Analog Engineer’s

Nadhem JEMLI

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. 34013KPCover_CS6_final.indd 2 6/5/15 5:32 PM 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Standard resistor values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Practical capacitor model and specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Practical capacitors vs frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Capacitor type overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Standard capacitance values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Capacitance marking and tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diodes and LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 13 14 15 16 17 17 18 Analog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Capacitor equations (series, parallel, charge, energy) . . . . . . . . . . . . . . . . . . . . . . . . . . . Inductor equations (series, parallel, energy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Capacitor charge and discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RMS and mean voltage definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RMS and mean voltage examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logarithmic mathematical definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . dB definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Log scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pole and zero definitions and examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time to phase shift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 21 23 24 24 27 28 29 30 34 Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Basic op amp configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Op amp bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Full power bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Small signal step response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noise equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Phase margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability open loop SPICE analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Instrumentation Amp filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 41 42 43 44 48 50 53 PCB and wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 PCB conductor spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Self-heating of PCB traces on inside layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCB trace resistance for 1oz and 2oz Cu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Package types and dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCB parallel plate capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCB microstrip capacitance and inductance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCB adjacent copper trace capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCB via capacitance and inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common coaxial cable specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coaxial cable equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resistance per length for different wire types (AWG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maximum current for wire types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 57 58 60 61 62 63 64 65 66 67 68 Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Temperature sensor overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resistive temperature detector (RTD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diode temperature characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermocouple (J and K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 71 72 74 76 A/D conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Binary/hex conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A/D and D/A transfer function (LSB, Data formats, FSR). . . . . . . . . . . . . . . . . . . . . . . . . . Quantization error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Signal-to-noise ratio (SNR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Total harmonic distortion (THD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Signal-to-noise and distortion (SINAD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effective number of bits (ENOB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noise free resolution and effective resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Setting time and conversion accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Texas Instruments Analog Engineer's Pocket Reference 83 84 90 91 92 94 94 95 96 5 6 Texas Instruments Analog Engineer's Pocket Reference Standard decimal preixes • Metric conversions • Temperature scale conversions • Error conversions (ppm and percentage) • Texas Instruments Analog Engineer's Pocket Reference 7 Conversions Conversions Conversions ti.com/precisionlabs Conversions Conversions ti.com/precisionlabs Table 1: Physical constants Constant Speed of light in a vacuum Permittivity of vacuum Symbol Value c 2.997 924 58 x 108 Units m/s -12 εo 8.854 187 817 620 x 10 F/m Permeability of free space µo 1.256 637 0614 x 10-6 H/m Plank’s constant h 6.626 069 57 x 10-34 J•s -23 Boltzmann’s constant k 1.380 648 8 x 10 Faraday’s constant F 9.648 533 99 x 104 C/mol Avogadro’s constant NA 6.022 141 29 x 1023 1/mol mu 1.660 538 921 x 10-27 kg -19 C Unified atomic mass unit Electronic charge J/K 1.602 176 565 x 10 q -31 Rest mass of electron me 9.109 382 15 x 10 kg Mass of proton mp 1.672 621 777 x 10-27 kg -11 Nm2/kg2 Gravitational constant G Standard gravity gn 9.806 65 m/s2 Ice point Tice 273.15 K Maximum density of water Density of mercury (0°C) Gas constant Speed of sound in air (at 273°K) 6.673 84 x 10 3 ρ 1.00 x 10 kg/m3 ρHg 1.362 8 x 104 kg/m3 R 8.314 462 1 J/(K•mol) 2 3.312 x 10 cair m/s Table 2: Standard decimal prefixes Multiplier Abbreviation 10 tera T 109 giga G 106 mega M 103 kilo k 10–3 milli m 10–6 micro µ 10–9 nano n 10–12 pico p 10–15 femto f atto a –18 10 8 Prefix 12 Texas Instruments Analog Texas Instruments Analog Engineer's Pocket Reference Engineer's Pocket Reference Conversions ti.com/precisionlabs Table 3: Imperial to metric conversions Unit Symbol Equivalent Unit Symbol inches in 25.4 mm/in millimeter mm mil mil 0.0254 mm/mil millimeter mm feet ft 0.3048 m/ft meters m yards yd 0.9144 m/yd meters m miles mi 1.6093 km/mi kilometers km circular mil cir mil 5.067x10-4 mm2/cir mil square millimeters mm2 2 2 square yards yd 0.8361 m square meters m2 pints pt 0.5682 L/pt liters L ounces oz 28.35 g/oz grams g pounds lb 0.4536 kg/lb kilograms kg calories cal 4.184 J/cal joules J horsepower hp 745.7 W/hp watts W Symbol Table 4: Metric to imperial conversions Unit Symbol Conversion Unit millimeter mm 0.0394 in/mm inch in millimeter mm 39.4 mil/mm mil mil meters m 3.2808 ft/m feet ft meters m 1.0936 yd/m yard yd kilometers km 0.6214 mi/km miles mi square millimeters mm2 1974 cir mil/mm2 circular mil cir mil square meters m2 1.1960 yd2/ m2 square yards yd2 liters L 1.7600 pt/L pints pt grams g 0.0353 oz/g ounces oz kilograms kg 2.2046 lb/kg pounds lb joules J 0.239 cal/J calories cal watts W 1.341x10-3 hp/W horsepower hp Example Convert 10 mm to mil. Answer 10 mm x 39.4 mil = 394 mil mm Texas Instruments Analog Engineer's Pocket Reference 9 Conversions ti.com/precisionlabs Table 5: Temperature conversions 5 �C � �� 5 �C�� C� � �� 5 � �� C� � �� C �5�7�.�5 � � �C � �7�.�5 �C � � � �7�.�5 �C � � � �7�.�5 Fahren Fahrenheit to Celsius Celsius Celsius to Fahrenheit Celsius to Kelvin Celsius Kelvin to Celsius Kelvin Table 6: Error conversions Table 6: Error conversions Table 6: Error conversions Meas�red � Idea� �rror�%� � � �00 Idea� � Idea� Meas�red �rror�%� � Meas�red � Idea�� 00 Idea� �rror�% �S�� 00 ��‐s�a�e ra��e Meas�red � Idea� �rror�% �S�� m � �00 ��‐s�a�e ra��e %� � �00 � �0 ��m %� � �00 ��m �0� � �00 � �000 m% � �0��m m% � � �00 � �000 �0� ��m � % � �0� ��m � % � �0� ��m � m% � �0 ��m � m% � �0 E Error in measured value Error Errorin percent of full-scale range Part Par per million to percent Par per million to milli-percent Part Per Percent to part per million MilliMilli-percent to part per million Example Example Compute the error for a measured value of 0.12V when the ideal value is 0.1V and the range is 5V. 0.��V � 0.�V �rror�%� � � �00 � �0% Answer 0.�V � 0.�V 0.��V V �rror�%� � 0.12V 0.�� 0.�V � �00 � �0% Error % 0.�V � �00 � 0.�% �rror�% �S�� 0.1V 5V � 0.�V 0.�� V� �00 � 0.�% �rror�% �S�� Error % FSR 5V 5V Error in measured value Percent FSR Example Convert 10 ppm to percent and milli-percent. �0 ��m Answer � �00 � 0.00�% � �0 �0 ��m 10 ppm � �00 � 0.00�% �0 ��m �0 10�� 00 � �000 � � m% � �0 �0 10��m ppm � �00 � �000 � � m% �0 10� 10 Texas Part per million to percent Part per million to milli-percent Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Discrete Components Resistor color code • Standard resistor values • Capacitance speciications • Capacitance type overview • Standard capacitance values • Capacitance marking and tolerance • 11 Texas Texas Instruments Analog Engineer's Pocket Reference Discrete Discrete Components Discrete Components ti.com/precisionlabs Discrete Table 7: Resistor color code Color Digit Additional Zeros Black 0 0 Tolerance Temperature Coefficient Failure Rate 250 Brown 1 1 1% 100 1 Red 2 2 2% 50 0.1 Orange 3 3 15 0.01 Yellow 4 4 25 0.001 Green 5 5 0.5% 20 Blue 6 6 0.25% 10 Violet 7 7 0.1% 5 0.05% 1 Grey 8 8 White 9 9 Gold -na- -1 5% Silver -na- -2 10% No Band -na- -na- 20% 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 10.0 10 14.7 14.9 15.0 15.2 15.4 15.6 15.8 16.0 16.2 16.4 16.5 16.7 16.9 17.2 17.4 17.6 17.8 18.0 18.2 18.4 18.7 18.9 19.1 19.3 19.6 19.8 20.0 20.3 20.5 20.8 21.0 21.3 10.2 10.5 10.7 11.0 11 11.3 11.5 11.8 12 12.1 12.4 12.7 13.0 13.3 13.7 14.0 14.3 13 1% 2% 5% 10% 14.7 15.0 15 15.4 15.8 16 16.2 16.5 16.9 17.4 17.8 18 18.2 18.7 19.1 19.6 20.0 20.5 21.0 20 0.1% 0.25% 0.5% 21.5 21.8 22.1 22.3 22.6 22.9 23.2 23.4 23.7 24.0 24.3 24.6 24.9 25.2 25.5 25.8 26.1 26.4 26.7 27.1 27.4 27.7 28.0 28.4 28.7 29.1 29.4 29.8 30.1 30.5 30.9 31.2 1% 2% 5% 10% 21.5 22.1 22 22.6 23.2 23.7 24 24.3 24.9 25.5 26.1 26.7 27 27.4 28.0 28.7 29.4 30.1 30.9 30 0.1% 0.25% 0.5% 31.6 32.0 32.4 32.8 33.2 33.6 34.0 34.4 34.8 35.2 35.7 36.1 36.5 37.0 37.4 37.9 38.3 38.8 39.2 39.7 40.2 40.7 41.2 41.7 42.2 42.7 43.2 43.7 44.2 44.8 45.3 45.9 1% 2% 5% 10% 31.6 32.4 33.2 33 34.0 34.8 35.7 36 36.5 37.4 38.3 39.2 39 40.2 41.2 42.2 43.2 44.2 45.3 43 0.1% 0.25% 0.5% 46.4 47.0 47.5 48.1 48.7 49.3 49.9 50.5 51.1 51.7 52.3 53.0 53.6 54.2 54.9 55.6 56.2 56.9 57.6 58.3 59.0 59.7 60.4 61.2 61.9 62.6 63.4 64.2 64.9 65.7 66.5 67.3 1% 2% 5% 10% 46.4 47 47.5 48.7 49.9 51.1 51 52.3 53.6 54.9 56.2 56 57.6 59.0 60.4 61.9 63.4 64.9 66.5 62 0.1% 0.25% 0.5% 68.1 69.0 69.8 70.6 71.5 72.3 73.2 74.1 75.0 75.9 76.8 77.7 78.7 79.6 80.6 81.6 82.5 83.5 84.5 85.6 86.6 87.6 88.7 89.8 90.9 92.0 93.1 94.2 95.3 96.5 97.6 98.8 1% 2% 5% 10% 68.1 68 69.8 71.5 73.2 75.0 75 76.8 78.7 80.6 82.5 82 84.5 86.6 88.7 90.9 93.1 95.3 97.6 91 Discrete Components 0.1% 0.25% 0.5% ti.com/precisionlabs 13 10.0 10.1 10.2 10.4 10.5 10.6 10.7 10.9 11.0 11.1 11.3 11.4 11.5 11.7 11.8 12.0 12.1 12.3 12.4 12.6 12.7 12.9 13.0 13.2 13.3 13.5 13.7 13.8 14.0 14.2 14.3 14.5 1% 2% 5% 10% Table 8: Standard resistor values Texas Instruments Analog Engineer's Pocket Reference Standard resistance values for the 10 to 100 decade 0.1% 0.25% 0.5% 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 ESR Equivalent series resistance Ideally this is zero Ceramic capacitors have the best ESR (typically in milliohms). Tantalum Electrolytic have ESR in the hundreds of milliohms and Aluminum Electrolytic have ESR in the ohms ESL Equivalent series inductance Ideally this is zero ESL ranges from 100 pH to 10 nH Rp Rp is a parallel leakage resistance (or insulation resistance) 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 Discrete Components Impedance (ohms) Practical capacitors vs. frequency of ESR ESL on capacitor frequency Figure 3:Figure Effect 3: of Effect ESR and ESL and on capacitor frequency responseresponse Texas Instruments Analog Engineer's Pocket Reference 15 Discrete Components ti.com/precisionlabs Table 10: Capacitor type overview Capacitor type Description C0G/NP0 (Type 1 ceramic) 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 X7R (Type 2 ceramic) 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 Y5V (Type 2 ceramic) 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 Aluminum oxide electrolytic 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 Tantalum electrolytic Capacitance range: 1 µF to 150 µF Similar to aluminum oxide but smaller size Polypropylene film 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 Discrete Components ti.com/precisionlabs 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 Tolerance B ± 0.1 pF J ± 5% C ± 0.25 pF K ± 10% D ± 0.5 pF M ± 20% F ± 1% Z + 80%, –20% G ± 2% Table 13: EIA capacitor tolerance markings (Type 2 capacitors) First letter symbol Low temp limit Second number symbol High temp 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 ti.com/precisionlabs Diodes and LEDs Anode (+) Cathode (-) Anode (+) Cathode (-) Anode (+) Cathode (-) Anode (+) Long Lead Cathode (-) Short Lead, Flat Figure 5: Diode and LED pin names Color Wavelength (nm) Voltage (approximate range) Infrared 940-850 1.4 to 1.7 Red 660-620 1.7 to 1.9 Orange / Yellow 620-605 2 to 2.2 Green 570-525 2.1 to 3.0 Blue/White 470-430 3.4 to 3.8 Table 14: LED forward voltage drop by color 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 Analog Analog Analog Capacitor equations (series, parallel, charge, energy) • Inductor equations (series, parallel, energy) • Capacitor charge and discharge • RMS and mean voltage deinition • RMS for common signals • Logarithm laws • dB deinitions • Pole and zero deinition with examples • Texas Instruments Analog Engineer's Pocket Reference 19 Analog ti.com/precisionlabs Capacitor equations C C 1 1 C 1 C 1 C C C (1) Series capacitors (2) Two series capacitors C C (3) Parallel capacitors Analog Where Ct = equivalent total capacitance C1, C2, C3…CN = component capacitors (4) Charge storage V (5) Charge deined 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) 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 2 (7) Energy stored in a capacitor Where E = energy stored in an capacitor in Joules (J) V = voltage in volts C = capacitance in farads (F) 20 Texas Texas Instruments Analog Engineer's Pocket Reference Analog ti.com/precisionlabs Inductor equations L� � L� � L� � � � L� L� � L� � � � � � � � �� L� L� L� L� L� L� � L� Series inductors (8)Series (8) inductors Parallel inductors (9)Parallel (9) inductors Two parallel inductors (10) parallel inductors (10)Two Where Where LLtt = equivalent total total inductance inductance LL11,, L L33…L …LNN == component componentinductance inductance L22,, L ��L di dt Instantaneousvoltage voltageacross acrossananinductor inductor (11)Instantaneous (11) Where Where v = instantaneous voltage across the inductor v = instantaneous voltage across the inductor L = inductance in Henries (H) L = inductance in Henries (H) di � = instantaneous rate of current change dt = the instantaneous rate of voltage change �� LI� � Energystored storedininananinductor Inductor (12)Energy (12) Where Where EE == energy energy stored stored in in an an inductor inductorininJoules Joules(J) (J) II ==current currentininamps amps L = inductance in Henries (H) L = inductance in Henries (H) Texas Instruments Analog Engineer's Pocket Reference 21 Analog ti.com/precisionlabs Equation for charging an RC circuit �� V� � V� �� e� � � � General relationship (13) (13) General relationship Where �� Where V� � V� �� e� � � � VC = voltage across the capacitor at any instant in time (t) VS = the source voltage charging the RC circuit t = time in seconds τ = RC, the time constant for charging and discharging capacitors  fully charged Graphing equation 13 produces the capacitor charging curve below. Note that the capacitor is 99.3% charged at ive time constants. It is common practice to consider this fully charged. fully charged Figure 7: RC charge curve 22 Texas Figure 6: RC charge curve Texas Instruments Analog Engineer's Pocket Reference Analog ti.com/precisionlabs Equation for discharging an RC circuit �� V� � V� �e� � � � (14) General Relationship (14) General �� Where Where V� � V� �e� � � � VC = voltage across the capacitor at any instant in time (t) Vi = the initial voltage of the capacitor at t=0s t = time in seconds τ = RC, the time constant for charging and discharging capacitors   Graphing equation 14 produces the capacitor discharge curve below. Note that the capacitor is discharged to 0.7% at ive time constants. It is common practice to consider this fully discharged. this fully fullydischarged. discharged Percentage Discharged vs. Number of Time Constants Percentage Discharged vs. Number of Time Consta 100 90 PercentagePercentage Charged Charged 80 70 60 50 40 30 20 10 0 0 1 2 3 4 5 Number of time Constants (τ = RC) Figure 8: RC discharge curve Figure 7: RC discharge curve Number of time Constants (τ = RC) Texas Instruments Analog Engineer's Pocket Reference 23 Analog ti.com/precisionlabs RMS voltage �� (15) General relationship (15) General relationship � �V�t�� dt �T� � T� � �� V�t�� dt V�� V�� V�t�� dt � � T�� Where �T�T � � T� � �� Where V(t) = continuous function of time V(t) = continuous function of time t = time in seconds t = time in seconds T1 ≤ t ≤ T2 = the time interval that the function is defined over T1 ≤ t ≤ T2 = the time interval that the function is deined over V�� ≤ ≤ Mean ≤ ≤voltage Mean voltage Mean voltage � V�� V�t�dt �T� � T� � �� V�� V�t�dt V�� T� � T�� V�t�dt �T� � T� � �� (16)(16) General relationship General relationship Where Where ≤ V(t)≤= continuous function of time t = time in seconds ≤ ≤ T1 ≤≤ t ≤ T2 = the time interval that the function is deined over V�� V�� √� V�� RMS for fullsine wave rectified V�� V�� (17) RMS for full wave rectiied wave V�� √� (17) � V�� sine wave V�� √� π � � V�� Mean for full wave rectified V�� V�� (18) Mean for full (18)wave rectiied sine wave � V�� π sine wave π Figure 8: Full wave rectified sine wave Figure 9: Full wave rectified sine wave 24 Texas Texas Instruments Analog Engineer's Pocket Reference Analog ti.com/precisionlabs RMS voltage and mean voltage V τ 2T V V π V RMS for a half-wave (19) (19) RMS for a half-wave sine wave rectified rectified sine wave τ T Mean for a half-wave (20) (20) Mean for a half-wave rectified sine wave rectified sine wave 9: sine Half-wave Figure 10: Half-wave Figure rectified wave rectified sine wave V V V V τ T (21) a square wave (21) RMSRMS for afor square wave τ T (22) Mean for a square wave Figure 11: Square wave Figure 10: Square wave Texas Instruments Analog Engineer's Pocket Reference 25 Analog ti.com/precisionlabs RMS voltage and mean voltage V (V V τ V 2T V V 3 V V τ (( T ( (23) RMS for afortrapezoid (23) RMS a trapezoid (24) Mean for afortrapezoid (24) Mean a trapezoid Figure 12: Trapezoidal wave Figure 11: Trapezoidal wave V V V τ 3T τ V 2T (26) Mean for a triangle (26) Mean for a triangle wave wave Figure 13: Triangle wave 26 (25) RMS a triangle wave wave (25) for RMS for a triangle Texas Figure 12: Triangle wave Texas Instruments Analog Engineer's Pocket Reference Analog ti.com/precisionlabs Logarithmic mathematical definitions A B log AB log A A B (27)ofLog of dividend (27) Log dividend A B (28) Log product (28)ofLog of product A (29)ofLog of exponent (29) Log exponent log log log (30) Changing the of base log function (30) Changing the base logof function log log log (31) Example changing to logtobase 2 (31) Example changing log base 2 ln X (32) Natural log is log log is base e (32) Natural log base e (33) Exponential function to 6 digits. (33) Exponential function to 6 digits Alternative Alternative notations notations exp x Different notation for exponential (34) Different notation for exponential function (34) function Different notation for scientific (35) Different notation for scientific notation, (35) notation, sometimes confused with sometimes confused with exponential function exponential function Texas Instruments Analog Engineer's Pocket Reference 27 Analog ti.com/precisionlabs dB definitions Bode plot basics The frequency response for the magnitude or gain plot is the change in voltage gain as frequency changes. This change is speciied on a Bode plot, a plot of frequency versus voltage gain in dB (decibels). Bode plots are usually plotted as semi-log plots with frequency on the x-axis, log scale, and gain on the y-axis, linear scale. The other half of the frequency response is the phase shift versus frequency and is plotted as frequency versus degrees phase shift. Phase plots are usually plotted as semi-log plots with frequency on the x-axis, log scale, and phase shift on the y-axis, linear scale. scale. Definitions V V ((36) 36 Voltage gain in decibels P P Power Measured (W) 1 mW Measured A (V/V) A (dB) 0.001 –60 0.01 –40 0.1 –20 1 0 10 20 100 40 1,000 60 10,000 80 100,000 100 1,000,000 120 10,000,000 140 28 ((37) 37 Power gain in decibels Texas (38) Used for input or (38) output power Table 15: Examples of common gain values and dB equivalent Roll-off rate is the decrease 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) 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. A (dB) 1. Given L = 1cm; D = 2cm, measured with a ruler. 2. L/D = log10(fp) 3. fP = 10(L/D) = 10(1cm/2cm)= 3.16 4. Adjust for the decade range (for this example, fp = 31.6 Hz) Figure14: 13:Finding Findingvalues valueson onlogarithmic logarithmic axis axis not not directly directly on on aa grid grid line line Figure Texas Instruments Analog Engineer's Pocket Reference 29 Analog ti.com/precisionlabs Bode plots: Poles Bode plots: Poles fP 100 0.707*GV/V = –3 dB Actual function G (dB) 80 Straight-line approximation –20 dB/decade 60 40 20 0 1 10 100 1k 10k 100k 1M 10M 100k 1M 10M Frequency (Hz) (degrees) +90 +45 0° 10 100 1k 10k 0 –45 –5.7° at fP 10 –45°/decade –84.3° at fP x 10 –90° –45° at fP –90 Figure 14: Pole gain and phase Figure 15: Pole gain and phase Pole Location fP (cutoff freq) Pole=Location = fP (cutoff freq) Magnitude (f < fP) = GDC (for example, 100 dB) Magnitude (f = fP) = –3 dB Magnitude (f > fP) = –20 dB/decade Phase (f = fP) = –45° Phase (0.1 fP < f < 10 fP) = –45°/decade Phase (f > 10 fP) = –90° Phase (f < 0.1 fP) = 0° 30 Texas Texas Instruments Analog Engineer's Pocket Reference Analog ti.com/precisionlabs Pole (equations) G V V G V V G j f f (39) As a complex number G f f f f G (40) Magnitude (41) Phase shift (42) Magnitude in dB Where Where Gv = voltage gain in V/V GdB = voltage gain in decibels GDC = the dc or low frequency voltage gain θ f = frequency in Hz 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 Analog ti.com/precisionlabs Bode plots (zeros) 80 Straight-line approximation +20 dB/decade G (dB) 60 40 Actual function 20 +3 dB 0 1 10 100 1k 10k 100k 1M 10M +90° +90 +45° at fZ (degrees) 84.3° at fZ x 10 +45 0° f 5.7° at Z 10 +45°/decade 0 10 100 1k 10k 100k 1M 10M Frequency (Hz) –45 –90 Figure 15: Zero gain and phase Figure 16: Zero gain and phase Zero location = fZ Magnitude (f < fZ) = 0 dB Magnitude (f = fZ) = +3 dB Magnitude (f > fZ) = +20 dB/decade Phase (f = fZ) = +45° Phase (0.1 fZ < f < 10 fZ) = +45°/decade Phase (f > 10 fZ) = +90° Phase (f < 0.1 fZ) = 0° 32 Texas Texas Instruments Analog Engineer's Pocket Reference Analog ti.com/precisionlabs Zero (equations) Zero (equations) G� � V�� G�� j � � � �� V�� G� � � � V�� G�� V�� ta�� G�� 0 Lo��G� � (43) As a complex number (44) Magnitude (45) Phase shift (46) Magnitude in dB Where Where GV = voltage gain in V/V GdB = voltage gain in decibels GDC = the dc or low frequency voltage gain f = frequency in Hz θ 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 Analog ti.com/precisionlabs P S Figure 17: Time to phaseFigure shift 16: Time to phase shift θ Where (47) Phase fromshift timefrom time (47) shift Phase • 360° Where TS = time shift from input to output signal θTP = period of signal θ = phase shift of the signal from input to output Example Calculate the phase shift in degrees for Figure 16. Answer θ= 34 Ts • 360° = Tp ( Texas 0.225 ms 1 ms ) • 360° = 81° Texas Instruments Analog Engineer's Pocket Reference Amplifier Amplifier ti.com/precisionlabs Amplifier Basic op amp conigurations • Op amp bandwidth • Full power bandwidth • Small signal step response • Noise equations • Stability equations • Stability open loop SPICE analysis • ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 35 Amplifier ti.com/precisionlabs Basic op amp configurations G�� Gain for buffer (48) Gain (48) for buffer coniguration configuration G�� VCC VOUT VIN VEE Figure 17: Buffer configuration Amplifier G�� G�� (49) forfor non-inverting coniguration Gain non-inverting configuration (49)Gain �� R1 Rf VCC VOUT VIN VEE Figure 18: Non-inverting configuration ti.com/amplifiers 36 Texas Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs �� G�� Amplifier �� Basic op amp configurations (cont.) G�� Gain for inverting (50) Gain(50) for inverting coniguration R1 Rf VCC VIN VOUT VEE Figure 19: Inverting configuration Figure 20: Inverting configuration V� V� V� for inverting V�� (51) Transfer function ( �� summing ampliier �� V � V � Transfer function for inverting summing V�� V �� V �VV� �V� (52) ( �� ampliier, assuming R1 = R2 = …=RN V�� VN RN �� V� � V� � � � V� � �� R2 V2 R1 Rf VCC V1 VOUT - + VEE + Figure 20: Inverting summing configuration ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference -+ + 37 Amplifier ti.com/precisionlabs Basic op amp configurations (cont.) Basic op amp configurations (cont.) V�� Where �� V� V� V� � �� N N N � �� Transfer function (53) Transfer function forfor noninverting summing amplifier (53)noninverting summing ampliier equalinput inputresistors resistors forforequal Where R1 = R2 = … = RN N = number of input resistors Rin R1 Rf VCC VOUT V1 R2 V2 RN VEE VN Figure 21: Non-inverting summing configuration ti.com/amplifiers 38 Texas Texas Instruments Analog Engineer's Pocket Reference Amplifier ti.com/precisionlabs Simple amp Cf filter Simplenon-inverting non-inverting amp withwith C filter �� G�� G�� Gain for non-inverting configuration (54) Gain(54) for non-inverting configuration for f < fc for f < fc G�� Gain for non-inverting configuration (55) Gain(55) for non-inverting configuration for f >> fc for f >> fc G �� π � � C� � �� π � � C� Cut off frequency for non-inverting (56) Cut off (56)frequency for non-inverting configuration configuration Cf R1 Rf VCC VOUT VIN VEE Figure 22: Non-inverting amplifier with Cf filter Figure 23: 24: Frequency Frequency response response for for non-inverting non-inverting op op amp amp with with C Cf filter ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 39 Amplifier ti.com/precisionlabs Simple inverting amp with Cf filter G G R R (57) Gain for inverting configuration for f < fC −�0dB/de�ade a�ter � C ��ti� o� am� ba�dwidth �imitatio� (58) Gain for inverting configuration for f > fC −20dB/decade after f 1until op amp bandwidth (59) Cutoff frequency for inverting configuration �π � C � Cf π R1 Rf VCC VIN VOUT VEE Figure 24: Inverting amplifier with Cf filter Figure 25: Frequency response for inverting op amp with Cf filter Figure 26: Frequency response for inverting op amp with C filter ti.com/amplifiers 40 Texas Texas Instruments Analog Engineer's Pocket Reference Amplifier ti.com/precisionlabs Op amp bandwidth GBW = Gain • BW GBW � Gai� x BW (60) Gain bandwidth product deined Where GBW = gain bandwidth product, listed in op amp data sheet speciication table Gain = closed loop gain, set by op amp gain coniguration BW = the bandwidth limitation of the ampliier Example Gai� � bandwidth �00 Determine using equation 60 Gain = 100 (from ampliier coniguration) GBW � ��MHz GBW = 22MHz (from data sheet) GBW 22MHz ��MHz GBW = ��0kHz 220 kHz BW BW = � Gai�=� �00 � 100 Gain Note that the same result can be graphically determined using the AOL curve as shown below. 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 Full power bandwidth S� �π�S� V� � �π� Where Maximum output without slew-rate induced (61) Maximum (61) output without slew-rate induced distortion distortion V� � Where VP = maximum peak output voltage before slew induced distortion occurs SR = slew rate f = frequency of applied signal Maximum output voltage vs. frequency �. ��/µ� �� . �� . �� . ��/µ� �� . �� . �� Figure 27: Maximum output without slew-rate induced distortion Figure 28: Maximum output without slew-rate induced distortion Notice that the above igure is graphed using equation 61 for the OPA277. The example calculation shows the peak voltage for the OPA277 at 40kHz. This can be determined graphically or with the equation. 0.�V/μs � �.��V�k or 6.�7V�� π�S� �π��0kHz� 0.�V/μs V� � � SR 0.8V/µs � �.��V�k or 6.�7V�� VP = �π�= �π��0kHz� = 3.18Vpk or 6.37Vpp S� Example V� � � 2πf 2π(40kHz) ti.com/amplifiers 42 Texas Texas Instruments Analog Engineer's Pocket Reference Amplifier ti.com/precisionlabs Small signal step response τ� � 0.�5 �� a small signal (62) (62) RiseRise timetime for afor small signal stepstep Where 0.�5 τ� �  �� Where τR = the rise time of a small signal step response fC = the closed-loop bandwidth of the op amp circuit  Small signal step response waveform Figure 29: Small signal step response Figure 28: Maximum output without slew-rate induced distortion ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 43 Amplifier ti.com/precisionlabs Op amp noise model Figure 30: Op amp noiseFigure model29: Op amp noise model  Op amp intrinsic noise includes:  • Noise caused by op amp (current noise + voltage noise) • Resistor noise ti.com/amplifiers 44 Texas Texas Instruments Analog Engineer's Pocket Reference Amplifier ti.com/precisionlabs Noise bandwidth calculation Noise bandwidth calculation BW� � � � �� BW� � � � �� ( Noise bandwidth (63) BW � � � �� Where� Where BWN = noise bandwidth of the system KN = the brick wall correction factor for different ilter order fC = –3 dB bandwidth of the system Figure 30: Op amp bandwidth for three different filters orders Table 16: Brick wall correction factors for noise bandwidth Number of poles KN brick wall correction factor 1 1.57 2 1.22 3 1.13 4 1.12 Broadband total total noise noise calculation calcula Broadband �� e�� BW� �� e�� BW� (64) Total rms noise from broadband e�� BW� �� Where Where EN = total rms noise from broadband noise eBB = broadband noise spectral density (nV/rtHz) BWN = noise bandwidth (Hz) ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 45 Amplifier ti.com/precisionlabs 1/f total noise calculation (65) Normalized 1/f noise at 1 Hz ��_�� e�� _�� e�� Where Where EN_NORMAL = 1/f noise normalized to 1 Hz eBF = noise spectral density measured in the 1/f region fO = the frequency that the 1/f noise eBF is measured at �� _�� _�� _�� _�� (66) 1/f total noise calculation Where Where EN_FLICKER = total rms noise from licker EN_NORMAL = 1/f noise normalized to 1Hz fH = upper cutoff frequency or noise bandwidth fL = lower cutoff frequency, normally set to 0.1Hz Table 17: Peak-to-peak conversion σ Number ofσstandard deviations σ σ as ±1σ) 2σ (same σ σ 3σ (same as ±1.5σ) σ σ σ σ 4σ (same σ σ as ±2σ) σ 5σ (sameσas ±2.5σ) σ σ 6σ (same σ σ σ as ±3σ) σ σ 6.6σ (same σas ±3.3σ) σ σ Percent chance reading is in range 68.3% 86.6% 95.4% 98.8% 99.7% 99.9% ti.com/amplifiers 46 Texas Texas Instruments Analog Engineer's Pocket Reference Amplifier ti.com/precisionlabs Thermal noise calculation En_R = en_R = (67) Total rms Thermal Noise √ 4kTR�f √ 4kTR (68) Thermal Noise Spectral Density ��_� � √� kT�Δ� Where En_R = Total rms noise from resistance, also called thermal noise (V rms) en_R = Noise spectral density from resistance, also called thermal noise (V/√Hz ) k = Boltzmann’s constant 1.38 x 10-23J/K T = Temperature in Kelvin ∆f = Noise bandwidth in Hz ∆ Noise Spectral Density (nV/rtHz) 1000 100 10 ‐55C 25C 1 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 Figure 31: Noise spectral density vs. resistance ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 47 Amplifier ti.com/precisionlabs Ac response versus frequency (Dominant 2-Pole System) Figure 32 illustrates a bode plot with four different examples of ac peaking. Figure 32: Stability – ac peaking relationship Figure 33: Stability – ac peaking relationship exampleexample Phase margin versus ac peaking graph illustrates thephase phasemargin margin for of of ac ac peaking. This This graph illustrates the for any anygiven givenlevel level peaking. NoteNote thatthat 45°45° of phase isrequired requiredforfor stable operation. of phasemargin marginor or greater greater is stable operation. Figure 34: Stability – phase margin vs. peaking for a two-pole system Figure 33: Stability – phase margin vs. peaking for a two-pole system ti.com/amplifiers 48 Texas Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs Amplifier Transient overshoot (Dominant 2-Pole System) Transient overshoot Figure 34 35 illustrates withtwo two different examples of Figure illustratesa atransient transient response response with different examples percentage overshoot. of percentage overshoot. Figure 35:Figure Stability transient overshootovershoot example example 34:–Stability – transient Phase margin versus percentage overshoot Phase margin versus percentage overshoot This graph illustrates the phase margin for any given level of transient This graph illustrates theof phase margin for any given level of overshoot. Note that 45° phase margin or greater is required for transient overshoot. Note that 45° of phase margin or greater is required stable operation. for stable operation. Figure Figure 35: 36:Stability Stability––phase phasemargin marginvs. vs.percentage percentageovershoot overshoot Note: The curves assume a two-pole system. ti.com/amplifiers Texas Instruments Analog Engineer's Pocket Reference 49 Amplifier ti.com/precisionlabs VFB R1 C1 1T RF L1 1T VIN V+ VO VOUT Riso CL V– Figure 36: Common spice test circuit used for stability A��_�� β � V�� V� V�� V�� β (69) Loaded open-loop gain (70) Feedback factor (71) Closed-loop noise gain A��_�� β � V� (72) Loop gain Where Where VO = the voltage at the output of the op amp. VOUT = the voltage output delivered to the load, which may be important to the application but is not considered in stability analysis. VFB = feedback voltage RF , R1, RiS0 and CL = the op amp feedback network and load. Other op amp topologies will have different feedback networks; however, the test circuit will be the same for most cases. Figure 37 shows the exception to the rule (multiple 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. ti.com/amplifiers 50 Texas Texas Instruments Analog Engineer's Pocket Reference Amplifier ti.com/precisionlabs VFB RF R1 CF L1 1T CIN VIN C1 1T V+ Riso - + VO VOUT CL V– Figure 37: Alternative (multiple feedback) SPICE test circuit used for stability A��_�� V� β� V�� V� V� � � V�� β A��_�� β � V�� (73) Loaded open loop gain (74) Feedback factor (75) Closed-loop noise gain (76) Loop gain Where Where VO = the voltage at the output of the op amp. VOUT = the voltage output delivered to the load. This may be important to the application but is not considered in stability analysis. VFB = feedback voltage RF, R1, Riso and CF = the op amp feedback network. Because there are two paths for feedback, the loop is broken at the input. 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. CIN = the equivalent 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 ti.com/precisionlabs R1 RF +Vs VOUT + Voffset + -Vs VIN Volts VOUT Voffset 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 ti.com/amplifiers 52 Texas Texas Instruments Analog Engineer's Pocket Reference Amplifier ti.com/precisionlabs +15V RIN1 VIN- CCM1 1nF CDIF 10nF 1kΩ RG RIN2 VIN+ Rg 1kΩ VOUT Out RG Ref U1 INA333 1kΩ CCM2 1nF -15V Figure 39: Input filter for instrumentation amplifier Se�e�t C C�� 0C �0C�� Se�e�t �� Se�e�t � �0C�� C� �� C �� C�� C � C �� C�� C�� π� �� C�� π� �� C�� π� �� C�� C�� C C�� π�� C � �� π�� π�� C�� C�� (77) Differential ilter is sized 10 times the common-mode ilter (78) Input resistors must be equal (79) Common-mode capacitors must be equal (80) Differential ilter cutoff (81) Common-mode ilter cutoff Where Where fDIF = differential cutoff frequency fCM = common-mode cutoff frequency RIN = input resistance CCM = common-mode ilter capacitance ≥ ≥ CDIF = differential ilter capacitance ≥ Note: Selecting CDIF ≥ 10 CCM sets the differential mode cutoff frequency 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 Reference 53 Amplifier ti.com/precisionlabs Notes ti.com/amplifiers 54 Texas Texas Instruments Analog Engineer's Pocket Reference PCB andWire Wire PCB and ti.com/precisionlabs PCB and wire 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 speciications • Coaxial cable equations • Resistance per length for wire types • Maximum current for wire types • Texas Instruments Analog Engineer's Pocket Reference 55 PCB and Wire ti.com/precisionlabs Table 18: Printed circuit board conductor spacing Minimum spacing PCB and wire Voltage between conductors (dc or ac peaks) Bare board Assembly B1 B2 B3 B4 A5 A6 A7 0-15 0.05 mm [0.00197 in] 0.1 mm [0.0039 in] 0.1 mm [0.0039 in] 0.05 mm [0.00197 in] 0.13 mm [0.00512 in] 0.13 mm [0.00512 in] 0.13 mm [0.00512 in] 16-30 0.05 mm [0.00197 in] 0.1 mm [0.0039 in] 0.1 mm [0.0039 in] 0.05 mm [0.00197 in] 0.13 mm [0.00512 in] 0.25 mm [0.00984 in] 0.13 mm [0.00512 in] 31-50 0.1 mm [0.0039 in] 0.6 mm [0.024 in] 0.6 mm [0.024 in] 0.13 mm [0.00512 in] 0.13 mm [0.00512 in] 0.4 mm [0.016 in] 0.13 mm [0.00512 in] 51-100 0.1 mm [0.0039 in] 0.6 mm [0.024 in] 1.5 mm [0.0591 in] 0.13 mm [0.00512 in] 0.13 mm [0.00512 in] 0.5 mm [0.020 in] 0.13 mm [0.00512 in] 101-150 0.2 mm [0.0079 in] 0.6 mm [0.024 in] 3.2 mm [0.126 in] 0.4 mm [0.016 in] 0.4 mm [0.016 in] 0.8 mm [0.031 in] 0.4 mm [0.016 in] 151-170 0.2 mm [0.0079 in] 1.25 mm [0.0492 in] 3.2 mm [0.126 in] 0.4 mm [0.016 in] 0.4 mm [0.016 in] 0.8 mm [0.031 in] 0.4 mm [0.016 in] 171-250 0.2 mm [0.0079 in] 1.25 mm [0.0492 in] 6.4 mm [0.252 in] 0.4 mm [0.016 in] 0.4 mm [0.016 in] 0.8 mm [0.031 in] 0.4 mm [0.016 in] 251-300 0.2 mm [0.0079 in] 1.25 mm [0.0492 in] 12.5 mm [0.492 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] 301-500 0.25 mm [0.00984 in] 2.5 mm [0.0984 in] 12.5 mm [0.492 in] 0.8 mm [0.031 in] 0.8 mm [0.031 in] 1.5 mm [0.0591 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 speciication can be downloaded at www.ipc.org 56 Texas Texas Instruments Analog Engineer's Pocket Reference ti.com/precisionlabs PCB and Wire Figure Self of heating of PCB on inside layer Figure 41: Self 40: heating PCB traces on traces inside layer � Example Find the current that will cause a 20°C temperature rise in a PCB trace that is 0.1 inch wide and uses 2 oz/ft2 copper. (Assume traces on outside of PCB.) Answer � First translate 0.1 inch to 250 sq. mils. using bottom chart. Next ind the current associated with 10°C and 250 sq. mils. using top chart (Answer = 5A). Extracted with permission from IPC-2152, Figure 5-1. For additional information the entire speciication can be downloaded at www.ipc.org 57 Texas Instruments Analog Engineer's Pocket Reference 57 PCB and Wire ti.com/precisionlabs PCB trace resistance for 1 oz-Cu PCB trace resistance for 1 oz Cu 5mil 10mil 25mil 50mil 100mil 1 100m 10m 1m 100µ 10µ 1µ 1 10 100 Trace length (mils) 1000 10000 Figure trace resistance vs. length width for 1 oz-Cu, 25°C Figure 42: 41: PCBPCB trace resistance vs. length andand width for 1 oz-Cu, 25°C Figure 43: 42: PCB trace resistance vs. length andand width for for 1 oz-Cu, 125°C Figure PCB trace resistance vs. length width 1 oz-Cu, 125°C Example What is the resistance of a 20 mil long, 5 mil wide trace for a 1 oz-Cu thickness at 25°C and 125°C? Answer Ω Ω R125C = 3Ω Ω R25C = 2 mΩ, mΩ. The points are circled on the curves. 58 Texas Texas Instruments Analog Engineer's Pocket Reference PCB and Wire ti.com/precisionlabs PCB trace resistance for 2 oz-Cu PCB trace resistance for 2 oz Cu 1 5mil 10mil 25mil 50mil 100mil 100m 10m 1m 100µ 10µ 1µ 1 10 100 Trace length (mils) 1000 10000 Figure PCB trace resistance length and width 2 oz-Cu, 25°C Figure 44:43: PCB trace resistance vs.vs. length and width forfor 2 oz-Cu, 25°C Figure 44: PCBtrace traceresistance resistancevs. vs.length length and and width width for 2 oz-Cu, 125°C Figure 45: PCB 125°C Example What is the resistance of a 200 mil long, 25 mil wide trace for a 2 oz-Cu thickness at 25°C and 125°C? Answer R25C = 2 mΩ, The points are circled on Ω R125C = 3 mΩ. ΩΩ the curves. Ω Texas Instruments Analog Engineer's Pocket Reference 59 PCB and Wire ti.com/precisionlabs Common package type and dimensions 120.2mil 3.05mm 60 Texas Texas Instruments Analog Engineer's Pocket Reference PCB and Wire ti.com/precisionlabs PCB parallel plate capacitance PCB parallel plate capacitance k ∙ ℓ ∙ w ∙ εr (82) Capacitance for parallel copper planes Where Where k = Permittivity of free space. ∙ℓ∙w∙ε Both the metric and imperial version of the constant are given. ℓ = length (metric in mm, or imperial in mil) k = 8.854∙10-3 pF/mm, or 2.247∙10-4 pF/mil ε = PCB relative dielectric constant (εr ≈ 4.5 for FR-4) ℓ = length (metric∙ in ℓ ∙ mm, w ∙ ε or imperial in mil) w = width (metric in mm, or imperial in mil) h= between (metric in mm, or imperial in mil) ℓ = separation length (metric in mm, or imperial inplanes mil) εr = PCB relative dielectric constant (εr ≈ 4.5 for FR-4) ε = PCB relative dielectric constant (εr ≈ 4.5 for FR-4) ℓ = length (metric in mm, or imperial in mil) w ε = PCB relative dielectric constant (εr ≈ 4.5 for FR-4) ε A l εr h Figure 45: PCB parallel plate capacitance (�.�5� ∙ �0 ε ��⁄mm) ∙ (5.0�mm) ∙ (��.7mm) ∙ (�.5) ε �.575mm ε = �.6�� Example Calculate the total capacitance for ℓ=5.08mm, (�.�5� ∙ �0 ��⁄mm) ∙ (5.0�mm) ∙ (��.7mm) ∙ (�.5) w=12.7mm, h=1.575mm, εr = 4.5 �.575mm ε (�.�5� ∙ �0–3 ��⁄mm) ∙ (5.0�mm) ∙ (��.7mm) ∙ (�.5) C(pF) = C(��) = (�.��7 ∙ �0 ��⁄mi�) ∙ (�00mi�) ∙ (500mi�) ∙ (�.5) �.575mm 6�mi� ε = �.6�� = �.6�� = �.6�� Example Calculate the total capacitance for∙ (�.5) ℓ=200mil, C(��) = (�.��7 ∙ �0 ��⁄mi�) ∙ (�00mi�) ∙ (500mi�) w=500mil, h=62mil, 6�mi� εr = 4.5 –4 C(��) = (�.��7 ∙ �0 ��⁄mi�) ∙ (�00mi�) ∙ (500mi�) ∙ (�.5) 6�mi� Texas Instruments Analog Engineer's Pocket Reference = �.6�� = �.6�� 61 PCB and Wire ti.com/precisionlabs Microstrip capacitance and inductance L(nH) = kL ∙ ℓ ∙ �� C(pF) = ( 0.�5.��∙ w∙ +h t ( kC ∙ ℓ ∙ (εr + 1.41) �� 5.�� ∙ h ( 0.� ∙w+t ( (83) Inductance for microstrip (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(��) = (� �H⁄�m) ∙ (�.5��m) ∙ �� ( 5.�� ∙ 0.�mm 0.� ∙ 0.�5�mm + 0.0�56mm ) = 15.2nH C(pF) = (0.�6��/�m) ∙ (�.5��m)(�.5 + �.��) = �.�� 5.�� ∙ 0.�mm �� ( ) 0.� ∙ 0.�5�mm + 0.0�56mm 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 PCB and Wire ti.com/precisionlabs Adjacent copper traces  ∙ t∙ ℓ k C(pF) ≈ C(pF) ≈  ≈ (85) Same layer d k∙ εr ∙ w∙ ℓ h (86) Different layers Where ℓ = length of the copper trace (mil, or mm) ε -3pF/mm, or k=2.247*10-4 pF/mil k = 8.854*10 t = thickness of trace (in mil, or mm) d = distance between traces if on same layer (mil, or mm) For imperial: Copper thickness (mils) = 1.37 • (number of ounces) w = width of trace. (mil, or mm) h = separation between planes. (mil, or mm) i.e. 1oz Cu = 1.37mils i.e. ½oz Cu = 0.684mils εr = PCB dielectric constant (εr = 4.5 for FR-4) Figure 47: Capacitance for adjacent copper traces Figure 48: Capacitance for adjacent copper traces 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) ≈ (�.�5� ∙ �0–� ��/mm) (0.0��mm) (�.5�mm) 63 0.�5�mm = 0.00�� Same �ayer (�.�5� ∙ �0–� ��/mm) (�.5mm) (0.6�5mm) (�.5�mm) = 0.04pF �.6mm Adja�e�t �ayers 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(pF) ≈ 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 � + �� C(pF) ≈ (�hd )] (87) Inductance for via kC ∙ εr ∙ h ∙ d1 d2 — d1 (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 Middle Layer GND Plane h 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.� �H⁄mm) ∙ (�.6mm) � + �� C(pF) ≈ ∙ �.6mm (�0.�mm )] = 1.2nH (0.0555��/mm) ∙ (�.5) ∙ (�.6mm) ∙ (0.�mm) �.5mm — 0.�mm = 0.�6�� 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 PCB and Wire ti.com/precisionlabs Type ZO Capacitance / length (pF/feet) Outside diameter (inches) dB attenuation /100 ft at 750 MHz Dielectric type Table 19: Coaxial cable information RG-58 53.5Ω 28.8 0.195 13.1 PE Application 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 9914 50Ω 26.0 0.405 4.0 PE RG-6 75Ω 20 0.270 5.6 PF RG-59/U 73Ω 29 0.242 9.7 PE 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 31 0.100 23.5 PE RG-178/U 50Ω 29 0.071 42.7 ST Texas Instruments Analog Engineer's Pocket Reference RF power to a few kW, up to several hundred MHz Video and CATV applications. RF to a few hundred watts, up to a few hundred MHz, sometimes to higher frequencies if losses can be tolerated Miniature coax used primarily for test equipment interconnection. Usually short runs due to higher loss. 65 PCB and Wire ti.com/precisionlabs Coaxial cable equations C ℓ L ℓ �πε D d μ ℓ 2π (89) Capacitance per length D�πε d L ℓC (90) Inductance per length μ1 μ 2π ε π (91) Characteristic impedance μ Where Where π ε L = inductance in henries (H) C = capacitance in farads (F) Ω Z = impedance in ohms (Ω) d = diameter of inner conductor ε ε ε ε D = inside diameter of shield, orΩdiameter of dielectric insulator ε = dielectric constant of insulator (ε = εr εo ) μ = magnetic permeability (μ = μr μo ) ε ε ε ε ℓ = length of the cable Insulation Figure 49: Coaxial cable cutaway Figure 49: Coaxial cable cutaway 66 Texas Texas Instruments Analog Engineer's Pocket Reference PCB and Wire ti.com/precisionlabs Table 20: Resistance per length for different wire types (AWG) Outside diameter Area dc resistance AWG Stds 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 in mm circular mils mm2 Ω / 1000 ft Ω / km 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 ti.com/precisionlabs Polypropylene Polyethylene (high density) at 90°C Polyvinylchloride Nylon at 105°C Imax (A) Imax (A) Imax (A) Imax (A) Kapton Teflon Silicon at 200°C Polyethylene Neoprene Polyvinylchloride (semi-ridged) at 80°C AWG Kynar Polyethylene Thermoplastic at 125°C Wire gauge Table 21: Maximum current vs. AWG Imax (A) 30 2 3 3 3 4 28 3 4 4 5 6 26 4 5 5 6 7 24 6 7 7 8 10 22 8 9 10 11 13 20 10 12 13 14 17 18 15 17 18 20 24 16 19 22 24 26 32 14 27 30 33 40 45 12 36 40 45 50 55 10 47 55 58 70 75 Note: Wire is in free air at 25°C Example What is the maximum current that can be applied to a 30 gauge Telon wire in a room temperature environment? What will the self-heating be? Answer Imax = 4A Wire temperature = 200°C 68 Texas Texas Instruments Analog Engineer's Pocket Reference Sensor Sensor ti.com/precisionlabs Sensor Thermistor • Resistive temperature detector (RTD) • Diode temperature characteristics• Thermocouple (J and K) • 69 Texas Instruments Analog Engineer's Pocket Reference Sensors Cost – –55°C < T < 150°C –55°C < T < 150°C –200°C < T < 850°C –200°C < T < 850°C Diode –55°C –55°C–55°C < T < 150°C < T < 150°C Thermocouple < T < 1800°C – –250°C –250°C < T < 1800°C High Low Low Accuracy Good accuracy at one temperature Less accurate over full range Excellent accuracy Poor accuracy without calibration Good accuracy with polynomial correction Linearity Very nonlinear. Follows reciprocal |of logarithmic function Fairly linear Nonlinearity < 4.5% of full scale Relatively simple quadratic function ≈ ≈ ≈linear Slope ≈ -2mV/C ≈ Fairly Slope varies according to current excitation, diode type, and diode processing Fairly linear Nonlinearity < 10% of full scale Complex 10th order polynomial Less rugged Depends on Type (can be rugged) Rugged Most rugged Construction Ω Ω ΩΩ Output range Applications General Ω Ω ΩΩ Ω Ω ΩΩ Typically 10s to 100s of kΩ full scale Very wide variation in resistance 18 to 390 Ω for PT100 180 to 3.9 kΩ for PT1000 0.4 to 0.8V 10s of millivolts General purpose Scientific and industrial Low cost temperature monitor Low cost linear response Industrial temperature measurement Requires excitation Requires excitation Requires excitation Self-powered Requires cold junction comp ti.com/precisionlabs Texas Instruments Analog Engineer's Pocket Reference Low Sensor Temp range Temp range RTD Table 22: Temperature sensor overview 70 Thermistor Sensor ti.com/precisionlabs Thermistor: Resistance to temperature, Steinhart-Hart equation 1 T R (92) Convert resistance to temperature for a thermistor R Where Where T = temperature in Kelvin a, b, c = Steinhart-Hart equation constants R = resistance in ohms Thermistor: Temperature to resistance, Steinhart-Hart equation x x [ x 1 T y c b 3c y x 2 y+ x x 4 x 2 [ (93) Convert temperature to resistance for a thermistor (94) Factor used in Equation 93 (95) Factor used in Equation 93 Where Where R = resistance in Ω T = temperature in Kelvin a, b, c = Steinhart-Hart equation constants x, y = Steinhart-Hart factors used in temperature to resistance equation Texas Instruments Analog Engineer's Pocket Reference 71 Sensor ti.com/precisionlabs RTD equation temperature to resistance R 0 0 0T R 0 0 0T (96) RTD resistance for T<0°C T 0 (97) RTD resistance for T>0°C Where Where Rrtd = resistance of RTD over temperature range of (–200°C < T < 850°C) Ω Ω RA0 = 100Ω for PT-100, 1000Ω for PT-1000 A0, B0, C0 = Callendar-Van Dusen coeficients Ω Ω T = temperature in degrees Celsius (°C) RTD equation resistance to temperature (T>0°C) RTD equation resistance to temperature (T>0° R R0 A (98) RTD resistance for T>0°C 2B Ω Where A Where RRTD = resistance of RTD over temperature range of (–200°C < T < 850°C) Ω RA0 = 100Ω A0, B0, C0 = Callendar-Van Dusen coeficients T = temperature in degrees Celsius (°C) Table 23: Callendar-Van Dusen coefficients for different RTD standards IEC-751 DIN 43760 BS 1904 ASTM-E1137 EN-60751 JISC 1604 US Industrial Standard D-100 American US Industrial Standard American A0 +3.9083E-3 ITS-90 +3.9739E-3 +3.9787E-3 +3.9692E-3 +3.9888E-3 B0 –5.775E-7 –5.870E-7 –5.8686E-7 –5.8495E-7 –5.915E-7 C0 –4.183E-12 –4.4E-12 –4.167E-12 –4.233E-12 –3.85E-12 Ω Ω Example What is the temperature given∙ an ITS-90 PT100 resistance of 120Ω? Answer ∙ 72 120 100 Texas Instruments Analog Engineer's Pocket Reference Sensor ti.com/precisionlabs RTD equation resistance to temperature (T<0°C) � T � � �� (99) RTD resistance for T<0°C � �� Where Where � T = temperature in degrees Celsius (°C) � RRTD = resistance of RTD over temperature range of (T<0°C) α � αi = polynomial coeficients for converting RTD resistance to temperature for T<0°C Table 24: Coefficients for 5th order RTD resistance to temperature α αα0 IEC-751 DIN 43760 BS 1904 ASTM-E1137 EN-60751 JISC 1604 US Industrial Standard D-100 American US Industrial Standard American ITS-90 –2.4202E+02 –2.3820E+02 –2.3818E+02 –2.3864E+02 –2.3791E+02 αα1 2.2228E+00 2.1898E+00 2.1956E+00 2.1973E+00 2.2011E+00 αα2 αα 2.5857E-03 2.5226E-03 2.4413E-03 2.4802E-03 2.3223E-03 3 –4.8266E-06 –4.7825E-06 –4.7517E-06 –4.7791E-06 –4.6280E-06 α4 –2.8152E-08 –2.7009E-08 –2.3831E-08 –2.5157E-08 –1.9702E-08 α5 1.5224E-10 1.4719E-10 1.3492E-10 1.4020E-10 1.1831E-10 α Ω Example T � ��.�7�� 0�� ∗ �60�� .�0�� 00� ∗ �60�� .�� 0�� ∗ �60�� Find the temperature given an ITS-90 resistance of 60 Ω. � ��.�� 0�� ∗ �60�PT100 � ��.6� Answer • • 60 • 60 • 60 60 Texas Instruments Analog Engineer's Pocket Reference 73 73 Sensor ti.com/precisionlabs Diode equation vs. temperature V� � I �kT I �kT �� I� q I� q (100) Diode voltage Where Where �kT I �kT I VV diode�� voltage vs.�temperature � � �� and current D�=� q I� q I� n = diode ideality factor (ranges from 1 to 2) k = 1.38 x 10-23 J/K, Boltzmann’s constant T = temperature in Kelvin q = 1.60 x 10-19 C, charge of an electron I = forward diode current in amps qV� � �T ��⁄�� ex� �� ISI�=�saturation current �kT I = saturation current I� � �T ��⁄�� ex� �� α Where qV� � �kT ( (101) Saturation current Where ISα= saturation current α = constant related to the cross sectional area of the junction VG = diode voltage vs. temperature and current n = diode ideality factor (ranges from 1 to 2) k = 1.38 x 10-23 J/K, Boltzmann’s constant T = temperature in Kelvin q = 1.60 x 10-19 C, charge of an electron 74 Texas Instruments Analog Engineer's Pocket Reference Sensor ti.com/precisionlabs Diode voltage versus temperature Figure 50 shows an example of the temperature drift for a diode. Depending on the characteristics of the diode and the forward current the slope and offset of this curve will change. However, typical diode drift is about –2mV/°C. A forward drop of about 0.6V is typical for room temperature. 0.6V is typical for room temperature. Figure 50: Diode voltage vs. temperature Figuredrop 50: Diode voltage drop vs. temperature 75 Texas Instruments Analog Engineer's Pocket Reference 75 Sensor ti.com/precisionlabs Type J thermocouples translating temperature to voltage (ITS-90 standard) � V� � � �� T�� (102) Thermoelectric voltage �� Where Where VT = thermoelectric voltage T = temperature in degrees Celsius ci = translation coeficients Table 25: Type J thermocouple temperature to voltage coefficients � 76 �to voltage Type�J thermocouple�temperature –219°C to 760°C 760°C to 1,200°C c0 0.0000000000E+00 2.9645625681E+05 c1 5.0381187815E+01 –1.4976127786E+03 c2 3.0475836930E-02 3.1787103924E+00 c3 –8.5681065720E-05 –3.1847686701E-03 c4 1.3228195295E-07 1.5720819004E-06 c5 –1.7052958337E-10 –3.0691369056E-10 c6 2.0948090697E-13 — c7 –1.2538395336E-16 — c8 1.5631725697E-20 — Texas Instruments Analog Engineer's Pocket Reference Sensor ti.com/precisionlabs Type J thermocouples translating voltage to temperature (ITS-90 standard) � T � � �� V� �� (103) Temperature �� Table 25: Type J thermocoup Table 26: Type J thermocouple voltage to temperature coefficients Type J thermocouple temperature to voltage c0 –219°C to 0°C 0°C to 760°C 760°C to 1,200°C 0.000000000E+00 0.000000000E+00 –3.113581870E+03 c1 1.952826800E-02 1.978425000E-02 3.005436840E-01 c2 –1.228618500E-06 –2.001204000E-07 –9.947732300E-06 c3 –1.075217800E-09 1.036969000E-11 1.702766300E-10 c4 –5.908693300E-13 –2.549687000E-16 –1.430334680E-15 c5 –1.725671300E-16 3.585153000E-21 4.738860840E-21 c6 –2.813151300E-20 –5.344285000E-26 — c7 –2.396337000E-24 5.099890000E-31 — c8 –8.382332100E-29 — — Texas Instruments Analog Engineer's Pocket Reference 77 Sensor ti.com/precisionlabs Type K thermocouples translating temperature to voltage (ITS-90 standard) � V� � � �� T�� V� � �� T�� e�� .�� Where (104) Thermoelectric voltage for T<0°C � (105) Thermoelectric voltage forT>0°C � Where VT = thermoelectric voltage T = temperature in degrees Celsius α α ci = translation coeficients α0, α1 = translation coeficients Table 27: Type K thermocouple temperature to voltage coefficients –219°C to 760°C 760°C to 1,200°C c0 0.0000000000E+00 –1.7600413686E+01 c1 3.9450128025E+01 3.8921204975E+01 c2 2.3622373598E-02 1.8558770032E-02 c3 –3.2858906784E-04 –9.9457592874E-05 c4 –4.9904828777E-06 3.1840945719E-07 c5 –6.7509059173E-08 –5.6072844889E-10 c6 –5.7410327428E-10 5.6075059059E-13 αc7 –3.1088872894E-12 –3.2020720003E-16 αc 78 8 –1.0451609365E-14 9.7151147152E-20 c9 –1.9889266878E-17 –1.2104721275E-23 c10 –1.6322697486E-20 — α0 — 1.1859760000E+02 α1 — –1.1834320000E-04 Texas Instruments Analog Engineer's Pocket Reference Sensor ti.com/precisionlabs Type K thermocouples translating voltage to temperature (ITS-90 standard) � T � � �� V� �� (106) Temperature �� Table 27: Type K thermocouple v Table 28: Type K thermocouple voltage to temperature coefficients c0 –219°C to 0°C 0°C to 760°C 760°C to 1,200°C 0.0000000E+00 0.0000000E+00 –1.3180580E+02 c1 2.5173462E-02 2.5083550E-02 4.8302220E-02 c2 –1.1662878E-06 7.8601060E-08 –1.6460310E-06 c3 –1.0833638E-09 –2.5031310E-10 5.4647310E-11 c4 –8.9773540E-13 8.3152700E-14 –9.6507150E-16 c5 –3.7342377E-16 –1.2280340E-17 8.8021930E-21 c6 –8.6632643E-20 9.8040360E-22 –3.1108100E-26 c7 –1.0450598E-23 –4.4130300E-26 — c8 –5.1920577E-28 1.0577340E-30 — c9 — –1.0527550E-35 — Texas Instruments Analog Engineer's Pocket Reference 79 Sensor ti.com/precisionlabs Table 29: Seebeck coefficients for different material Material Seebeck coefficient Material Seebeck coefficient Material Seebeck coefficient Aluminum 4 Gold 6.5 Rhodium 6 Antimony 47 Iron 19 Selenium 900 Bismuth –72 Lead 4 Silicon 440 Cadmium 7.5 Mercury 0.6 Silver 6.5 Carbon 3 Nichrome 25 Sodium –2.0 Constantan –35 Nickel –15 Tantalum 4.5 Copper 6.5 Platinum 0 Tellurium 500 Germanium 300 Potassium –9.0 Tungsten 7.5 Note: Units are μV/°C. All data at temperature of 0°C 80 Texas Instruments Analog Engineer's Pocket Reference A/D Conversion A/D conversion ti.com/precisionlabs ti.com/adcs 81 Texas Instruments Analog Engineer's Pocket Reference A/D conversion 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/precisionlabs Numbering systems: Binary, decimal, and hexadecimal Binary (Base-2) 0 1 0 1 2 3 4 5 6 7 8 9 01 2 3 4 5 6 7 8 9 A B C D E F Decimal (Base-10) Hexadecimal (Base-16) 2(1000) + 3(100) + 4(10) + 1(1) = 2,341 2(1000) + 3(100) + 4(10) + 1(1) = 2,341 Example conversion: todecimal decimal Example conversion: Binary Binary to Decimal Binary = LSD LSD 8 + 4 + 0 + 1 8 + 4 + 0 + 1 Example conversion: Decimal to binary Example conversion: Decimal to binary Binary Decimal LSD = LSD 128 + 64 + 32 + 8 + 4 = 236 A/D conversion MSD 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 Example conversion: Binary to hexadecimal Example conversion: Binary to hexadecimal Binary MSD LSD 128 + 64 + 16 + 8 + 1 = 217 Hexadecimal Conversion 128 + 64 + 16 + 8 + 1 = 217 8 + 4 + 1 = 13 (D) 8 8++14=+91 = 13 (D) 8+1=9 161 160 Hexadecimal D 9 MSD LSD 208 + 9 = 217 208 + 9 = 217 Example Conversion: Hexadecimal to decimal Example Conversion: Hexadecimal binary and decimal totohexadecimal Decimal (Base-10) Hexadecimal (Base-16) 0 1 2 3 4 5 6 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 A BCDE F Decimal Hexadecimal x16 3 x16 2 x16 1 x16 0 16 9903 R = 15 (F) = 2 6 A F MSD 7 LSD LSD 16 618 R = 10 (A) 16 38 R = 6 (6) 16 38 R = 2 (2) LSD MSD 2(4096) + 6(256) + 10(16) + 16(1) = 9903 LSD = Least Significant Digit MSD = Most Significant Digit ti.com/adcs Texas Instruments Analog Engineer's Pocket Reference 83 A/D Conversion ti.com/precisionlabs A/D Converter with PGA 5V VREF FSR 0 to 2.5V PGA x2 ADC 12 bits Digital I/O ADC in 0 to 5V Figure 51: ADC full-scale range (FSR) unipolar Full Scale Range (FSR) Unipolar VREF �S� = PGA �LSB = �S� 2n Example calculation for the circuit above. �S� = VREF �LSB = PGA �S� 2n 5V = 2.5V 2 = = 2.5V = 6�0.�5µV 212 ti.com/adcs 84 Texas Instruments Analog Engineer's Pocket Reference A/D Conversion ti.com/precisionlabs A/D Converter with PGA 2.5V VREF FSR 0 to ±1.25V PGA x2 ADC 12 bits Digital I/O ADC in 0 to ± 2.5V Figure 52: ADC full-scale range (FSR) Bipolar Full Scale Range (FSR) Bipolar �S� = VREF PGA �LSB = �S� 2n Example calculation for the circuit above. �S� = ±VREF ±2.5V = = ±1.25V ⇒ 2.5V PGA 2 �LSB = �S� 2n = 2.5V = 6�0.�5µV 212 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 2’s complement Decimal value Binary Decimal value Decimal value 11111111 255 127 –1 11000000 192 64 –64 10000000 128 0 –128 01111111 127 –1 127 01000000 64 –64 64 00000000 0 –128 0 Converting two’s complement to decimal: Converting two’s complement to decimal: Negative number example Negative number example Converting two’s complement to decimal: SIGN x4 x2 x1 Negative number example Step 1: Check sign bit This case is negative 1 0 1 1 LSD MSD Step 2: Invert all bits 0 1 0 0 Step 3: Add 1 0 1 0 1 Final result –(4+1) = –5 Converting two’s complement to decimal: –(4+1) = –5 Positive number example Converting two’s complement to decimal: Converting two’s complement to decimal: Positive number example Positive number example SIGN x4 Just add bit weights x2 0 4+1 1 = 50 1 LSD MSD Final result x1 4+1 = 5 ti.com/adcs 86 Texas Instruments Analog Engineer's Pocket Reference A/D Conversion ti.com/precisionlabs Table 31: LSB voltage vs. resolution and reference voltage voltage FSR Reference (Full-Scale Range) 1.024V 1.25V 2.048V 2.5V 4 mV 4.88 mV 8 mV 9.76 mV 10 1 mV 1.22 mV 2 mV 2.44 mV 12 250 µV 305 µV 500 µV 610 µV 14 52.5 µV 76.3 µV 125 µV 152.5 µV 16 15.6 µV 19.1 µV 31.2 µV 38.14 µV 18 3.91 µV 4.77 µV 7.81 µV 9.53 µV 20 0.98 µV 1.19 µV 1.95 µV 2.384 µV 22 244 nV 299 nV 488 nV 596 nV 24 61 nV 74.5 nV 122 nV 149 nV Resolution 8 Table 32: LSB voltage vs. resolution and reference voltage voltage FSR Reference (Full-Scale Range) Resolution 3V 3.3V 4.096V 5V 8 11.7 mV 12.9 mV 16 mV 19.5 mV 10 2.93 mV 3.222 mV 4 mV 4.882 mV 12 732 µV 806 µV 1 mV 1.221 mV 14 183 µV 201 µV 250 µV 305 µV 16 45.77 µV 50.35 µV 62.5 µV 76.29 µV 18 11.44 µV 12.58 µV 15.6 µV 19.07 µV 20 2.861 µV 3.147 µV 3.91 µV 4.768 µV 22 715 nV 787 nV 976 nV 1.192 µV 24 179 nV 196 nV 244 nV 298 nV ti.com/adcs Texas Instruments Analog Engineer's Pocket Reference 87 A/D Conversion ti.com/precisionlabs DAC definitions Resolution = n Number of Codes = 2n Full-Scale Range output = FSR LSB = FSR / 2n Full-scale output voltage = (2n – 1) • 1LSB Full-scale input code = 2n – 1 Transfer Function: Vout = Number of Codes • (FSR/2n) The number of bits used to quantify the output The number of input code combinations Sets the converter output range and the LSB voltage The voltage step size of each LSB Full-scale output voltage of the DAC Largest code that can be written Relationship between output voltage and input code FSR = 5V Output voltage (V) Full-scale voltage = 4.98V Resoluion 1LSB = 19mV Full-scale code = 255 Resoluion = 8bits Number of codes = 2n Figure 53: DAC transfer function Figure 51: DAC transfer function ti.com/adcs 88 Texas Instruments Analog Engineer's Pocket Reference A/D Conversion ti.com/precisionlabs ADC definitions Resolution = n Number of Codes = 2n Full-Scale Range input 1) = FSR LSB = FSR / 2n Full-scale input voltage = (2n – 1) • 1LSB Full-scale output code = 2n – 1 Transfer Function: Number of Codes = Vin / (FSR/2n) The number of bits used to quantify the input The number of output code combinations Sets the converter input range and the LSB voltage The voltage step size of each LSB Full-scale input voltage of the ADC Largest code that can be read Relationship between input voltage and output code Full-scale code=255 Input voltage (V) Figure 54: ADC transfer function Figure 52: ADC transfer function ti.com/adcs Full-scale Range FSR = 5V 87 Texas Instruments Analog Engineer's Pocket Reference 89 A/D Conversion ti.com/precisionlabs Quantization error of ADC Quantization error of ADC Quantization error 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 a function of the resolution of the converter. The quantization ⁄√�� LSBis 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 ti.com/adcs 90 Texas Instruments Analog Engineer's Pocket Reference A/D Conversion ti.com/precisionlabs Signal-to-noise ratio (SNR) from quantization noise only Max�MSSi��a� � �MSNoise � SN� � �S�/� �LSB √�� √� � �LSB � �� (107) √� �rom q�a�tizatio� o��y (108) Max�MSSi��a� �LSB � �� /√� � � �� √6 �MSNoise �LSB⁄√�� SN��dB� � �0�o��SN�� 0 �o��N � �0�o� � SN��dB� � 6.0�N � �.76 √6 � � (109) (110) (111) Where Where FSR = full-scale range of the A/D converter 1LSB = the voltage of 1LSB, VREF/2n N = the resolution of the A/D converter MaxRMSSignal = the rms equivalent of the ADC’s full-scale input RMSNoise = the rms noise from quantization SNR = the ratio of rms signal to rms noise Example �� SN� �is�� for √6 �� A/D converter with 5V reference, What the√6 SNR an�8-bit assuming only quantization noise? SN��dB� � �0�o�� .� dB Answer SN��dB� � 6.0�� .76 ��.� dB SNR = 2N-1 √6 = 28-1 √6 =�314 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 89 91 A/D Conversion ti.com/precisionlabs Total harmonic distortion (Vrms) % THD dB RMSDistortion MaxRMSSignal • V 100 V V V V • 100 RMSDistortion MaxRMSSignal (112) (107 (113) (108 Where • • Where THD = total harmonic distortion, the ratio of the rms distortion to the rms signal RMSDistortion = the rms sum of all harmonic components MaxRMSSignal = the rms value of the input signal V1 = the fundamental, generally the input signal V2, V3, V4, …Vn = harmonics of the fundamental Figure 56: Fundamental and harmonics in Vrms Figure 54: Fundamental and harmonics in Vrms ti.com/adcs 92 Texas Instruments Analog Engineer's Pocket Reference A/D Conversion ti.com/precisionlabs Total harmonic distortion (dBc) �� THD(dBc) THD � �0 �o� ��0� �� 0� �� 0� �� 0� �� THD � �0 �� o� ��0� �� 0� �� 0� �� (114) � �0� �� Where Where THD = total harmonic distortion. The ratio of the rms distortion to the rms signal D1 = the fundamental, generally the input signal. This is normalized to 0 dBc D2, D3, D4, …Dn = harmonics of the fundamental measured relative to the fundamental Figure 57: Fundamental and harmonics in dBc Figure 55: Fundamental and harmonics in dBc Example Determine THD for the example above. �� 0 ��0 �o� ��0 � �0 � ��0 �� 0 � �0 � �0 � �0 THDTHD � �0��o� -75 ) ) ) -95 ) -92 -110 ) ) Answer ) 10 10 10 � �7�.76 dB10 THDTHD �= �7�.76 dB10 THD(dBc) 10 log +10 +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 Ac signals Signal-to-noise and distortion (SINAD) and effective number of bits (ENOB) SINAD�dB� � �0 �o� � SINAD�dB� � ��0�o� ��0 �N�B � Max�MSSi��a� √�MSNoise� � �MSDistortio�� 0 � �� SINAD�dB� � �.76dB 6.0� (115) (110) (116) (111) (117) (112) Where Where MaxRMSSignal = the rms equivalent of the ADC’s full-scale input RMSNoise = the rms noise integrated across the A/D converters RMSDistortion = the rms sum of all harmonic components 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. SNR = the ratio of rms signal to rms noise Example Calculate the SNR, THD, SINAD and ENOB given the following information: MaxRMSSignal = 1.76 Vrms RMSDistortion = 50 μVrms RMSNoise = 100 �.76 μVrms Vrms SN��dB� � �0 �o� � � � ��.� dB �00 μVrms Answer THD�dB� SNR dB � �0 �o� � 50 μVrms 1.76 Vrms � � � �0.� dB �.76 Vrms �.76V rms � � ��.� dB SINAD�dB� THD dB � �0 �o� � μVrms�� 50 μVrms�� 00 1.76 Vrms ��.�1.76V �� .� �� rms� �� 0 � SINAD dB � ��0 �o� ��0� SINAD�dB� ��.�dB � �.76dB �N�B � ��.65 SINAD�dB 10 6.0� � ��.� dB 6.02 ti.com/adcs 94 Texas Instruments Analog Engineer's Pocket Reference A/D Conversion ti.com/precisionlabs Dc signals Noise free resolution and effective resolution Noise�ree�eso��tio� � �o� � � �� PeaktoPeakNoisei�LSB �� e�ti�e�eso��tio� � �o� � � � rmsNoisei�LSB (118) (119) PeaktoPeakNoisei�LSB � 6.6 � rmsNoisei�LSB (120) ��e�ti�e�eso��tio� � Noise�ree�eso��tio� � �.7 (121) Note: The maximum effective resolution is never greater than the A Note: The maximum effective resolution is never greater than the ADC resolution. For example, a 24-bit converter cannot have an effective resolution greater than 24 bits. Example What is the noise-free resolution and effective resolution for a 24-bit converter assuming the peak-to-peak noise is 7 LSBs? �� Answer Noise�ree�eso��tio� � �o� � � � � ��.� 72 7 �� e�ti�e�eso��tio� � �o� � � � � ��.� 7 2 6.6 7 6.6 ��e�ti�e�eso��tio� � ��.� � �.7 � ��.� ti.com/adcs Texas Instruments Analog Engineer's Pocket Reference 93 95 A/D Conversion ti.com/precisionlabs Time Constant R VIN A/D VIN C Figure 58: Settling time for RC circuit-related to A/D converters Table 33: Conversion accuracy achieved after a specified time Settling time in time constants (NTC) Accuracy in bits (N) Settling time in time constants (NTC) Accuracy in bits 1 1.44 10 14.43 2 2.89 11 15.87 3 4.33 12 17.31 4 5.77 13 18.76 5 7.21 14 20.20 6 8.66 15 21.64 7 10.10 16 23.08 8 11.54 17 24.53 9 12.98 18 25.97 N � �o� � �e�� (122) (117) Where Where N = the number of bits of accuracy the RC circuit has settled to after NTC number of 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 A/D Conversion ti.com/precisionlabs Table 34: Time required to settle to a specified conversion accuracy Accuracy in bits (N) Settling time in time constants (NTC) Accuracy in bits (N) Settling time in time constants (NTC) 8 5.5 17 11.78 9 6.24 18 12.48 10 6.93 19 13.17 11 7.62 20 13.86 12 8.32 21 14.56 13 9.01 22 15.25 14 9.70 23 15.94 15 10.40 24 16.64 16 11.04 25 17.33 N�� (123) (118) Where Where NTC = the number of time constants required 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 97 Texas Instruments Analog Engineer's Pocket Reference 95 ti.com/precisionlabs Notes 6 98 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. 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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 TI E2E™ Community 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 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 Applications Audio www.ti.com/audio Automotive and Transportation www.ti.com/automotive Amplifiers amplifier.ti.com Communications and Telecom www.ti.com/communications Data Converters dataconverter.ti.com Computers and Peripherals www.ti.com/computers DLP® Products www.dlp.com Consumer Electronics www.ti.com/consumer-apps DSP dsp.ti.com Energy and Lighting www.ti.com/energy Clocks and Timers www.ti.com/clocks Industrial www.ti.com/industrial Interface interface.ti.com Medical www.ti.com/medical Logic logic.ti.com Security www.ti.com/security Power Mgmt power.ti.com Space, Avionics and Defense www.ti.com/space-avionics-defense Microcontrollers microcontroller.ti.com Video and Imaging www.ti.com/video RFID www.ti-rfid.com OMAP Applications Processors www.ti.com/omap TI E2E Community e2e.ti.com Wireless Connectivity www.ti.com/wirelessconnectivity Mailing Address: Texas Instruments, Post Office Box 655303, Dallas, Texas 75265 Copyright © 2016, Texas Instruments Incorporated

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