TI模擬工程師計算手冊

AnalogEngineefs

PocketReference

ArtKayandTimGreen,Editors

DownloadeBookat

www.ticom/analogrefguide

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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