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1、Analog EngineersPocket ReferenceArt Kay and Tim Green, EditorsDownload eBook atAnalog Engineers Pocket ReferenceThird EditionEdited by:Art Kay and Tim GreenSpecial thanks for technical contribution and review: Kevin DukeRafael Ordonez John Caldwell Collin Wells Ian WilliamsThomas Kuehl© Copyrig

2、ht 2014, 2015 Texas Instruments Incorporated.Texas Instruments Analog Engineer's Pocket Reference3Message from the editors:This pocket reference is intended as a valuable quick guide for often used board- and system- level design formulae. This collection of formulae is based on a combined 50 ye

3、ars of analog board- and system-level expertise. Much of the material herein was referred to over the years via a folder stuffed full of printouts. Those worn pages have been organized and the informa- tion is now available via this guide in a bound and hard-to-lose format!Here is a brief overview o

4、f the key areas included: Key constants and conversions Discrete components AC and DC analog equations Op amp basic configurations OP amp bandwidth and stability Overview of sensors PCB trace R, L, C Wire L, R, C Binary, hex and decimal formats A/D and D/A conversionsWe hope you find this collection

5、 of formulae as useful as we have. Please send any comments and/or ideas you have for the next edition of the Analog Engineer's Pocket Reference to artkay_timgreenAdditional resources: Search for complet-and-system level circuits in the TI Designs Precisionreference design library ().how-to blog

6、s from TI precision analog experts at the Precision Hub).( Find solutions, get help, share knowledge and solve problems with fellow engineers andTI experts in the TI E2E Commu().4Texas Instruments Analog Engineer's Pocket ReferenceContentsConversions7Physical constants8Standard decimal prefixes9

7、Metric conversions9Temperature conversions10Error conversions (ppm and percentage)10Discrete components11Resistor color code12Standard resistor values13Practical capacitor mand specifications14Practical capacitors vs . frequency15Capacitor type overview16Standard capacitance values17Capacitance mark

8、ing and tolerance17Diodes and LEDs18Analog19Capacitor equations (series, parallel, charge, energy)20Inductor equations (series, parallel, energy)21Capacitor charge and discharge22RMS and mean voltage definition24RMS and mean voltage examples25Logarithmic mathematical definitions27dB definitions28Pol

9、e and zero definitions and examples30Amplifier35Basic op amp configurations36Op amp bandwidth41Full power bandwidth42Small signal step response43Noise equations44Stability equations48Stability open loop SPICE analysis50PCB and wire55PCB conductor spacing56Self-heating of PCB traces on inside layer57

10、PCB tracefor 1oz and 2oz Cu58Package types and dimensions60PCB parallel plate capacitance61PCB via capacitance and inductance62Common coaxial cable specifications64Coaxial cable equations65per length for different wire types (AWG)66um current for wire types67Sensor69Temperature sensor overview70Ther

11、mistor71Resistive temperature detector (RTD)72Diode temperature characteristics74Thermocouple (J and K)76A/D conversion81Binary/hex conversions82A/D and D/A transfer function86Quzation error88Signal-to-noise ratio (SNR)89Signal-to-noise and distortion (SINAD)90Total harmonic distortion (THD)89Effect

12、ive number of bits (ENOB)92Noiseresolution and effective resolution93Texas Instruments Analog Engineer's Pocket Reference56Texas Instruments Analog Engineer's Pocket ReferenceCoCnovneversrsioionnss Standard decimal prefixes Metric conversions Temperature scale conversions Error conversions (

13、ppm and percentage)Texas Instruments Analog Engineer's Pocket Reference7ConversionsConversionsTable 1: Physical constantsConstantSpeed of light in a vacuum Permittivity of vacuumSymbolc o µoValue3.00 x 108 8.85 x 10-12 1.26 x 10-66.63 x 10-341.38 x 10-239.65 x 1046.02 x 10231.66 x 10-271.60

14、 x 10-199.11 x 10-311.67 x 10-276.67 x 10-11Units m/s F/m H/mPermeability ofspacePlanks constant Boltzmanns constant Faradays constanth k FJs J/K C/molAvogadros constant Unified atomic mass unit Electronic chargeNAmu q/mol kg CRest mass of electron Mass of proton Gravitational constantme mp Gkg kgNm

15、2/kgm/s2 Kkg/m3kg/m3 J/(Kmol) m/sStandard gravity Ice pointum density of watergn Tice 9.81273.151.00 x 1031.36 x 104 8.313.31 x 102Density of mercury Gas constantSpeed of sound in air (at 273 K)Hg Rcair8Texas Instruments Analog Engineer's Pocket ReferenceConversionsConversionsTable 2: Standard d

16、ecimal prefixesTable 3: English to metric conversionsTable 4: Metric to English conversionsUnitSymbolConversionUnitSymbolmillimeter millimeter meters meters kilometersmm mm m m km0.0394 in/mm39.4 mil/mm 3.2808 ft/m 1.0936 yd/m 0.6214 mi/kminch mil feet yardin mil ft yd mimm2 m2 Lg kg1974 cir mil/mm2

17、1.1960 yd2/ m21.7600 pt/L0.0353 oz/g2.2046 lb/kgsquare millimeters square meters litersgramskilogramscircular mil square yards pintsouncespoundscir mil yd2 pt oz lbjoules wattsJ W0.239 cal/J 1.341x10-3 hp/Wcalories horsepowercal hpExampleConvert 10 mm to mil.Answer Texas Instruments Analog Engineer&

18、#39;s Pocket Reference9UnitSymbolEquivalentUnitSymbolinchesin25.4 mm/inmillimetermm milmil0.0254 mm/milmillimetermmfeetft0.3048 m/ftmetersm yardsyd0.9144 m/ydmetersm mi1.6093 km/mikilometerskmcircular milcir mil5.067x10-4 mm2/cir mil square millimetersmm2 square yardsyd20.8361 m2square metersm2 pint

19、spt0.5682 L/ptlitersL ouncesoz28.35 g/ozgramsg poundslb0.4536 kg/lbkilogramskgcaloriescal4.184 J/caljoulesJ horsepowerhp745.7 W/hpwattsWMultiplierPrefixAbbreviation1012teraT109gigaG106megaM103kilok103millim106microµ109nanon1012picop1015femtof1018attoaConversionsTable 5: Temperature conversions5

20、 9 F 2F 5 2 2.15Fahrenheit to Celsius9Celsius to FahrenheitCelsius to Kelvin 2.15Kelvin to CelsiusTable 6: Error conversionsError% easured Ideal 100Error in measured valueIdealError% FSR easured Ideal 100Error in percent of full-scale rangeFullscale range% ppm 100Part per million to percent10m% ppm

21、100 1000Part per million to milli-percent10ppm % 10Percent to part per millionppm m% 10Milli-percent to part per millionExampleCompute the error for a measured value of 0.12V when the ideal value is 0.1V and the range is 5V.AnswerError% 0.12V 0.1V 100 20%Error in measured value0.1VError% FSR 0.12 0.

22、1V 100 0.%Percent FSR5VExampleConvert 10 ppm to percent and milli-percent.Answer10 ppm 100 0.001%Part per million to percent1010 ppm 100 1000 1 m%Part per million to milli-percent1010Texas Instruments Analog Engineer's Pocket Reference DisDcirsectreetceocmomppoonneennttss Resistor color code Sta

23、ndard resistor values Capacitance specifications Capacitance type overview Standard capacitance values Capacitance marking and toleranceTexas Instruments Analog Engineer's Pocket Reference11DiscreteDiscrete componentsTable 7: Resistor color codeExampleYellow, violet, orange and silver indicate 4

24、, 7, and 3 zeros. or a 47 k, 10% resistor.Figure 1: Resistor color code12Texas Instruments Analog Engineer's Pocket ReferenceDiscreteColorDigitAdditional ZerosToleranceNone-na-na-20%Silver-na-210%Gold-na-15%Black00Brown11Red222%Orange33Yellow44Green55Blue66Violet77Grey8White9vSatlaunedsfaorrtdhe

25、10to100decadeDiscrete componentsTable 8: Standard resistor valuesTexas Instruments Analog Engineer's Pocket Reference130.1%0.25%0.5%1%2%5%10%0.1%0.25%0.5%1%2%5%10%0.1%0.25%0.5%1%2%5%10%0.1%0.25%0.5%1%2%5%10%0.1%0.25%0.5%1%2%5%10%0.1%0.25%0.5%1%2%5%10%10.010.01010.110.210.210.410.510.510.610.710.

26、710.911.011.01111.111.311.311.411.511.511.711.811.812.01212.112.112.312.412.412.612.712.712.913.013.01313.213.313.313.513.713.713.814.014.014.214.314.314.514.714.714.915.015.01515.215.415.415.615.815.816.01616.216.216.416.516.516.716.916.917.217.417.417.617.817.818.01818.218.218.418.718.718.919.119.

27、119.319.619.619.820.020.02020.320.520.520.821.021.021.321.521.521.822.122.12222.322.622.622.923.223.223.423.723.724.02424.324.324.624.924.925.225.525.525.826.126.126.426.726.727.12727.427.427.728.028.028.428.728.729.129.429.429.830.130.13030.530.930.931.231.631.632.032.432.432.833.233.23333.634.034.

28、034.434.834.835.235.735.736.13636.536.537.037.437.437.938.338.338.839.239.23939.740.240.240.741.241.241.742.242.242.743.243.24343.744.244.244.845.345.345.946.446.447.04747.547.548.148.748.749.349.949.950.551.151.15151.752.352.353.053.653.654.254.954.955.656.256.25656.957.657.658.359.059.059.760.460.

29、461.261.961.96262.663.463.464.264.964.965.766.566.567.368.168.16869.069.869.870.671.571.572.373.273.274.175.075.07575.976.876.877.778.778.779.680.680.681.682.582.58283.584.584.585.686.686.687.688.788.789.890.990.99192.093.193.194.295.395.396.597.697.698.8Discrete componentsPractical capacitor mand s

30、pecificationsFigure 2: Mof a practical capacitor.Table 9: Capacitor specifications14Texas Instruments Analog Engineer's Pocket ReferenceParameterDescriptionCThe nominal value of the capacitance. Table 11 lists standard capacitance values.ESREquivalent series.Ideally this is zero. Ceramic capacit

31、ors have the best ESR (typically in milliohms). Tantalum Electrolytic have ESR in the hundreds of milliohms and Aluminum Electrolytic have ESR in the ohms.ESLEquivalent series inductance.Ideally this is zero. ESL ranges from 100 pH to 10 nH.RpRp is a parallel leakage(or insulation). Ideally this is

32、infinite. This can range from tens of megaohms for some electrolytic capacitors to tens of gigohms for ceramic.Voltage ratingTheum voltage that can be applied to the capacitor.Exceeding this rating damages the capacitor.Voltage coefficientThe change in capacitance with applied voltage in ppm/V.A hig

33、h-voltage coefficient can introduce distortion. C0G capacitors have the lowest coefficient. The voltage coefficient is mostimportn applications that use capacitors in signal processing such as filtering.Temperature coefficientThe change in capacitance with across temperature in ppm/. Ideally, the te

34、mperature coefficient is zero. Theum specified drift generally ranges from 10 to 100ppm/°C depending on the resistor type.Discrete componentsPractical capacitors vs. frequencyFigure 3: Effect of ESR and ESL on capacitor frequency responseTexas Instruments Analog Engineer's Pocket Reference1

35、5Impedance (ohms)Discrete componentsTable 10: Capacitor type overview16Texas Instruments Analog Engineer's Pocket ReferenceCapacitor typeDescriptionC0G/NP0(Type 1 ceramic)Use in signal path, filtering, low distortion, audio, and precisionLimited capacitance range: 0.1 pF to 0.47 µF Lowest t

36、emperature coefficient: ±30 ppm/ Low-voltage coefficientMinimal piezoelectric effect Good tolerance: ±1% to ±10%Temperature range: 55 to 125 (150 and higher) Voltage range may be limited for larger capacitance valuesX7R(Type 2 ceramic)Use for decoupling and other applications where ac

37、curacy and low distortion are not requiredX7R is an example of a type 2 ceramic capacitorSee EIA capacitor tolerance table fors on other types Capacitance range: 10 pF to 47 µFTemperature coefficient: ±833 ppm/ (±15% across temp range) Substal voltage coefficientTolerance: ±5% to

38、 20%/+80% Temperature range: 55 to 125Voltage range may be limited for larger capacitance valuesY5V(Type 2 ceramic)Use for decoupling and other applications where accuracy and low distortion are not requiredY5V is an example of a type 2 ceramic capacitorSee EIA capacitor tolerance table fors on othe

39、r types Temperature coefficient: 20%/+80% across temp range Temperature range: 30 to 85Other characteristics are similar to X7R and other type 2 ceramicAluminum oxide electrolyticUse for bulk decoupling and other applications where large capacitance is requiredNote that electrolytic capacitors are p

40、olarized and will be damaged, if a reverse polarity connection is Capacitance range: 1 µF to 68,000 µFTemperature coefficient: ±30 ppm/ Substal voltage coefficient Tolerance: ±20%Temperature range: 55 to 125 (150 and higher) Higher ESR than other typesTantalum electrolyticCapacit

41、ance range: 1 µF to 150 µF Similar to aluminum oxide but smaller sizePolypropylene filmCapacitance range: 100 pF to 10 µFVery low voltage coefficient (low distortion) Higher cost than other typesLarger size per capacitance than other types Temperature coefficient: 2% across temp range

42、 Temperature range: 55 to 100Discrete componentsTable 11: Standard capacitance tableExampleTranslate the capacitor markingFigure 4: Capacitor marking codeTable 12: Ceramic capacitor tolerance markingsTable 13: EIA capacitor tolerance markings (Type 2 capacitors)ExampleX7R: 55 to +125, ±15.0%Tex

43、as Instruments Analog Engineer's Pocket Reference17First letter symbolLow temp. limitSecond number symbolHigh temp. limitSecond letter symbolMax. capacitance change over temperature ratingZ+10°C2+45°CA±1.0%Y30°C4+65°CB±1.5%X55°C5+85°CC±2.2%6+105°

44、CD±3.3%7+125°CE±4.7%F±7.5%P±10.0%R±15.0%S±22.0%T±22% 33%U±22% 56%V±22% 82%CodeToleranceCodeToleranceB± 0.1 pFJ± 5%C± 0.25 pFK± 10%D± 0.5 pFM± 20%F± 1%Z+ 80%, 20%G± 2%Standard capacitance table11.11.21.31.51.61.

45、822.22.42.733.33.63.94.34.75.15.66.26.87.58.29.1Discrete componentsDiodes and LEDsFigure 5: Diode and LED pin namesFigure 6: LED forward voltage drop by color18Texas Instruments Analog Engineer's Pocket ReferenceColorVoltageInfrared1.4Red1.7 to 1.9Orange / yellow2Green2.1Blue / white3.4AAnnaallo

46、ogg Capacitor equations (series, parallel, charge, energy) Inductor equations (series, parallel, energy) Capacitor charge and discharge RMS and mean voltage definition RMS for common signals Logarithm laws dB definitions Pole and zero definition with examplesTexas Instruments Analog Engineer's P

47、ocket Reference19AnalogAnalogCapacitor equations1C 1 1 1Series capacitors(1)C CC CC CTwo series capacitors(2)C CC C C C(3)Parallel capacitorsWhereCt = equivalent total capacitanceC1, C2, C3CN = component capacitors CVCharge storage(4) tWhereQ = charge in coulombs (C) C = capacitance in farads (F) I

48、= current in amps (A)t = time in seconds (s)Charge defined(5)dvInstantaneous current through a capacitor C (6)dtWherei = instantaneous current through the capacitor C = capacitance in farads (F) = the instantaneous rate of voltage change1 CV(7)Energy stored in a capacitor2WhereE = energy stored in a

49、n capacitor in Joules (J) V = voltage in voltsC = capacitance in farads (F)20Texas Instruments Analog Engineer's Pocket ReferenceAnalogAnalogInductor equationsL L L LSeries inductors(8)1L 1 1 1(9)Parallel inductorsL LL LL L(10)Two parallel inductorsL LWhereLt = equivalent total inductanceL1, L2,

50、 L3LN = component inductancediInstantaneous voltage across an inductorv L (11)dtWherev = instantaneous voltage across the inductor L = inductance in Henries (H) = the instantaneous rate of voltage change1 LIEnergy stored in an Inductor(12)2WhereE = energy stored in an inductor in Joules (J) I = current in ampsL = inductance in Henries (H)Texas Instruments Analog Engineer's Pocket Reference21AnalogEquation for charging a capacitorV V General relatio