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AnalogEngineefs
PocketReference
ArtKayandTimGreen,Editors
DownloadeBookat
www.ticom/analogrefguide
卷TEXASINSTRUMENTS
THESEMATERIALSAREPROVIDED“空6”TtMAKESNOWARRANTIESORREPRESENTAHONSWITHREGARDTO
THESEMATERIALSORUSEOFTHESEMATERIAL^EXPRESS,IMPLIEDORSTATUTORYINCLUDINGFORACCURACY,
COMPLETENESS,ORSECURDYTtDISCLAIMSANYIMPLIEDWARRANTIESOFMERCHANTABHHY,FTOESSFORA
PARTICULARPURPOSE;QUIETENJOYMENT,QUIETPOSSESSIONANDNON4NFRINGEMENTOFANYTHIRDPARTY
INTELLECTUALPROPERTYRIGHTSWITHREGARDTOTHESEMATERIALSORUSETHEREOEUSIALLNOTBEHABLE
FORANDSHALLNOTDEFENDORINDEMNIFYYOUAGAINSTANYTURDPARTYCLAIMTHATRELATESTOORIS
BASEDONTHESEMATEREALSINNOEVENTSHALLUBEHABLEFORANYACTUALSPECIALINCIDENTAL
CONSEQUENTIALORINDIRECTDAMAGE忖HOWEVERCAUSED,ONANYTHEORYOFUABMTYANDWHETHEROR
NOTITHASBEENADVISEDOFTHEPOSSIBtUTYOFSUCHDAMAGES,ARHNGINANYWAYOUTOFTHESE
MATERIALSORYOURUSEOFTHESEMATEREALS
AnalogEngineefsPocketReference
FourthEdition
Editedby:
ArtKayandUmGreen
Specialthanksfcrtechnicalcontributionandreview:
KevinDuke
RafedOrdonez
JohnCaldwell
CollinWells
IanWilliams
ThomasKuehl
©Copyright20142015TexasInstrumentsInccrpcratedAllightsresaved
Messagefromtheeditors:
Thispocketreferenceisintendedasavaluablequickglideftrcftenusedboard-andsystan-
leveldesignformulaeThiscdlecticncffcrmulaeisbasedonacombined50yearscfanalog
board-andsystemTevelexpertiseMuchofthematerialhereinwasreferredtoovertheyears
viaafolderstiffedfullcfpintoutsThosewornpageshavebeenorganizedandtheinftrma^
isnowavailableviathisguideinaboundandharcHcdosefirmat!
Hereisabriefoverviewcfthekeyareasincluded:
•Keyconstantsandconversions
•Discretecomponents
•ACandDCanalogequaticns
•8ampbasicconfiguraticns
•OPampbandwidthandstability
•Overviewcfsensors
•PCBtraceRLC
•岫PLRC
•Binaryhexanddecimalformats
•andD/Aconversions
WehopeyoufindIhiscollecticncffcrmulaeasusefulaswehavePleasesendanycomments
and/crideasyouhavefcrthenextcftheAnalogEngineersPocketReferenceto
artkay_timgreen@
Additicnalresources:
•towseHPrecisionLabs(www.ticoin/precisionlabs),acomprehensivecnlinetraining
cunicuLumfcranalogenginegwhichappliestheorytoleaHvcddhands-onexamples
•Searchftrcomplyboard-and-systemlevelcircuitsintheKDesigns-Predsicn
referencedesignIbrary(www.ticom/precisiondesign。
•ReadhowHx)blogsfirunHfrecisicnanalogexpertsatthePrecisionHub
(www.ticom/thehub).
•Hndsduticn^蜓helpshareknowledgeandsolveproblemswithfelkwengineersand
TIexpatsintheT[E2E™Community(www.ticom/e2es).
Contents
Conversions7
Physicalconstants8
Standarddecimalprefixes9
Metricconversions9
Temperatureconversions10
Errorconversions(ppmandpercentage)10
Discretecomponents11
Resistorcolorcode12
Standardresistorvalues13
Practicalcapacitormodelandspecifications14
Practicalcapacitorsvsfrequency15
Capacitortypeoverview16
Standardcapacitancevalues17
Capacitancemarkingandtolerance17
DiodesandLEDs18
Analog19
Capacitorequations(series,parallel,charge,energy)20
Inductorequations(series,parallel,energy)21
23
Capacitorchargeanddischarge24
RMSandmeanvoltagedefinition24
RMSandmeanvoltageexamples27
Logaiithmicmathematicaldefinitions28
29
dBdefinitions30
Logscale34
Poleandzerodefinitionsandexamples35
Timetophaseshift36
41
Amplifier42
Basicopampconfigurations43曲
Opampbandwidth
Fullpowerbandwidth48
50
Smallsignalstepresponse53
Noiseequations55
Phasemargin56
StabilityopenloopSPICEanalysis57
InstrumentationAmpfilter58
60
PCBandwire61
62
PCBconductorspacing63
Self-heatingofPCBtracesoninsidelayer64
PCBtraceresistanceforlozand2ozCu65
Packagetypesanddimensions66
PCBparallelplatecapacitance67
68
PCBmicrostripcapacitanceandinductance
PCBadjacentcoppertracecapacitance
PCBviacapacitanceandinductance
Commoncoaxialcablespecifications
Coaxialcableequations
Resistanceperlengthfordifferentwiretypes(AWG)
Maximumcurrentforwiretypes
Sensor69
Temperaturesensoroverview70
Thermistor71
Resistivetemperaturedetector(RTD)72
Diodetemperaturecharacteristics74
Thermocounle(landK)76
A/Dconversion81
Binary/hexconversions83
A/DandD/Atransferfunction(LSB,Dataformats,FSR)84
90
Quantizationerror91
SignaPtcrnoiseratio(SNR)92%
Totalharmonicdistortion(THD)%
Signaldo-noiseanddistortion(SINAD)
Effectivenumberofbits(ENOB)95
Noisefreeresolutionandeffectiveresolution96
Settingtimeandconversionaccuracy.
Conversions
Standarddecimalprefixes•
Metricconversions•
Temperaturescaleconversions,
Errorconversions(ppmandpercentage),
ConversionstLcom/precisionlabs
Table1:Physicalconstants
ConstantSymbolValueUnits
299792458x108
Speedcflightinavacuumcm/s
8.854187817620x10-12
Permittivitycfvacuum%F/m
1.2566370614x10-6
PermeabilitycffreespaceMbH/m
662606957x10-34
PlanksconstanthJ,s
1.3806488x10-23
BoltzmaniisconstantkJ/K
9.64853399x104
Farada#sconstantFC/mol
a02214129x1023
Avogadrdsconstant1/mol
NA1.660538921x10-27
Unifedatomicmassunitkg
mu1.602176565x10-19
Electronicchargeq9.10938215x10知C
Restmasscfelectrcn1.672621777x10-27kg
me
Masscfproton6.67384x10-nkg
mp
Nm2/kg2
GravitationalconstantG9.80665
m/s2
Standardgravitygn
IcepointTice27315K
33
MaximumdensitycfwaterP1.00x10kg/m
4kg/m3
Densityofmercury001.3628x10
P也
J/(K*mo])
GasconstantR&3144621
2
Speedcfsoundinair俄273K)3312x10m/s
Cair
Table2:Standarddecimalprefixes
MultiplierPrefixAbbreviation
1012
taaT
9
10gigaG
106
megaM
3
10kilok
10-3
millim
10-6
microN
10-9
nanon
10-12
picoP
10-15
femtof
1018
attoa
tLcom/precisionlabsConversions
Table3:Imperialtometricconversions
UnitSymbolEquivalentUnitSymbol
inchesin254mm/inmillimetermm
milmil0.0254mm/milmillimetermm
feetftQ3048n^tmetersm
yardsydQ9144n/ydmetersm
milesmiL6093km/mikilometerskm
-422
circularmildrmil5067x10mm/cirmilsquaremillimetersmm
yd20.8361m2m2
squareyardssquaremeters
pintsptQ5682l7ptL
ouncesoz2835g/ozgramsg
pounds]bQ4536kg/LbIdlogramskg
caLori.escal4184JMjiiesJ
horsepowerhp7457WwattsW
Table4:Metrictoimperialconversions
UnitSymbolConversionUnitSymbol
millimetermm0.0394in/mminchin
millimetermm39.4mil/mnimilmil
metersm3.2808fVmfeetft
metersm1.0936y〃myardyd
kilometerskm0.6214mi/kmmilesmi
mm21974drnri]/mm2
squaremillimeterscircularnrilcirmil
m21.1960yd2/m2yd2
squaremeterssquareyards
litersL1.7600pt/Lpintspt
gramsg0.0353oz/gouncesoz
kilogramskg22046Mgpoundslb
joulesJ0.239ca]/Jcalcriescal
1.341x10-3hp/w
wattsWhorsepowerhp
Example
Convert10mmtomil
Answer小社
10mmx39.4=394mil
mm
Conversionsticom/precisionlabs
Table5:Temperatureconversions
5
℃=-(°F=32(FahrenheittoCelsius
9
°F=-(℃(=32CelsiustoFahrenheit
K=℃=233.15CelsiustoKelvin
℃=K=233.15KelvintoCelsius
Table6:Errorconversions
Measured=Ideal
Error(%(=x100Errorinmeasuredvalue
Ideal
Measured=Ideal
Error(%FSR(=——x100Errorinpercentoffull-scalerange
Full-scalerange
ppm
%=i^xlOOPartpermilliontopercent
ppm
m%=x100x1000Partpermilliontomilli-percent
106
ppm=%X106Percenttopartpermillion
ppm=m%X10Milli-percenttopartpermillion
Example
Computetheerrorfarameasuredvalueof0.12Vwhentheidealvalueis0.IV
andtherangeis5V.
Answer
0.12V-0.1V「.
Error(%)=——x100=20%Errorinmeasuredvalue
01?—01V
Error(%FSR)=—~x100=0.4%PercentFSR
Example
Convert10ppmtopercentandmilli-percent.
Answer
10ppm
Partpermilliontopercent
106x100=0.001%
10ppm
Partpermilliontomilli-percent
106X100X1000=1m%
DiscreteComponents
Resistorcolorcode•
Standardresistorvalues•
Capacitancespecifications•
Capacitancetypeoverview,
Standardcapacitancevalues•
Capacitancemarkingandtolerance•
DiscreteComponentstLcom/precisionlabs
Table7:Resistorcolorcode
AdditionalTemperatureFailure
ColorDigitZerosToleranceCoefficientRate
Black00250
Brown111%1001
Red222%500.1
Orange33150.01
Yellow44250.001
Green550.5%20
Blue660.25%10
Videt770.1%5
Grey880.05%1
White99
GoldFb-15%
Silv&-210%
NoBand-na--na-20%
4Bandexample:yellowvioletorangesilverindicate4,7,and3zeros.
ie.a47k。,10%resistor
3band.I==4/I||HIJ2R,2e0d0,R,0e0d0,G0,r2e0e%n
Yellow.Violet,Red,Black
4band4,7000,1%
5bandBrown,Brown,Orange,Red,Violet
°dlQ11,3000,0.1%
6bHiittuy
Brown,Green,Red,Black,Blue,Red
152Q,0.25%,15ppm/°C
1-digitTemperatureCoefficient
2nddigitTolerance
3rddigitAlsoUsedasFailureRateonMilitarySpec.
Additionalzeros
Figure1:Resistorcolorcode
tLcom/precisionlabsDiscreteComponents
Table8:Standardresistorvalues
a
p
e
s
a
p
0
0
L
O
L
3
£
S
E
P
A
s
o
u
e
sl
w
a
l
P
」
P
P
U
4SS
DiscreteComponents
Practicalcapacitormodelandspecifications
Rp
ESRcESL
A/W/YYY\
Figure2:Modelofapracticalcapacitor
Table9:Capacitorspecifications
ParameterDescription
Thenominalvalueofthecapacitance
C
Table11listsstandardcapacitancevalues
Equivalentseriesresistance
Ideallythisiszero
ESRCeramiccapacitcrshavethebestESR6ypicallyinnriBiohms).TantalumElectro
lytichaveESRinthehundredscfnrilliohnsandAluminumElectrolytichaveESR
intheohms
Equivalentseriesinductance
ESLIdeallythisiszero
ESLrangesfinm100pHto10nH
Rpisaparallellea
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