joy(s), Inez, Olivia, Luisa, Amelia,
Juliana,andMolly,mygrandchildren,andtheirparents,SoniaandCliff,Dianeand
Adrian,andDavidandEmily.
And a special thank you, with gratitude, to my wife Norma for her constant
supportandlove.
Enjoy!
Vista,CA,USA AgustinOchoa
Contents
1 TheConceptofFeedback:WhyWeCareandComplications. . . . . 1
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
TheProblemwithOpen-LoopDesign. . . . . . . . . . . . . . . . . . . . . . . . . 3
TheIdealLoop:Black’sFeedbackRelation. . . . . . . . . . . . . . . . . . . . . 4
ComplicationsinFeedbackDesign. . . . . . . . . . . . . . . . . . . . . . . . . . . 5
RealLoops. . . . . .. . . . . . . .. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . 6
TheDrivingPointImpedance/SignalFlowGraphApproach. . . . . . . . . 9
Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 DrivingPointImpedanceandSignalFlowGraphBasics:
ASystematicApproachtoCircuitAnalysis. . . . . . . . . . . . . . . . . . . 13
DrivingPointImpedance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
SomeSimpleApplicationsoftheDPILaw. . . . . . . . . . . . . . . . . . . . . 15
IntroducingFlowGraphstotheAnalysis. . . . . . . . . . . . . . . . . . . . . . . 19
SimplifiedFlowGraphAlgebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
AFewMoreExamples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
TheDifferentialInputStage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
TheCascodeConfiguration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
InitialTimeConstantResponseforaResetComparator. . . . . . . . . . . . 29
Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 DPI/SFGGeneralizationsandExpansions:TheRoad
toFeedback. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
FlowGraphComponents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
TheFlowGraphTemplate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
AdditionalAnalysisfromtheSystemGraph. . . . . . . . . . . . . . . .. . . . . 41
BranchCurrentandPower. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
PortImpedances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
ExtendingtheFlowGraphstoIncludeEmbeddedCells. . . . . . . . . . . . 43
ix