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SLUA398 AT103 bq20z70 bq20z80 bq20z90 - Datasheet Archive

Application Report SLUA398 SLUA398 October 2006 Thermistor Coefficient Calculator for TI Advanced Fuel Gauges Doug Williams . Battery Management ABSTRACT TI advanced fuel-gauge battery-management ICs use a polynomial model to translate the voltage measured across the thermistor terminals into a temperature value. While the recommended Semitec AT103 AT103 is readily available, some customers prefer to use an alternate device. This report describes the use of a companion Excel® spreadsheet that automates coefficient calculation for a given thermistor. 1 Introduction The firmware algorithm in TI advanced fuel gauge battery management ICs uses a polynomial model to translate voltage measured across the thermistor terminals into temperature. While the recommended Semitec AT103 AT103 is readily available in various shapes, some customers prefer to use an alternate device. This report describes the use of a companion Excel spreadsheet that automates the calculation of coefficients for a given thermistor. The Thermistor Coefficient Calculator is a Microsoft® Excel spreadsheet, which is available as a zip file in the same location as this report. It can be used for various advanced fuel gauge ICs such as the bq2084, bq20z70 bq20z70, bq20z80 bq20z80, bq20z90 bq20z90, etc. 2 Theory of Operation Solver, an add-in tool for Excel, which is part of the standard installation, is used in this case to find a solution to a set of 3rd order polynomials. Given a few points on an unknown curve, it finds the coefficients of a cubic polynomial equation that best fits the available data. The fuel-gauge device firmware uses the cubic polynomial along with the dataflash-based coefficients at 1-s intervals when converting the A/D reading from the thermistor into a temperature value. Solver's job is to minimize the value in cell B33 (see Figure 1), which is the sum of the norms for each known data point. The norms are simply the square of the difference between what you want and what you get. Solver updates the polynomial coefficients in E25 ~ E28 for the best overall fit. You can, of course, change the coefficients manually to see what happens. The values in E31 ~ E36 should be programmed into the respective fuel gauge dataflash locations. Excel, Microsoft are registered trademarks of Microsoft Corporation. SLUA398 SLUA398 October 2006 Submit Documentation Feedback Thermistor Coefficient Calculator for TI Advanced Fuel Gauges 1 www.ti.com Thermistor Tables A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Temperature -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 R1 R2 Vref Vadref ADres Vadmax 30 Rs 31 Vs 32 33 Sum of Norms: 34 35 36 37 B Resistance Calculation of A/DData Flash Thermistor Constants E Count Calculation of best-fit Calculation of (using 3rd order A/D Count polynomial) Norm 67770 53410 42470 33900 27280 22050 17960 14690 12090 10000 8313 6940 5827 4911 4160 3536 3020 2588 2228 1924 1668 25982 25309 24537 23646 22657 21562 20391 19143 17853 16537 15220 13920 12668 11469 10344 9293 8328 7445 6648 5927 5283 8450 61900 3.3 3.3 0.000100708 2.64 7435.03909 2.903624733 -19.55338015 -15.13893104 -10.40258881 -5.334192226 -0.155141665 5.103094832 10.26512627 15.35518484 20.30002249 25.1540882 29.96452929 34.80931675 39.69777558 44.70168577 49.78340483 54.9514734 60.11969589 65.25409511 70.25884332 75.11718798 79.74269257 Polynomial coefficients A0 A1 A2 A3 0.199469 0.019302 0.162078 0.111684 0.024069 0.010629 0.070292 0.126156 0.090013 0.023743 0.001258 0.03636 0.09134 0.088991 0.046913 0.002355 0.014327 0.064564 0.067 0.013733 0.066207 F G HI Instructions 1. Insert Temperature and Resistance values in colums A&B 2. Verify A/D count value in cell C2 does not exceed 27000 If necessary, raise value of R1 in cell B24 to a higher standard resistor value so that C2 is under 27000. 3. Select Solver from Tools menu. Use Add-Ins menu if not available. 4. Set Target Cell to $B$33 5. Choose Equal to: Value Of 0 (choose "Value Of", enter 0 6. Set "By Changing Cells" to $E$25:$E$28 7. Press Solve button - Accept the solution, even though not "feasible" 8. Compare columns A and D to evaluate the accuracy A lower number in B33 indicates a better fit 9. Linearity may be improved by changing R2 in some cases 10. Insure none of the values in columns J or K exceed +/- 32767 J K L Partial Result Bounds Check 10248.5197 -3774.69 10557.1208 -3760.757 10911.1179 -3752.579 11319.6818 -3753.509 11773.1833 -3767.55 12275.2905 -3799.063 12812.2472 -3851.329 13384.5119 -3928.155 13976.0355 -4030.476 14579.4813 -4158.854 15183.3856 -4311.593 15779.4947 -4486.165 16353.5936 -4676.647 16903.3895 -4879.628 17419.2531 -5088.375 17901.1844 -5299.392 18343.6807 -5506.755 18748.5763 -5707.915 19114.0371 -5898.852 19444.6483 -6079.239 19739.9516 -6246.513 Value 4032.48 -7837.818 22162.45 -30050.77 Data Flash Thermistor Constants A0 (* Coefficient 4) 4032 A1 (* Coefficient 3) -7838 A2 (* Coefficient 2) 22162 A3 (* Coefficient 1) -30051 Min A/D 0 Max Temp (K) 4032 * The polynomial coefficients have alternate names in some fuel gauges 1.330484661 Figure 1. Thermistor Coefficient Calculator Spreadsheet 3 Thermistor Tables Enter the data for the desired thermistor into cells B2 ~ B22 which correspond to the temperatures in column A. Some vendors include resistance tables in their catalog; others provide a calculator for you to generate them. If a given vendor only supplies a small table with multiples of 10°C, then use it as-is in the spreadsheet, but include some of the degree-resistance pairs twice to fill up the table of 21 pairs. 4 Circuit Modifications For maximum accuracy, the voltage input voltage to the A/D converter in the fuel gauge should be limited to around 82% of the reference voltage, which is the same as V CC in this case. Looking at it another way, the A/D count should not exceed 27000 (82% of full scale 32767) counts for low temperature readings that must be accurate. Column C displays the expected A/D count for a given temperature. Measurements between 27000 and 32767 will be degraded somewhat, but still useful. The recommended thermistor circuit, where R1 = 8.45 k, R2 = 61.9 k and Thermistor = 10 k at 25°C, should satisfy the above requirement in most cases. However, if a 10-k thermistor cannot be used, the fixed resistors should be modified in cells B24 and B25 to optimize the measurement. B25 is used to linearize the thermistor curve somewhat, enhancing the polynomial curve-fitting accuracy. 2 Thermistor Coefficient Calculator for TI Advanced Fuel Gauges SLUA398 SLUA398 October 2006 Submit Documentation Feedback IMPORTANT NOTICE Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, modifications, enhancements, improvements, and other changes to its products and services at any time and to discontinue any product or service without notice. Customers should obtain the latest relevant information before placing orders and should verify that such information is current and complete. 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