APPLICATION NOTE RX21A Group Calibration and Compensation for the ΔΣ A/D Converter R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Abstract This document describes the methods of calibration and compensation for the 24-bit ΔΣ A/D converter (DSAD) in the RX21A Group. The RX21A is designed to achieve a low cost solution of the 3-phase power meter that satisfies IEC 62052-11 and IEC 62053-22 requirements. IEC 62053-22 standardizes measurement errors in the range of current 0.01In ≤ I ≤ Imax. To measure current which varies in this wide range, the RX21A DSAD can amplify differential input from x1 to x64 and single-ended input from x1 to x4 using the on-chip PGA. Furthermore the G version of RX21A has the calibration data of the accurate gains, which are programmed before shipping, for available gain settings. With these calibration data, the user can calibrate gains for all gain settings by choosing only one gain setting and calibrating the gain for the selected gain setting. The measurement accuracy after calibration at the reference temperature satisfies the class 0.2S meter requirements standardized in IEC 62053-22. IEC 62052-11 and IEC 62053-22 also standardize measurement errors due to temperature fluctuations in the ranges of temperature. The measurement values with the RX21A DSAD are influenced by temperature. However the temperature characteristics of the RX21A have been clarified. Thus the measured values can be compensated using the powerful calculation ability of the RX21A. Even if not using an external reference power supply with high precision, the measurement accuracy after compensation by the RX21A DSAD satisfies the requirement for the class 0.5S meter standardized by IEC 62053-22 in the temperature range from -25°C to +75°C. This range is wider than the required range, which is from -25°C to +55°C, for outdoor use meters by IEC 62052-11. Products - RX21A Group 100-pin package with a ROM size between 256 KB and 512 KB - RX21A Group 80-pin package with a ROM size between 256 KB and 512 KB - RX21A Group 64-pin package with a ROM size between 256 KB and 512 KB Note: Only the G-version (operating temperature: -40°C to +105°C) of RX21A is the target device in this application note. R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 1 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter Contents 1. Specifications ..................................................................................................................................... 3 2. Operation Confirmation Conditions .................................................................................................... 3 3. Hardware ............................................................................................................................................ 4 4. Mechanism of Gain Calibration .......................................................................................................... 5 4.1 Gain Calibrations Among Channels and Among Gains on a Channel ........................................ 5 4.2 Device Gain ................................................................................................................................. 5 4.3 Influences of External Input Resistor and Internal Input Resistor................................................ 6 4.4 System Gain Calibration .............................................................................................................. 7 5. Result of the System Gain Calibration ............................................................................................... 9 6. Temperature Characteristics and Compensation Method................................................................ 10 6.1 Temperature Characteristics...................................................................................................... 10 6.2 Device Gain ............................................................................................................................... 11 6.3 VBGR ......................................................................................................................................... 12 6.4 Input Impedance ........................................................................................................................ 13 6.5 Compensation for the Temperature Characteristics of the System Gain .................................. 13 6.6 Coefficients of the Temperature Characteristics in the RX21A Group ...................................... 14 7. Compensation Results of the Temperature Characteristics............................................................. 15 7.1 Temperature Characteristics of the VBGR ................................................................................ 15 7.2 System Gain of the Differential Input Pins ................................................................................. 16 7.3 System Gain of Single-Ended Input Pin .................................................................................... 18 8. Software ........................................................................................................................................... 20 8.1 Operation Overview ................................................................................................................... 20 8.2 Required Memory Size .............................................................................................................. 20 8.3 File Composition ........................................................................................................................ 20 8.4 Constants ................................................................................................................................... 21 8.5 Variables .................................................................................................................................... 21 8.6 Functions.................................................................................................................................... 23 8.7 Function Specifications .............................................................................................................. 24 8.8 Flowcharts .................................................................................................................................. 26 8.8.1 Main Processing ................................................................................................................. 26 8.8.2 Coefficient Initialization for Gain Calibration and Temperature Compensation.................. 27 8.8.3 System Gain Calibration ..................................................................................................... 29 8.8.4 Temperature Compensation for the System Gain .............................................................. 29 9. Sample Code .................................................................................................................................... 30 10. Reference Documents ...................................................................................................................... 30 R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 2 of 30 RX21A Group 1. Calibration and Compensation for the ΔΣ A/D Converter Specifications This document describes the methods of calibration and compensation for gains in the RX21A DSAD. Table 1.1 lists the Peripheral Functions and Their Applications. Table 1.1 Peripheral Functions and Their Applications Peripheral Function 24-bit ΔΣ A/D converter (DSAD) Temperature sensor (TEMPSa) 10-bit A/D converter (AD) Application Measures electrical power Measures temperature These peripheral functions are not operated in the sample code. Some dummy functions are used instead. 2. Operation Confirmation Conditions The sample code accompanying this application note has been run and confirmed under the conditions below. Table 2.1 Operation Confirmation Conditions Item Integrated development environment C compiler iodefine.h version Endian Operating mode Processor mode Sample code version Simulator R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Contents Renesas Electronics Corporation High-performance Embedded Workshop Version 4.09.01 Renesas Electronics Corporation C/C++ Compiler Package for RX Family V.1.02 Release 01 Compile options -cpu=rx200 -output=obj="$(CONFIGDIR)\$(FILELEAF).obj" -debug -nologo (The default setting in the integrated development environment is used.) Version 1.1A Little endian Single-chip mode Supervisor mode Version 1.00 RX200 Simulator Target Platform V.1.00.01.000 Page 3 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter 3. Hardware Figure 3.1 shows the Configuration of the 3-Phase Power Meter with the RX21A. 1.22 V BGR N P1 P2 P3 Temperature sensor PGA Reference generator BGR_BO ANDS0P PGA ΔΣ Modulator + Filter PGA ΔΣ Modulator + Filter ANDS0N ANDS1P ANDS1N 10 bit ADC XTAL PCLKC Main Clock EXTAL HOCO ANDS2P PGA ΔΣ Modulator + Filter PGA ΔΣ Modulator + Filter PGA ΔΣ Modulator + Filter PGA ΔΣ Modulator + Filter PGA ΔΣ Modulator + Filter ANDS2N ANDS3P ANDS3N ANDS4 ANDS5 ANDS6 ANDSSG CPU RX21A Figure 3.1 Configuration of the 3-Phase Power Meter with the RX21A R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 4 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter 4. Mechanism of Gain Calibration 4.1 Gain Calibrations Among Channels and Among Gains on a Channel The RX21A has seven independent units of the DSAD and can measure 3-phase of currents and voltages simultaneously. Having multiple channels is an advantage in measuring multi-phase power while gain errors for all channels must be minimized. Offset and gain mismatches among channels occur not only in the RX21A but also in the external devices. The user must calibrate the system gain (the total gain from the sensor input through the digital output of the DSAD) for all channels at least once in the finalized product. Also the user must compensate mismatch among gains on a channel. The calibration data for gains on the RX21A is measured and stored before shipping for each device. Therefore the user does not have to obtain calibration data for each gain setting. Figure 4.1 shows the concept of the gain calibration. The left chart shows the raw gains, the center shows the gains after calibration of mismatches among channels at x1, and the right shows the gains after the compensation of mismatches among gains using the calibration data stored in the device. Gain-to-gain mismatch compensation by the calibration data internally stored Calibrated at x1 64.0 64.0 32.0 32.0 32.0 16.0 16.0 16.0 8.0 4.0 Actual Gain 64.0 Actual Gain Actual Gain Raw gain 8.0 4.0 8.0 4.0 2.0 2.0 2.0 1.0 1.0 1.0 x1 x2 x4 x8 x16 x32 x64 PGA Gain setting x1 x2 x4 x8 x16 x32 x64 PGA Gain setting x1 x2 x4 x8 x16 x32 x64 PGA Gain setting Note: This figure shows concept only. Errors in these charts are exaggerated. Figure 4.1 Gain Calibration and Compensation 4.2 Device Gain The calibration data for gains on each device (device gain) is measured and stored in the GCD[15:0] bits in the ΔΣ A/D gain calibration data registers (DSADGmXn) before factory shipping. The device gain for each channel and gain setting can be obtained using the formula below. Note that DSADGmX64 does not exist. The gain of x32 is digitally amplified and used for the gain of x64. Twice the gain of x32 for the gain of x64. Formula 4.1 DeviceGain (m, n) = n × DSADGmXn.GCD[15:0] / 47971 DeviceGain (m, 64) = DeviceGain (m, 32) × 2 m: Input channel (0 to 6) n: Gain (1, 2, 4, 8, 16, and 32) selected with ΔΣ A/D gain select registers 0 to 6 (DSADGSRm) R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 5 of 30 RX21A Group 4.3 Calibration and Compensation for the ΔΣ A/D Converter Influences of External Input Resistor and Internal Input Resistor Figure 4.2 shows the Connection Diagram of the Differential Input Channel. Rp Rf Ri PGA Ri ΔΣ Modulator + Filter Rf Rp Rp: External input resistor, Ri: Internal input resistor, Rf: Feedback resistor Figure 4.2 Connection Diagram of the Differential Input Channel A low-pass filter (anti-aliasing filter) composed of the external input resistor Rp and the capacitor must be connected to the input pins of the DSAD for preventing an aliasing error. The device gain is proportional to the ratio between the input resistor and the feedback resistor. The input resistor is the sum of the internal input resistor Ri within the DSAD and the external input resistor Rp. Formula 4.2 DeviceGain (m, n) ∝ Rf(n) / { Ri(n) + Rp(m) } m: Input channel (0 to 3) n: Gain (1, 2, 4, 8, 16, 32 and 64) selected with ΔΣ A/D gain select registers 0 to 3 (DSADGSRm) Rf(n): Feedback resistor at gain n Ri(n): Internal input resistor at gain n Rp(m): External input resistor of channel m Table 4.1 shows the internal resistor (Ri and Rf) for each gain setting. Table 4.1 Internal Resistor Values when Setting Each Gain DSADGSRm. GAIN[2:0] 000b 001b 010b 011b 100b 101b 110b Gain x1 x2 x4 x8 x16 x32 x64 Internal Input Resistor Ri(n) Ri0 Ri0 Ri0 Ri0 Ri0 / 2 Ri0 / 2 Ri0 / 2 Feedback Resistor Rf(n) Rf0 2Rf0 4Rf0 8Rf0 8Rf0 8Rf0 8Rf0 Gain of the ΔΣ Modulator 1 1 1 1 1 2 4 Ri0 and Rf0 values in Table 4.1 are designed to 100 kΩ. In practice, these values vary depending on devices. This variation in Ri0 is proportional to variation in impedance. Thus the accurate value of Ri0 for each device can be obtained by using the value of the IICD[15:0] bits in the ΔΣ A/D input impedance calibration data register (DSADIIC). The formula is shown below. Formula 4.3 Ri0 = 100.0 × DSADIIC.IICD[15:0] / 32768 [kΩ] R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 6 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter The system gain is a product of the sensor gain and the device gain. The sensor gain is the gain of all elements except the DSAD. Formula 4.4 SystemGain (m, n) = SensorGain (m) × DeviceGain (m, n) m: Input channel (0 to 6) n: Gain selected with ΔΣ A/D gain select registers 0 to 6 (DSADGSRm) (1, 2, 4, 8, 16, and 32) SystemGain (m, n): Total of the sensor gain and the device gain on channel m with gain setting n SensorGain (m): Sensor gain on channel m When the gain setting is for x16, x32, and x64, the input resistor becomes half the value of the input resistor with gain setting for x1, x2, x4 and x8. Therefore the influence of the external input resistor Rp on the system gain varies depending on the gain setting. The following formula shows the influence ratio. Formula 4.5 SystemGain (nH = 16, 32, 64) / SystemGain (nL = 1, 2, 4, 8) ∝ {Ri0 / 2 + Rp} / (Ri0 + Rp) ≈ 1 + Rp / Ri0 4.4 System Gain Calibration To calibrate the system gain, follow the procedure below. 1. Initialize the DSAD and specify an appropriate value for gain settings of all channels. x1 is set here as an example. 2. Connect the power supply and load for testing and provide signals to all phases. 3. Repeat A/D conversion in appropriate periods for an appropriate number of times, and read the A/D converted data from the ΔΣ A/D data registers (DSADDR0 to DSADDR6) for each channel. Then calculate the root mean square value (RMS value) of the A/D converted data. 4. Calibrate the system gain at gain x1 for each channel. Formula 4.6 SystemGain (m, 1) = (RMS value of DSADDRm) / Itest [digit / A] m: Input channel (0 to 3) Itest: RMS value [A] of the test current Formula 4.7 SystemGain (m, 1) = (RMS value of DSADDRm) / Vtest [digit / V] m: Input channel (4 to 6) Vtest: RMS value [V] of the test voltage 5. Calculate the sensor gain for each channel based on formula 4.4. Formula 4.8 SystemGain (m, n) = SensorGain (m) × DeviceGain (m, n) (from formula 4.4) ∴ SensorGain (m) = SystemGain (m, 1) / DeviceGain (m, 1) m: Input channel (0 to 6) R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 7 of 30 RX21A Group 6. Calibration and Compensation for the ΔΣ A/D Converter Calculate the system gain for gain x2 to x8 based on formulas 4.1 and 4.4 Formula 4.9 DeviceGain (m, n) = n × DSADGmXn.GCD[15:0] / 47971 (from formula 4.1) SystemGain (m, n) = SensorGain (m) × DeviceGain (m, n) (from formula 4.4) ∴ SystemGain (m, n) = SensorGain (m) × n × DSADGmXn.GCD[15:0] / 47971 m: Input channel (0 to 3), n: Gain (2, 4, 8) selected with ΔΣ A/D gain select registers 0 to 3 (DSADGSRm) or m: Input channel (4 to 6), n: Gain (2, 4) selected with ΔΣ A/D gain select registers 4 to 6 (DSADGSRm) 7. Calculate the system gain for gain x16 to x32 based on formulas 4.1, 4.3 and 4.5 Formula 4.10 DeviceGain (m, n) = n × DSADGmXn.GCD[15:0] / 47971 (from formula 4.1) Ri0 = 100.0 × DSADIIC.IICD[15:0] / 32768 [kΩ] (from formula 4.3) SystemGain (n = 16, 32, 64) / SystemGain (n = 1, 2, 4, 8) ≈ 1 + Rp / Ri0 (from formula 4.5) ∴ SystemGain (m, n) = SystemGain (m, 1) / DSADGmX1.GCD[15:0] × DSADGmXn.GCD[15:0] × n × (1 + Rp/100k × 32768 / DSADIIC.IICD[15:0]) m: Input channel (0 to 3), n: Gain (16, 32) selected with ΔΣ A/D gain select registers 0 to 3 (DSADGSRm) 8. For the gain of x64, the gain of x32 is digitally amplified. Twice the gain of x32 for the gain of x64. Formula 4.11 System Gain (m, 64) = System Gain (m, 32) × 2 m: Input channel (0 to 3) R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 8 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter 5. Result of the System Gain Calibration Figure 5.1 shows an example of the system gain calibration. In the example, the gain is calibrated for each channel with each gain setting based on the gain with channel 0 and gain x4 using formulas 4.9 and 4.10. In the result, the gain errors have been reduced from 0.6% to 0.2% or less. To make the measurement conditions consistent for all channels, in this example, 14.06 mV of voltage is input taking into account the limit of x32 gain (14.4 mV). To raise the precision of the calibration, use the test voltage appropriate to the reference gain selected. Calibrated Gain 1.006 1.006 1.004 1.004 Real Gain / Nominal Gain Real Gain / Nominal Gain Raw Gain 1.002 1.000 0.998 0.996 0.994 1.002 1.000 0.998 0.996 0.994 x1 x2 x4 x8 x16 x32 Gain x1 x2 x4 x8 x16 x32 Gain Measurement conditions: - Number of samples: 5 - Channels: 0 to 3 - Gains: x1 to x32, - Input: AC 50.664 Hz ± 14.06 mV (peak-to-peak: 28.12 mV) for all gains - External input resistor: 0 Ω Figure 5.1 Result of the System Gain Calibration R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 9 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter 6. Temperature Characteristics and Compensation Method 6.1 Temperature Characteristics Suppressing the measurement error due to temperature fluctuations is another challenge. The temperature characteristics of the device gain have been clarified. Thus the system gain can be compensated by using Tj (junction temperature on the chip) measured with the built-in temperature sensor in the RX21A. The accuracy of the temperature measured with the temperature sensor affects the accuracy of gain compensation. Therefore the temperature sensor must be calibrated beforehand. For details on the temperature sensor, refer to the reference application note listed in section 10. Figure 6.1 shows the Elements that Have Temperature Characteristics in the Power Meter System. VBGR: See section 6.3. Voltage Reference (Optional) 1.22 V BGR BGR_BO VREFDSH (output) PGA RL VBG: See formulas 6.1 and 6.2 Reference generator ΔΣ Modulator + Filter ZI Device gain: See section 6.2. System gain (Differential) System gain (Single-ended) See section 6.5. CPU Input impedance: See formula 6.2 and section 6.4. Figure 6.1 Elements that Have Temperature Characteristics in the Power Meter System The system gain of differential input is proportional to the device gain and inversely proportional to the reference voltage VBG which comes from the on-chip BGR or the external reference voltage. Formula 6.1 System gain (differential input) ∝ Device gain / VBG The system gain of the single-ended input is affected also by the input impedance (ZI). Formula 6.2 System gain (single-ended input) ∝ Device gain / VBG × (1 + RL / ZI) RL: External load resistor [Ω] ZI: Input impedance [Ω] R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 10 of 30 RX21A Group 6.2 Calibration and Compensation for the ΔΣ A/D Converter Device Gain Figure 6.2 shows the theoretical temperature characteristics of the device gain shown in Figure 6.1 when the reference voltage (VBG) assumes to stay constant regardless of temperature fluctuations. 0.08 Device gain error (%) 0.04 x8 x2 x1 x4 0.00 -0.04 x16, x32, x64 -0.08 -25 0 25 50 75 Temperature (degC) degC: Degrees Celsius Figure 6.2 Temperature Characteristics of the Device Gain The temperature characteristics of the device gain can be calculated with the following formula. Formula 6.3 Device gain (Tj) = Device gain(Tj = 25) × {1 + CXn (Tj - 25)} Tj: Junction temperature on the chip [°C] CXn: (n = 1, 2, 4, 8, 16, 32, and 64): Coefficient of the temperature characteristics. Refer to Table 6.1 for coefficient values. R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 11 of 30 RX21A Group 6.3 Calibration and Compensation for the ΔΣ A/D Converter VBGR 1.2205 0.04 1.2200 0.00 1.2195 -0.04 1.2190 -0.08 1.2185 Error (%) VBGR (V) The on-chip BGR voltage (VBGR) is usually used as the reference voltage (VBG). Figure 6.3 shows the Temperature Characteristics of the VBGR. If the external reference voltage (BGR_BO) is used instead of the on-chip BGR, the influence of the VBGR can be excluded. -0.12 -25 0 25 50 75 Temperature (degC) degC: Degrees Celsius Figure 6.3 Temperature Characteristics of the VBGR The temperature characteristics of the VBGR is calculated with the following formula. Formula 6.4 VBGR(Tj) = VBGR(Tj = 25) × {1 + CBA(Tj - 25)2 + CBB(Tj - 25)} Tj: Junction temperature on the chip [°C] CBA: Coefficient of quadratic slope. Refer to Table 6.1 for the coefficient values. CBB: Coefficient of linear slope. Refer to Table 6.1 for coefficient values. VBGR(Tj = 25): Typical voltage of BGR: 1.220 [V] R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 12 of 30 RX21A Group 6.4 Calibration and Compensation for the ΔΣ A/D Converter Input Impedance Figure 6.4 shows the temperature characteristics of input impedance ZI for the single-ended input at gain x1 shown in Figure 6.1. Input Impedance (kΩ) 86 84 82 80 78 76 74 -25 0 25 Temperature (degC) 50 75 degC: Degrees Celsius Figure 6.4 Temperature Characteristics of the Input Impedance The temperature characteristic of input impedance ZI at each gain setting can be calculated with the following formula. Formula 6.5 ZI (Tj) = ZI (Tj = 25) × DSADIIC.IICD[15:0] / 32768 × {1 + CZ × (Tj - 25)} Tj: Junction temperature on the chip [°C] ZI (Tj = 25): Typical value of the input impedance. The value differs depending on the gain setting. Refer to the ΔΣ A/D Conversion Characteristics section in the User’s Manual: Hardware for details. CZ: Coefficient of linear slope. See Table 6.1 for coefficient values. 6.5 Compensation for the Temperature Characteristics of the System Gain Formulas 6.1 to 6.5 can be combined and approximated into the following formulas. Make sure the sign of each member in the formulas is correct. Formula 6.6 System gain (differential input) (Tj) ≈ System gain (differential input) (Tj = 25) × {1 - CBA(Tj - 25)2 + (CXn - CBB) (Tj - 25)} Formula 6.7 System gain (single-ended input) (Tj) ≈ System gain (single-ended input) (Tj = 25) × {1 - CBA(Tj - 25)2 + (CXn - CBB + RL / ZI (Tj = 25) / DSADIIC.IICD[15:0] × 32768 × CZ) (Tj - 25)} R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 13 of 30 RX21A Group 6.6 Calibration and Compensation for the ΔΣ A/D Converter Coefficients of the Temperature Characteristics in the RX21A Group Table 6.1 shows the Coefficients of the Temperature Characteristics in the RX21A Group. Table 6.1 Coefficients of the Temperature Characteristics in the RX21A Group Element Coefficient Input impedance Value Unit -6 Quadratic slope CBA -0.26 × 10 Linear slope CBB 5.5 × 10-6 x1 CX1 -5 × 10-6 x2 CX2 -4 × 10-6 x4 CX4 -7 × 10-6 CX8 -2 × 10-6 x16 CX16 -14 × 10-6 x32 CX32 -14 × 10-6 x64 CX64 -14 × 10-6 BGR Device Gain Symbol x8 Linear slope Linear slope R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 CZ -1200 × 10-6 K-2 K-1 K-1 K-1 Page 14 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter 7. Compensation Results of the Temperature Characteristics 7.1 Temperature Characteristics of the VBGR The typical VBGR voltage can be calculated by assigning the coefficients shown in Table 6.1 and the temperature measured by the temperature sensor to formula 6.4. The Figure 7.1 shows the Temperature Characteristics of the VBGR (Difference Between the Measured Values and Typical Values). Difference from the typical value Raw data 1.0005 1.0005 VBGR / VBGR at 25 degC Typical value 1.0000 1.0000 0.9995 0.9995 0.9990 0.9990 Compensation error caused by the measurement error of temperature sensor 0.9985 0.9985 -50 -25 0 25 50 75 100 Temperature (degC) -50 -25 0 25 50 75 100 Temperature (degC) degC: Degrees Celsius Figure 7.1 Temperature Characteristics of the VBGR (Difference Between the Measured Values and Typical Values) Error of temperature causes an error for the calculation value of the VBGR. To minimize the temperature measurement error, it is recommended to calibrate the temperature sensor at room temperature. Refer to the reference application note listed in section 10. The temperature characteristics of the VBGR can be decreased virtually from 30 ppm/°C to 10 ppm/°C by compensating with formula 6.4. Table 7.1 Results of the VBGR Compensation Reference Voltage Temperature Coefficient Electrical characteristics in the User’s Manual: Hardware Maximum value of the raw data Residual error after compensation R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 -40 to +105 °C ±30 ppm/°C +30 ppm/°C -24 ppm/°C (-40°C to +25°C) (+25°C to +105°C) ±10 ppm/°C Page 15 of 30 RX21A Group 7.2 Calibration and Compensation for the ΔΣ A/D Converter System Gain of the Differential Input Pins The following figure shows the system gain of the differential input pins. The temperature characteristics for the differential input pins before compensation appear as parabola. Gain Test voltage (Peak-to-peak) 1.002 1.001 1.000 0.999 0.998 Relative Gain 900 mV Relative Gain x1 -25 0 25 50 75 Temperature (degC) -50 -25 0 25 50 75 Temperature (degC) 100 100 -50 -25 0 25 50 75 Temperature (degC) 100 -50 -25 75 0 25 50 Temperature (degC) 100 -50 -25 0 25 50 75 Temperature (degC) 100 -50 -25 0 25 50 75 Temperature (degC) 100 -50 -25 0 25 50 75 Temperature (degC) 100 1.004 1.002 1.000 0.998 0.996 100 1.006 1.003 1.000 0.997 0.994 0 25 50 75 Temperature (degC) 1.002 1.001 1.000 0.999 0.998 100 Relative Gain Relative Gain 28.12 mV 0 25 50 75 Temperature (degC) 1.004 1.002 1.000 0.998 0.996 -50 x32 -25 -25 1.002 1.001 1.000 0.999 0.998 100 Relative Gain Relative Gain 56.25 mV 50 75 0 25 Temperature (degC) 1.002 1.001 1.000 0.999 0.998 -50 x16 -25 -50 1.002 1.001 1.000 0.999 0.998 100 Relative Gain Relative Gain 112.5 mV 0 25 50 75 Temperature (degC) 1.002 1.001 1.000 0.999 0.998 -50 x8 -25 1.002 1.001 1.000 0.999 0.998 100 Relative Gain Relative Gain 225 mV 0 25 50 75 Temperature (degC) 1.002 1.001 1.000 0.999 0.998 -50 x4 -25 Relative Gain 450 mV Relative Gain -50 x2 The ratio of Row data / Compensated Raw data 1.006 1.003 1.000 0.997 0.994 degC: Degrees Celsius Measurement condition: - Test input: AC 50.664 Hz Figure 7.2 System Gain of the Differential Input Pins R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 16 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter Table 7.2 lists the Results of the Compensation for Temperature Characteristics of the System Gain on the Differential Input Pins. The temperature characteristics vary depending on devices. The values shown in the table are compensated so that the temperature characteristics appear as flat. Table 7.2 Results of the Compensation for Temperature Characteristics of the System Gain on the Differential Input Pins Gain Setting x1 x2 x4 x8 x16 x32 Temperature Characteristic Coefficient [ppm/K] Raw data Data after compensation (1) (2) Every 25 K -25°C to +75°C Every 25 K (1) -25°C to +75°C (2) -38 -24 16 14 +21 +25 -39 -17 14 10 +17 +23 -31 -13 15 14 +21 +24 -48 -21 18 10 +29 +30 -96 -57 33 23 +45 +64 -136 -97 41 31 +94 +111 Notes: 1. The range between -25°C and +75°C is divided every 25 K, the temperature characteristic coefficients are calculated for all divided ranges, and the minimum and maximum values are picked up and shown in the table. 2. Value calculated with the box method. Temperature characteristic coefficient = Gain range (maximum value - minimum value) / Temperature range (75 - (-25)) R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 17 of 30 RX21A Group 7.3 Calibration and Compensation for the ΔΣ A/D Converter System Gain of Single-Ended Input Pin Figure 7.3 shows the temperature characteristics of the system gain for single-ended input pins when compensating with formula 6.7. External load resistor Raw Data / Compensated gain 1.010 1.010 1.005 1.005 Relative Gain Relative Gain 1.8 kΩ Raw Data Gain x1 1.000 0.995 0.990 1.000 0.995 0.990 -50 -25 0 25 50 75 100 -50 -25 1.010 1.010 1.005 1.005 Relative Gain Relative Gain Temperature (degC) 5.4 kΩ 0 25 50 75 100 75 100 Temperature (degC) 1.000 0.995 0.990 1.000 0.995 0.990 -50 -25 0 25 50 75 100 Temperature (degC) -50 -25 0 25 50 Temperature (degC) degC: Degrees Celsius 1.33 MΩ 50.664 Hz Peak-to-peak +/- 20 V 100 Ω PGA External load resistor ΔΣ Modulator + Filter Figure 7.3 System Gain of the Single-Ended Input Pins R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 18 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter Table 7.3 lists the Results of the Compensation for Temperature Characteristics of the System Gain on the SingleEnded Input Pins. The temperature characteristics vary depending on devices. The values shown in the table are compensated so that the temperature characteristics appear as flat. Table 7.3 Results of the Compensation for Temperature Characteristics of the System Gain on the Single-Ended Input Pins External Load Resistor [kΩ] 1.8 5.4 Temperature Characteristic Coefficient [ppm/K] Raw data Data after compensation (1) (2) Every 25 K -25°C to +75°C Every 25 K (1) -25°C to +75°C (2) -186 -145 54 43 +114 +167 -249 -136 90 55 +104 +176 Notes: 1. The range between -25°C and +75°C is divided every 25 K, the temperature characteristic coefficients are calculated for all divided ranges, and the minimum and maximum values are picked up and shown in the table. 2. Value calculated with the box method. Temperature characteristic coefficient = Gain range (maximum value - minimum value) / Temperature range (75 - (-25)) R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 19 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter 8. Software 8.1 Operation Overview This application note provides functions to calibrate and compensate gains on the DSAD using formulas described in sections 4.4 System Gain Calibration and 6.5 Compensation for the Temperature Characteristics of the System Gain. 8.2 Required Memory Size Table 8.1 lists the Required Memory Size. Table 8.1 Required Memory Size Memory Used Size Remarks ROM 2396 bytes Required in the r_dsad_compensate.c RAM 592 bytes Maximum user stack usage 92 bytes Maximum interrupt stack usage 0 bytes Note: • The required memory sizes vary depending on the C compiler version and compile options. 8.3 File Composition Table 8.2 lists the Files Used in the Sample Code and Table 8.3 lists the Standard Include Files. Table 8.2 Files Used in the Sample Code File Name main.c r_dsad_compensate.c r_dsad_compensate.h Outline Main processing Gain calibration and temperature compensation on the DSAD Header file for r_dsad_compensate.c Table 8.3 Standard Include Files File Name stdbool.h stdint.h float.h Outline Defines macros associated with Boolean and its value. Defines macros declaring the integer type with the specified width. Defines various limit values relating to the limits of floating-point numbers. R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 20 of 30 RX21A Group 8.4 Calibration and Compensation for the ΔΣ A/D Converter Constants Table 8.4 and Table 8.5 list the Constant Used in the Sample Code. Table 8.4 Constants Used in the Sample Code (r_dsad_compensate.c) Constant Name RI0TYP Setting Value 100e3 Contents Designed value of the internal input resistor [Ω] Table 8.5 Constants Used in the Sample Code (r_dsad_compensate.h) Constant Name DSAD_CH_NUM DSAD_DIFFER_CH_NUM DSAD_SINGLE_CH_NUM DSAD_GAIN_NUM Setting Value 7 4 3 7 DSAD_DIFFER_GAIN_NUM 7 DSAD_SINGLE_GAIN_NUM 3 DSAD_GAIN_X1 DSAD_GAIN_X2 DSAD_GAIN_X4 DSAD_GAIN_X8 DSAD_GAIN_X16 DSAD_GAIN_X32 DSAD_GAIN_X64 0 1 2 3 4 5 6 8.5 Contents Number of channels of the DSAD Number of channels for the differential input Number of channels for the single-ended input Number of gains the DSAD can select Number of gains that can be selected with the differential input channel Number of gains that can be selected with the single-ended input channel Gain number to be selected Variables Table 8.6 lists the static Variables, and Table 8.7 and Table 8.8 list the const Variables. Table 8.6 static Variables Type Variable Name static volatile float coef_temp_quad static volatile float static volatile float static volatile float coef_temp_linear [DSAD_CH_NUM] [DASD_GAIN_NUM] device_gain[DSAD_ CH_NUM][DSAD_ GAIN_NUM] system_gain[DSAD_ CH_NUM][DSAD_ GAIN_NUM] R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Contents Linear coefficient of the temperature characteristics for temperature compensation Function R_DSAD_InternalCalibration R_DSAD_ Calibration R_DSAD_CompensatedGain R_DSAD_InternalCalibration R_DSAD_Calibration R_DSAD_CompensatedGain Device gain for each gain setting and channel of the DSAD at 25°C R_DSAD_InternalCalibration R_DSAD_Calibration System gain including the sensor for each gain setting and channel of the DSAD at 25°C R_DSAD_Calibration R_DSAD_CompensatedGain Quadratic coefficient of the temperature characteristics for temperature compensation Page 21 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter Table 8.7 const Variables (main.c) Type Variable Name const bool valid_dsad_channel [DSAD_CH_NUM] const bool use_internal_dsad_bgr const float dsad_ext_input_res [DSAD_DIFFER_CH_ NUM] const float dsad_ext_load_res [DSAD_SINGLE_CH_ NUM] Contents Indicates whether the channel is valid or not. Specify an appropriate value according to the user system. Indicates whether to use the on-chip BGR or not. Specify an appropriate value according to the user system. Value of the external input resistor [Ω] for differential input channels (channels 0 to 3). Specify an appropriate value according to the user system. Value of the external load resistor [Ω] for singleended input channels (channels 4 to 6). Specify an appropriate value according to the user system. Function main main main main Table 8.8 const Variables (r_dsad_compensate.c) Type Variable Name static const typ_zi[DSAD_SINGLE float _GAIN_NUM] static const coef_temp_cba float static const coef_temp_cbb float static const coef_temp_cxn[DSAD float _GAIN_NUM] static const float coef_temp_cz static const float gain_val [DSAD_GAIN_NUM] R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Contents Typical value [Ω] of the input impedance (x1, x2, and x4) of the single-ended input. Refer to the ΔΣ A/D Conversion Characteristics section in the User’s Manual: Hardware for details. Quadratic coefficient of the temperature characteristics for the on-chip BGR. The coefficient value is listed in Table 6.1. Linear coefficient of the temperature characteristics for the on-chip BGR. The coefficient value is listed in Table 6.1. Coefficient of the temperature characteristics for the device gain. The coefficient value is listed in Table 6.1. Coefficient of the temperature characteristics for the input impedance. The coefficient value is listed in Table 6.1. Amplification factor of a gain Function R_DSAD_Internal Calibration R_DSAD_Internal Calibration R_DSAD_Internal Calibration R_DSAD_Internal Calibration R_DSAD_Internal Calibration R_DSAD_Internal Calibration Page 22 of 30 RX21A Group 8.6 Calibration and Compensation for the ΔΣ A/D Converter Functions Table 8.9 lists the Functions. Table 8.9 Functions Function Name main initialize_system_and_peripherals measure_temperature measure_calibration_data Outline File Main processing main.c System and peripheral initializations Temperature measurement (1) (1) Power measurement for calibration main.c main.c (1) (1) main.c measure_power Power measurement main.c R_DSAD_InternalCalibration Coefficient initialization for gain calibration and temperature compensation r_dsad_compensate.c R_DSAD_Calibration System gain calibration r_dsad_compensate.c R_DSAD_CompensatedGain Temperature compensation for the system gain r_dsad_compensate.c Note: 1. This is the dummy function for testing in the sample code. R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 23 of 30 RX21A Group 8.7 Calibration and Compensation for the ΔΣ A/D Converter Function Specifications The following tables list the sample code function specifications. main Outline Header Declaration Description Arguments Return Value Main processing None void main(void) Calls the following functions: R_DSAD_InternalCalibration, R_DSAD_Calibration, and R_DSAD_CompensatedGain None None R_DSAD_InternalCalibration Coefficient initialization for gain calibration and temperature compensation Outline r_dsad_compensate.h Header bool R_DSAD_InternalCalibration(bool use_internal_dsad_bgr, const float Declaration dsad_ext_input_res[DSAD_DIFFER_CH_NUM], const float dsad_ext_load_res[DSAD_SINGLE_CH_NUM]) Prepares the intermediate calculation result required for the gain calibration and Description temperature compensation. bool use_internal_dsad_bgr: Indicates whether to use the on-chip BGR or not. Arguments Return Value const float dsad_ext_input_res[DSAD_ DIFFER_CH_NUM]: External input resistor for the differential input channels (channels 0 to 3) [Ω]. const float dsad_ext_load_res[DSAD_ SINGLE_CH_NUM]: External load resistor for the single-ended input channels (channels 4 to 6) [Ω]. true: Values written in the ΔΣ A/D input impedance calibration data register and ΔΣ A/D gain calibration data registers are valid. false: Values written in theΔΣ A/D input impedance calibration data register and ΔΣ A/D gain calibration data registers are invalid. * Gain calibration using the ΔΣ A/D input impedance calibration data register and ΔΣ A/D gain calibration data registers are not performed in this application note. The designed value is used for the internal input resistor Ri0, and the typical values, that are described in the ΔΣ A/D Conversion Characteristics section in the User’s Manual: Hardware, are used for the gain and the input impedance of the single-ended input. Remarks Execute this function before executing the R_DSAD_Calibration and R_DSAD_CompensatedGain functions. Otherwise calibration and compensation cannot be performed correctly. R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 24 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter R_DSAD_Calibration System gain calibration Outline r_dsad_compensate.h Header void R_DSAD_CALIBRATION(uint16_t channel, uint16_t gain_setting, float Declaration acculate_rms_value, uint32_t measured_rms_digital, int16_t junction_temp) Calculates the system gain before temperature compensation. Description unit16_t channel: Input channel (0 to 6) Arguments uint16_t gain_setting: Reference gain for calibration - Specify a value from 0 to 6 (gains x1 to x64) for input channels 0 to 3. - Specify a value from 0 to 2 (gains x1 to x4) for input channels 4 to 6. Return Value Remarks float acculate_rms_value: RMS value of a current or voltage input from the reference power supply, e.g. 10[A] for channels 0 to 3, 230[V] for channels 4 to 6. This value must be positive. If the value is 0 or negative, R_DSAD_COMPENSATED_GAIN() returns 0. uint32_t measured_rms_digital: The reference power is A/D converted with the DSAD. This is the RMS value of the conversion result. int16_t junction_temp: The device temperature measured by the temperature sensor. The value should be from -40°C to +105°C. None Execute the R_DSAD_InternalCalibration function before executing this function. Otherwise calibration and compensation cannot be performed correctly. If the channel and gain_setting arguments have invalid values, this function exits the processing without performing calibration. R_DSAD_CompensatedGain Temperature compensation for the system gain Outline r_dsad_compensate.h Header float R_DSAD_CompensatedGain(uint16_t channel, uint16_t gain_setting, int16_t Declaration junction_temp) Calculates the system gain after temperature compensation and returns the calculation Description result. uint16_t channel: Input channel (0 to 6) Arguments uint16_t gain_setting: Gain to be performed temperature compensation - Specify a value from 0 to 6 (gains x1 to x64) for input channels 0 to 3. - Specify a value from 0 to 2 (gains x1 to x4) for input channels 4 to 6. int16_t junction_temp: The device temperature measured by the temperature sensor. The value should be from -40°C to +105°C. The system gain after temperature compensation Return Value Execute the R_DSAD_Calibration function before executing this function. Otherwise Remarks calibration and compensation cannot be performed correctly. If the channel and gain_setting arguments have invalid values, the return value will be 0. R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 25 of 30 RX21A Group 8.8 8.8.1 Calibration and Compensation for the ΔΣ A/D Converter Flowcharts Main Processing Figure 8.1 shows the Main Processing. main System and peripheral function initializations (1) initialize_system_and_peripherals() Coefficient initialization for gain calibration and temperature compensation R_DSAD_InternalCalibration() Power measurement for calibration (1) measure_calibration_data() Temperature measurement (1) measure_temperature() System gain calculation R_DSAD_Calibration() Has calibration for all channels been completed? No Yes Temperature measurement (1) measure_temperature() System gain compensation R_DSAD_CompensatedGain() Has compensation for all channels been completed? No Yes Power measurement (1) measure_power() return Note: 1. In the sample code, this is the dummy function only for testing. Figure 8.1 Main Processing R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 26 of 30 RX21A Group 8.8.2 Calibration and Compensation for the ΔΣ A/D Converter Coefficient Initialization for Gain Calibration and Temperature Compensation Figure 8.2 and Figure 8.3 show the Coefficient Initialization for Gain Calibration and Temperature Compensation. R_DSAD_InternalCalibration Set "true" to the return value (isvalid_reg) Read the calibration data for input impedance Is the calibration data valid data? Arguments: - bool use_internal_dsad_bgr: On-chip BGR usage - const float dsad_ext_input_res[DSAD_DIFFER_CH_NUM]: Value of the external input resistor - const float dsad_ext_load_res[DSAD_SINGLE_CH_NUM]: Value of the external load resistor Reads the DSADIIC register. No Verifies DSADIIC.IICD[15:0]. Yes Is the return value (isvalid_reg) "true"? Set "false" to the return value (isvalid_reg) No Yes Calculate the calibration coefficient for calibration with resistor Is the return value (isvalid_reg) "true"? Calibration coefficient = DSADIIC.IICD[15:0] / 32768 Set 1 as the calibration coefficient for calibration with resistor No Yes Calculate device gains for gains x1 to x32 using the calibration data Compensate device gains for gains x16 and x32 with input resistor value Calculate the device gain for gain x64 Have all gains for channels 0 to 3 been calculated? Reads the DSADGmXn register and calculates device gains. Set 1, ..., 32 as device gains for gains x1 to x32, respectively When the gain setting is for x16 to x64, the input resistor becomes half the value of the input resistor with gain setting for x1 to x8. Then the influence of the external input resistor on the system gain changes. Therefore the compensation here is performed using the external input resistor and internal input resistor. Calculates the gain using the value of gain x32. No Yes A Figure 8.2 Coefficient Initialization for Gain Calibration and Temperature Compensation (1/2) R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 27 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter A Is the return value (isvalid_reg) "true"? No Yes Calculate device gains for gains x1 to x4 using the calibration data Have all gains for channels 4 to 6 been calculated? Reads the DSADGmXn register and calculates device gains. Set 1, ..., 4 as the device gains for gains x1 to x4, respectively No Yes Is the on-chip BGR used? No Yes Set the quadratic slope coefficient of the temperature characteristics Is the on-chip BGR used? Calculates the coefficient based on the parameter (coef_temp_cba). Set 0 as the quadratic slope coefficient of the temperature characteristics No Yes Set the linear slope coefficients of the temperature characteristics for gains x1 to x64 Have all gains for channels 0 to 3 been calculated? Calculates the coefficients based on the parameter (coef_temp_cxn, coef_temp_cbb) according to gains. Set the linear slope coefficient of the temperature characteristics for gains x1 to x64 Calculates the coefficients based on the parameter (coef_temp_cxn) according to gains. Set the linear slope coefficient of the temperature characteristics for gains x1 to x4 Calculates the coefficients based on the parameter (typ_zi, coef_temp_cxn, coef_temp_cz) and the external load resistor according to gains. No Yes Is the on-chip BGR used? No Yes Set the linear slope coefficients of the temperature characteristics for gains x1 to x4 Have all gains for channels 4 to 6 been calculated? Calculates the coefficients based on the parameter (typ_zi, coef_temp_cxn, coef_temp_cbb, coef_temp_cz) and the external load resistor according to gains. No Yes return (isvalid_reg) Figure 8.3 Coefficient Initialization for Gain Calibration and Temperature Compensation (2/2) R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 28 of 30 RX21A Group 8.8.3 Calibration and Compensation for the ΔΣ A/D Converter System Gain Calibration Figure 8.4 shows the System Gain Calibration. Arguments: - uint16_t channel: Input channel - uint16_t gain_setting: Reference gain for calibration (0: x1, 1: x2, ..., 5: x32, 6: x64) - float accurate_rms_value: RMS value of a current or voltage input from the reference power supply - uint32_t measured_rms_digital: RMS value of the reference power that is A/D converted with the DSAD - int16_t junction_temp: Device temperature R_DSAD_Calibration Are the channel and gain setting valid? No Yes Is the value of accurate_rms_value a positive value? No Yes Calculate the sensor gain at 25°C Is the channel for differential input? Calculates the sensor gain with the RMS value and device temperature passed by arguments, and device gain and coefficient of the temperature characteristics that are calculated in the R_DSAD_InternalCalibration function. Set the sensor gain to 0 No Yes Calculate the system gain for gains x1 to x4 at 25°C Calculate the system gain for gains x1 to x64 at 25°C System gain = sensor gain × device gain return Figure 8.4 System Gain Calibration 8.8.4 Temperature Compensation for the System Gain Figure 8.5 shows the Temperature Compensation for the System Gain. R_DSAD_CompensatedGain Are the channel and gain setting valid? Arguments: - uint16_t channel: Input channel - uint16_t gain_setting: Gain to be performed temperature compensation (0: x1, 1: x2, ..., 5: x32, 6: x64) - int16_t junction_temp: Device temperature No Yes Set the system gain after temperature compensation as the return value (ret) Calculates the system gain with the calibrated system gain, device temperature, and the coefficient of the temperature characteristics. Set the return value (ret) to 0 return Figure 8.5 Temperature Compensation for the System Gain R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 29 of 30 RX21A Group Calibration and Compensation for the ΔΣ A/D Converter 9. Sample Code Sample code can be downloaded from the Renesas Electronics website. 10. Reference Documents User’s Manual: Hardware RX21A Group User’s Manual: Hardware Rev.1.10 (R01UH0251EJ) The latest version can be downloaded from the Renesas Electronics website. Technical Update/Technical News The latest information can be downloaded from the Renesas Electronics website. User’s Manual: Development Tools RX Family C/C++ Compiler Package V.1.01 User’s Manual Rev.1.00 (R20UT0570EJ) The latest version can be downloaded from the Renesas Electronics website. Application Note Using the Temperature Sensor to Calculate the Ambient Temperature (R01AN1923EJ) The latest version can be downloaded from the Renesas Electronics website. Website and Support Renesas Electronics website http://www.renesas.com Inquiries http://www.renesas.com/contact/ R01AN2180EJ0100 Rev. 1.00 Oct. 1, 2014 Page 30 of 30 REVISION HISTORY Rev. Date 1.00 Oct. 1, 2014 RX21A Group Application Note Calibration and Compensation for the ΔΣ A/D Converter Page — Description Summary First edition issued All trademarks and registered trademarks are the property of their respective owners. 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