AN1001 IC Temperature Sensor Accuracy Compensation with a PIC® Microcontroller Author: SOLUTION APPROACH Ezana Haile Microchip Technology Inc. INTRODUCTION Microchip Technology Inc. provides a number of analog and serial output Integrated Circuit (IC) temperature sensors. Typically, these sensors are accurate at room temperature within one degree Celsius (±1°C). However, at hot or cold temperature extremes, the accuracy decreases nonlinearly. Normally, that nonlinearity has a parabolic shape. This application note derives an equation to describe the typical nonlinear characteristics of a sensor, which is used to determine compensation for the sensor's accuracy error over a specified range of operating temperatures. A PIC® microcontroller unit (MCU) can compute the equation and provide a temperature reading with higher accuracy. This application note is based on MCP9700 and MCP9701 analog-output temperature sensors and MCP9800 serial-output temperature sensors. Silicon characterization data is used to determine the nonlinear sensor characteristics. From this data, an equation is derived that describes the typical performance of a sensor. When the corresponding coefficients for the equation are determined, the coefficients are used to compute the compensation for the typical sensor’s nonlinearity. The error distribution is provided using an average and ±1 standard deviation (± before and after compensation. A total of 100 devices were used as representative for the MCP9700 and MCP9701, while 160 devices were used for the MCP9800. Figure 1 shows the typical sensor accuracy before and after compensation. It illustrates that the compensation provides an accurate and linear temperature reading over the sensor operating temperature range. A PIC MCU is used to compute the equation and compensate the sensor output to provide a linear temperature reading. Typical Accuracy (°C) 3.0 2.0 Sensor Accuracy 1.0 0.0 -1.0 Compensated Sensor Accuracy -2.0 -3.0 -55 -35 -15 FIGURE 1: 5 25 45 65 Temperature (°C) 85 105 125 Typical Sensor Accuracy Before and After Compensation. 2010-2015 Microchip Technology Inc. DS00001001C-page 1 AN1001 SENSOR ACCURACY The typical sensor accuracy over the operating temperature range has an accuracy error curve. At hot and cold temperatures, the magnitude of the error increases exponentially, resulting in a parabolic-shaped error curve. The following figures show the average and ±1°C standard deviation of the sensor accuracy curve for the MCP9800, MCP9700 and MCP9701 sensors. The accuracy specification limits for these sensors are published in the corresponding data sheets as plotted in Figure 2, Figure 3 and Figure 4. Note that due to the sensor nonlinearity at temperature extremes, the accuracy specification limits are widened. The reduced accuracy at temperature extremes can be compensated to improve sensor accuracy over the range of operating temperatures. 3.0 Accuracy (°C) 2.0 1.0 Spec. Limit 0.0 -1.0 + V Average - V -2.0 -3.0 -55 -35 -15 5 25 45 65 Temperature (°C) FIGURE 2: (160 parts). 85 105 125 MCP9800 Accuracy 6.0 Accuracy (°C) 4.0 Spec. Limit 2.0 0.0 -2.0 + V Average - V -4.0 -55 -35 -15 5 25 45 65 Temperature (°C) FIGURE 3: (100 parts). 85 105 125 MCP9700 Accuracy 6.0 Accuracy (°C) 4.0 Spec. Limit 2.0 0.0 -2.0 -4.0 + V Average - V -15 5 FIGURE 4: (100 parts). DS00001001C-page 2 25 45 65 85 Temperature (°C) 105 125 MCP9701 Accuracy 2010-2015 Microchip Technology Inc. AN1001 SENSOR THEORY Temperature sensors use a fully turned-on PNP transistor to sense the ambient temperature. The voltage drop across the base-emitter junction has the characteristics of a diode. The junction drop is temperature dependent, which is used to measure the ambient temperature. Equation 1 shows a simplified equation that describes the diode forward voltage. EQUATION 1: DIODE FORWARD VOLTAGE VPTAT provides a linear voltage change with a slope of (86 µV/°C)*ln(N)|N=10 = 200 µV/°C. The voltage is either amplified for analog output sensors or is interfaced to an Analog-to-Digital Converter (ADC) for digital sensors. The accuracy of VPTAT over the specified temperature range depends on the matching of both forward current (IF) and saturation current (IS) of the two sensors . Any mismatch in these variables creates inaccuracy in the temperature measurement. The mismatch contributes to the temperature error or nonlinearity. The nonlinearity is described using a 2nd order polynomial equation. kT A I F VF = --------- ln -----, IF » I S q IS Where: k = Boltzmann’s Constant (1.3807 x 10-23 J/K) q = Electron Charge (1.602 x 10-19 coulombs) TA = Ambient Temperature IF = Forward Current IS = Saturation Current IS is a constant variable defined by the transistor size. A constant forward current (IF) is used to bias the diode, which makes the temperature TA the only changing variable in the equation. However, IS varies significantly over process and temperature. The variation makes it impossible to reliably measure the ambient temperature using a single transistor. To minimize IS dependency, a two-diode solution is used. If both diodes are biased with constant forward currents of IF1 and IF2, and the currents have a ratio of N (IF2/IF1 = N), the difference between the forward voltages (VF) has no dependency on the saturation currents of the two diodes, as shown in Equation 2. VF is also called Voltage Proportional to Absolute Temperature (VPTAT). EQUATION 2: VPTAT V F = V F1 – VF2 I F1 ------kT A IS V F = --------- ln ---------------q N I F1 ----------------IS kT A VF = --------- ln N q V F = VPTAT Where: VF = Forward Voltages IF = Forward Currents VPTAT = Voltage Proportional to Absolute Temperature 2010-2015 Microchip Technology Inc. DS00001001C-page 3 AN1001 FITTING POLYNOMIALS TO THE ERRORS The accuracy characterization data is used to derive a 2nd order equation that describes the sensor error. The equation is used to improve the typical sensor accuracy by compensating for the sensor error. 1ST ORDER ERROR Error T_1 = EC 1 T A – T cold + Error T_cold Where: ErrorT_1 = 1st order temperature error Quadratic Fit Derivation Linear Fit Derivation To capture the parabolic-shaped accuracy error between the temperature extremes (Figure 5), a 2nd order term and the corresponding coefficient must be computed. 3.0 2.0 Accuracy (°C) EQUATION 4: 1.0 0.0 -1.0 MCP9800 MCP9700 -2.0 -3.0 -55 -35 -15 5 25 45 65 Temperature (°C) FIGURE 5: 85 105 125 Typical Accuracy Plot. Figure 5 shows a typical accuracy curve which indicates that the accuracy error magnitudes are not the same at hot and cold temperatures. There is a 1st order error slope, or temperature error coefficient (EC1), from -55° to +125°C. The error coefficient is calculated using an end-point-fit method: EQUATION 3: ERROR SLOPE T A = T hot – T cold Error EC 1 = ------------------T A Where: Thot = Highest Operating Temperature Tcold = Lowest Operating Temperature ErrorT_hot = Error at Highest Operating Temperature ErrorT_cold = Error at Lowest Operating Temperature EC1 = 1st Order Error Coefficient Once the error slope is calculated, the corresponding offset is determined at cold by adjusting the error at cold temperature as shown in Equation 4. DS00001001C-page 4 Equation 5 shows that the 2nd order temperature error coefficient, EC2, is solved by specifying a temperature TA where the calculated 2nd order error, ErrorT_2, is equal to the known error at TA. For example, if TA is +25°C and ErrorT_2 is equal to the temperature error at +25°C, then Equation 5 is rearranged to solve for EC2 as shown in Equation 6. EQUATION 5: 2ND ORDER ERROR Error T_2 = EC2 T hot – T A T A – T cold + Error T_1 Where: ErrorT_2 = 2nd order temperature error EC2 = 2nd order error coefficient Equation 5 shows that when TA is equal to Thot or Tcold , the 2nd order term is forced to zero with no error added to the 1st order error term. This is because the error at the Thot and Tcold temperature extremes is included in the 1st order error (ErrorT_1). EQUATION 6: 2ND ORDER ERROR COEFFICIENT Error T_2 – Error T_1 EC 2 = ------------------------------------------------------------- T hot – T A T A – T cold Equation 7 shows the complete 2nd order polynomial equation that is used to compensate the sensor error. EQUATION 7: 2ND ORDER POLYNOMIAL EQUATION Error T_2 = EC 2 T hot – T A T A – T cold +EC 1 T A – T cold + Error T_cold 2010-2015 Microchip Technology Inc. AN1001 ACCURACY COMPENSATION Typical Results nd Equations 8, 9 and 10 show the 2 order error equation of the tested parts for the MCP9800, MCP9700 and MCP9701, respectively. Since these devices have functional differences, the operating temperature range and temperature error coefficients differ. To achieve higher accuracy in a temperature monitoring application, using Equations 8, 9 and 10 can compensate for the sensor error as shown in Equation 11. EQUATION 11: MCP9800 2ND ORDER EQUATION EQUATION 8: Error T_2 = EC 2 125 C – T A T A – – 55 C T compensated = T sensor – Error T_2 Tsensor = Sensor Output Tcompensated = Compensated Sensor Output Where: EC1 = 7 x 10-3 °C/°C Error-55 = -1.5°C For example, if the MCP9800 temperature output Tsensor = +65°C, the compensated temperature Tcompensated is 64.6°C as shown below. T compensated = 65 C – Error T_2 MCP9700 2ND ORDER EQUATION EQUATION 9: +EC 1 T A – – 55 C + Error -55 T compensated = 64.6 C +EC 1 T A – – 40 C + Error -40 EC2 = -244 x 10-6°C/°C2 EC1 = 2 x 10-12°C/°C 0 °C/°C Error-40 = 2°C Figures 6, 7 and 8 show the average sensor accuracy with the 2nd order error compensation for all tested devices. The figures indicate that, on average, the sensor accuracy over the operating temperature can be improved to ±0.2°C for the MCP9800, and ±0.05°C for the MCP9700 and MCP9701. MCP9701 2ND ORDER EQUATION Error T_2 = EC 2 125 C – T A T A – – 15 C +EC 1 T A – – 15 C + Error -15 Where: EC2 = -200 x 10-6 °C/°C2 EC1 = 1 x 10-3 °C/°C Error-15 = 1.5°C The preceding equations describe the typical device temperature error characteristics. 2010-2015 Microchip Technology Inc. 0.3 0.2 Accuracy (°C) EQUATION 10: T A = 65 C = 65 C + EC2 125 C – 65 C 65 C – – 55 C Error T_2 = EC 2 125 C – T A T A – – 40 C Where: T A = T sensor Where: +EC 1 T A – – 55 C + Error -55 EC2 = 150 x 10-6 °C/°C2 TEMPERATURE COMPENSATION 0.1 0.0 -0.1 -0.2 Average -0.3 -55 -35 -15 5 25 45 65 Temperature (°C) 85 105 125 FIGURE 6: MCP9800 Average Accuracy After Compensation (160 parts). DS00001001C-page 5 0.3 6.0 0.2 4.0 Accuracy (°C) Accuracy (°C) AN1001 0.1 0.0 -0.1 2.0 0.0 + V Average - V -2.0 -0.2 Average -0.3 -4.0 -55 -35 -15 5 25 45 65 Temperature (°C) 85 105 125 -55 -35 -15 6.0 0.2 4.0 Accuracy (°C) 0.3 0.1 0.0 -0.1 85 105 125 Spec. Limit 2.0 0.0 + V Average - V -2.0 -0.2 5 25 45 65 Temperature (°C) FIGURE 10: MCP9700 Accuracy After Compensation (100 parts). FIGURE 7: MCP9700 Average Accuracy After Compensation (100 parts). Accuracy (°C) Spec. Limit Average -4.0 -0.3 -15 5 25 45 65 85 Temperature (°C) 105 125 -15 5 25 45 65 85 Temperature (°C) 105 125 FIGURE 8: MCP9701 Average Accuracy After Compensation (100 parts). FIGURE 11: MCP9701 Accuracy After Compensation (100 parts). Figures 9, 10 and 11 show an average and ±1 standard deviation of sensor accuracy for the tested parts with the 2nd order error compensation. When comparing the compensated accuracy from Figures 9, 10 and 11 with the uncompensated accuracy from Figures 2, 3 and 4, the accuracy error distribution is shifted towards 0°C accuracy, providing a linear temperature reading. 3.0 Accuracy (°C) 2.0 1.0 Spec. Limit 0.0 -1.0 + V Average - V -2.0 -3.0 -55 -35 -15 5 25 45 65 Temperature (°C) 85 105 125 FIGURE 9: MCP9800 Accuracy After Compensation (160 parts). DS00001001C-page 6 2010-2015 Microchip Technology Inc. AN1001 The 2nd Order Temperature Coefficient nd Among the compensations, the 2 order temperature coefficient variable EC2 was evaluated at +25°C. For most applications, the compensation characteristics at this temperature are adequate. However, changing the temperature at which EC2 is evaluated provides relatively higher accuracy at narrower temperature ranges. For example, Figure 12 shows the MCP9700 EC2 evaluated at 0°, +25° and +90°C. CALIBRATION Calibration of individual IC sensors at a single temperature provides superior accuracy for high-performance, embedded-system applications. Figure 13 shows that if the MCP9700 is calibrated at +25°C and the 2nd order error compensation is implemented, the typical sensor accuracy becomes ±0.5°C over the operating temperature range. 0.05 0.04 0.03 0.02 0.01 0.00 -0.01 -0.02 -0.03 -0.04 -0.05 4.0 MCP9700 Accuracy (°C) Accuracy (°C) 6.0 2.0 Spec. Limits 0.0 + V Average - V -2.0 EC2 @ 90°C EC2 @ 25°C EC2 @ 0°C -55 -35 -15 -4.0 -50 0 25 50 75 100 125 Temperature (°C) 5 25 45 65 85 105 125 Temperature (°C) FIGURE 12: MCP9700 Average Accuracy with Varying EC2 . -25 FIGURE 13: Accuracy. MCP9700 Calibrated Sensor When comparing EC2 at 0° and +25°C, accuracy is higher at cold rather than hot temperatures. However, for EC2 evaluated at temperatures higher than +25°C, accuracy is higher at hot rather than cold temperatures. However, the magnitude of accuracy error difference among the various EC2 values is not significant. Therefore, EC2 evaluated at +25°C provides practical results. 2010-2015 Microchip Technology Inc. DS00001001C-page 7 AN1001 COMPENSATION USING PIC® MICROCONTROLLERS A PIC MCU can implement the 2nd order accuracy error compensation for embedded temperature-monitoring systems. The equation is relatively easy to implement in a 16-bit core MCU since built-in math functions are readily available. However, 12 and 14-bit cores require firmware implementation of some math functions, such as 16-bit add, subtract, multiply and divide. This application note includes firmware that can compute and implement the compensation variables. The file AN1001 Source Code.zip includes the MCP9700 and MCP9800 compensation firmware versions. These firmware versions are intended to be included in an existing embedded system firmware that uses a PIC MCU. All registers required to execute this routine are listed within the firmware. Once the temperature data from the device is retrieved using a serial interface or ADC input, the binary data must be loaded to the Bargb0 and Bargb1 registers. Detailed instructions are included in the firmware files. Figure 14 shows the firmware flowchart. Load TA Determine 2nd Order Error Determine 1st Order Error Add 1st and 2nd Order Error to ErrorT_cold Subtract Total Error from TA Load Compensated TA FIGURE 14: Firmware Flowchart. TEST RESULTS The MCP9800 and MCP9700 demo boards (MCP9800DM-PCTL and MCP9700DM-PCTL, respectively) were used to evaluate the compensation firmware. A constant temperature air stream was applied directly to the temperature sensors. A thermocouple was used to accurately measure the air stream temperature and compare the sensor outputs. TABLE 1: MEASUREMENT ACCURACY TEST RESULTS Temperature Error Temperature MCP9700 MCP9800 W/O W W/O W -40°C 0.9 0.2 -1.0 0.1 -25°C 0.6 0.2 -0.4 0.2 0°C 0.4 0.4 0.2 0.1 +25°C 0.3 0.6 0.1 0.1 +40°C 0.4 0.7 0.1 0.2 +90°C 1.2 0.8 0.3 0.3 +110°C 1.8 0.7 0.6 0.3 +125°C 2.3 0.6 0.9 0.1 Note 1: The “W/O” and “W” columns indicate accuracy without and with compensation. The test result in Table 1 shows the accuracy improvement achieved using compensation firmware routines. At hot and cold temperatures, accuracy is improved by approximately 1° to 2°C, respectively. CONCLUSION The nonlinear accuracy characteristics of a temperature sensor is compensated for higher-accuracy embedded systems. The nonlinear accuracy curve has a parabolic shape that is described using a 2nd order polynomial equation. Once the equation is determined, it is used to compensate the sensor output. On average, the accuracy improvement using compensation is ±2°C (for all tested devices) over the operating temperature range. The compensation also improves the wide temperature accuracy specification limits at hot and cold temperature extremes. A PIC MCU can compute the equation and compensate the sensor output using the attached firmware. WORK CITED . Bakker, A., and Huijsing, J. (2000). High-Accuracy CMOS Smart Temperature Sensors. Boston: Kluwer Academic Publishing. 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