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Analog Engineer’s Pocket Reference Art Kay and Tim Green, Editors Download eBook at www.ti.com/analogrefguide THESE MATERIALS ARE PROVIDED “AS IS.” TI MAKES NO WARRANTIES OR REPRESENTATIONS WITH REGARD TO THESE MATERIALS OR USE OF THESE MATERIALS, EXPRESS, IMPLIED OR STATUTORY, INCLUDING FOR ACCURACY, COMPLETENESS, OR SECURITY. TI DISCLAIMS ANY IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, QUIET ENJOYMENT, QUIET POSSESSION, AND NON-INFRINGEMENT OF ANY THIRD PARTY INTELLECTUAL PROPERTY RIGHTS WITH REGARD TO THESE MATERIALS OR USE THEREOF. TI SHALL NOT BE LIABLE FOR AND SHALL NOT DEFEND OR INDEMNIFY YOU AGAINST ANY THIRD PARTY CLAIM THAT RELATES TO OR IS BASED ON THESE MATERIALS. IN NO EVENT SHALL TI BE LIABLE FOR ANY ACTUAL, SPECIAL, INCIDENTAL, CONSEQUENTIAL OR INDIRECT DAMAGES, HOWEVER CAUSED, ON ANY THEORY OF LIABILITY AND WHETHER OR NOT TI HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES, ARISING IN ANY WAY OUT OF THESE MATERIALS OR YOUR USE OF THESE MATERIALS. Analog Engineer’s Pocket Reference Fourth Edition Edited by: Art Kay and Tim Green Special thanks for technical contribution and review: Kevin Duke Rafael Ordonez John Caldwell Collin Wells Ian Williams Thomas Kuehl © Copyright 2014, 2015 Texas Instruments Incorporated. All rights reserved. Texas Instruments Analog Engineer's Pocket Reference 3 Message from the editors: This pocket reference is intended as a valuable quick guide for often used board- and systemlevel design formulae. This collection of formulae is based on a combined 50 years 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 information is now available via this guide in a bound and hard-to-lose format! Here is a brief overview of 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 conversions We hope you find this collection 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_timgreen@list.ti.com Additional resources: • Browse TI Precision Labs (www.ti.com/precisionlabs), a comprehensive online training curriculum for analog engineers, which applies theory to real-world, hands-on examples. • Search for complete board-and-system level circuits in the TI Designs – Precision reference design library (www.ti.com/precisiondesigns). • Read how-to blogs from TI precision analog experts at the Precision Hub (www.ti.com/thehub). • Find solutions, get help, share knowledge and solve problems with fellow engineers and TI experts in the TI E2E™ Community (www.ti.com/e2e). 4 Texas Instruments Analog Engineer's Pocket Reference Contents Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Physical constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Standard decimal prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Metric conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Temperature conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Error conversions (ppm and percentage) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Discrete components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Resistor color code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Standard resistor values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Practical capacitor model and specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Practical capacitors vs frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Capacitor type overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Standard capacitance values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Capacitance marking and tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Diodes and LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Analog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Capacitor equations (series, parallel, charge, energy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Inductor equations (series, parallel, energy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Capacitor charge and discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 RMS and mean voltage definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 RMS and mean voltage examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Logarithmic mathematical definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 dB definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Log scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Pole and zero definitions and examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Time to phase shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Basic op amp configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Op amp bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Full power bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Small signal step response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Noise equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Phase margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Stability open loop SPICE analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Instrumentation Amp filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 PCB and wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 PCB conductor spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Self-heating of PCB traces on inside layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 PCB trace resistance for 1oz and 2oz Cu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Package types and dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 PCB parallel plate capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 PCB microstrip capacitance and inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 PCB adjacent copper trace capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 PCB via capacitance and inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Common coaxial cable specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Coaxial cable equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Resistance per length for different wire types (AWG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Maximum current for wire types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Temperature sensor overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Thermistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Resistive temperature detector (RTD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Diode temperature characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Thermocouple (J and K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 A/D conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Binary/hex conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 A/D and D/A transfer function (LSB, Data formats, FSR) . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Quantization error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Signal-to-noise ratio (SNR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Total harmonic distortion (THD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Signal-to-noise and distortion (SINAD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Effective number of bits (ENOB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Noise free resolution and effective resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Setting time and conversion accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Texas Instruments Analog Engineer's Pocket Reference 5 6 Texas Instruments Analog Engineer's Pocket Reference Conversions ti.com/precisionlabs CoCnovnevresrsioionns Standard decimal prefixes • Metric conversions • Temperature scale conversions • Error conversions (ppm and percentage) • Texas Instruments Analog Engineer's Pocket Reference 7 Conversions Conversions ti.com/precisionlabs Table 1: Physical constants Constant Speed of light in a vacuum Permittivity of vacuum Permeability of free space Plank’s constant Boltzmann’s constant Faraday’s constant Avogadro’s constant Unified atomic mass unit Electronic charge Rest mass of electron Mass of proton Gravitational constant Standard gravity Ice point Maximum density of water Density of mercury (0°C) Gas constant Speed of sound in air (at 273°K) Symbol c εo µo h k F NA mu q me mp G gn Tice ρ ρHg R cair Value 2.997 924 58 x 108 8.854 187 817 620 x 10-12 1.256 637 0614 x 10-6 6.626 069 57 x 10-34 1.380 648 8 x 10-23 9.648 533 99 x 104 6.022 141 29 x 1023 1.660 538 921 x 10-27 1.602 176 565 x 10-19 9.109 382 15 x 10-31 1.672 621 777 x 10-27 6.673 84 x 10-11 9.806 65 273.15 1.00 x 103 1.362 8 x 104 8.314 462 1 3.312 x 102 Units m/s F/m H/m J•s J/K C/mol 1/mol kg C kg kg Nm2/kg2 m/s2 K kg/m3 kg/m3 J/(K•mol) m/s Table 2: Standard decimal prefixes Multiplier 1012 109 106 103 10–3 10–6 10–9 10–12 10–15 10–18 Prefix tera giga mega kilo milli micro nano pico femto atto Abbreviation T G M k m µ n p f a 8 Texas Instruments Analog Texas Instruments Analog Engineer's Pocket Reference Engineer's Pocket Reference ti.com/precisionlabs Conversions Table 3: Imperial to metric conversions Unit Symbol Equivalent inches in 25.4 mm/in mil mil 0.0254 mm/mil feet ft 0.3048 m/ft yards yd 0.9144 m/yd miles mi 1.6093 km/mi circular mil square yards cir mil yd2 5.067x10-4 mm2/cir mil 0.8361 m2 pints pt 0.5682 L/pt ounces oz 28.35 g/oz pounds lb 0.4536 kg/lb calories cal 4.184 J/cal horsepower hp 745.7 W/hp Unit millimeter millimeter meters meters kilometers square millimeters square meters liters grams kilograms joules watts Symbol mm mm m m km mm2 m2 L g kg J W Table 4: Metric to imperial conversions Unit Symbol Conversion millimeter mm 0.0394 in/mm millimeter mm 39.4 mil/mm meters m 3.2808 ft/m meters m 1.0936 yd/m kilometers km square millimeters mm2 0.6214 mi/km 1974 cir mil/mm2 square meters m2 1.1960 yd2/ m2 liters L 1.7600 pt/L grams g 0.0353 oz/g kilograms kg 2.2046 lb/kg joules watts J 0.239 cal/J W 1.341x10-3 hp/W Unit inch mil feet yard miles circular mil square yards pints ounces pounds calories horsepower Symbol in mil ft yd mi cir mil yd2 pt oz lb cal hp Example Convert 10 mm to mil. Answer mil 10 mm x 39.4 mm = 394 mil Texas Instruments Analog Engineer's Pocket Reference 9 Conversions ti.com/precisionlabs TTaabbllee 55:: TTeemmppeerraattuurree ccoonnvveerrssiioonnss Ta���b�Fl�e�����F�59559�:�����T��9559�eF2��m�������F�p��.e��12�r25�a��t2u2�re FcaFohanrhverenerhnsehiieotinttostoCCeleslisuisus Fahrenheit to Celsius CCeleslisuisustotoFaFharhernehnehiet it Celsius to Fahrenheit CCeleslisuisustotoKeKlevlivnin � � �� � 2��.15 Celsius to Kelvin �� � � � 2��.15 KKelevlivnintotoCCeleslisuisus �� � � � 2��.15 Kelvin to Celsius Table 6: Error conversions EETrrarrbETEoolrrrrae��rrboo%%6lrre:���F%%E6�Smr:R�rF%E�o��Smrr�Re%�rp%co�a�pso�rp��1me%�uFnpc0aeIrumvdosea��p�pl�11euelFdsnpp‐00eIaurrus%�vmdm�sea�l�prcl1eeldsieap1‐o0Iarudsl���md0�seln�rce�0ieas11r1oIadla�d0�00elnInde��00sr1�g1aea�0e0lIan1d0l0�g10e0�e0a01l0100�000100 Error in measured value EErrrroorrininmmeeaassuurreeddvvaaluluee Error in percent of full-scale range EErrrroorrininppeerrcceennttooff ffuullll--ssccaallee rraannggee Part per million to percent PPaarrttppeerrmmiilllliioonn ttoo ppeerrcceenntt Part per million to milli-percent PPaarrttppeerrmmiilllliioonn ttoo mmiillllii--ppeerrcceenntt Percent to part per million ppm � % � 10� ppm � m% � 10 PPeerrcceennttttoo ppaarrtt ppeerr mmiilllliioonn Milli-percent to part per million ppm � m% � 10 MMiillllii--ppeerrcceenntt ttoo ppaarrtt ppeerr mmiilllliioonn Example ComExpaumtepthlee error for a measured value of 0.12V when the ideal value is 0.1V and theCrEaoxnmgapemuitspel5tehVe. error for a measured value of 0.12V when the ideal value is 0.1V and thCeormanpgueteisth5eVe.rror for a measured value of 0.12V when the ideal value is 0.1V Ansawnedr the range is 5V. EEErrxrraAEEooAmEErrrrn��rrrrnpsoo%%rrsoowlrre���rrwFe%%�S%%reR�Fr�0F�S.S�R1R�2000V0.�1...1112�2V02000V..51�1�..V11V20VV05�..5V11�VV0VV.11��0VV011�00�00120��00%02�.0�%%0.�% Error in measured value PerEcErerrnrootrrFiniSnmRmeeaassuurreeddvvaaluluee PPeercrceennt tFFSSRR ConEEvxexaramt m1p0lpeplepm to percent and milli-percent. AnsCCwoonenvrveertrt1100ppppmmtotoppeercrceennt taannddmmilillil-ip-peercrceennt.t. 110011ppA1100A11pp00��n1100mmnspp1100sppwpp00��pp��wmmemmr11e��00r0011�00�0010��0.00100001.00�%0011�%m1%m% Part per million to percent PPaartrtppeer rmmilliilolionntotoppeercrceennt t Part per million to milli-percent PPaartrtppeer rmmilliilolionntotommilliil-lip-peercrceennt t 10 Texas Texas Instruments Analog Engineer's Pocket Reference 10 Discrete Components Discretti.ecomC/poremcispionolanbsents Resistor color code • Standard resistor values • Capacitance specifications • Capacitance type overview • Standard capacitance values • Capacitance marking and tolerance • Discrete 11 Texas Texas Instruments Analog Engineer's Pocket Reference Discrete Discrete Components ti.com/precisionlabs Table 7: Resistor color code Color Digit Black 0 Brown 1 Red 2 Orange 3 Yellow 4 Green 5 Blue 6 Violet 7 Grey 8 White 9 Gold -na- Silver -na- No Band -na- Additional Zeros 0 1 2 3 4 5 6 7 8 9 -1 -2 -na- Tolerance 1% 2% 0.5% 0.25% 0.1% 0.05% Temperature Coefficient 250 100 50 15 25 20 10 5 1 5% 10% 20% Failure Rate 1 0.1 0.01 0.001 4 Band example: yellow violet orange silver indicate 4, 7, and 3 zeros. i.e. a 47kΩ, 10% resistor. Figure 1: Resistor color code 12 Texas Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Table 8: Standard resistor values Texas Instruments Analog Engineer's Pocket Reference Standard resistance values for the 10 to 100 decade 0.1% 2% 0.1% 2% 0.1% 2% 0.1% 2% 0.1% 2% 0.1% 2% 0.25% 1% 5% 0.25% 1% 5% 0.25% 1% 5% 0.25% 1% 5% 0.25% 1% 5% 0.25% 1% 5% 0.5% 10% 0.5% 10% 0.5% 10% 0.5% 10% 0.5% 10% 0.5% 10% 10.0 10.0 10 14.7 14.7 21.5 21.5 31.6 31.6 46.4 46.4 68.1 68.1 68 10.1 14.9 21.8 32.0 47.0 47 69.0 10.2 10.2 15.0 15.0 15 22.1 22.1 22 32.4 32.4 47.5 47.5 69.8 69.8 10.4 15.2 22.3 32.8 48.1 70.6 10.5 10.5 15.4 15.4 22.6 22.6 33.2 33.2 33 48.7 48.7 71.5 71.5 10.6 15.6 22.9 33.6 49.3 72.3 10.7 10.7 15.8 15.8 23.2 23.2 34.0 34.0 49.9 49.9 73.2 73.2 10.9 16.0 16 23.4 34.4 50.5 74.1 11.0 11.0 11 16.2 16.2 23.7 23.7 34.8 34.8 51.1 51.1 51 75.0 75.0 75 11.1 16.4 24.0 24 35.2 51.7 75.9 11.3 11.3 16.5 16.5 24.3 24.3 35.7 35.7 52.3 52.3 76.8 76.8 11.4 16.7 24.6 36.1 36 53.0 77.7 11.5 11.5 16.9 16.9 24.9 24.9 36.5 36.5 53.6 53.6 78.7 78.7 11.7 17.2 25.2 37.0 54.2 79.6 11.8 11.8 17.4 17.4 25.5 25.5 37.4 37.4 54.9 54.9 80.6 80.6 12.0 12 17.6 25.8 37.9 55.6 81.6 12.1 12.1 17.8 17.8 26.1 26.1 38.3 38.3 56.2 56.2 56 82.5 82.5 82 12.3 18.0 18 26.4 38.8 56.9 83.5 Discrete Components 12.4 12.4 18.2 18.2 26.7 26.7 39.2 39.2 39 57.6 57.6 84.5 84.5 12.6 18.4 27.1 27 39.7 58.3 85.6 12.7 12.7 18.7 18.7 27.4 27.4 40.2 40.2 59.0 59.0 86.6 86.6 12.9 18.9 27.7 40.7 59.7 87.6 13.0 13.0 13 19.1 19.1 28.0 28.0 41.2 41.2 60.4 60.4 88.7 88.7 13.2 19.3 28.4 41.7 61.2 89.8 13.3 13.3 19.6 19.6 28.7 28.7 42.2 42.2 61.9 61.9 62 90.9 90.9 91 13.5 19.8 29.1 42.7 62.6 92.0 13.7 13.7 20.0 20.0 20 29.4 29.4 43.2 43.2 43 63.4 63.4 93.1 93.1 13.8 20.3 29.8 43.7 64.2 94.2 14.0 14.0 20.5 20.5 30.1 30.1 30 44.2 44.2 64.9 64.9 95.3 95.3 14.2 20.8 30.5 44.8 65.7 96.5 14.3 14.3 21.0 21.0 30.9 30.9 45.3 45.3 66.5 66.5 97.6 97.6 13 14.5 21.3 31.2 45.9 67.3 98.8 Discrete Components ti.com/precisionlabs Practical capacitor model and specifications Rp ESR C ESL Figure 2: Model of a practical capacitor Table 9: Capacitor specifications Parameter Description C The nominal value of the capacitance Table 11 lists standard capacitance values Equivalent series resistance Ideally this is zero ESR Ceramic capacitors have the best ESR (typically in milliohms). Tantalum Electro- lytic have ESR in the hundreds of milliohms and Aluminum Electrolytic have ESR in the ohms Equivalent series inductance ESL Ideally this is zero ESL ranges from 100 pH to 10 nH Rp is a parallel leakage resistance (or insulation resistance) Rp Ideally this is infinite This can range from tens of megaohms for some electrolytic capacitors to tens of gigohms for ceramic Voltage rating The maximum voltage that can be applied to the capacitor Exceeding this rating damages the capacitor Voltage coefficient The change in capacitance with applied voltage in ppm/V A high-voltage coefficient can introduce distortion C0G capacitors have the lowest coefficient The voltage coefficient is most important in applications that use capacitors in signal processing such as filtering Temperature coefficient The change in capacitance with across temperature in ppm/°C Ideally, the temperature coefficient is zero The maximum specified drift generally ranges from 10 to 100ppm/°C or greater depending on the capacitor type (See Table 10 for details) 14 Texas Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Practical capacitors vs. frequency Practical capacitors vs. frequency Discrete Components Impedance (ohms) Figure 3:FEigffuercet 3o:fEEfSfeRctaonfdEESSRLaonndcEaSpLacointocrafrpeaqcuiteonrcfyrerqeusepnocnyseresponse Texas Instruments Analog Engineer's Pocket Reference 15 Discrete Components ti.com/precisionlabs Table 10: Capacitor type overview Capacitor type C0G/NP0 (Type 1 ceramic) X7R (Type 2 ceramic) Y5V (Type 2 ceramic) Aluminum oxide electrolytic Tantalum electrolytic Polypropylene film Description Use in signal path, filtering, low distortion, audio, and precision Limited capacitance range: 0.1 pF to 0.47 µF Lowest temperature coefficient: ±30 ppm/°C Low-voltage coefficient Minimal piezoelectric effect Good tolerance: ±1% to ±10% Temperature range: –55°C to 125°C (150°C and higher) Voltage range may be limited for larger capacitance values Use for decoupling and other applications where accuracy and low distortion are not required X7R is an example of a type 2 ceramic capacitor See EIA capacitor tolerance table for details on other types Capacitance range: 10 pF to 47 µF Temperature coefficient: ±833 ppm/°C (±15% across temp range) Substantial voltage coefficient Tolerance: ±5% to –20%/+80% Temperature range: –55°C to 125°C Voltage range may be limited for larger capacitance values Use for decoupling and other applications where accuracy and low distortion are not required Y5V is an example of a type 2 ceramic capacitor See EIA capacitor tolerance table for details on other types Temperature coefficient: –20%/+80% across temp range Temperature range: –30°C to 85°C Other characteristics are similar to X7R and other type 2 ceramic Use for bulk decoupling and other applications where large capacitance is required Note that electrolytic capacitors are polarized and will be damaged, if a reverse polarity connection is made Capacitance range: 1 µF to 68,000 µF Temperature coefficient: ±30 ppm/°C Substantial voltage coefficient Tolerance: ±20% Temperature range: –55°C to 125°C (150°C and higher) Higher ESR than other types Capacitance range: 1 µF to 150 µF Similar to aluminum oxide but smaller size Capacitance range: 100 pF to 10 µF Very low voltage coefficient (low distortion) Higher cost than other types Larger size per capacitance than other types Temperature coefficient: 2% across temp range Temperature range: –55°C to 100°C 16 Texas Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Discrete Components Table 11: Standard capacitance table Standard capacitance table 1 1.1 1.2 1.3 1.5 1.6 1.8 2 2.2 2.4 2.7 3 3.3 3.6 3.9 4.3 4.7 5.1 5.6 6.2 6.8 7.5 8.2 9.1 CK06 223K Figure 4: Capacitor marking code Example Translate the capacitor marking 2 2 3 K "K" = ±10% 22 000 pF = 22nF = 0.022µF Table 12: Ceramic capacitor tolerance markings Code Tolerance Code B ± 0.1 pF J C ± 0.25 pF K D ± 0.5 pF M F ± 1% Z G ± 2% Tolerance ± 5% ± 10% ± 20% + 80%, –20% Table 13: EIA capacitor tolerance markings (Type 2 capacitors) First letter Low temp symbol limit Second number High temp symbol limit Second letter symbol Max. capacitance change over temperature rating Z +10°C 2 +45°C A ±1.0% Y –30°C 4 +65°C B ±1.5% X –55°C 5 +85°C C ±2.2% 6 +105°C D ±3.3% 7 +125°C E ±4.7% F ±7.5% P ±10.0% R ±15.0% S ±22.0% T ±22% ~ 33% U ±22% ~ 56% V ±22% ~ 82% Example X7R: –55°C to +125°C, ±15.0% Texas Instruments Analog Engineer's Pocket Reference 17 Discrete Components Diodes and LEDs Anode (+) ti.com/precisionlabs Cathode (-) Anode (+) Anode (+) Cathode (-) Anode (+) Cathode (-) Anode (+) Long Lead Cathode (-) Cathode (-) Anode (+) Long Lead Cathode (-) Short Lead, Flat Figure 5: Diode and LED pin names Color Infrared Red Orange / Yellow Green Blue/White Wavelength (nm) 940-850 660-620 620-605 570-525 470-430 Table 14: LED forward voltage drop by color Voltage (approximate range) 1.4 to 1.7 1.7 to 1.9 2 to 2.2 2.1 to 3.0 3.4 to 3.8 Note: The voltages given are approximate, and are intended to show the general trend for forward voltage drop of LED diodes. Consult the manufacturer’s data sheet for more precise values. 18 Texas Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs AnAnaalologg 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 examples • Analog Texas Instruments Analog Engineer's Pocket Reference 19 Analog Analog ti.com/precisionlabs CCappaaccitiotroerqeuaqtuioantsions 1 C 11 1 CC C (1) Series capacitors CC C C (2) Two series capacitors C (3) Parallel capacitors Where Ct = equivalent total capacitance C1, C2, C3…CN = component capacitors V (4) Charge storage Where Q = charge in coulombs (C) C = capacitance in farads (F) V = voltage in volts (V) I = current in amps (A) t = time in seconds (s) (5) Charge defined dv dt (6) Instantaneous current through a capacitor Where i = instantaneous current through the capacitor C = capacitance in farads (F) dv = the instantaneous rate of voltage change dt 1 CV (7) Energy stored in a capacitor 2 Where E = energy stored in an capacitor in Joules (J) V = voltage in volts C = capacitance in farads (F) 20 Texas 2Te0xas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Analog Indduucctotroerqeuqatuioantsions L� � L� � L� � � � L� ((88))SerSieesriiensdiuncdtuocrstors L� � 1 L� � 1 L� 1 � � � 1 L� ((99))ParPaalleral lilnedl iuncdtuocrstors L� � L�L� L� � L� ((1100))TwTowopapraarllaellleinl dinudcutcotrosrs WWhheerree LLtt == eeqquuiivvaalleenntt ttoottaall iinndduuccttaannccee LL11,, LL22,, LL33……LLNN==ccoommppoonneennttinindduucctatannccee v � L di dt ((1111))InIsntsatnatnatnaenoeuosusvovlotaltgaegeacarcorsosssananinidnudcutcotor r ddWvL�WvL�it�h==h====eeiirnnriiitennnhesdsdsteuattucaaninctnntastattantaanancnnenceeeoteaooiunnuuisnessHvHoevrouaeonlttsnraletiraegriaoegsetfsee(acH(acoHu)rcfro)rrveosonssltsttahctgehheeainncidnghudaecuntcgoteror � � 1 2 LI� ((1122))EnEenregrygystsotroerdedininananinIdnudcutcotror WWhheerree EE ==eenneerrggyy ssttoorreeddiinnaanniinndduuccttoorrininJJoouuleless(J(J)) II ==cucrurrernetnitninamampsps LL ==inindduucctatanncceeininHHeennrireiess(H(H)) Texas Instruments Analog Engineer's Pocket Referen2c1e 21 Analog ti.com/precisionlabs EEqquuaatitoionnffoorr cchhaarrggininggaacnapRaCcitcoirrcuit EV�qu�atiVo�n�f�or�ch�a�r��g�i�n�g a capa(c1i3t(o1) r3G)enGereanl ereralaltrioenlasthioipnship Where WVVh�Cer=�e voVl�ta�g�e �acr�o�s�s���th�e capacitor(a1t3a) nyGinesntearnatl irneltaimtioen(st)hip VCVS==vtohletasgoeuarccerovsoslttahgeeccahpaarcgiitnogr athteanRyCincsirtcaunitt in time (t) tτGV=S=WVctttGVrhaa==CS==trRi=hpsipam==tteCRRapiihtfmmrhuecth,vCCeihenileeoittlin,,ehyonglstgttiiernnahhcsoseighoeeeteusssiqeauqmcreett9crruuiioccmmagce9eaanoocee.eetcd3tnnvridioovoo%sddocc.onsnlssoontslsactnn1atg1htss3ahgeatt3naaeeprtcnngrpccohftteaorhdaffdopraoourdgarrrcacgicuhtcceniinhhacfstgiogvaaregtrterrhshtigganheteiittigennmhcaRggRaaeenCnpaaCyccdanncoiacddcnidnripistcrddisoctsauiiatrusscacintcccihnitthhthatoisaaarng.rrrrgggtiIcnitiiminnnghisgggeaccrccc(agotaaup)mipprnavaamcgecciotiicbottnooeursrrlprssovrwaec. tbNiceoeltoetowthc.aoNtnotshtiedeer thGartatphheincgaepqaucaittioonr i1s39p9ro.3d%ucecshtahregceadpaactitfoivrechtiamrgeincgocnusrvtaenbtesl.oIwt.isNoctoemthmatotnhe prcaacptaiccietotroisc9o9n.3s%idecrhathrgisedfualtlyfivcehatimrgeecdo.nstants. It is common practice to consider this fully charged. Figure 7: RC charge curve Figure 7: RC charge curve Figure 6: RC charge curve 22 Texas T2ex2as Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Analog Equation for discharging a capacitor Equation for discharging an RC circuit V� � V� �������� (14) General R(e1la4ti)onsGhipeneral relationship Equation for discharging a capacitor WVWVCVh�C=eh�r=eveoVrv�elt�oa�gl�t��ea��g�aceroascsrothsesctahpeaccita(o1pr4aa) tcaGitnoeynreianrastltaraennlatytiioninntsismhtipaen(tt) in time (t) VtτtV=i=WVtV==I==CItRhi==tm=tetChiRimtrmevhtee,hCeoetiilehnentii,naneitgsitiiistnhnaeiteeailmeciclastvooviceeaotonrniollcdlmcdttsaasovossggeonnetehsldcotetoaasfocfntgnhatteehpsfaeotcocaarciftpncaoattrhphcaafaietotrocgarrictinanocaytgrhptin=aaaas0tnrtsctagd=inti0dtnosiingrsctaiahmtnaetrd=g(ti0)dnsgisccahpaarcgitionrgs capacitors Gra=phRiCn,gtheeqtuimateiocnon1s4tapntrofodruccheasrgtinhge acnadpdaicscithoarrgdiinsgchcaaprgaceitcoursrve below. Note tmhcGcGoaaatrnrppaatapphapchrechaiitnoiccitgnratoiiegpcsrqea0iuecs.ta7qiott%0iouocr.naco7ihs1tn%ia4sodrigpndicsereochd1rdhaa4utahtrcrgfiepgisvseerefodtduhtdilemtlayoucetdca0cfpie.sio7avcsn%cehsitttaohatarringemtdtesfisic.edvcIa.ethcpiastoriagmcnceoesmicttcuomarorvonnendtssbpits.earaclnIocthtwtsiiac..seNrItgctooieotsecmcocthnoumasmtridvot-heener belo prac tthhiiss ffuullyllydisdcihsacrgheadr. ged. PePrecerncteagnetDaigscehaDrgisecdhvas.rNguemdbevrso.fNTiumme CboenrstoanftsTime Consta 100 19000 8900 678000 5700 4600 30 2500 1400 300 0 1 2 3 4 5 20 Number of time Constants (τ = RC) Figu1r0e 8: RC discharge cFuigrvuere 7: RC discharge curve 0 0 1 2 3 4 Number of time Constants (τ = RC) Figure 8: RC discharge curve PercentagePeCrchearntgaegedCharged Texas Instruments Analog Engineer's Pocket Reference 23 Analog ti.com/precisionlabs RRMMSSvvolotaltgaege WRVWVV��RV(Mhh��t�)eMeS���r=rSe���evc�ovo��lont���alt��ti�gna���eug���11oe�1u��s������f��u���n������c����t���iVVo��V�ntt���ot���f���ddt�itmtdte (15(1) 5G)enGeeranlerrealal rteiolantsiohnipship (1(51)5) GGeneenrearlarlerlealtaiotinosnhsihpip VtTWVtTtTM1=(==1WVtT1(teht)≤=≤1≤)(ttateh=tiii≤m=)mmtntrtteiec=m≤≤≤rteceevoe≤oceToTTiniinnnno2l2T2tittnni=s=asin=s2nteeeg=uisuttntcchcheoehoutoooeechueuonnnoessttutdddniiimmfstmsfssduiumeesfnenuecciininntntciiittnotoeeteitnnrorervvvnrooaavafflolalttttfltiihhhmmttaaihameettattettthhhteeheefffuuufnnunccncttcitiooitoinnonniissisisdddeedeffeiifnnifnieeneddeddooovvoveeverrerr MMVVWV��MV(ehet���)aee��a�=na�r��enn�cv��oovv�n��loot��t�ali��ntl�gatu���11aego�1eg��u���se���f���u���n�������c��VVt�i�V�ott�n��tdd�ottdfttime (16) General relationship (16(1)(61G)6e)nGeGeranelenrreearllaartleiroleanltasiohtinoipsnhsihpip WVtTVWVtTVVtT1=(���==1VWVtT1(thh�t�)≤��=≤1≤)(tetteh=���t�iii≤mr=)mmttrt�tee��i�ec=m≤≤≤rtecee��oe≤oVVceTTTiniinnnn�o�√2√V22T2ti��tnni�√=2s=2sin=s2���n�teee=�2u�si�uttntcVcπhcheo�houto�ooeechueuo�nnnoes�sttutdddnii�immfstmsfssduiumeesfnenuecciininntntciiittnotoeeteitnnrorervvvnrooaavafflolalttttfltiihhhmmttaaihameettattettthhhteeheefffuu(u1fnnun7ccnc)ttcitiRooitoiMnnonniSissisisfddodeedreffeififnnuif(((ni111eenl(le778d1dewd)))7dooa)ovvovRsRsMsveeveiiieRsMnrMnnreeirreeeMnraeSSencwwwSfftwoofaaaioffrirvovvaereeefrfvduufeufllullslllwiwlnwwaaeavvavweeveaerrvreereeccecttciitffitiifieeifeiddedd V�V���������2 2��Vπ�Vπ������� (18) Mean for f(u1(l81l )w8)aMsviMseneienaereenawcnwfatoivffarioeevfrdueflulslwilnwaevawevaerverecetciftiiefided Figure 9: Full wave rectified sine wave FiFgiugruere9:9F: uFlullwl wavaFevigeruerrceetcift8ii:efiFdeudsllisnwienaewvweavareevcetified sine wave 24 Texas 2T4exas Instruments Analog Engineer's Pocket Reference 24 ti.com/precisionlabs Analog RMMSSvovlotaltgaegaendamnedanmveoaltnagveoltage τ V V 2T (19) RMS fo(r19a)haRrlefM-cwtSiafievfoedr a half-wave rseincetifwieadvseine wave V V τ πT (20) Mean f(o2r0a) harMelfec-tawifniaevfdoersraiencehtaiwflifea-wdveasvinee wave Figure 10: Half-wave Freigcutirfeie9d: sHianlef-wwaavvee rectified sine wave τ V V T τ V V T (21(2) 1R)MSRMfoSr afosrqauasrqeuwaraevwe ave (22) Mean for a square wave Figure 11: Square wave Figure 10: Square wave Texas Instruments Analog Engineer's Pocket Referen2c5e 25 Analog RMS voltage and mean voltage RMS voltage and mean voltage (( V ( ( V V V V τ 3 T τ V VV 2T ti.com/precisionlabs (23(2)3R)MSRMfoSr afotrraapterazpoeidzoid (24(2)4M) eaMnefaonr afotrrapterazpoeidzoid Figure 12: Trapezoidal wavFeigure 11: Trapezoidal wave τ V V 3T τ V 2T V (25) R(2M5)S fRorMaStrfoiarnaglteriawnagvlee wave (26) M(2e6a) n Mfoeraantrfoiarnaglteriawnagvlee wave Figure 13: Triangle wave Figure 12: Triangle wave 26 Texas Texas Instruments Analog Engineer's Pocket Reference 26 ti.com/precisionlabs Analog LLooggaarirtihtmhmic imcamtheamthateicmaladteicfianiltidonesfinitions A A B B log AB A B (27) L(o27g)oLf odgiviodfednivdidend (28) L(o28g)oLf opgroodfupcrtoduct log A A (29) L(o29g)oLf oegxpoofneexnptonent log log log (30) C(3h0a)ngCinhganthgeingbathse obfalsoegoffulnocgtifounnction log log log (31) E(3x1am) pElxeacmhpalnegcinhgantgoinloggtobalosge b2ase 2 ln X (32) N(3a2tu) raNlalotugraisl lloogg ibsalosge bease e (33) E(3x3p)onEexnptoianl efunnticatliofunnctotio6ndtiogi6tsdigits. AAlltteerrnnaattiivvee nnoottaattiioonnss exp x (34) D(3if4fe)reDfunintffcentroieotnnattionontafotiroenxfpoorneexnptoianlefnutniacltion (35) Ds(o3ifm5fe)eretenDinmxoitfptfeaenostronieotcenanontt,nitonsiafnooultmsfafueotendirotcisnmwtcioiefitoenhsnr ctsiofcinicefunnstoieftiacdtiwonith, exponential function Texas Instruments Analog Engineer's Pocket Reference 27 27 Analog ti.com/precisionlabs dB definitions BdoBddeepfilnoittiobnassics The frequency response for the magnitude or gain plot is the change in vBooltdaegpelogtabinasaiscsfrequency changes. This change is specified on a Bode plot, a plot of frequency versus voltage gain in dB (decibels). Bode plots are uTshueaflrleyqpuleontcteydreassposnesmeif-olor gtheplmotasgnwitiuthdefroerqguaeinncpyloot ins thhee cxh-aanxgise,inlovgosltacgaeleg, ain aansdfrgeqauinenocny tchheanyg-easx.isT,hliisnechaarnsgceailse.spTehceifioetdhoenr haaBlfodoef tphloet,fraepqluoet onfcfyrequency rvvwheeeasirtrlhpsfsuouofrfssnetsqvhdoeueeletgifansrregcetqeyheugeoseannppincthhhyiaaenrssexdees-Bapssxo(hhidnsiies,ffttcel.oivbPigesehrsltsshac)ueas. sleBep,hfopraadelonseqedtupsgsleoahantriisfncet yavourenaesrnustuhduasesluliyysafr-leaplpyqxlloopuistlet,ottneeltitcnddeyedaaaaasrsnssdsfcsreieaesmqlmepu.ili-o-eTlltoontheggcedpyoalotshtser pfrleoqtsuewnictyhvferersquusednecgyreoens tphheasxe-asxhiisft,. lPohgassecaplleo,tsaanrde upshuaaslley sphloitftteodnasthseemi-log yp-laotxsisw,itlihnfereaqr usecnacley.on the x-axis, log scale, and phase shift on the y-axis, linear scale. Definitions V V ((3366)) VVooltltaaggeeggaaininininddeeccibibeelsls P P ((3377)) PPoowweerr ggaaiinniinnddeecciibbeellss Measured Power Measured (W) 1 mW (38) (38) UPsoewdefrograininpiunt omuitllpiwuat tpt ower doer cibel A (V/V) A (dB) Table 15: Examples of common gain Table 14: Examples of covamlumeosnagnadindBvaelquueisvalnedntdB equivalent 0.001 –60 A (V/V) A (dB) 0.000.101 –40–60 Roll-off rate is the decrease in gain with frequency 0.010.1 0.1 1 1 –20–40 0 –20 0 Decade is a tenfold increase or decrease in frequency (from 10 Hz to 100 Hz is one decade) 10 10 100100 1,000 101,0,00000 20 20 40 40 60 60 80 Octave is the doubling or halving of frequency (from 10 Hz to 20 Hz is one octave) 10100,,000000 80 100 11,0100,00000,00,00,000000 100114200 1,000,000 120 R1o0l,l0-o00ff,0r0a0te is th1e40decrease in gain with frequency Decade is a tenfold increase or decrease in frequency.(from 10 Hz to 100 Hz is one decade) Octave is the doubling or halving of frequency (from 10 Hz to 20 Hz is one octave) 28 Texas Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Analog Figure 13 illustrates a method to graphically determine values on a logarithmic axis that are not directly on an axis grid line. Figure 14 illustrates a method to graphically determine values on a logarithmic axis 1. GthiavteanreLn=ot1dcirmec;tDly o=n2acnma,xims geraidsulinreed. with a ruler. 2. 3. L/D fP = =1120..lo(LGLg//DiD1v)0e(==nfpl1L)o0g=1(101(cfmPc)m/2c; mD)== 2cm, 3.16 measured with a ruler. 4. Adjus3t. ffoPr=t1h0e(Ld/De) =ca1d0(e1CrMa/2nCMg)e= 3(f.o1r6this example, fp = 31.6 Hz) 4. Adjust for the decade range (for example, 31.6 Hz) A (dB) FFigiguurere1143: :FFininddininggvvaalulueessoonnllooggaarriitthhmmiiccaaxxiissnnoottddiirreeccttllyy oonn aa ggrriidd lliinnee Texas Instruments Analog Engineer's Pocket Reference 29 Analog ti.com/precisionlabs Bode pBloodtesp: lPotos:lePsoles fP 100 80 Actual function 60 0.707*GV/V = –3 dB Straight-line approximation –20 dB/decade G (dB) 40 20 0 1 +90 10 100 1k 10k 100k 1M 10M Frequency (Hz) (degrees) +45 0° 10 100 1k 10k 100k 1M 10M 0 –45 –5.7° at fP 10 –45°/decade –90 –45° at fP –84.3° at fP x 10 –90° Figure 15: Pole gaiFnigaunrdep1h4a: sPeole gain and phase MPMoaalggennLiittouucddaeeMPti((ooaffnl<=ge=nffLPPift))oPu==c(dcaG–uet3tdioo(cfdfnfB<(ff=roefrPqf)eP)x=(acGmutDpoCleff,(f1for0er0qed)xBa)mple, 100 dB) MagnitudeM(af >gnfPit)u=d–e2(0f d=Bf/Pd)e=ca–d3e dB Phase (f =MfPa)g=n–it4u5d°e (f > fP) = –20 dB/decade Phase Phase Phase (((0ff .><1PP10hhfP0.aa1 10 fP) = –90° Phase (f < 0.1 fP) = 0° 30 Texas Texas Ins3tr0uments Analog Engineer's Pocket Reference ti.com/precisionlabs Analog Pole (equations) Pole (equations) V G G V j f f V G GV f f (39) As (a3c9o) mApsleax cnoummpbleexr number (40) Mag(4n0it)udMeagnitude f f (41) Pha(4se1)shPifht ase shift G (42) Mag(4n2it)udMeaingnditBude in dB Where Gv = voltage gain in V/V WGhdeBre= voltage gain in decibels GGv =dc =vothlteagdce ograloinwinfreVq/uVency voltage gain GfdB= f=revqouletancgyeingaHizn in decibels GfDPC==frethqeuednccyoartlowwhicfhretqheuepnolceyovcocultrasge gain f =θ f=repqhuaseencshyifitnoHf tzhe signal from input to output fP = frequency at which the pole occurs θ = phase shift of the signal from input to output j = indicates imaginary number or √ –1 Texas Instruments Analog Engineer's Pocket Reference 31 31 Analog ti.com/precisionlabs BodeBpoldoetsplo(ztse(rzoesro) s) G (dB) 80 60 40 20 0 1 +90 +45 0 –45 Straight-line approximation +20 dB/decade Actual function 10 100 +3 dB 1k 10k 100k 1M 10M +45° at fZ 0° 5.7° at 1fZ0 +90° 84.3° at fZ x 10 +45°/decade 10 100 1k 10k 100k 1M 10M Frequency (Hz) (degrees) –90 Figure 16: Zero gaiFnigaunrde p1h5a: sZeero gain and phase MMZMeaaargggonnnliiiotttuuucdddaMMZeeetieoaa(((rnfffggo=> fZ) = +20 dB/decade Phase (0P.1hfaZsh1a0sefZ)(0=.1+f9Z0<° f < 10 fZ) = +45°/decade Phase (f P 01°0 fZ) = +90° Phase (f < 0.1 fZ) = 0° 32 Texas Texas In3s2truments Analog Engineer's Pocket Reference ti.com/precisionlabs Analog ZZeerroo ((eeqquuataiotniosn) s) G� � V��� V�� � G�� �j �ff�� � �� (43) As(4a3c)omApsleaxcnoummpbleexr number G� � V��� V�� � G����ff��� � � (44) Ma(g44n)ituMdeagnitude � � ����� �ff�� (45) Ph(a4s5e) shPihftase shift G�� � �������G�� (46) Ma(g46n)ituMdeaginndituBde in dB Where WGhVe=revoltage gain in V/V GGGf θffGG=VdDZ=BCdD=f==BrCf=e=rpf=v=eqrhovetquvhatolqhtuoeeslauteelneatgedancgdenscgcycechyegoiyiongafirgtnraaiHnlaooiltHnoifznwiwnwztihnhifnVefrircde/edVhseqqeicugtuchienbiebenaeneclzlcslfyseyrorvvomooollttiacnacgpgueuertsggtaoaiinnoutput fZ = frequency at which the zero occurs θ = phase shift of the signal from input to output j = indicates imaginary number or √ –1 Texas Instruments Analog Engineer's Pocket Reference 33 33 Analog Time to phase shift ti.com/precisionlabs P S Figure 17: Time to phaseFsighuifrte 16: Time to phase shift θ • 360° (47) P(h4a7s)e shPifhtafrsoemshtiimft efrom time Where TWS h=etrime e shift from input to output signal TTPS==pteimrioedsohf isftigfnroalm input to output signal θTP= =phpaesreiosdhifot fosf itghenaslignal from input to output θ = phase shift of the signal from input to output Example Calculate the phase shift in degrees for Figure 17. Example ACnaslcwuelar te the phase shift in degrees for Figure 16. AnsTwer 0.225 ms ( ) θ T = Ts • 360° 1 = 0.225mms s • 360° = 81° Tp 1 ms 34 Texas 3Te4xas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs AmAmpplilfiifeier Basic op amp configurations • Op amp bandwidth • Full power bandwidth • Small signal step response • Noise equations • Stability equations • Stability open loop SPICE analysis • Amplifier ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 35 Amplifier ++ Amplifier ti.com/precisionlabs BasicBoaspicamopp acmonpficgounrfaitgiuornastions BGa�s�ic�op�amp configurations (48) Gain (f4or8b)uffeGr acoinnffigourrabtuiofnfer configuration G�� � � (48) Gain for buffer configuration VCC VOUT VIN VEE Figure 17: Buffer configuration Figure 18: Buffer configuration GF�i�gu�reRR�1� 8�: Buffer � configuration (4(499) )GaGinafionrfnoor nn-oinnv-ienrvteinrgtincgocnofingfuigrautriaotnion G�� � R� R� �� R1 Rf (49) Gain for non-inverting configuration VCC VOUT VIN VEE Figure 19: NonF-iignuvreert1in8g: Ncoonn-fiingvuerarttiinogn configuration + + Figure 19: Non-inverting configuration 36 Texas ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference Basic op amp configurations (cont.) BGtia.�cs�oicm�Bo/p�parsaeRRimcc��ispoiocpnolnaafbimgsupractioonnsfi(gcuonrta.)tio(n5s0)(contG.)ain for invertingAcmonpfilgiufireartion G�� � � R� R� (50) Gain(f5o0r )invertinGgacionnffiogurriantivoenrting configura + + R1 Rf VIN VCC VOUT VEE Figure 20: InvertinFgigucroen1f9i:gIunvrearttiiongnconfiguration V��� F�ig�uRre��RV2��0:�InRVv��e�rti�ng�cRVo��n�fig(5u1)raTsrutaimnosmnfeinrgfuan(m5ctp1iol)ifniefrorTsiunravmenrmstinfiegnrgfuanmcptiloifniefror i V��� V����� RR��� ��VR� ���RVV�����RV��� �� V���� RV(5��2�) Transfer function for i Tarmanpsliffeierr,fua(ns5cs2tuio)mni(n5fog1rsRR)iun11vm==emrRtTsRi2nuir2ng=amg=ns…musa…m=fmieRnm=rNgpiRnfluiagfNinmecrpt,iloaifnis V��� � � R� R� �V� � V� � � � RVN�� VN RN R2 Transfer function (52) summing amplifi R1 = R2 = …=RN VN V2 R2 RRN1 Rf V2 VN V1 R1 RVfCC R2 V2 V1 Vcc R1 - + VEE Rf + Vcc Figure 2V01: Inverting summing configuration ti.com/amplifiers Vee - + Texas Instruments Analog Engineer's Pocket Reference + Figure 21: Inverting summing configuration VOUT Vout Vout 37 Amplifier ti.com/precisionlabs BaBsaiscicopopamamp pcocnofnigfiugruartaiotinosns(c(ocnotn.)t.) V��� � �RR��� � �� �VN� � V� N � � � V� N � Where WRh1er=eR2 = … = RN R1N==Rn2u=m…ber=oRf Ninput resistors N = number of input resistors (53) TrTanrasnfesrfefrunfucnticotnionfofror non(53)noinnvinevrteinrtginsgusmummimnginagmapmlipfielifrier fofroerqeuqaulainl ipnupturterseissitsotrosrs V1 V2 VN Rin R1 R2 RN Rf VCC VEE VOUT Figure 22: Non-inverting summing configuration Figure 21: Non-inverting summing configuration 38 Texas ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Amplifier SiSmimpplelennoonn--ininvveretirntginagmapmwipthwCfitfhilteCr f filter G�S� i�mRpR�l�e�n1on-inverting(5a4m) pGawinit(h5fo4Cr) fnfoilGfntoe-arirnifnveiffn>orau>triaofctnion f� G��2� π�R11� C� f� � 2π 1 R� C� (56) Cut o(5ff6(5f)r5e)qCcuoeuGfnnotfcaroigyiffnfu>ffrofra>oertrqifnocnuonoennn--icninyvvefeorrrttininngogncc-oionnnvffeiiggrutuirnraagttiioonn (56) Cf Cut off frequency for non-inverting configuration R1 Rf VCC VOUT VIN VEE Figure 23: Non-inverting amplifier with Cf filter Figure 22: Non-inverting amplifier with Cf filter Figure 23: Non-inverting amplifier with Cf filter Figure 24: Frequency response for non-inverting op amp with Cf filter FFiigguurree 2234:: FFrreeqquueennccyy rreessppoonnssee ffoorr nnoonn--iinnvveerrttiinnggooppaammppwwiitthh CCff ffiilltteerr ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 39 39 Amplifier ti.com/precisionlabs Simple inverting amp with Cf filter SimpleRinverting G amp with Cf (f5il7te) rGain for inverting configuration for f < fC R GG R −2R0dB/decade after fC until op amp bandwidth (5(85)7G)ainGfofoar rifni fC G li−m2i0tadtBio/ndecade after fC f 1until op amp bandwidth (59) Cutoff frequency for inverting configuration 2π RlimCitation 1 f 2π R C (59) CCfutoff frequency for inverting configuration RC1 f Rf R1 Rf VIN VCC Vcc Vin VOUT -+ Vout + VEE FiguVreee24: Inverting amplifier with Cf filter Figure 25: Inverting amplifier with Cf filter FigureFi2g6u:reFr2e5q:uFernecqyuerenscpyornesspeofonrseinfvoerritninvgerotipngamopp awmithp CwfitfhiltCerf filter ti.com/amplifiers 40 Texas Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Amplifier Op aOmp apmbpabnadndwwididtthh GBGWBW= G�ainGa•iBnW���BW (60) G(6a0in) baGnadinwibdatnhdpwroiddthucptrdodeufincteddefined WGBhWerWGGe=BahsgiWenparee=in=ccibgflioaacsnianedtdibwoanliodnottdahpwbpgilderaothind,pusrcoet,dt lubiscytte,odlpisiatnemdoppingaoampinpacdmoanptfaidgsauhtraeaetsitohneet specification table Gain B=Wclo=stehde lboaonpdgwaidint,hsleimt ibtaytioopn aomf tphegaaimnpcloifinefriguration BW =Etxhaembpalnedwidth limitation of the amplifier Determine bandwidth using equation 60 Example DeteGrmainin�e �b1a0n0dwidth using equation 60(from amplifier configuration) GGaBiWnG=B=W1202�0M�(2fH2roMzmH(fzraommpdliafitear schoenefitg)uration()from data sheet) BW B=WGG�BaWiGGnBaiWn=�2�221M201M00H0Hzz �= 222200�HkHz z Note that the same result Notesthhoawt tnhebeslaomw.e result can can be graphically determined using the be graphically determined using the AOL AcuOrLvceurve as as shown below. Open-loop gain and phase vs. frequency Open-loop gain and phase vs. frequency Figure 27: Using AOL to find closed-loop bandwidth Figure 26: Using AOL to find closed-loop bandwidth ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 41 Amplifier ti.com/precisionlabs FFuulll ppoowweer brabnadnwdidwthidth WV�hFV�e�url�2eSlπRp2fSoπRwf er bandwidth (61) Maxi(m61u(6)m1)oMduisaMdttpxiosaiumrtxttoiiuowmrtmniiuothmnoouuotptuustptleuwwtitw-hriaothtueot uisntledswulec-wread-treadtiiensdtionurdctuieocdned SWVSfVPRh=RP=SWVe==fr=RPrmehesm=esql=aelraumxewesxeiwmlainemrxarcwuiautymmetmreoaupftmpeeaeappakpeklaoioekuudtotppsuuiutgtptnvuvaotollvlttaoaglgteaegbbeeefbfooerrfeeorsselleeswwleiiwnnddinuudccueecddedddiissdttioosrrtttoiioortnniooonccoccucucrrsusrs f M=affrx=eiqmfrueueqmnuceoynuoctyfpauopftpavlpoiepldtlaiesgdigesnviagsln.afrl equency Maximum output voltage vs. frequency Maximum output voltage vs. frequency �� � �� ������������ ������. �������. ���/������/�������� �. � ����� �� �. �. ����� �� ����� �. ����� Figure 28: Maximum output without slew-rate induced distortion NoFtiicgeuFrthiega2ut 8rteh: eM27aa:bxMoimvaeuxfmiimguourumetpisouugttrwpaupiththewoduituthssoilnuegtwse-lqreauwtae-triioanntde6ui1cnefdodurcdtheisedtoOdriPtsiAtoo1nr8t8io.nThe NTedhoxeetNeatiecexmoreaxtmpiamtclhimeenpaeplcttehdalteachlgctaceurtlaachlaalpuecbthliuoaoailctvnabiaoetosilnolvfhyinegsoohuwsfriorhgsewwoutiiwrshtsehestghitsphrteaheegpepareheakpqeapevudkhaoaekuvlttdiosaovilgunontaes.lgtgianfeeoggqrefouethfraqoetutrihoaOtenthiPoOe6An1PO26APf71o2A7r7f2oat77hrt7eat4ht0aOe4ktP0HO4Ak0zP2Hk.A7zHT71.hz.8T.is8h.cisTacnhaebnebe TEhxisdaecmtaepnrlmebieneddetgerrampihniecdallgyraopr hwicithalltyheorewquitahtitohne. equation. Example VEVPx�aV=�m� �2SSpπRRl2fSeπR�f=�2π02�.08π�0.V0�.88�/kVVμ0�//sk�µμ��ss��� 3.�8Vpk or 6.37Vpp � 3.�8Vpk or 6.37Vpp = 3.18Vpk or 6.37Vpp 2πf 2π(40kHz) 42 Texas ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 42 ti.com/precisionlabs Amplifier SmSmaalllssiignnaal lsstetpepresrpeosnpsoense τ� � 0.35 f� (62(6) 2R)iseRtiismeetifmoreafosrmaasllmsaigllnsailgsntaelpstep Small signal step response WtRhWf=CRe=h=rtehettehrheeeriscreilsoestiemtτidme�-leo�oofo0paff.3a�bs5amsnmadlalwlslidisgtinhganolafsltthsetepeporeprseapsmopnopsnces(i6rec2u)it Rise time for a small signal step fC S=mthaellcsloigsneadlW-Rlsoht=oeeptprheberearsnispdeowtniidmsteeh wooffaatvhesefmooarpmllasmigpnaclirsctueipt response fC = the closed-loop bandwidth of the op amp circuit Small sSimgnaalll ssitgenparlesstpeopnrseespwoanvseefowrmaveform Figure 29: Small signal step response Figure 2F8ig: uMreax2i9m:uSmmoalultspiugtnwalitshtoeuptrselsepwo-nrastee induced distortion ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 43 43 Amplifier OpOapmamppnnooiisseemmoodedlel ti.com/precisionlabs Figure 30: Op amp noiseFmigoudreel29: Op amp noise model Op amp intrinsic noise includes: OpamNRpoeiisnsitesrtinocsar iuncsoneisodeisbey ionpclaumdeps:(current noise + voltage noise) • Noise caused by op amp (current noise + voltage noise) • Resistor noise 44 Texas ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Amplifier NNooisisee bbaNanondidswewidbitdahntcdhawlcciduatllahcticuoalnlactuiloatnion BW�No�is�eB�Wbf�a�n�dw�i�dft�h calculatio(6n(36)3N) oiNseo(i6bs3ae)nbdawNnioddiwtsheidtbhandwidth WBKfCNWKfWBhC=NWe=N=h–=reKBfWBeNt=–3ChrWtNW3=e=hhend=�eeNodBn–brtBiKfWBo�3b=erhsCbiirNWecesbd=hnia�cke=aBebonbNk�–nrwiadbrtsf3=ebhwid�nacweaaewdakdnnlinlbdBlowdbiwldcdatiwrcishowtbaindhcoeiralddtioklrrdhontewrbcfhtewfdchaooitcdthwtaonrfhitotreolfidhiteelofdhntwccsnhttoeshhotyifefidyfaeosrsaosttrcstnyhhectsfetyesetcyomtfosotmhatsrestfirecoetmfyetftonmhosom(retr6yrfeads3dfsmocti)iyfeftrffsoemedtrrNreieeffmfoonneirttsredfefiinliltftbfeteearfrrinloeotdenrrdwdrt eeoifdirrrlttdeherrorder Figure 3F1i:gOuprea3m1p: Obpanadmwpidbtahnfdowr tidhtrheefodriftfherreeentdfiiflfteerresnot rfdileterrss orders FigureF3i1g:uOrep3a0m: Oppbaanmdpwbidatnhdfworidtthhrefoerdtihffreereendtifffeilrteernst ofirltdeerrssorders Table 15T:aBbrlieck15w: aBllriccokrrweacltliocnorfraeccttoiorsn ffoarctnoorissefobrannodisweidbtahndwidth NTumaNbbuleemr1234T1bNoa5efub:r123pmlBoeoNbfrlu1eiepcm6sro1234k:bloeBewfsrr2341paiooclflkepccoswoolKerrarscNreleolbcKcr1111crtriNti....oeoci5211obcckrn7232111rrotniiweKf...ocra521rcfakNneca723tlbtcclwifoo1111arttaiir....nococK5211ltkrlnN7232ofsawrfbacfraocitclortlkornrswoafiosll1111rec....5211nob7232roraeinscdetiwobniadfnatchdtworidth 4 1.12 BroadbaBBnrrodoaatdodbtbaaalnnnddotitsooettaacllannlocoiuissleaetcicoaanllccuullaattiioonn E� �Bro��a�Ed��bBa�Wnd���t�o�taBlWno�ise calc(u6(l46a)4tTi)oontaTlor(tm6a4ls)rnmosTisonetoafilsroremmfrsobnmrooaibsdreobafardonbmdanbdroadband WEeBBNWhB=eWEEeN=rB�N=tehBbo=�ertn=aorWEBeoWEeBtelaboB�NiWBNWrshdrtB�hBmaoe=eb�=NeN==lasr�abrter==tdenombobanBbdtrtnnnroWasaaooodoinllnsaa�niwirorsesdddommeiiebbdsifnssrsaetabbooehnnannaimssdfd(noonpreHodidiebnssnzmwswcroeeo)optiiiirdsfafdesbarretedocrtohlohtbmmsdsra(aap(epHHdnlebbnebzzddcrrsc)aoo)eti(tnrtnaar6nyaoaddd4sl(libbis)dnntdayeaeVoennn(i/TnsdnrdstoseVHinittntya/zoyorl)t(iiHs(rnsnmeeVzV)s//rrtntHHozizs))e from broadband BWN = noise bandwidth (Hz) ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 45 45 45 Amplifier ti.com/precisionlabs 1//fftototatlanlonisoeicsaelccualaltciounlation 1/f total noise calculation E�_������ � � ����f� E�_������ � � ����f� ((6655)) NNoromrmalaizliezded1/1f/nf oniosieseata1t 1HHz z (65) Normalized 1/f noise at 1 Hz Where eWEeEfOBNBNeWEh=FF__BeNNN==hFt_OrhONee=RnneORrMooeRMnAfMiirLosAseAeLie=Lsq=es=us1ppe/1s1fenep//ncfccfeotyntncrriaoostatrhlieilassdadleenetedonntnehrososmneirritstmmya1yitl/ayamimfzlliemniezzedoaeeeaisddsstaoueusttrooru1eeerdB11dHeFdizHHininsizznttmhhteheeea11s//1fuf/rfrreeergedgigoioainont n fOfO==thtehefrferqeuqeunecnycyththaat tththee11/f/fnnooisiseeeeBBFFisismmeeaassuurreeddaatt E�E_���_��������������� E��E_��_������������������ff���ff��� � (66) 1/f total noise calculation (66()616/)f tota1l/fntooitsael ncoalicseulacatiolcnulation Where ENW_FhLIeCrKeER = total rms noise from flicker WENEh_eN_OrFeRLMICAKLER= =1/tfontaolisrme snonromisaelizfreodmtofli1ckHezr EfHNE=_NFu_LNIpCOpKReEMrRALc=u=ttoo1ft/faf flnrreomqisuseennoocirsymeoafrrloinzomeidsfeltiocbk1aenrHdzwidth EfLNf=H_N=loOwuRMpeprAeLcru=cto1uf/tffoffnrfeofqriseueqeunneconyrm,cynaoolirzrmendaoliltsyoes1ebHtaztnod0w.i1dtHhz fHf=L =ulpopweerrccuuttooffff ffrreeqquueennccyy,onronromisaellybasentdtwoid0t.h1 Hz fTLa=blloew1e6r: cPuetaokff-tfore-qpueeankccyo, nnovremrsailolynset to 0.1Hz Table 16: Peak-to-peak conversion Number of Percent chance Tasbtlaen1d7aN:rPduemdaebkve-itraoot-ifopnesak converersaidPoiennrgceisntinchrangce 2σs(tsaanmNdueamradbsedr±eo1fvσsi)atatinodnasrd deviatiorensadi6n8g.3is%in ranPgeercent chance reading is in range 3σ2σ(s(asmame easa2s±σ1±.(15saσσm))e as ±1σ) 866.86.%3% 68.3% 4σ3σ(s(asmame easa3s±σ2±(sσ1a).m5eσ)as ±1.5σ) 958.64.%6% 86.6% 5σ4σ(s(asmame easa4s±σ2±.(25saσσm))e as ±2σ) 989.58.%4% 95.4% 6σ5σ(s(asmame easa5s±σ3±(sσ2a).m5eσ)as ±2.5σ) 999.87.%8% 98.8% 6.66σσ ((ssaammee aa6ssσ±±(33saσ.3m)σe)as ±3σ) 999.99.%7% 99.7% 6.6σ (sam6e.6aσs(s±a3m.3eσas) ±3.3σ) 99.9% 99.9% 46 Texas ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 46 ti.com/precisionlabs Thermal noise calculation Amplifier √ TEhn_eRr=ma4l knToRi�sef calculation (67) Total rms Thermal Noise √ en_R = 4kTR (68) Thermal Noise Spectral Density E�_� � √4 kTRΔf (67) Total rms thermal nois Where WEnh_Re=reTotal rms noise from resistance, also called thermal noise (V rms) EkTekNn===__RRBBT=eo=omlNtlzttpoozmeismtraaeantalsnurnp’rsmeencci’snotsrnKancsleotodlaviennsinntses1tita.fy3rn8ofrtmox1m1.r03re-e28ss3iJisxs/tKta1an0nce-c2,3ea,Jls/aoKlscaollecdatlhleerdmtahl enormisea(lVn/√oHizse) T∆f==tNeomispeebraantduwriedthininKHezlvin ∆f = noise bandwidth in Hz 1000 Noise Spectral Density (nV/rtHz) 100 10 ‐55C 1 25C 125C 0.1 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 Resistance (Ω) 1.E+06 1.E+07 FFiigguurree313:2N:oNisoe isspeecstrpael dcetnrasiltydvesn. rseistiystavnsc.eresistance ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 47 Amplifier ti.com/precisionlabs Ac rAecsrpeospnosneseveverrssuuss ffrreeqquuenecnycy (Dominant 2-Pole System) Ac response versus frequency FiguFreig3u2reil3lu3siltlruastterasteasbaobdoedepplolottwwiitthh ffoouurrddififfeferernetnetxeaxmapmlepsleosf aocf paecakpienga.king. Figure 33 illustrates a bode plot with four different examples of ac peaking. Figure 33F:igSutarebi3li2ty: S–taacbipliteya–kiancgpreelaaktiiongnsrheilpateioxnasmhpipleexample Figure 33: Stability – ac peaking relationship example Phase margin versus ac peaking PhaPsheasmeamragrigninvveerrssussaaccpepaekainkging This graph illustrates the phase margin for any given level of ac peaking. TNhoitseNTNgthoorhiattseaeptgtthhhr4aaa5iplttl°hu44os55iltl°f°urpaoosfftthreppaashhtseaateshsseemtehmmeapraahpgrrahgginasiinnseoeoomrrrmggagarrrrereggaaiinntteeeffrrrooiirissrsararrneeneyqqyquuguiigrirvieeirevddenedffnoolefrrolvesserttvalaseobbtlfllaeeoabfocoleppapeeceorraaappktteeiiioonrannagk..t.iinogn.. Figure 34: Stability – phase margin vs. peaking for a two-pole system FigFuigruere343:3S: tSatbaibliitlyity– –phpahsaesemmaragrigninvsvs. .ppeeaakkininggfoforraatwtwoo-p-poolelesyssystetemm 48 Texas ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Amplifier Transient overshoot (Dominant 2-Pole System) Transient overshoot FiguFriegu3re4 3il5luisllutrsatrtaetsesaatrtarannssieienntt rreessppoonnsseewwithithtwtowdoiffdeirfefenrteenxtamexpalemsples of percoTefrapnnetarscgieenttoaovgveeerosrvshehoroosoht.toot. Figure 35 illustrates a transient response with two different examples of percentage overshoot. Figure 35:FSigtaubreili3ty4:–Sttraabnisliiteyn–t torvaenrssiehnotoot veexrasmhopolet example PFhigausreem35a:rgSitnabvielirtsyu–stpraenrcseienntat goeveorvsehrosohtoeoxtample PhaTshies gmraaprhgililunstvraetresuthse phearsceemnatragginefoor vaneyrsgihveonoltevel of tPrahnassienmt oavrgerinshvoeorts. uNsotpeetrhcaetn4t5a°goefopvhearssehmooatrgin or greater is required TosthvaeisbfTtfroorslhagerrhinrsssooasttagpaipoebrbtehna.lleretpiNaloholotuovippioeslteleeunrtrrsrsa.aathtthtrtoiiaoeoaotnnstet...s4tNh5tohe°teepopfthhhapaashtseea45smm°eaaomrrfggpainihnrgafofsionreraomnarynagryggrieigvnaeivonteerlrnegvirsleeealrvetoeeqflr uoisifrreterdqaunfoisreriednt Figure 36: Stability – phase margin vs. percentage overshoot FNFiioggtueur:reeT3h35e6::cSSutrtavabebisliiltiaytsy–s–upmphheaasaseetwmmoa-arpgrogilneinvsvsys.sp.tepemerc.rceenntataggeeooveversrhshoooot t Note: The curves assume a two-pole system. ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 49 49 Amplifier ti.com/precisionlabs VFB R1 RF C1 1T VIN L1 1T V+ VO Riso VOUT CL V– Figure 36: Common spice test circuit used for stability Figure 37: Common spice test circuit used for stability A��_������ � � V� V�� (69) Loade(d6o8)pen-Lloooapdegdaionpen-loop gain β � � V�� (70) Feedb(a6c9k) factFoeredback factor 1 β � � 1 V�� (71) Closed(7-l0o)op nColiosesegda-ilnoop noise gain A��_������ � β � � V� (72) Loop g(7a1in) Loop gain Where WVOhe=rethe voltage at the output of the op amp. VVOOU=T t=hethveovltoalgtaegaetothuetpouut tdpeulitvoefrethdetooptheamlopa.d, which may be important to the VaVOpFUBpTl=itc=hfaeettheiaoedpnbpvbaoliuccltktaaitgvsiooennltooabtuguctepot unistsidndoeeltrivecedorneinsdisdttoearbtehidleityilnoaasndtaa,lbywislhiitsyic. hanmalayysibs.e important to VRtoFFBp,o=Rlof1ge,ieeRdsISbwOaicallknhdvaoCvletLa=dgieftfheereonpt amp feedback network and load. feedback networks; however, the Other op amp test circuit will be the RsFam, Re1f,oRr imS0oasntdcaCsLe=s.tFhieguorpea3m8pshfeoewdsbtahcekenxectewpotiroknatnodthloeardu.le (multiple feedback). C1 anOdthLe1raorep caommpptoonpeonlotsgtiehsatwfaillchiliatavteedSifPfeICreEntafneaeldysbiasc. kThneeytwaorerklsa;rge (1TF, 1TH) to mahkoewtehveerc,irtchueittecslotsceirdc-uloitowp iflol br edct,hbeustaompeenfolor ompofsotrcaacsferse.quencies. SPICE requiFreigsucrelo3s7eds-hlooowpsotpheeraetxiocnepattiodnc tfoorthceonruvelerg(menuclteip. le feedback). C1 and L1 are components that facilitate SPICE analysis. They are large (1TF, 1TH) to make the circuit closed-loop for dc, but open loop for ac frequencies. SPICE requires closed-loop operation at dc for convergence. 50 Texas ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Amplifier R1 R1 VFB VFB CIN Cin RF RF CF CF L1 1T VIN Vin C1 1CT1 1T V+ V- - + ++ V– V+ Riso Riso VO Vo VOUT VoCutL CL Figure 37: Alternative (multiple feedback) SPICE test circuit used for stability Figure 38: Alternative (multiple feedback) SPICE test circuit used for stability A��_������ � V� (73)(L7o2a) dedLoopadeendloooppengaloinop gain β� V�� V� (74)(F7e3e) dbaFcekefdabcatocrk factor 1 β � V� V�� (75)(C74lo)sedC-loloospedn-oloisoepgnaoinise gain A��_������ � β � V�� (76)(L7o5o) p gLaionop gain Where WVVVOOOhU=e=Tre=tthhetehvveoovllttoaalgtgaeegeaattottuhhteepuootuudttppeuulittvoeofrfetthdheetoooptphaeammloppa..d. This may be important to the VaOppUTlic=attihoen vboulttaisgenootuctopnust iddeelrievderiendsttoabthilietyloaanda.lyTshisis. may be important to VFB =thfeeeadpbpalcickavtiooltnagbeut is not considered in stability analysis. VRfeFFeB,dR=b1af,ecRekId,SObthaaecnkldoovCopFltisa=gbtehroekoepn amp feedback at the input. network. Because there are two paths for RtCoF1,maRnap1dk,aeRLtht1ihssaoefraoecnricrdfcoeuCmeidtFpcb=olaontcsehkene,dtstohlpotehoaalpomtoffpoaprcfiedisliectba,drtbboeuakStceoPknpInCaeetnEttwhlaoeonoraipknl.ypfoBsuriest.ac. caTuhfrseeeyqtuahereenrcelaieargsre.eSt(wP1ToICFE, 1TH) Cre1qaunirdesL1claorseedco-lomoppoonpeenrtasttiohnataftadccilitfoatrecoSnPvICerEgeanncaely.sis. They are large CcHaIoNpwa=ec(ac1tvicohtTeanefFrnrv,,eecew1qqerTghuunHeeievonnn)arcctmluoeeiesna.msitlnl.yaignSkdptPehouIietCtshscEseanimrpcoeaiturqccnluaiuteitariieteondcsncleotcmosltoeaebstdkeheedolanod-dolfodrtphoeoemfdpocbrotahedppecceaa,rocaubpitstuiaoeatnnmotchappeetedidmsnacioltsoadfoooselhpraletifeneodctr.lubTdyheiss it. CthIeN 1=TtHheinedquucivtoarl.ent input capacitance taken from the op amp datasheet. This capacitance normally does not need to be added because the model includes it. However, when using this simulation method the capacitance is isolated by the 1TH inductor. ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 51 Amplifier R1 Voffset VIN + RF +Vs + -Vs ti.com/precisionlabs VOUT Volts Voffset VOUT 50mVpp Figure 38: Transient real world stability test Test tips • Choose test frequency << fcl • Small signal (Vpp ≤ 50 mV) ac output square wave (for example, 1 kHz) • Adjust VIN amplitude to yield output ≤ 50 mVpp • Worst cases is usually when Voffset = 0 (Largest RO, for IOUT = 0A). • Use Voffset as desired to check all output operating points for stability • Set scope = ac couple and expand vertical scope scale to look for amount of overshoot, undershoot, and ringing on VOUT • Use 1x attenuation scope probe on VOUT for best resolution 52 Texas ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Amplifier RIN1 CCM1 1nF VIN- 1kΩ CDIF RIN2 10nF Rg 1kΩ VIN+ 1kΩ CCM2 1nF +15V RG VOUT Out RG Ref U1 INA333 -15V FFiigguurree 4400:: IInnppuuFttigffiuillttreeerr3ff9oo:rrIiinnnpssuttrrtuufmimlteeennr ttfaaottriiooinnnsaatrmmupmplliieffinieetrration amplifier Figure 40: Input filter for instrumentation amplifier SSeelleecctt CC������ �� 11��CC������ RRSe����le��c��t CRR���������� 1�C��� CCR��������� ��� RCC��������� ffCf�������������222πππCRRR��������111����CCC��������� (c((777o789m))) DICmniopoffmunet((((((((r-(((m7777e7777777mre6879n6879867oos))))t)))))))nidias-elmtoDDtCmIfDtDCmICmDtIfiinininomrimlmiioiiotloiupsupupffdfftfeffffmfmeemesuesusueeeeeermrtststtsttrrrrmrmmiceeeebseburbrrttteeaeohnnohnneohnesessspsnettnetttnetiiiiieieieiziaaaaa-a-s-bssccmqcqmeqmllclltltteooooudouuffffifoootiiiimimrmraraellalloldttsdtts1dtsleeqleelermmmee0esmmrrmrrurooocccitacicimuusussinnanauamulsss-u-ps-pstpstttmtmomoeisiaiaazzbzbbfsftococfocfeeeeeebiididtdddtdtthooeeoeeeeee11r1rqrqqsesfsff000uuiuiiqlllttataaeeeulllrrral (80) Differ(e7n9t)ial fDiltifefer rceunttoiaffl filter cutoff ff������ f��� �� � 11 22ππ��22RR����������CC1������ 2π�2R�����C��� �� � 12121 2 CC�������� C���� ((8800)) CCoommmmoonn--mmooddee ffiilltteerr ccuuttooffff (81) Com(m80o)n-mCoodme mfilotenr-mcuotdoeff filter cutoff WffRDCfCCWfRfCCWfRWfRDCIDCDCIMNhFICDIMICDIMICIMNFNFhNhFheIMIMM=F=F=e=e==e===r==e====rrridccedcendecidiinnnocidcodcooipififfpfpofpomoimimffmfueffeeueumufmfmtreemmmrrmtrtteeemremrrmrrrneeooeoonneneeotsoonnnnnnttstsisiiinainnt--t-a-asiaiiiismsmmsml--aa-tlllmmttmatcllcacaocaooonuffuouonuondndddiictlltdtdctdctecteoeeoooeeeeeeeeffffcrcrfccfffffufuuccfufififilrlrrltrtatatttteeoeoeoeeoeppqqfqfqfrrrfffafafuuuucccfffceferereraaariieeenttnennpppaaqqqccqccaaannuuuyyyyucccceeeeiiieettntnnanaacccncnnyyyyccceee CCNlfNlfNCloororCDoooowDowwIMFmmItttFeeeeee==r=r:r::bbdtSctStSeehdhhoieeieifaiaannffmlllfennenegegercmccrtettcchtehthtniiooionnenneetnnnggtgiacicvcv-amColCoeCoelfmmrmrDDifDottliIIetIelFFmdmFmtedede≥≥≥roooriicnnfn1n11cia-l-0t-0ta0tomommpepCCCarododaocCCcCdidicdffMMiMfafeieteeteapasssrrcccnnaeeeeeuuuccctntnttststseeiootottiiatfatfatfhfhfhfnllefefefcnrnrreeeeododdqqqiiiiisfsffuuufffeeeeeeerrrnndndeeeccucunnnyyyeettt.i.i.iaaattTTToolllhhhmmmcciiisssooooommdpdpdperererppeeeoocccvvvnunueueeetetntnnooonntttffsfsstftff tftcfcfcororroooeeelleemmmqqqrruuumamameeennooonnnccnnncccee--y-yyssmmm..111ooo000dddtteteeiiimmmnnneeeooosssiiissseee Nforotem: SbeeilnegctcinognvCeDrItFe≥d i1n0toCdCiMffesreetnstitahlenodiisffeerdeunetiatol mcoomdepocnuetonftftforleeqraunecnecsy.10 times lower than the common-mode cutoff frequency. This prevents common-mode noise from being converted into differential noise due to component tolerances. ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Referen5c5e33 53 53 Amplifier Notes ti.com/precisionlabs 54 Texas ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs PCPBCaBnadndWWiriree PCB trace resistance for 1oz and 2oz Cu • Conductor spacing in a PCB for safe operation • Current carrying capacity of copper conductors • Package types and dimensions • PCB trace capacitance and inductance • PCB via capacitance and inductance • Common coaxial cable specifications • Coaxial cable equations • Resistance per length for wire types • Maximum current for wire types • PCB and wire Texas Instruments Analog Engineer's Pocket Reference 55 PCB and Wire ti.com/precisionlabs Table 18: Printed circuit board conductor spacing Voltage between conductors (dc or ac peaks) B1 Bare board B2 B3 Minimum spacing B4 A5 0-15 0.05 mm 0.1 mm 0.1 mm 0.05 mm 0.13 mm [0.00197 in] [0.0039 in] [0.0039 in] [0.00197 in] [0.00512 in] 16-30 0.05 mm 0.1 mm 0.1 mm 0.05 mm 0.13 mm [0.00197 in] [0.0039 in] [0.0039 in] [0.00197 in] [0.00512 in] 31-50 0.1 mm 0.6 mm 0.6 mm 0.13 mm 0.13 mm [0.0039 in] [0.024 in] [0.024 in] [0.00512 in] [0.00512 in] 51-100 0.1 mm 0.6 mm 1.5 mm 0.13 mm 0.13 mm [0.0039 in] [0.024 in] [0.0591 in] [0.00512 in] [0.00512 in] 101-150 0.2 mm 0.6 mm [0.0079 in] [0.024 in] 3.2 mm [0.126 in] 0.4 mm [0.016 in] 0.4 mm [0.016 in] 151-170 0.2 mm 1.25 mm 3.2 mm [0.0079 in] [0.0492 in] [0.126 in] 0.4 mm [0.016 in] 0.4 mm [0.016 in] 171-250 0.2 mm 1.25 mm 6.4 mm [0.0079 in] [0.0492 in] [0.252 in] 0.4 mm [0.016 in] 0.4 mm [0.016 in] 251-300 0.2 mm 1.25 mm 12.5 mm [0.0079 in] [0.0492 in] [0.492 in] 0.4 mm [0.016 in] 0.4 mm [0.016 in] 301-500 0.25 mm 2.5 mm 12.5 mm [0.00984 in] [0.0984 in] [0.492 in] 0.8 mm [0.031 in] 0.8 mm [0.031 in] Assembly A6 0.13 mm [0.00512 in] 0.25 mm [0.00984 in] 0.4 mm [0.016 in] 0.5 mm [0.020 in] 0.8 mm [0.031 in] 0.8 mm [0.031 in] 0.8 mm [0.031 in] 0.8 mm [0.031 in] 1.5 mm [0.0591 in] A7 0.13 mm [0.00512 in] 0.13 mm [0.00512 in] 0.13 mm [0.00512 in] 0.13 mm [0.00512 in] 0.4 mm [0.016 in] 0.4 mm [0.016 in] 0.4 mm [0.016 in] 0.8 mm [0.031 in] 0.8 mm [0.031 in] B1 Internal conductors B2 External conductors uncoated sea level to 3050m B3 External conductors uncoated above 3050m B4 External conductors coated with permanent polymer coating (any elevation) A5 External conductors with conformal coating over assembly (any elevation) A6 External component lead/termination, uncoated, sea level to 3050m A7 External component lead termination, with conformal coating (any elevation) Extracted with permission from IPC-2221B, Table 6-1. For additional information, the entire specification can be downloaded at www.ipc.org PCB and wire 56 Texas Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs PCB and Wire Figure 4F1i:gSuerelf 4h0ea: tSineglf ohfePaCtiBngtroacf ePsCoBn tirnascidees loanyeirnside layer Example Example Find the current that will cause a 20Ԩ temperature rise in a PCB trace that is 0.1 inch Find the cuwridreenatndthuastesw2illocz/aftu2 scoepape2r.0(°ACsstuemmeptrearcaetsuorne oriustseidien oaf PPCCBB.) trace that is 0.1Ainncshwewr ide and uses 2 oz/ft2 copper. (Assume traces on outside ofFPirCstBtr.a)nslate 0.1 inch to 250 sq. mils. using bottom chart. Next find the current Answer associated with 10Ԩ and 250 sq. mils. using top chart (Answer = 5A). FthirestcturrarnesnEFltaoxattrersaas0cdotd.e1cidtiioaiwnnticaethlhdinptwfeoorirmtm2hi5sas10tiio0osnn°qCtfhr.oeammenindIlPsti.rC2eu-52ss01pin5es2cgqi,fi.Fbcmiaogtutiiotlrsone.mc5ua-1snc.ihbneagrdtto.owNpnelcoxhatdaferintddat www.ipc.org (Answer = 5A). Extracted with permission from IPC-2152, Figure 5-1. For additional information the entire specification can be downloaded at www.ipc.org 57 Texas Instruments Analog Engineer's Pocket Reference 57 PCB and Wire ti.com/precisionlabs PPPCCCBBBttrrtaarccaeecrreeessriiseststaaninsccteeafnfoocrr1e1oofzozCrCu1u oz-Cu 11 110000mm 1100mm 11125012500505005050mmmmmmmmmmiiiiilllliiiililllll 11mm 110000µµ 1100µµ 11µµ11 1100 TTrraacceelele1n1n00gg0t0thh((mmilisls)) 11000000 1100000000 FFiigguuFrreieg4u42r2e::P4PC1C:BBPtCtrraBacceterarrecesesiisrsettasaninsccteaenvvcsse..llevesnn.ggltethhnagantnhddawwnididdtwthhifdfootrhr11fooorzz1--CCouuz,-,2C255u°°,CC25°C FFiigguFuriregeu44r3e3::4PP2CC:BPBCttrrBaaccterearcreeessirissettsaainsnctcaeenvcvsse..lvlesen.nglgetthnhgaatnhnddawnwdiiddwtthhidffotohrrf11ooroz1z--CoCuzu-,,C11u225,5°1°C2C5°C EExxaammppllee EWW2W25x5hh°ha°aCaaCmtttaiasiipnssnltdetdhthhe1e1e22rr5e5re°se°sCiCssis?it?staatnnaccneecooeffaoaf22a00m2m0ilillmoloninlggl,o,55nmgm,ilil5wwimdideiel twtrraaicdceeeffotorraraca1e1ofoozz-r-CCauutthhicickknneessssaatt 1ARARARn2n2on255ssz5sCwCw-CwCe=ee=rurr222tmhmmiΩcΩΩk,,nR,ReR11s212s525CaC5tC==23=53m°m3CΩΩm.a.TnΩThdh.eeT1php2oeo5ini°nptCtsos?aianrretesccairircrceleledcdiorocnnletthdheeoccnuurrtvvheeess..curves. 58 Texas Texas Instruments Analog Engineer's Pocket Reference 5588 ti.com/precisionlabs PCB and Wire PCB trace resistance for 2 oz Cu PCPCBBtrtraa1cceerreessisitsatnacnecfoer f2oorz2Cou z-Cu 100m1 11000mm 110mm 5mil 10mil 52m5iml il 105m0iml il 2150m0iml il 50mil 100mil 1010mµ 11000µµ 10µ 1µ 1µ 1 1 10 100 1000 10 Trace l1e0n0gth (mils) 1000 10000 10000 Figure 44: PCB trace resistaTnraccee vlesn.gltehn(gmthils)and width for 2 oz-Cu, 25°C FigFuigreur4e4:4P3:CPBCtBratcraecreesriesstiasntacnecves.vsle.nlegnthgtahnadnwdiwdtihdtfhorfo2r o2zo-Cz-uC, u2,52°C5°C FFiiggFuuigrrueer44e554::4PP:CCPBBCBttrratarccaeecrereersseiissstitsaatnancnceceevvsvs.s.l.elelnengngtghtthhaanandnddwwwidiidtdhtthhfoffroo2rr 22ozoo-zzC--uCC,uu1,,211522°55C°°CC EExxaammppllee EWxW2hW2a55ahmh°°taCaCipttsaaiilssetnnhttddhhee1e1r22err5e5es°s°siCCsiisst??ttaaannnccceee ooffaa220000mmilillolonngg, ,2255mmiliwl widideetrtarcaecefofroar of a 200 mil long, 25 mil wide trace a2 2ozo-zC-uCuthitchkicnkensessast for a at 2 oz-Cu thickness at 25°C and 125°C? AnAAsnnwsswwereerr Rth2ReR522cC55uCCr=v==e2s22m. mmΩΩΩ, ,,RRR111222555CCC === 333mmmΩΩΩ...TTThhheeeppopoionintisntstasareraerceicriccrlceirldecdloenodnthotehnecucruvrevse.s. Texas Instruments Analog Engineer's Pocket Reference 59 PCB and Wire CCoommmmoonnpapcakcagkeatgyepetyanpdedaimnednsdiiomnsensions ti.com/precisionlabs 120.2mil 3.05mm 60 Texas T6e0xas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs PCB and Wire PPCCBBpparaarllaelllpellatpelacatpeacciatapnacce itance k ∙ ℓ ∙ w ∙ εr (82) Cap(a8c1i)tance fCpolaarpnpaeacsriatallenlcceofporpeprarpalallenlecsopper WWPhhCeerBreeparallel plate capacitance kk ==PerPmiettivrimty oitf tfrieveitsypacoef. free space. Bk o=tBh8.t8oh5et4hm·1e0tt-rh3icpeaFn/mdmimme,pktoerrr∙ii2acℓ.l2v∙4ae7wrn·s1ido0∙n-4εiomrpfFth/pmeeicl orniastal nvt aerresgiivoenn. ℓ =PleCngBth w = widkth ((=pmmaee8ttrrrii.cca8iilnn5le4mmlmm∙1p,, o0olarr-iit3mmepppeecrrFiiaaa/ll pmiinnammmciill))i,taonr c2e.247∙10-4 Capacitance for of (t8h1e)constpalnatnaerse given. pF/mil parallel copper h = separation between planes (metric in mm, or imperial in mil) ℓεr ==WPhClBeerrneelagtitvhe d(iemlecetrticrikccon∙isℓnta∙nmwt (εmr∙ ≈ε,4r.o5 rforimFRp-4e) rial in mil) (81) w k== Pwermiditttivhity (omf freeetsrpicacei.n mm, or imperial in mil) Capacitance for parallel copper planes Both the metric and imperial version of the constant are given. h W=ℓ = hslkenee=gpr8the.8a(5mr4ae·1trt0ici-o3inpnFm/bmmme, o,trowirm2ep.2ee4ri7an·l1in0p-m4laipl)Fn/meils (metric in mm, or imwperial in mil) ε ε r = PCB relative dielectric constant ( r ≈ 4.5 for FR-4) w = width (metric in mm, or imperial in mil) khεr === PBsPeeoCprtBhmartirathettielviaoimttnyivebeoterfditcfwireeaeleenecdnstpripimaclacpceneo.ernisasl(tamvneetrts(rεiicorni≈no4fm.5thmfeo,rcooFrnRims-t4pa)enrtiaalreingmiviel)n. k = 8.854·10-3 pF/mm, or 2.247·10-4 pF/mil l ℓ = length (metric in mm, or imperial in mil) w = width (metric in mm, or imperial in mil) A h = separation between planes (metric in mm, or imperial in mil) w εr = PCB relative dielectric constant (εr ≈ 4.5 for FR-4) h l Aw εr Figure 45: PCBl parallel plate capacitancAe h εr Example Calculate the total capacitance for ℓ=5.08mm, Fhigure 45: PwC=B1p2a.r7amlleml p,laht=e1c.a5p7a5cimtamnc,eεr = 4.5 εr Examp(8le.85C4a∙lc1u0–la3tpeFt⁄hmemto) t∙a(5l .c0a8pmamc)it∙a(n1c2e.7mfomr )ℓ=∙ (54..058) mm, C(FpigFu) r=e 45: PwCB=1p2ar.7almlelmp,1lah.5te=71c5a.m5pm7a5cimtamnc,eεr = 4.5 = 1.63pF EECx(axpamFm)p=ple(le8C.8C5awa4lc=l∙cu11ul20ala–.t73teempFttmh⁄heme,1mhtt.o5o=)7tt1∙a5a(.mll55c.cm70aa85ppmmaammcc)ii,tt∙aaε(n1nr2cc=.e7em4ffo.mo5rr)ℓ∙ℓ=(=452..500)80mm= m1il.,6,3pF (8.8w54=5∙ 1000–m3 piFl,⁄hm=m6)2∙ m(5i.0l,8εmrm=) 4.5 ∙ (12.7mm) ∙ (4.5) C(CEp(xFpa)Fm)==p(l2e.2C47al∙c1u0l–a4tepFth⁄em1t.i5lo)7t∙5a(ml2c0ma0pmailc)i∙ta(5n0c0emfiol)r = 1.63pF ∙ℓ(=42.50)0mi=l, 1.63pF w=500mil, h=6622mmiill, εr = 4.5 EC(xpaFm) =pl(e2.C24a7lc∙ u1l0a–t4eptFh⁄emtiol)t∙a(l2c0a0pmailc) i∙t(a5n0c0emfilo)r∙ (ℓ4=.52)00mil, w=500mil, h=6622mmiill, εr = 4.5 = 1.63pF C(pF) = (2.247 ∙ 10–4 pF⁄mil) ∙ (200mil) ∙ (500mil) ∙ (4.5) 62mil = 1.63pF Texas Instruments Analog Engineer's Pocket Reference 61 61 PCB and Wire ti.com/precisionlabs Microstrip capacitance and inductance ( L(nH) = kL ∙ ℓ ∙ ln 5.98 ∙ h 0.8 ∙ w + t (83) Inductance for microstrip ( ( kC ∙ ℓ ∙ (εr + 1.41) ( C(pF) = ln 5.98 ∙ h 0.8 ∙ w + t (84) Capacitance for microstrip Where kL = PCB inductance per unit length. Both the metric and imperial version of the constant are given. kL = 2nH/cm, or 5.071nH/in kC = PCB capacitance per unit length. Both the metric and imperial version of the constant are given. kC = 0.264pF/cm, or 0.67056pF/in ℓ = length of microstrip (metric in cm, or imperial in inches) w = width of microstrip (metric in mm, or imperial in mil) t = thickness of copper (metric in mm, or imperial in mil) h = separation between planes (metric in mm, or imperial in mil) εr = relative permittivity, approximately 4.5 for FR-4 PCB For imperial: Copper thickness (mils) = 1.37 • (number of ounces) i.e. 1oz Cu = 1.37mils i.e. ½oz Cu = 0.684mils ℓ W t h Figure 46: PCB Microstrip capacitance and inductance Example Calculate the total inductance and capacitance for ℓ=2.54cm, w=0.254mm, t=0.0356mm, h=0.8mm, εr = 4.5 for FR-4 ( L(pF) = (2 nH⁄cm) ∙ (2.54cm) ∙ ln 5.98 ∙ 0.8mm ) = 15.2nH 0.8 ∙ 0.254mm + 0.0356mm C(pF) = (0.264pF/cm) ∙ (2.54cm)(4.5 + 1.41) = 1.3pF ( ) ln 5.98 ∙ 0.8mm 0.8 ∙ 0.254mm + 0.0356mm Example Calculate the total inductance and capacitance for ℓ=1in, w=10mil, t=1.4mil, h=31.5mil, εr = 4.5 for FR-4 L = 15.2nH, C=1.3pF. Note: this is the same problem as above with imperial units. 62 Texas Texas Instruments Analog Engineer's Pocket Reference Where l = length of copper trace (mils) t = thickness of copper trace (mils) ti.com/precisionlaceboxsp: p1eorzt.hcicokpnpeesrsth(miciklsn)e=ss1=.317.3* 7(nmumilsber of ounPceCs)B and Wire ex: ½ oz. copper thickness = 0.685 mils Adjacedn=t dcisotpanpceerbetrtwaeceenstraces (mils) C(pF) ≈ kr w h ===∙dstPwe∙CipdℓBathrdaoitefiolcenocpbtrpeicetwrceotrenansctepaln(amtn(eilss(r8)≈(5m4) .Sil2sa)fmoreFlaRy-e4r) C(pF) ≈ kEx∙amεrphl∙ew ∙ ℓ (86) Different layers l = 100 mils Where t = 1.37 mils (1 oz. copper) ℓ = lengthd o=f1t0hemcilospper trace (mil, or mm) k = 8.854ε*r1=04-3.p2F/mm, or k=2.247*10-4 pF/mil t = thicknwhes==s62o35f mmtraiillscse (in mil, or mm) d = distance between traces if on same layer (mil, or mm) w = widthAnosf wtraecre. (mil, or mm) εhr==sPeCpaBrCCadt((iiesdoalinefmfcebterereitclnwatcyeleoaernyn)es=ptrasl0an).nt=0e(0ε0s3r..0(=pm3F47il.,5poFfromr FmR)-4) For imperial: Copper thickness (mils) = 1.37 • (number of ounces) i.e. 1oz Cu = 1.37mils i.e. ½oz Cu = 0.684mils FigurFeig4u8r:eC4a7p:aCcaitpaanccietafnocreadfojarcaednjat cceonptpceor ptrpaecretsraces Example: Calculate the total capacitance for both cases: ℓ=2.54mm, t=0.0348mm, d=0.254mm, w=0.635mm, h=1.6mm, εr = 4.5 for FR-4 C(pF) ≈ (8.854 ∙ 10–3 pF/mm) (0.0348mm) (623.54mm) = 0.0031pF Same 0.254mm layer (8.854 ∙ 10–3 pF/mm) (4.5mm) (0.635mm) (2.54mm) C(pF) ≈ = 0.04pF 1.6mm Adjacent layers Example: Calculate the total capacitance for both cases: ℓ=100mil, t=1.37mil, d=10mil, w=25mil, h=63mil, εr = 4.5 for FR-4 C = 0.0031pF (Same layer), C=0.4pF (Adjacent layers). Note: this is the same problem as above with imperial units. Texas Instruments Analog Engineer's Pocket Reference 63 PCB and Wire ti.com/precisionlabs PCB via capacitance and inductance [ ( )] L(nH) ≈ kL ∙ h 1 + ln 4h d C(pF) ≈ kC ∙ εr ∙ h ∙ d2 — d1 d1 (87) Inductance for via (88) Capacitance for via Where kL = PCB inductance per unit length. Both the metric and imperial version of the constant are given. kL = 0.2nH/mm, or 5.076∙10-3nH/mil kC = PCB capacitance per unit length. Both the metric and imperial version of the constant are given. kC = 0.0555pF/mm, or 1.41∙10-3pF/mil h = separation between planes d = diameter of via hole d1 = diameter of the pad surrounding the via d2 = distance to inner layer ground plane. εr = PCB dielectric constant (εr = 4.5 for FR-4) d1 d Top Layer Trace h Middle Layer GND Plane d2 Bottom Layer Trace Figure 48: Inductance and capacitance of via Example: Calculate the total inductance and capacitance for h=1.6mm, d=0.4mm, d1=0.8mm, d2=1.5mm [ ( )] L(nH) ≈ (0.2 nH⁄mm) ∙ (1.6mm) 1 + ln 4 ∙ 1.6mm = 1.2nH 0.4mm C(pF) ≈ (0.0555pF/mm) ∙ (4.5) ∙ (1.6mm) ∙ (0.8mm) = 0.46pF 1.5mm — 0.8mm Example: Calculate the total inductance and capacitance for h=63mil, d=15.8mil, d1=31.5mil, d2=59mil L=1.2nH, C=0.46pF. Note: this is the same problem as above with imperial units. 64 Texas Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Table 19: Coaxial cable information PCB and Wire Capacitance / length (pF/feet) Outside diameter (inches) dB attenuation /100 ft at 750 MHz Dielectric type Type RG-58 ZO Application 53.5Ω 28.8 0.195 13.1 PE Test equipment and RF power to a few hundred watts, and a couple hundred MHz RG-8 52Ω 29.6 0.405 5.96 PE RG-214/U 50Ω 30.8 0.425 6.7 PE RF power to a few kW, up to several hundred MHz 9914 50Ω 26.0 0.405 4.0 PE RG-6 75Ω 20 0.270 5.6 PF Video and CATV applications. RF to a few hundred watts, up to a few hundred MHz, RG-59/U 73Ω 29 0.242 9.7 PE sometimes to higher frequencies if losses can be tolerated RG-11/U 75Ω 17 0.412 3.65 PE RF power to a few kW, up to several hundred MHz RG-62/U 93Ω 13.5 0.242 7.1 ASP Used in some test equipment and 100Ω video applications RG-174 50Ω RG-178/U 50Ω 31 0.100 23.5 PE Miniature coax used primarily for test equipment interconnection. Usually short 29 0.071 42.7 ST runs due to higher loss. Texas Instruments Analog Engineer's Pocket Reference 65 PCB and Wire ti.com/precisionlabs CCooaaxxiiaal lcacbalebleequeaqtiuonastions C 2πε ℓ D Codaxial cable equations L μC D2πε ℓ 2πℓ d D d LL μ1 μD ℓ C 2π2π εd ((8894))CapacCitanpcaecitpaenrcleenpgetrhlength ((9805))In(d8u4c)tIanndcuectpCaeanrpcleaecnpigteatrhnlceengptehr length ((9816))Ch(8a5ra) cCthearirsatIicnctdeiumricspttaiecndciamenpcpeeedralenncegth L 1μ WWhheerree C 2π ε LL==inindduuccttaannccee iinn hheennrriieess ((HH)) (86) Characteristic impedance CC==ccaappaacciittaannccee iinn ffaarraaddss ((FF)) ZZd===idmimiaWLppmee=hdedeiatnarenednrcucoeecftiaiinnnnnoocehehrmmicnssohn((ΩeΩdn)u)rcietosr (H) dD==diinaCsmid=eetcedaripaoamfcienittanenercroecf oisnnhdfieaulrdca,tdoosrr(dFi)ameter of dielectric insulator Dε == idniseZilde=ectirdmiciapcmeodenatsentrcaeonftinoshfoiihenmlsdus,lao(tΩrod)r i(aεm=eεter rεoo)f dielectric insulator εlµ==ldemineadDglegt=ch=ntedroiinticfaisctmchidpoeeeentcresdmartiabaeomlneaftbeinoitlenfitreyinro(sfcµuosl=ahntidµeourlrdcµ(,tεooo)=rr εdriaεmo )eter of dielectric insulator μ = maεg=nedtiieclepcetrrmic ecaobnislittayn(tμo=f iμnrsμuola)tor (ε = εr εo ) ℓ = lenµgt=h mofatghneectiacbpleermeability (µ = µr µo ) l = length of the cable Insulation Figure 49: Coaxial cable cutaway Figure 49: Coaxial cable cutaway Figure 49: Coaxial cable cutaway 66 Texas Texas Instruments Analog Engineer's Pocket Reference 65 ti.com/precisionlabs PCB and Wire Table 20: Resistance per length for different wire types (AWG) Outside diameter Area dc resistance AWG Stds in mm circular mils mm2 Ω / 1000 ft Ω / km 36 Solid 0.005 0.127 25 0.013 445 1460 36 7/44 0.006 0.152 28 0.014 371 1271 34 Solid 0.0063 0.160 39.7 0.020 280 918 34 7/42 0.0075 0.192 43.8 0.022 237 777 32 Solid 0.008 0.203 67.3 0.032 174 571 32 7/40 0.008 0.203 67.3 0.034 164 538 30 Solid 0.010 0.254 100 0.051 113 365 30 7/38 0.012 0.305 112 0.057 103 339 28 Solid 0.013 0.330 159 0.080 70.8 232 28 7/36 0.015 0.381 175 0.090 64.9 213 26 Solid 0.016 0.409 256 0.128 43.6 143 26 10/36 0.021 0.533 250 0.128 41.5 137 24 Solid 0.020 0.511 404 0.205 27.3 89.4 24 7/32 0.024 0.610 448 0.229 23.3 76.4 22 Solid 0.025 0.643 640 0.324 16.8 55.3 22 7/30 0.030 0.762 700 0.357 14.7 48.4 20 Solid 0.032 0.813 1020 0.519 10.5 34.6 20 7/28 0.038 0.965 1111 0.562 10.3 33.8 18 Solid 0.040 1.020 1620 0.823 6.6 21.8 18 7/26 0.048 1.219 1770 0.902 5.9 19.2 16 Solid 0.051 1.290 2580 1.310 4.2 13.7 16 7/24 0.060 1.524 2828 1.442 3.7 12.0 14 Solid 0.064 1.630 4110 2.080 2.6 8.6 14 7/22 0.073 1.854 4480 2.285 2.3 7.6 Texas Instruments Analog Engineer's Pocket Reference 67 PCB and Wire Table 21: Maximum current vs. AWG ti.com/precisionlabs Wire gauge Polyethylene Neoprene Polyvinylchloride (semi-ridged) at 80°C Polypropylene Polyethylene (high density) at 90°C Polyvinylchloride Nylon at 105°C Kynar Polyethylene Thermoplastic at 125°C Kapton Teflon Silicon at 200°C AWG Imax (A) 30 2 28 3 26 4 Imax (A) 3 4 5 24 6 7 22 8 9 20 10 12 18 15 17 16 19 22 14 27 30 12 36 40 10 47 55 Note: Wire is in free air at 25°C Imax (A) 3 4 5 7 10 13 18 24 33 45 58 Imax (A) 3 5 6 8 11 14 20 26 40 50 70 Example What is the maximum current that can be applied to a 30 gauge Teflon wire in a room temperature environment? What will the self-heating be? Answer Imax = 4A Wire temperature = 200°C Imax (A) 4 6 7 10 13 17 24 32 45 55 75 68 Texas Texas Instruments Analog Engineer's Pocket Reference Sensor ti.com/precisioSnlaebsnsor Thermistor • Resistive temperature detector (RTD) • Diode temperature characteristics• Thermocouple (J and K) • Sensor 69 Texas Instruments Analog Engineer's Pocket Reference Sensors TheTrmheTisTrhTtmhoeheiresmrrtmoisritsottroorr RTDRTRDRTDTD RTD DiodDeioDdDieoidoede Diode TheTrmheTorhcTmoehoruemcprmoloeucoTpochluoeepurlpmeleocouple Sensor TabTTlaaebb2llee2:22T11e::mTTepemmerppaeeturraarettuusrreeenssseeonnrssooovrreoorvvveieerrwvviieeww Table 21: Temperature sensor overview Table 21: Temperature sensor overview 70 Te7x7a00s Instruments Analog Engineer's Pocket Reference 70 TemTpemraTpnemgrTaeeTpnmegrmapenprgarenagne–g5e5–°–C5555–<°°5–CTC55°<5s0is°tCance for RWRARRTWRWRAR0r0htOroro,d=tthh=dd,eB==ee=Br==t10eerr11Oee,r0mrr00e,eeC000spCssΩ00iΩΩeiisOss=rtfttaa=oaaffCntoornnuCcarrccPrealeeePPTl0el-loTTiooen1nf--ffnd011RdRRda000eTarTT,00-g0Dr1DDV,,-rT0Vae11ooo0nea00vvv0s00neDeeΩ00rCDrruΩΩtfstteueoeeelsmsrmmffneooiPupppnrrcsTeeeoPPc-rrr(1eaoTTaa0ftett--fuuu110i)fcrfrr000ieieece00irnerr00aaatnnsnntgsggeee ooff of ((––220000°°CC<(<9T2T)<<88RT55>T00D°°CCr)e) sistance (–200°C < T < 850°C) for TAR=OT,DtBemeO,qpCueaOrat=itouCnrearlielnesndisdetagarrn-eVceaesntCoDeutlsesimeunsp(ce°orCae)tfuficreien(Tts>0°C) T = temperature in degrees Celsius ( ) RRTTDDeeqquuataiotAniornesrisetsaniscteatnoRRct0eemtpoertaetmurep(eTr>a0t°uCr)e (T>0(9°3C) ) 2B RTD resistance for T>0°C Where RRTD = A resistance2oBf RTD R R0 over temperature (98) range of R(–T2D00re°(Cs9i3s<)taTnc°rTC0e>°s)0Cis°tCance WRRRTWRARhOoRoT=h,TeD==eDBrteer=11=Oem00,rre00pCesΩΩesOirissa=ttatauCnnrcaecelelienoonfdfdReRagTrT-rDVDeeaoosnvveCDerreutltseseemimunpspcee(orraeat)ftufuicrreeiernraatnsnggeeooff ((––220000°°CC<g0e°C forT>0� Where WVThe=rethermoelectric voltage VTT==tethmeprmeroaetulercetrinicdveogltraegees Celsius Tαci0==, αtter1am=nptsrelaarnatisotulnarteciooinnefcdfoiecegiefrfneictesisenCtselsius ci = translation coefficients αT0a,bαl1e=26tr:aTnsylpaetioKn tchoeerfmficoiecnotusple temperature to voltage coefficients –219°C to 760°C 760°C to 1,200°C Tabcle0 27: Ty0p.e00K00th00e0rm00o0cEo+u0p0le tem–p1e.r7a6t0u0re41to36v8o6lEta+g0e1coefficients c1 3.9450128–022159°EC+t0o1760°C 3.8921204975E+01 760°C to 1,200°C ccc230 2.3622373598E-02 1.8558770032E-02 –3.2858900.600708040E0-000400E+00 –9.9457592874E-05–1.7600413686E+01 cc4 1 –4.9904832.894757071E2-800625E+01 3.1840945719E-07 3.8921204975E+01 cc5 2 –6.7509052.931672233E7-305898E-02 –5.6072844889E-10 1.8558770032E-02 cc6 3 –5.74103–237.2482588E90-160784E-04 5.6075059059E-13 –9.9457592874E-05 ccccc78945 –3.10888–742.9899044E82-182777E-06–3.2020720003E-16 3.1840945719E-07 –1.0451609365E-14 9.7151147152E-20 –1.98892–666.7857089E05-197173E-08–1.2104721275E-23–5.6072844889E-10 cc106 –1.63226–957.7448160E32-270428E-10 -- 5.6075059059E-13 αc0 7 –-3-.1088872894E-12 1.1859760000E+02 –3.2020720003E-16 αc1 8 –-1-.0451609365E-14–1.1834320000E-04 9.7151147152E-20 c9 –1.9889266878E-17 –1.2104721275E-23 c10 –1.6322697486E-20 — α0 — 1.1859760000E+02 α1 — –1.1834320000E-04 78 Texas Instruments Analog Engineer's Pocket Reference 78 ti.com/precisionlabs Sensor Type K thermocouples translating voltage to temperature (ITTSy-p9e0Ksttahenrdmaorcdo)uples translating voltage to temperature (ITS-90 standard) � � � � �� �V��� ��� (106) Temperature (101) Temperature Table 27: Type K thermocouple voltage to temperature coefficients Table 28: Type K thermocouple voltage to temperature coefficients –219°C to 0°C 0°C to 760°C 760°C to 1,200°C –219°C to 0°C 0°C to 760°C 760°C to 1,200°C c0cc01 00..0000000000000E0+E0+000 2.5173462E-02 00.0.00000000000E0+00E0+00 2.5083550E-02 –1–.131.3801588005E+8002E+02 4.8302220E-02 c1c2 –21..5116763426827E8-0E2-06 27.5.80863051500E6-00E2 -08 4–.813.062426200E3-1020E-06 c2c3 ––11..0168632386783E8-E06-09 –7.28.65001306103E1-008E-10 –15.6.44660437103E1-006E-11 c3c4 ––81..9087373365384E0-E09-13 –82..5301351321700E0-1E0-14 5–.496.467530107E1-5110E-16 c4c5 ––38..7973743253407E7-E13-16 –8.13.12522870003E4-104E-17 –98.6.58007211509E3-016E-21 c5c6 ––83..6736432236774E3-E16-20 c6c7 ––18..0664352065439E8-E20-23 cc78cc98 ––51..1049520055987E7-E23-28 –5.1920-57-7E-28 –91..2820840304306E0-1E7-22 –9.48.04410336003E0-202E-26 –14..4015370370304E0-2E6-30 –1.10.50757234705E5-300E-35 8–.830.211190308E1-0210E-26 –3.110810-0E--26 — -— -- c9 — –1.0527550E-35 — Texas Instruments Analog Engineer's Pocket Reference 79 Sensor ti.com/precisionlabs Table 29: Seebeck coefficients for different material Material Aluminum Antimony Bismuth Cadmium Carbon Constantan Copper Germanium Seebeck coefficient 4 47 –72 7.5 3 –35 6.5 300 Material Gold Iron Lead Mercury Nichrome Nickel Platinum Potassium Seebeck coefficient 6.5 19 4 0.6 25 –15 0 –9.0 Note: Units are μV/°C. All data at temperature of 0°C Material Rhodium Selenium Silicon Silver Sodium Tantalum Tellurium Tungsten Seebeck coefficient 6 900 440 6.5 –2.0 4.5 500 7.5 80 Texas Instruments Analog Engineer's Pocket Reference A/D Conversion ti.cAom//Dpreccisoionnlvabes rsion Binary/hex conversions • A/D and D/A transfer function • Quantization error • Signal-to-noise ratio (SNR) • Signal-to-noise and distortion (SINAD) • Total harmonic distortion (THD) • Effective number of bits (ENOB) • Noise-free resolution and effective resolution • A/D conversion ti.com/adcs 81 Texas Instruments Analog Engineer's Pocket Reference A/D Conversion ti.com/precisionlabs Numbering systems: Binary, decimal, and hexadecimal Numbering systems: Binary, decimal, and hexadecimal Numbering systems: Binary, decimal, and hexadecimal Binary (Base-2) Decimal (Base-10) Hexadecimal (Base-16) 0 1 01 2 3 4 5 6 7 89 012 3 4 5 678 9 A B C D E F 2(1000) + 3(100) + 4(10) + 1(1) = 2,341 MS2D(1=00M0)o+st3(s1ig00n)if+ic4a(n1t0d) +igi1t (1) = 2,341 ExaEmxapmleplecocnonveversrsMioioSnnD::B=BiiMnnaoasrryyt sttioognddiefiecccaimnimtadlaigl it Example convBeirnsaioryn: Binary to decimal Decimal Binary Decimal = = LSD 8+4 +0 +1 8+4 +0 +1 Example conversion: Decimal to binary EExxaammpplleeccoonnvevresrisoino:nD:eDceimcaiml taolbtionabriynary Decimal Decimal LSD Binary Binary LSD = = MSD 128 + 64 + 32 + 8 + 4 = 23L6SD 128 + 64 + 32 + 8 + 4 = 236 LSD = Least Significant Digit MSD = Most Significant Digit ti.com/adcs 82 Texas Instruments Analog Engineer's Pocket Reference A/D conversion ti.com/precisionlabs A/D Conversion Example conversEioxnam: Bpliencaornyvteorshioenx: aBdineacryimtoahlexadecimal Binary Example conversion: BinMaSrDy to hexadecimal LSD 128 + 64 + 16 + 8 + 1 = 217 Hexadecimal Conversion 128 + 64 + 16 + 8 + 1 = 217 8 + 4 + 1 = 13 (D) 88++14=+91 = 13 (D) 8 + 1 = 9 161 160 161 160 Hexadecimal D9 MSD 208 + 9 = 217 D9 MSD LSD 208 + 9 = 217 Example Conversion: Hexadecimal to decimal Example Conversioan:nHdedxeadceimciamlatlotohbeixnaadryecimal Decimal (Base-10) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Hexadecimal (Base-16) 0 1 2 3 4 5 6 7 8 9 A B C D E F Hexadecimal x163 x162 x161x160 2 6 AF = MSD LLSSDD 2(4096) + 6(256) + 10(16) + 16(1) = 9903 Decimal 16 9903 R = 15 (F) 16 618 R = 10 (A) 16 38 R = 6 (6) 16 38 R = 2 (2) LSD MSD LSD = Least Significant Digit MSD = Most Significant Digit83 ti.com/adcs Texas Instruments Analog Engineer's Pocket Reference 83 A/D Conversion ti.com/precisionlabs A/D Converter with PGA 5V FSR 0 to 2.5V PGA x2 ADC in 0 to 5V VREF ADC 12 bits Digital I/O Figure 51: ADC full-scale range (FSR) unipolar Full Scale Range (FSR) Unipolar VREF FSR = PGA FSR 1LSB = 2n Example calculation for the circuit above. VREF FSR = PGA = 5V 2 = 2.5V 1LSB = FSR 2n = 2.5V 212 = 610.35µV ti.com/adcs 84 Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs A/D Conversion A/D Converter with PGA 2.5V FSR 0 to ±1.25V PGA x2 ADC in 0 to ± 2.5V VREF ADC 12 bits Digital I/O Figure 52: ADC full-scale range (FSR) Bipolar Full Scale Range (FSR) Bipolar FSR = VREF PGA 1LSB = FSR 2n Example calculation for the circuit above. FSR = ±VREF PGA = ±2.5V 2 = ±1.25V ⇒ 2.5V 1LSB = FSR 2n = 2.5V 212 = 610.35µV ti.com/adcs Texas Instruments Analog Engineer's Pocket Reference 85 A/D Conversion ti.com/precisionlabs Table 30: Different data formats Code Straight binary Offset binary Binary Decimal value Decimal value 1111T1a1b1le1 29: Different d2a5ta5 formats 127 1100C00o0d0e 19S2traight binary Offs6e4t binary 1000B00in0a0ry 128Decimal value Decim0 al value 011T1Ca111bo111ld101e101e210910:1010Different da1t2aS7tfroarimgha21tt59sb52inary 0100B10i00n00a00r0y000 64Decim1a2l 8value 000010011011011011111111 0 21525 7 1011000000000000 19624 Offse–t116b24i7nary Deci–m6a40l value –1122–871 6–464 1000000000000000 1208 –0128 CNoegnavetiNCr000vt110eoie100nng100ng100vua100temtw100ir100vboteei’snrngceuoxtmmawmpboplee’lsmer ceeoxnmat16mt20p4o7lpedlemeceimnatl:to –1 de–c6i4mal: –128 Converting two’s compleSmIGenNt xto4 dexc2imaxl1: NTStheeigspac1at:sivCeehisencnkuegmsiagtbniveberitexampSleIG1N x04 x12 x11 Step 1: Check sign bit This case is negative Step 2: Invert all bits MSD LSD 10 11 MS0D 1 0 0 2’s complement Decimal value –1 2’s comple–m64ent Decimal –v1a2lu8e 2’s com–p–6l1e4m12e7nt Decim–a1l2v8a6lu4e –1127 0 –6644 –1208 127 64 0 Step 2: Invert all bits Step 3: Add 1 01 00 01 01 SFtienpal3r:eAsudldt 1 0–(41+1) =0–51 FPCinooanslivrteievsruetltinnugmtwboe’rsecxoammpplleem–e(n4t+1to) =de–c5imal: CPoosnivtievPCretooinnnsguivtmietvwrbetoei’nnrsuegcxmotawmmbopepl’rleseemcxoeanmmt ptpolleedmSecIeGinmNtatl:xo4decxi2maxl:1 Just add bit weights JFuisntaal dredsbuiltt weights Final result SIG0N x14 x02 x11 MSD 0 4+11 = 50 1 MSD LSD 4+1 = 5 84 ti.com/adcs 86 Texas Instruments Analog Engineer's Pocket Reference 84 ti.com/precisionlabs A/D Conversion Table 31: LSB voltage vs. resolution and reference voltage Resolution 1.024V 8 4 mV 10 1 mV 12 250 µV 14 52.5 µV 16 15.6 µV 18 3.91 µV 20 0.98 µV 22 244 nV 24 61 nV FSR R(Fefuelrle-nScceavloeltaRgae nge) 1.25V 2.048V 4.88 mV 8 mV 1.22 mV 2 mV 305 µV 500 µV 76.3 µV 125 µV 19.1 µV 31.2 µV 4.77 µV 7.81 µV 1.19 µV 1.95 µV 299 nV 488 nV 74.5 nV 122 nV 2.5V 9.76 mV 2.44 mV 610 µV 152.5 µV 38.14 µV 9.53 µV 2.384 µV 596 nV 149 nV Table 32: LSB voltage vs. resolution and reference voltage Resolution 3V 8 11.7 mV 10 2.93 mV 12 732 µV 14 183 µV 16 45.77 µV 18 11.44 µV 20 2.861 µV 22 715 nV 24 179 nV FSR R(Feufelrle-nScceavloeltaRgaenge) 3.3V 4.096V 12.9 mV 16 mV 3.222 mV 4 mV 806 µV 1 mV 201 µV 250 µV 50.35 µV 62.5 µV 12.58 µV 15.6 µV 3.147 µV 3.91 µV 787 nV 976 nV 196 nV 244 nV 5V 19.5 mV 4.882 mV 1.221 mV 305 µV 76.29 µV 19.07 µV 4.768 µV 1.192 µV 298 nV ti.com/adcs Texas Instruments Analog Engineer's Pocket Reference 87 A/D Conversion ti.com/precisionlabs DDAACC ddeefifniintiiotniosns Resolution = n The number of bits used to quantify the output ReCsoolduteiosn== 2nn Number of Codes = 2n FuRll-eSfcearleenRcaengveooluttapgute==FSVRREF LSB = FSR / 2n FuLllS-sBca=le VouRtEpFut/v2onltage = (2n – 1) • 1LSB Full-scale input code = 2n – 1 The nTuhme bnuemr boefr ionfpbuitst ucsoeddetocqoumanbtifiynathteioonustput The number of input code combinations Sets tSheetsLthSeBcovnoveltrategreouotpruct urarnrgeenatnsdiztheeaLnSBdvoltage conveTrhteervorlatanggeestep size of each LSB The oFuutlpl-usctavleooltuatpguet voorltacguerroef tnhtesDtAeCp size of each code Largest code that can be written TrFanuslfle-sr cFuanlecticono:dVeou=t =2Nn u–m1ber of Codes • (FSRT/h2en) laRreglaetisotnschoipdbeettwhaeetncoauntpbutevowltraigtteeannd input code Full-scale voltage = VREF – 1LSB Full-scale output voltage of the DAC Transfer function = VREF x (code/ 2n) Relationship between input code and output voltage or current FSR = 5V Full-scale voltage = 4.98V Output voltage (V) Resolution 1LSB = 19mV Number of codes = 2n Figure 51: DAC transFfeigrufruen5c3ti:oDnAC transfer function Full-scale code = 255 Resolution = 8bits ti.com/adcs 88 8Te6xas Instruments Analog Engineer's Pocket Reference AtiD.cComde/pfirneitcioisniosnlabs A/D Conversion Resolution = n ACDodCesd=e2fninitions The number of bits used to quantify the output The number of input code combinations RReesfoelurteionnc=e nvoltage = VREF Number of Codes = 2n Sets theThLeSnBumvboelrtaofgbeitsourscedurtoreqnutanstiizfyethaenindput converteThreranunmgbeer of output code combinations FLuSll-BSc=aleVRRaEnFg/e(i2nnpu–t 1=)FSR LSB = FSR / 2n The voltSaegtsethsetecopnvseirzteer oinfpeutarcanhgceoadndet.hNe oLSteB vtholatatge some toTphoelvoogltiaegse smteapysiuzesoef 2eancahsLSoBpposed to Full-scale input voltage = (2n – 1) • 1LSB 2n – 1 inFutlhl-escdaleeninopmutivnoalttaogre. of the ADC FFuulll-ls-scaclaeleouctpoudteco=de2=n –2n1– 1 The largLearsgtesctocdoedetthhaatt ccaannbebreeawdritten. TFraunlls-fsecraFluencvtoioltna: gNeum=bVerRoEfFCodes = Vin / (FFSuRll/-2snc) aRleelaotiuontpshuitpvboetlwtaegeen ionpfutthveoltDagAeCa.ndNooutteputthcaodt e the full-scale voltage will differ if the alternative definition for resolution is used. Transfer function = VREF x (code/ 2n) Relationship between input code and output voltage or current Full-scale code=255 Input voltage (V) Figure 52: ADC transFfeigr ufurenc5t4io: nADC transfer function Full-scale Range FSR = 5V 87 ti.com/adcs Texas Instruments Analog Engineer's Pocket Reference 89 A/D Conversion Quantization error of ADC Quantization error of ADC ti.com/precisionlabs Quantization error Figure 53: Quantization error of an A/D converter Figure 55: Quantization error of an A/D converter Quantization error The error introduced as a result of the quantization process. The amount of this error is a function of the resolution of the converter. The quantization error of an A/D Quantcioznavteirotenr ies r½roLrSB. The quantization error signal the difference between the actual The ervrooltraginetraopdpluiecdeadndatsheaArDesCuoltutopuf tth(Feigquruea5n3t)i.zTahteiornmsproof ctheesqsu.aTnhtizeataiomn osiugnnatloisf this er1rLoSrBi⁄s√a12function of the resolution of the converter. The quantization error of an A/D converter is ½ LSB. The quantization error signal is the difference between the actual voltage applied and the ADC output (Figure 55). The rms of the quantization signal is 1LSB ⁄√12 88 ti.com/adcs 90 Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs A/D Conversion SSiiggnnaall--toto-n-onisoeisraetiora(tSiNoR()SfNroRm)qfuraonmtizqatuioannntoizisaetioonnlynoise only MaxRMSSignal � FSR/2 √2 � 1LSB � 2��� √2 RMSNoise � 1LSB √12 from quantization only SNR � MaxRMSSignal RMSNoise � 1LSB � 2���/√2 1LSB⁄√12 � 2���√6 SNR�dB� � 2�log�SNR� � �2� log�2��N � 2�log �√26� ((110027)) ((110038)) ((110049)) ((110150)) SNR�dB� � 6��2N � 1��6 ((110161)) Where WFNF1ShLSR=eSRr=Bteh=fe=ufulrtleh-lls-sescocvaluaoletlleitoaranrganeongfogetfeho1eofLftAShth/BeDe,AcVA/oRD/DnEFvc/ce2oornntnevvreerrteterr 1MLSaBxR=MtSheSivgonlatal g=ethoef RMSNoise = the rms n1rmoLiSssBee,fqrVuoRimvEaFq/le2unnatnotifztahteioAnDC’s full-scale input NS=NRthe= rtehseorlauttiioonoforfmthsesAig/nDacl toonrvmerstenroise MaxRMSSignal = the rms equivalent of the ADC’s full-scale input REMxSamNopilsee = the rms noise from quantization SNR = the ratio of rms signal to rms noise What is the SNR for an 8-bit A/D converter with 5V reference, assuming only quantization noise? Answer Example WSNhRat�is2�th��e√S6N�R2�fo��r√a6n�8-3b1i4t A/D converter with 5V reference, assuming only quantization noise? SNR�dB� � 2�log�314� � 4��� dB Answer SSNNRR�d=B2� N�-16√��62=�82� 8�-11√��66=�341�4�� dB SNR(dB) = 20log(314) = 49.9 dB SNR(dB) = 6.02(8) + 1.76 = 49.9 dB ti.com/adcs Texas Instruments Analog Engineer's Pocket Reference 91 89 A/D Conversion ti.com/precisionlabs Total harmonic distortion (Vrms) Total harmonic distortion (Vrms) RMSDistortion VVV % • 100 MaxRMSSignal V V • 100 ((110172)) THD dB RMSDistortion MaxRMSSignal Total harmonic distortion (Vrms) ((110183)) Where RMSDistortion VVV V WTRhHMeDSreD=istototartliohnar=m%tohneicrMmdaissxRtsoMurtSmiSoingon,fatalhlel• h1r0aa0rtmiooonficthceormmpsoVdniesntotsrtion to t•h1e00rms(1s0ig7n) al TMHaDx=RMtoStaSlihgTHanrDamld=oBnthicedrimstsorvRtaiMolunSeD, itsohtfoertthrioaentiionpoufttshiegnrmals distortion to the rms signal (108) RVM1 S=Dthisetofurtniodnam= ethnetarlm, gsesnueMmraaxlolRyfMtahSlSleihginanarplmutosniigcncaol mponents V2, V3, V4, …Vn = harmonics of the fundamental MaxRMSSigWnahler=e the rms value of the input signal V1 = the fundTRaHMmDSeD=nistottaotarl,tliohgnaer=mnetohrneaiclrlmydisstthsouertmioinnop,f tuahltel hsraaigrtminoaoonlfitchceormmpsodniesntotsrtion to the rms signal V2, V3, V4, …MVV1an=xR=thMehSafuSrnmigdnaoamnl ie=cntsthaeol,frgmtehsneevrafaluullynedtohafetmhineepinunttpasuiltgsniaglnal V2, V3, V4, …Vn = harmonics of the fundamental Figure 54: FFiugunrdeFai5gm4u:eFrneutna5dl6aa:mnFeudnnthadlaaarnmmdeohnnatriacmlsoaninnicdsVhirnmaVrsrmmosnics in Vrms ti.com/adcs 90 92 Texas Instruments Analog Engineer's Pocket Reference 90 ti.com/precisionlabs A/D Conversion TotaTlohtaal rhmaromnonicicddiissttoorrttioionn(d(BdcB) c) THD(d Bc)TൌotͳaͲl hŽ‘a‰rm൤ͳoͲnቀୈଵic଴మቁd൅isͳtoͲrቀtୈଵi଴oయቁn൅(dͳBͲcቀୈଵ)଴రቁ ൅ ‫ ڮ‬൅ ͳͲቀୈଵ଴౤ቁ൨   ൌ ͳͲŽ‘‰ ൤ͳͲቀୈଵ଴మቁ ൅ ͳͲቀୈଵ଴యቁ ൅ ͳͲቀୈଵ଴రቁ ൅ ‫ ڮ‬൅ ͳͲቀୈଵ଴౤ቁ൨ (114) (109) (109) Where tWTDDhH12eh,D=eDfurDfTDt=eu3nhH12,nd,etDD=doaDDfWTDfat4umuta=3,Hhm12n,hnl,…eeD=dtDedheDonarfanatD4t=3teuhma,a,rmtnnaeml…tlDeodleh=fno4tunaDaa,tnhnamtrl…naiamdlch=elra,Daomndmhgrnntimoaesa=iectnrnlon,omhiendtcgraariotiscesariln,omtnlodloignyceoifres.srtntttniaThhooiocelheernlfsyrte.iatifoonhtuTlrhnlfpyaenh.ettudehtTfihotuiaenhernsmapoefiduigtufneiranontaptnmdhastutoiaeaoilteg.fmlsnrnoTtmmhietgfahaenentslil.hstaaramdeTmslil.siheusrmTsminartsheoedossidirasiurstsdmsirrtoiniuesoesanordlrtnealotritizodrmtrooeitervnirmalodteaehlntailtotzateilovoteitoztiervhd0meteethdtodsoetrtBomtos0hrcimtgs0ehdnsesBdaisBcglicgnnaal l FiguFriegu5r5e: 5F5uF:nigFduuarnmedea5nm7t:eaFnlutaannlddaanhmdaerhmnatroamnl aoicnnsdicinshaidnrBmdcBoncics in dBc ExamExpalme ple DeteDrmetienremTinHeDTHfoDr tfhoer tehxeaemxapmlepaleboavbeo.ve. ExamAnpslAwenesrwer Determine THD for the example above.  ൌ ͳͲൌŽ‘ͳ‰Ͳ൤Žͳ‘Ͳ‰ቀ൤ିͳଵଽ଴Ͳଶቀቁିଵ൅ଽ଴ଶቁͳ൅ͲቀͳିଵͲ଻଴ହቀቁିଵ଻൅଴ହቁͳ൅ͲቀͳିଵͲଽ଴ቀହିቁଵଽ଴൅ହቁ ‫ڮ‬൅ ൅‫ͳ ڮ‬൅ͲͳቀିͲଵଵቀ଴ଵି଴ଵଵቁ଴ଵ൨଴ቁ൨ Answer -92 THD(d Bcൌ ) =െൌ͹1Ͷ0െǤ͹l͹͸oͶg†Ǥ͹͸10†10 ) -75 +10 10 ) )) ) ) -95 10 +10 + ... ) -110 10 +10 ) THD(dBc) = -74.76 dB ti.com/adcs Texas Instruments Analog Engineer's Pocket Reference 91 91 93 A/D Conversion ti.com/precisionlabs AAcc ssigignnalasls Signal-to-noise and distortion (SINAD) and effective number of bits (ENOB) SINAD�dB� � 20 log �√RMSNoMisaex�R�MRSSMigSnDaisl �or�ion�� ((111105)) SINAD�dB� � �20log ��10������������ � 10������������ ((111116)) �N�B � SINAD�dB� � 6.02 1.76dB ((111127)) Where WMhaexRreMSSignal = the rms equivalent of the ADC’s full-scale input MRMaxSRNMoSisSeig=ntahle=rmthse nrmoisseeqinuteivgarlaetnetdoaf cthroesAsDthCe’sAf/uDll-csocnavleeritneprsut RMSDistortion = the rms sum of all harmonic components RSMINSANDo=iseth=e trhaetiormofstnhoeisfuelli-nstceaglerasteigdnaacl-rtoos-nsotihsee Ara/tDiocaonndvedristetorsrtion RTMHDSD=istototartliohnar=mtohneicrmdisstsourtmiono.fTahllehraarmtiooonficthceomrmpsodniesntotsrtion to the rms signal. SNR = the ratio of rms signal to rms noise SINAD = the ratio of the full-scale signal-to-noise ratio and distortion THD = total harmonic distortion. The ratio of the rms distortion to the rms signal. SENxaRm=ptlhee ratio of rms signal to rms noise Calculate the SNR, THD, SINAD and ENOB given the following information: EMxaaxmRpMleSSignal = 1.76 Vrms CRaMlcSuDliastteorttihoen =SN50Rµ, VTrHmDs, SINAD and ENOB given the following iRnfMoSrmNoaitsioen=: 100 µVrms MaxRMSSignal = 1.76 Vrms RAMnsSwDeirstortion = 50 μVrms RSNMRS�dNBo�is�e2=0 l1o0g0�11μ0.V706rμmVVrsrmmss� � ��.� dB Answer TSHNDR�ddBB� � 20 log �151.0.776μ6VVVrrrmmmsss� � � �0.� dB STIHNDADd�BdB� � 20 log1�.7�6�1V0r0mμsVr1m.7s6��V�rm�5s0 μVrms��� � ��.� dB SSIINNAADD�ddBB� � �20 log ��10�����.��1�.7�6� V�r1m0s�����.�� ���� � ��.� dB �SNIN�ABD�d�B�.�dB6.�021.76dB1�0 1�.65 6.02 94 ti.com/adcs 9Te2xas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs A/D Conversion DDccssigignanlsals Noise free resolution and effective resolution Noise�ree�eso��tion � �o�� �PeaktoPea2k�NoiseinLSB� ���e�ti�e�eso��tion � �o�� �rmsNo2is�einLSB� PeaktoPeakNoiseinLSB � 6.6 � rmsNoiseinLSB (118()113) (119()114) (120()115) ���e�ti�e�eso��tion � Noise�ree�eso��tion � 2.7 (121()116) Note: The maximum effective resolution is never greater than the ADC resolution. FNoortee:xTahmepmlea, xaim24u-mbitecffoencvtievreterrecsaonluntoiotnhaisvneeavneregffreecattiveer trheasnoltuhtieonADgrCearetesrotlhuationn. 2F4orbeitxsa. mple, a 24-bit converter cannot have an effective resolution greater than 24 bits. Example WExhaamt ipsltehe noise-free resolution and effective resolution for a 24-bit converter aWsshuamt iinsgththeenpoeiaske--tofr-epeearkesnooilsuetiiosn7aLnSdBse?ffective resolution for a 24-bit converter assuming the peak-to-peak noise is 7 LSBs? Answer NAonisswe�erree�eso��tion � �o�� �27�2�� � 2�.2 7 ���e�ti�e�eso��tion � �o�� � 2�� 672.6 � � 2�.� 7 6.6 ���e�ti�e�eso��tion � 2�.2 � 2.7 � 2�.� ti.com/adcs Texas Instruments Analog Engineer's Pocket Referen9c3e 95 A/D Conversion Time Constant ti.com/precisionlabs R VIN A/D VIN C Figure 58: Settling time for RC circuit-related to A/D converters Figure 56: Settling time for RC circuit-related to A/D converters TaTblaeb3l3e:3C2o:nvCeorsnivonerascicounraaccycaucrhaiecvyedacahftieervaedspaefctiefiredatsimpeecified time Settling time in time Settling time in time cStoimenstettlaincnogtnstsi(mNtaTenC)tins AAcccucurarcaycyininbits (NSt)imetetlicnognctsiomtnasentatisnnts (NTAC)ccuracy iAnccuracy in bits (N1 TC) bit1s.44 (NTC) 10 bits 14.43 21 1.424.89 10 11 14.43 15.87 32 2.849.33 11 12 15.87 17.31 434 45..37537.77 12 13 13 17.31 18.76 18.76 55 7.271.21 14 14 20.20 20.20 66 8.686.66 15 15 21.64 21.64 77 10.1100.10 16 16 23.08 23.08 889 11.1514.54 12.98 17 18 17 24.53 25.97 24.53 9 12.98 18 25.97  ൌ Ž‘‰ଶሺ‡ି୒౐ిሻ (122) (117) Where WNhe=rethe number of bits of accuracy the RC circuit has settled to after N t=imteheconnusmtabnetsr .of bits of accuracy the RC circuit has settled to after NNTTCC number number of of timNeTCc=onthsetannutsm. ber of RC time constants NTC = the number of RC time constants Note: For a FSR step. For single-ended input ADC with no PGA front end FSR (Full Scale Range) = VREF ti.com/adcs 96 Texas Instruments Analog Engineer's Pocket Reference 94 ti.com/precisionlabs A/D Conversion Table 34: Time required to settle to a specified conversion accuracy AccTuarabclye i3n3b:itTsime reSqetutliirnegdtitmoesientttilme eto a spAeccciufireadcycionnbvitesrsionSaecttcliunrgatcimye in time (N) A8ccuracy in bits (N) 98 Sectotlninsgtatnimtse(NinTC) time con5s.5tants (5N.56TC.52)4 (N) Settling timecionnstants (NTC) Accuracy 17 time constants 11.78 in bits (N) 17 18 (NTC) 11.78 12.48 10 9 6.26.493 18 19 12.48 13.17 11 10 12 11 12 13 13 6.97.362 78..638.2232 9.09.101 19 20 20 21 21 22 22 13.17 13.86 14.56 15.25 13.86 14.56 15.25 14 14 9.79.070 23 23 15.94 15.94 15 15 16 16 101.40.040 11.09 11.04 24 24 25 25 16.64 17.33 16.64 17.33 N�� � ������ (123) (118) Where WherNeTC = the number of time constants required to achieve N bits of settling NTC =Nt=hethneunmubmebreorfotfimbietscoofnasctacunrtascryequired to achieve N bits of settling N = the number of bits of accuracy Note: For a FSR step. For single-ended input ADC with no PGA front end FSR (Full Scale Range) = VREF ti.com/adcs Texas Instruments Analog Engineer's Pocket Reference 97 95 Notes ti.com/precisionlabs 698 Texas Instruments Analog Engineer's Pocket Reference IMPORTANT NOTICE Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, enhancements, improvements and other changes to its semiconductor products and services per JESD46, latest issue, and to discontinue any product or service per JESD48, latest issue. Buyers should obtain the latest relevant information before placing orders and should verify that such information is current and complete. All semiconductor products (also referred to herein as “components”) are sold subject to TI’s terms and conditions of sale supplied at the time of order acknowledgment. TI warrants performance of its components to the specifications applicable at the time of sale, in accordance with the warranty in TI’s terms and conditions of sale of semiconductor products. Testing and other quality control techniques are used to the extent TI deems necessary to support this warranty. Except where mandated by applicable law, testing of all parameters of each component is not necessarily performed. TI assumes no liability for applications assistance or the design of Buyers’ products. Buyers are responsible for their products and applications using TI components. To minimize the risks associated with Buyers’ products and applications, Buyers should provide adequate design and operating safeguards. TI does not warrant or represent that any license, either express or implied, is granted under any patent right, copyright, mask work right, or other intellectual property right relating to any combination, machine, or process in which TI components or services are used. Information published by TI regarding third-party products or services does not constitute a license to use such products or services or a warranty or endorsement thereof. Use of such information may require a license from a third party under the patents or other intellectual property of the third party, or a license from TI under the patents or other intellectual property of TI. Reproduction of significant portions of TI information in TI data books or data sheets is permissible only if reproduction is without alteration and is accompanied by all associated warranties, conditions, limitations, and notices. TI is not responsible or liable for such altered documentation. Information of third parties may be subject to additional restrictions. 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Buyer acknowledges and agrees that any military or aerospace use of TI components which have not been so designated is solely at the Buyer’s risk, and that Buyer is solely responsible for compliance with all legal and regulatory requirements in connection with such use. TI has specifically designated certain components as meeting ISO/TS16949 requirements, mainly for automotive use. In any case of use of non-designated products, TI will not be responsible for any failure to meet ISO/TS16949. Products Audio Amplifiers Data Converters DLP® Products DSP Clocks and Timers Interface Logic Power Management Microcontrollers RFID OMAP™ Applications  Processors Wireless Connectivity www.ti.com/audio amplifier.ti.com dataconverter.ti.com www.dlp.com dsp.ti.com www.ti.com/clocks interface.ti.com logic.ti.com power.ti.com microcontroller.ti.com www.ti-rfid.com www.ti.com/omap www.ti.com/wirelessconnectivity Applications Automotive and Transportation Communications and Telecom Computers and Peripherals Consumer Electronics Energy and Lighting Industrial Medical Security Space, Avionics and Defense Video and Imaging www.ti.com/automotive www.ti.com/communications www.ti.com/computers www.ti.com/consumer-apps www.ti.com/energy www.ti.com/industrial www.ti.com/medical www.ti.com/security www.ti.com/space-avionics-defense www.ti.com/video TI E2E™ Community e2e.ti.com SSZZ022H Mailing Address: Texas Instruments, Post Office Box 655303, Dallas, Texas 75265 Texas Instruments Analog Engineer's Pocket Reference 99 © 2014, 2015 Texas Instruments Incorporated Printed in U.S.A. by (Printer, City, State) SLYW038B IMPORTANT NOTICE Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, enhancements, improvements and other changes to its semiconductor products and services per JESD46, latest issue, and to discontinue any product or service per JESD48, latest issue. Buyers should obtain the latest relevant information before placing orders and should verify that such information is current and complete. All semiconductor products (also referred to herein as “components”) are sold subject to TI’s terms and conditions of sale supplied at the time of order acknowledgment. TI warrants performance of its components to the specifications applicable at the time of sale, in accordance with the warranty in TI’s terms and conditions of sale of semiconductor products. Testing and other quality control techniques are used to the extent TI deems necessary to support this warranty. Except where mandated by applicable law, testing of all parameters of each component is not necessarily performed. TI assumes no liability for applications assistance or the design of Buyers’ products. Buyers are responsible for their products and applications using TI components. To minimize the risks associated with Buyers’ products and applications, Buyers should provide adequate design and operating safeguards. TI does not warrant or represent that any license, either express or implied, is granted under any patent right, copyright, mask work right, or other intellectual property right relating to any combination, machine, or process in which TI components or services are used. Information published by TI regarding third-party products or services does not constitute a license to use such products or services or a warranty or endorsement thereof. Use of such information may require a license from a third party under the patents or other intellectual property of the third party, or a license from TI under the patents or other intellectual property of TI. Reproduction of significant portions of TI information in TI data books or data sheets is permissible only if reproduction is without alteration and is accompanied by all associated warranties, conditions, limitations, and notices. TI is not responsible or liable for such altered documentation. Information of third parties may be subject to additional restrictions. Resale of TI components or services with statements different from or beyond the parameters stated by TI for that component or service voids all express and any implied warranties for the associated TI component or service and is an unfair and deceptive business practice. TI is not responsible or liable for any such statements. Buyer acknowledges and agrees that it is solely responsible for compliance with all legal, regulatory and safety-related requirements concerning its products, and any use of TI components in its applications, notwithstanding any applications-related information or support that may be provided by TI. Buyer represents and agrees that it has all the necessary expertise to create and implement safeguards which anticipate dangerous consequences of failures, monitor failures and their consequences, lessen the likelihood of failures that might cause harm and take appropriate remedial actions. Buyer will fully indemnify TI and its representatives against any damages arising out of the use of any TI components in safety-critical applications. In some cases, TI components may be promoted specifically to facilitate safety-related applications. With such components, TI’s goal is to help enable customers to design and create their own end-product solutions that meet applicable functional safety standards and requirements. Nonetheless, such components are subject to these terms. No TI components are authorized for use in FDA Class III (or similar life-critical medical equipment) unless authorized officers of the parties have executed a special agreement specifically governing such use. Only those TI components which TI has specifically designated as military grade or “enhanced plastic” are designed and intended for use in military/aerospace applications or environments. Buyer acknowledges and agrees that any military or aerospace use of TI components which have not been so designated is solely at the Buyer's risk, and that Buyer is solely responsible for compliance with all legal and regulatory requirements in connection with such use. TI has specifically designated certain components as meeting ISO/TS16949 requirements, mainly for automotive use. In any case of use of non-designated products, TI will not be responsible for any failure to meet ISO/TS16949. Products Audio Amplifiers Data Converters DLP® Products DSP Clocks and Timers Interface Logic Power Mgmt Microcontrollers RFID OMAP Applications Processors Wireless Connectivity Applications www.ti.com/audio Automotive and Transportation amplifier.ti.com Communications and Telecom dataconverter.ti.com Computers and Peripherals www.dlp.com Consumer Electronics dsp.ti.com Energy and Lighting www.ti.com/clocks Industrial interface.ti.com Medical logic.ti.com Security power.ti.com Space, Avionics and Defense microcontroller.ti.com Video and Imaging www.ti-rfid.com www.ti.com/omap TI E2E Community www.ti.com/wirelessconnectivity www.ti.com/automotive www.ti.com/communications www.ti.com/computers www.ti.com/consumer-apps www.ti.com/energy www.ti.com/industrial www.ti.com/medical www.ti.com/security www.ti.com/space-avionics-defense www.ti.com/video e2e.ti.com Mailing Address: Texas Instruments, Post Office Box 655303, Dallas, Texas 75265 Copyright © 2015, Texas Instruments Incorporated

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