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MAQ473GQE-AEC1-Z

MAQ473GQE-AEC1-Z

  • 厂商:

    MPS(美国芯源)

  • 封装:

    VFQFN16_EP

  • 描述:

    霍尔效应 传感器 角度 外磁铁,不含 SMD(SMT)接片

  • 数据手册
  • 价格&库存
MAQ473GQE-AEC1-Z 数据手册
MAQ473 9-Bit to 14-Bit, MagAlpha Automotive Angle Sensor with ABZ Incremental and PWM Outputs DESCRIPTION FEATURES The MAQ473 detects the absolute angular position of a permanent magnet, typically a diametrically magnetized cylinder on a rotating shaft. Fast data acquisition and processing provide accurate angle measurement at speeds from 0rpm to 60,000rpm.  The MAQ473 supports a wide range of magnetic field strengths and spatial configurations. Both end-of-shaft and off-axis (side-shaft mounting) configurations are supported. The MAQ473 features magnetic field strength detection with programmable thresholds to allow sensing of the magnet position relative to the sensor for creation of functions such as the sensing of axial movements or for diagnostics. The on-chip non-volatile memory provides storage for configuration parameters, including the reference zero-angle position, ABZ encoder settings, and magnetic field detection thresholds. The MAQ473 is AEC-Q100 qualified, and is available in a QFN-16 (3mmx3mm) package.          9-Bit to 14-Bit Resolution Absolute Angle Encoder Contactless Sensing for Long Lifespan SPI Serial Interface with Parity Bit for Angle Readout and Chip Configuration Configuration Programmable Magnetic Field Strength Detection for Diagnostic Checks Incremental 12-Bit ABZ Quadrature Encoder Interface with Programmable Pulses Per Turn from 1 to 1024 14-Bit PWM Output 3.3V, 12mA Supply Current -40°C to +150°C Operating Temperature Available in a QFN-16 (3mmx3mm) Package with Wettable Flanks Available in AEC-Q100 Grade 1 APPLICATIONS     Automotive Angle Encoders Automotive Angle or Speed Sensors Robotics All MPS parts are lead-free, halogen-free, and adhere to the RoHS directive. For MPS green status, please visit the MPS website under Quality Assurance. “MPS”, the MPS logo, and “Simply, Easy Solutions” are registered trademarks of Monolithic Power Systems, Inc. or its subsidiaries. TYPICAL APPLICATION MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 1 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS ORDERING INFORMATION Part Number* MAQ473GQE-AEC1 Package QFN-16 (3mmx3mm) Top Marking See Below MSL Rating 1 * For Tape & Reel, add suffix -Z (e.g. MAQ473GQE–AEC1-Z). TOP MARKING ____ BNXY LLLL BNX: Product code of MAQ473GQE Y: Year code LLLL: Lot number PACKAGE REFERENCE TOP VIEW QFN-16 (3mmx3mm) MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 2 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS PIN FUNCTIONS Pin # Name 1 SSD 2 3 4 5 6 A Z MOSI CS B 7 MISO 8 9 10 11 12 GND PWM TEST MGL SCLK Supply ground. PWM output. Connect to ground. Digital output indicating field strength below the MGLT level. Clock (SPI). The SCLK pin has an internal pull-down resistor. 13 14 15 16 VDD NC SSCK MGH Exposed pad 3.3V supply. No connection. Leave the NC pin unconnected. Clock (SSI). The SSCK pin has an internal pull-down resistor. Digital output indicating field strength above the MGHT level. 17 Description Data out (SSI). Incremental output. Incremental output. Data in (SPI). The MOSI pin has an internal pull-down resistor. Chip select (SPI). The CS pin has an internal pull-up resistor. Incremental output. Data out (SPI). MISO has an internal pull-down resistor that is enabled when the device is in a high-impedance state. Recommend not to solder. Leave floating. θJA θJC ABSOLUTE MAXIMUM RATINGS (1) Thermal Resistance (3) Supply voltage ............................ -0.5V to +4.6V Input pin voltage (VI) ................... -0.5V to +6.0V Output pin voltage (VO) ............... -0.5V to +4.6V Continuous power dissipation (TA = 25°C) (2) ..................................................................2.0W Junction temperature ............................... 160°C Lead temperature .................................... 260°C Storage temperature ................ -65°C to +160°C QFN-16 (3mmx3mm) ............ 50 ....... 12 ... °C/W Notes: 1) Exceeding these ratings may damage the device. 2) The maximum allowable power dissipation is a function of the maximum junction temperature TJ (MAX), the junction-toambient thermal resistance θJA, and the ambient temperature TA. The maximum allowable continuous power dissipation at any ambient temperature is calculated by PD (MAX) = (TJ (MAX) - TA) / θJA. 3) Measured on JESD51-7, 4-layer PCB. ESD Ratings Human body model (HBM) .......................... 2kV Charged device model (CDM) ....................750V MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 3 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS ELECTRICAL CHARACTERISTICS Parameter Symbol Condition Recommended Operating Conditions Min Typ Max Units Supply voltage Supply current Operating (ambient) temperature Applied magnetic field 3.0 10.2 3.3 12 3.6 13.8 V mA +150 °C MAQ473 Rev. 1.1 8/8/2022 VDD IDD From -40°C to +125°C TA -40 B 30 60 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. mT 4 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS GENERAL CHARACTERISTICS VDD = 3.3V, 45mT < B < 100mT, TA = -40°C to +125°C, unless otherwise noted. Parameter Absolute Output (Serial) Symbol Condition Effective resolution (±3σ) Noise root mean square (RMS) Min Typ Max Units filter window τ = 64µs filter window τ = 16ms filter window τ = 64µs 9.0 13.0 0.04 9.8 13.8 0.07 10.5 14.5 0.12 bits bits deg filter window τ = 16ms 0.003 850 16 0.004 980 0.007 1100 16 deg kHz bits 0.6 260 10 ms ms µs Refresh rate Data output length Response Time filter window τ = 64µs filter window τ = 16ms Constant speed propagation delay Start-up time (4) Latency (4) Filter cutoff frequency (4) fCUTOFF fCUTOFF 8 filter window τ = 64µs filter window τ = 16ms 6 23 kHz Hz 0.7 deg 1.1 deg 1.16 deg 0.015 deg/°C From 25°C to 85°C 0.5 deg From 25°C to 125°C 1.0 deg Accuracy Integral nonlinearity (INL) at 25°C INL between -40°C and +125°C (5) INL at 150°C Output Drift At room temperature across the full field range Across the full temperature range and field range Across the full field range Temperature-induced drift at room temperature (5) Temperature-induced variation (5) Magnetic field induced (5) 0.005 Voltage supply induced (5) Absolute Output (PWM) PWM frequency fPWM PWM resolution Incremental Output (ABZ) ABZ update rate Resolution (edges per turn) Pulses per channel per turn ABZ hysteresis (5) Systematic jitter (5) MAQ473 Rev. 1.1 8/8/2022 deg/mT 0.3 deg/V 840 970 1090 Hz 13 13.8 14.0 bits 16 Programmable PPT + 1 Programmable H Programmable 4 1 0.08 MHz 4096 1024 2.8 deg For PPT = 1023, up to 60mT 11 % For PPT = 127 7 % MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 5 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS GENERAL CHARACTERISTICS (continued) VDD = 3.3V, 45mT < B < 100mT, TA = -40°C to +125°C, unless otherwise noted. Parameter Symbol Condition Magnetic Field Detection Thresholds Accuracy (5) Hysteresis (5) Temperature drift (5) Digital I/O VIH Input low voltage VIL voltage (5) Output high voltage (5) Typ Max 5 6 -600 MagHys Input high voltage Output low Min 2.5 -0.3 VOL IOL = 4mA VOH IOH = 4mA Units mT mT ppm/°C 5.5 +0.8 0.4 2.4 V V V V Pull-up resistor RPU 46 66 97 kΩ Pull-down resistor Rising edge slew rate (4) Falling edge slew rate (4) RPD tR tF 43 55 0.7 0.7 97 kΩ V/ns V/ns CL = 50pF CL = 50pF Notes: 4) 5) Guaranteed by design. Guaranteed by characterization. MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 6 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS TYPICAL CHARACTERISTICS VDD = 3.3V, TA = 25°C, unless otherwise noted. ABZ Jitter PPT = 255, τ = 1ms Error Curve 50mT Current Consumption Nonlinearity (INL and Harmonics) Filter Transfer Function τ = 16ms Effective Resolution 3σ Noise Spectrum 50mT and τ = 16ms MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 7 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS FUNCTIONAL BLOCK DIAGRAM Figure 1: Functional Block Diagram MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 8 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS OPERATION Sensor Front End The magnetic field is detected with integrated Hall devices located in the center of the package. The angle is measured using MPS’s proprietary SpinAxisTM method, which directly digitizes the direction of the field without the need for complex arctangent computation or feedback loop-based circuits (interpolators). The SpinAxisTM method is based on phase detection, and generates a sinusoidal signal with a phase that represents the angle of the magnetic field. The angle is then obtained by a time-to-digital converter, which measures the time between the zero crossing of the sinusoidal signal and the edge of a constant waveform (see Figure 2). The time-to-digital is outputted from the front end to the digital conditioning block. Start Sensor Magnet Mounting The MAQ473’s sensitive area (where the Hall devices are placed) is confined within a region less than 100µm wide and has multiple integrated Hall devices. This volume is located both horizontally and vertically within 50µm of the center of the QFN package. The sensor detects the angle of the magnetic field projected in a plane parallel to the package’s upper surface. This means that the only relevant magnetic field is the in-plane component (X and Y components) in the mid-point of the package. By default, when looking at the top of the package, the angle increases when the magnetic field rotates clockwise. Figure 3 shows the zero angle of the unprogrammed sensor, where the plus sign indicates the sensitive point. Both the rotation direction and the zero angle can be programmed. Stop Figure 2: Phase Detection Method across the Sine Waveform (Top) and Time-to-Digital Converter Clock (Bottom) The output of the front end delivers a digital number proportional to the angle of the magnetic field at the rate of 1MHz in a straightforward, open-loop manner. Digital Filtering The front-end signal is further treated to achieve the final effective resolution. This treatment does not add any latency in steady conditions. The filter transfer function can be calculated with Equation (1): H(s) = 1+ 2τs (1+ τs)2 (1) Where τ is the filter time constant related to the cutoff frequency by: τ = 0.38 / fCUTOFF. See the General Characteristics section on page 5 for the value of fCUTOFF. MAQ473 Rev. 1.1 8/8/2022 Figure 3: Detection Point and Default Positive Direction This type of detection provides flexibility for angular encoder design. The sensor only requires the magnetic vector to lie within the sensor plane with a field amplitude of at least 30mT. The MAQ473 can work with fields smaller than 30mT, but the linearity and resolution performance may deviate from the specifications. The most straightforward mounting method is to place the MAQ473 sensor on the rotation axis of a permanent magnet (e.g. a diametrically magnetized cylinder) (see Figure 4 on page 10). MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 9 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS The recommended magnet is a Neodymium alloy (N35) cylinder with dimensions Ø5x3mm, inserted into an aluminum shaft with a 1.5mm air gap between the magnet and the sensor (surface of package). For good linearity, position the with a precision of 0.5mm. Figure 4: End-of-Shaft Mounting If the end-of-shaft position is not available, the sensor can be positioned away from the rotation axis of a cylinder or ring magnet (see Figure 5). In this case, the magnetic field angle is not directly proportional to the mechanical angle. The MAQ473 can be adjusted to compensate for this effect and recover the linear relation between the mechanical angle and the sensor output. With multiple pole pair magnets, the MAQ473 indicates multiple rotations for each mechanical turn. Figure 6: Supply Decoupling Connection In general, the MAQ473 works well with or without the exposed pad connected. For optimum electrical, thermal, and mechanical conditions, it is recommended that the exposed pad be connected to ground. Serial Interface The sensor supports the serial peripheral interface (SPI) standard for angle reading and register programming. Alternatively, the synchronous serial interface (SSI) bus can be used for angle reading (programming through the SSI is not supported). The data length is 16 bits. For checking the integrity of the data received (angle or register content) the master sends a 17th clock count and receives a parity bit. SPI The SPI is a four-wire, synchronous, serial communication interface. The MAQ473 supports SPI Mode 3 and Mode 0 (see Table 1 and Table 2). The SPI mode (0 or 3) is detected automatically by the sensor, and therefore does not require any action from the user. The maximum clock rate supported on the SPI is 25MHz. There is no minimum clock rate. Realworld data rates depend on the PCB layout quality and signal trace length. See Figure 7 and Table 3 on page 11 for SPI timing. Table 1: SPI Specification Figure 5: Side-Shaft Mounting Electrical Mounting and Power Supply Decoupling It is recommended to place a 1µF decoupling capacitor close to the sensor with a lowimpedance path to GND (see Figure 6). Mode 0 SCLK Idle State Data Capture Data Transmission CS Idle State Data Order Mode 3 Low High On SCLK rising edge On SCLK falling edge High MSB first Table 2: SPI Standard Mode 0 CPOL CPHA Data Order (DORD) Mode 3 0 1 0 1 0 (MSB first) All commands to the MAQ473 (whether for writing or reading register content) must be transferred through the SPI MOSI pin and must be 16 bits long. MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 10 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS See the SPI Communication section on page 12 for details. Figure 7: SPI Timing Diagram Figure 8: Minimum Idle Time Table 3: SPI Timing Parameter (6) Min Max Idle time between two subsequent angle transmissions 150ns - Idle time before and after a register readout 750ns - tNVM Idle time between a write command and a register readout (delay necessary for non-volatile memory update) 20ms - tCSL Time between the CS falling edge and SCLK falling edge 80ns - tSCLK SCLK period 40ns - tSCLKL Low level of SCLK signal 20ns - tSCLKH High level of SCLK signal 20ns - tCSH Time between SCLK rising edge and CS rising edge 25ns - tMISO SCLK setting edge to data output valid - 15ns tMOSI Data input valid to SCLK reading edge 15ns - tIDLE_ANGLE tIDLE_REG Description Note: 6) Guaranteed by design. MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 11 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS SPI Communication The sensor supports three types of SPI operation:    Read angle Read configuration register Write configuration register Angle reading can be therefore optimized without any loss of information by reducing the number of clock counts. In the case of a 12-bit data output length, only 12 clock counts are required to get the full sensor resolution. MSB Each operation has a specific frame structure, described below. SPI Read Angle Every 1µs, new data is transferred into the output buffer. The master device triggers the reading by pulling CS low. When a trigger event is detected, the data remains in the output buffer until the CS signal is de-asserted (see Table 4). LSB MISO Angle[15:4] MOSI 0 If less resolution is needed, the angle can be read by sending even fewer clock counts (since the MSB is first). In case of fast reading, the MAQ473 continues sending the same data until the data is refreshed. See the refresh rate section in the General Characteristics section on page 5. Table 4: Sensor Data Timing Event CS falling edge CS rising edge Action Start reading and freeze the output buffer Release the output buffer Figure 9 shows a diagram of a full SPI angle reading. Figure 10 shows a partial SPI angle reading. A full angle reading requires 16 clock pulses. The sensor MISO line returns: MSB LSB MISO Angle[15:0] MOSI 0 The MagAlpha family has sensors with different features and levels of resolution. See the data output length section in the General Characteristics section on page 5 for the number of useful bits delivered at the serial output. If the data length is less than 16, the rest of the bits sent are 0s. For example, a data output length of 12 bits means that the serial output delivers a 12bit angle value with 4 bits of 0s padded at the end (the MISO state remains 0). If the master sends 16 clock counts, the MAQ473 replies with: MSB MISO MOSI MAQ473 Rev. 1.1 8/8/2022 Figure 9: Full 16-Bit SPI Angle Reading Diagram Figure 10: Partial 8-Bit SPI Angle Reading Diagram LSB Angle[15:4] 0 0 0 0 0 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 12 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS SPI Read Register A read register operation consists of two 16-bit frames. The first frame sends a read request, which contains the 3-bit read command (010) followed by the 5-bit register address. The last 8 bits of the frame must all be set to 0. The second frame returns the 8-bit register value (MSB byte). Figure 11 shows a complete transmission overview. First 16-bit SPI frame (read request): MISO MSB MISO MSB LSB Angle[15:0] LSB Command MOSI 0 1 0 Angle[15:0] Command Reg. Address MOSI 0 1 0 A4 A3 A2 A1 A0 0 0 0 0 0 0 0 0 Register Value MISO V7 V6 V5 V4 V3 V2 V1 V0 0 0 0 0 0 0 0 0 MSB Reg. Address 1 1 0 1 1 LSB 0 0 0 0 0 0 0 0 0 In the second frame, the MagAlpha replies: Register Value MISO MGH MGL X X X X X X Second 16-bit SPI frame (response): MOSI For example, to get the value of the magnetic level high and low flags (MGH and MGL), read register 27 (bit[6], bit[7]) by sending the following first frame: 0 0 0 0 0 0 0 0 MSB MOSI LSB 0 Figure 12 shows a complete example overview. Figure 11: Two 16-Bit Frames Read Register Operation Figure 12: Example Read Magnetic Level Flags High and Low (MGH, MGH) on Register 27, Bits[6:7] SPI Write Register The Register Map section on page 18 shows the programmable 8-bit registers. Data written to MAQ473 Rev. 1.1 8/8/2022 these registers is stored in the on-chip nonvolatile memory (NVM) and reloaded automatically at start-up. MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 13 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS A write register operation consists of two 16-bit frames. The first frame sends a write request, which contains the 3-bit write command (100), followed by the 5-bit register address and the 8bit value (MSB first). The second frame returns the newly written register value (acknowledge). The NVM is guaranteed to endure 1,000 write cycles at 25°C. It is critical to wait 20ms between the first and the second frame. This is the time taken to write to the NVM. Failure to implement this wait period results in the register’s previous value being read. Note that this delay is only required after a write request. A read register request or read angle does not require this wait time. The second 16-bit SPI frame (response) is: Register Value MISO V7 V6 V5 V4 V3 V2 V1 V0 0 0 0 0 0 0 0 0 MSB LSB MOSI 0 The readback register content can be used to verify the register programming. Figure 13 shows a complete transmission overview. For example, to set the value of the output rotation direction (RD) to counterclockwise (high), write register 9 by sending the following first frame: MSB MISO LSB Angle[15:0] The first 16-bit SPI frame (write request) is: MSB MISO LSB Angle[15:0] Command Reg. Address Register Value MOSI 1 0 0 A4 A3 A2 A1 A0 V7 V6 V5 V4 V3 V2 V1 V0 MOSI Command 1 0 0 Reg. Address 0 1 0 0 1 Register Value 1 0 0 0 0 0 0 0 Send the second frame after a 20ms wait time. If the register is written correctly, the reply is: Register Value MISO 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 MSB MOSI LSB 0 See Figure 14 for a complete example. Figure 13: Overview of Two 16-Bit Frames Write Register Operation MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 14 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS Figure 14: Example Write Output Rotation Direction (RD) to Counterclockwise (High), on Register 9, Bit 7 SSI The SSI is a two-wire, synchronous serial interface for data reading only. The sensor operates as a slave to the external SSI master and only supports angle reading. It is not possible to read or write registers via the SSI. SSI Communication Unlike the SPI, the sensor SSI only supports angle reading. It is not possible to read or write registers using the SSI. Figure 15 and Table 5 show the SSI timing communication details. tSSCK tM tSSCKH tSSCKL tP SSCK tSSD SSD MSB MSB-1 LSB MSB Figure 15: SSI Timing Table 5: SSI Timing Parameter Description Min Max - 15ns tSSD Delay between the SSCK rising edge and the start of data transfer tSSCK SSCK period 0.2µs 16µs tSSCKL Low level of the SSCK signal 0.1µs 8µs tSSCKH High level of the SSCK signal 0.1µs 8µs tM Transfer timeout (monoflop time) 25µs - tP Dead time: SSCK high time for next data reading 40µs - SSI Read Angle The bit order of the transmitted data is MSB first and LSB last. Every 1µs, new data is transferred into the output buffer. The master device triggers the reading by driving SSCK high. A full reading requires up to 17 clock counts (see Figure 16). MAQ473 Rev. 1.1 8/8/2022 The first clock is a dummy clock to start the transmission. The data length is up to 16 bits long. See the data output length section in the General Characteristics section on page 5 for the number of useful bits delivered at the serial output. MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 15 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS The first MSB are transmitted on the second clock count. If the data length is less than 16 bits, the 16-bit output word is completed by 0s. Therefore, the reading can also be performed with fewer than 16 clock counts. For example, for a part with a 12-bit data length, it is only necessary to send the first dummy clock to start the transmission + 12 clocks to read the angle data. When a trigger event is detected, the data remains in the output buffer until the clock falling edge for the LSB bit = 0 and the transfer timeout time has passed (see Table 6). Table 6: Sensor Data Timing Trigger Event Output Buffer Release First SSCK pulse rising edge SSCK falling edge + timeout tM Figure 16: Diagram of a Full 16-Bit SSI Angle Reading (with First Dummy Clock) Figure 17 shows the timing for consecutive angle readings. Figure 17: Diagram of Two Consecutive 16-Bit SSI Angle Readings with the Required Dead Time between the Frames Parity Bit The parity bit, or check bit, is added to the output string to ensure that the total number of 1s in the string is even. It is used as error detecting code for angle or register reading. The MAQ473 transmits the parity bit at the 17th clock edge (see Table 7 and Figure 18). Table 7: Example of Parity Bit 16-Bit Output 0000000000000000 1000110001100010 0101110100000000 MAQ473 Rev. 1.1 8/8/2022 Number of Bits Set to 1 0 6 5 Output with the Parity Bit 00000000000000000 10001100011000100 01011101000000001 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 16 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS Figure 18: SPI Angle Reading with Parity Bit MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 17 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS REGISTER MAP Table 8: Register Map # of Registers Hex Binary Bit[7] (MSB) 0 0x0 00000 Z[7:0] 1 0x1 00001 Z[15:8] 2 0x2 00010 BCT[7:0] 3 0x3 00011 4 0x4 00100 5 0x5 00101 6 0x6 00110 9 0x9 01001 14 0xE 01110 FW[7:0] 16 0x10 10000 HYS[7:0] 27 0x1B 11011 - Bit[6] - Bit[5] - Bit[4] Bit[3] - PPT[1:0] - Bit[2] Bit[1] Bit[0] (LSB) - ETY ETX - - - - - - - - ILIP[3:0] PPT[9:2] MGLT[2:0] RD - MGH MGHT[2:0] - - MGL - - MIR[3:0] Table 9: Factory Default Values # of Registers Hex Binary Bit[7] (MSB) Bit[6] Bit[5] Bit[4] Bit[3] Bit[2] Bit[1] Bit[0] (LSB) 0 0x0 00000 0 0 0 0 0 0 0 0 1 0x1 00001 0 0 0 0 0 0 0 0 2 0x2 00010 0 0 0 0 0 0 0 0 3 0x3 00011 0 0 0 0 0 0 0 0 4 0x4 00100 1 1 0 0 0 0 0 0 5 0x5 00101 1 1 1 1 1 1 1 1 6 0x6 00110 0 0 0 1 1 1 0 0 9 0x9 01001 0 0 0 0 0 0 0 0 14 0xE 01110 0 1 1 1 0 1 1 1 16 0x10 10000 1 0 0 1 1 1 0 0 MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 18 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS Table 10: Programming Parameters Parameters Symbol # of Bits Zero setting Z 16 Bias current trimming BCT 8 Enable trimming X ETX 1 Enable trimming Y ETY 1 Pulses per turn Index length/position Magnetic field high threshold Magnetic field low threshold Rotation direction Filter window Hysteresis PPT ILIP 10 4 Sets the zero position For side-shaft configuration: reduces the bias current of the X or Y Hall device Biased current trimmed in the X-direction Hall device Biased current trimmed in the Y-direction Hall device Number of pulses per turn of the ABZ output Parametrization of the ABZ index pulse MGHT 3 Sets the field strength high threshold 16 MGLT 3 Sets the field strength low threshold 16 RD FW HYS 1 8 8 Determines the sensor positive direction Size of the digital filter window ABZ output hysteresis 13 18 21 MAQ473 Rev. 1.1 8/8/2022 Description MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. See Table 11 14 15 15 19 Figure 27 19 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS REGISTER SETTINGS Zero Setting The MAQ473’s zero position (a0) can be programmed with 16 bits of resolution. The angle streamed out by the MAQ473 (aOUT) is calculated with Equation (2): aOUT = aRAW - a0 (2) Where aRAW is the raw angle provided by the MAQ473’s front end. The parameter Z[15:0], which is 0 by default, is the complementary angle of the zero setting. In decimals, it can be calculated with Equation (3): a0 = 216 - Z[15 : 0] (3) Table 11 shows the zero-setting parameter. Table 11: Zero-Setting Parameter Z[15:0] 0 1 2 … 65534 65535 Zero Position a0 (16-Bit Decimal) 65536 65535 65534 … 2 1 Zero Position a0 (deg) 360.000 359.995 359.989 … 0.011 0.005 Example To set the zero position to 20°, the Z[15:0] parameter must be equal to the complementary angle, and can be calculated with Equation (4): 20 16 Z [15 : 0]  2  2  61895 360 16 Figure 19: Positive Rotation Direction of the Magnetic Field Table 13: Rotation Direction Parameter RD 0 1 Positive Direction Clockwise (CW) Counterclockwise (CCW) BCT Settings (Bias Current Trimming) Side-Shaft When the MAQ473 is mounted on the side of the magnet, the relationship between the field angle and the mechanical angle is no longer directly linear. This effect is related to the fact that the tangential magnetic field is usually smaller than the radial field. Calculate the field ratio (k) with Equation (5): k = BRAD /BTAN (5) Where BRAD and BTAN are the maximum radial and tangential magnetic fields (see Figure 20). BRAD (4) In binary, it is written as 1111 0001 1100 0111. Table 12 shows the content of registers 0 and 1. BTAN BTAN Table 12: Register 0 and 1 Content Reg Bit[7] Bit[6] Bit[5] Bit[4] Bit[3] Bit[2] Bit[1] Bit[0] 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 Rotation Direction By default, when looking at the top of the package, the angle increases when the magnetic field rotates clockwise (CW) (see Figure 19 and Table 13). MAQ473 Rev. 1.1 8/8/2022 BRAD Figure 20: Side-Shaft Field The k ratio depends on the magnet geometry and the distance to the sensor. Having a k ratio different than 1 results in the sensor output response not being linear with respect to the mechanical angle. Note that the error curve has the shape of a double sinewave (see Figure 22 on page 21). E is the amplitude of this error. MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 20 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS The X-axis and Y-axis bias currents can be reduced by programming in order to recover an equal Hall signal for all angles, and therefore suppress the error. Parameter ETX and ETY control the direction in which sensitivity is reduced. The current reduction is set by the parameter bias current trimming register, BCT[7:0], which is an integer from 0 to 255. In side-shaft configuration (i.e. the sensor center is located beyond the magnet’s outer diameter), k is greater than 1. For optimum compensation, the sensitivity of the radial axis should be reduced by setting the BCT parameter, calculated with Equation (6):  1 BCT[7 : 0] = 258  1    k Determining k with the MagAlpha It is possible to deduce the k ratio from the error curve obtained with the default BCT setting (BCT = 0). Rotate the magnet more than one revolution and record the output. Next, plot the error curve (the output minus the real mechanical position vs. the real mechanical position) and extract two parameters: the maximum error (E) and the position of this maximum with respect to a zero crossing aM (see Figure 22). k can be calculated with Equation (7): k= (6) (7) 40 Figure 21 shows the optimum BCT value for a particular k ratio. Error (deg) 20 Error (deg) 200 tan(E + aM ) tan(aM ) aMm 2E 2E 0 -20 150 BCT -40 0 100 50 100 150 200 250 300 350 rotor angle (deg) Rotor Angle (deg) 50 Figure 22: Error Curve in Side-Shaft Configuration with BCT = 0 0 Table 14 provides some examples. Alternatively, the k parameter can be obtained using Figure 23. 1 1.5 2 2.5 3 3.5 4 4.5 5 k 5 Figure 21: Relation between the k Ratio and the Optimum BCT to Recover Linearity 4.5 Table 14 shows some typical BCT values. 4 Table 14: Example of BCT Settings MAQ473 Rev. 1.1 8/8/2022 Magnet Ratio k 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 BCT[7:0] 0 86 129 155 172 184 194 201 207 k E (deg) 0 11.5 19.5 25.4 30.0 33.7 36.9 39.5 41.8 3.5 3 2.5 2 1.5 1 0 5 10 15 20 25 30 35 40 E (deg) Figure 23: Relation between the Error Measured with BCT = 0 and the Magnet Ratio k MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 21 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS Sensor Orientation From the dot marked on the package, it is possible to know whether the radial field is aligned with sensor coordinate X or Y (see Figure 24). MagHys, the typical hysteresis on the MGH and MGL signals, is 6mT. The MGLT and MGHT thresholds are coded on 3 bits and stored in register 6 (see Table 16). Table 16: Register 6 Register 6 Bit[7] Bit[6] Bit[5] Bit[4] Bit[3] Bit[2] Bit[1] Bit[0] MGLT MGHT The 3-bit MGLT and MGHT values correspond to the magnetic field (see Table 17). Table 17: MGLT and MGHT: Binary to mT Relationship Figure 24: Package Top View with X- and Y-Axes Determine which axis needs to be reduced based on the qualitative field distribution around a ring (see Figure 20 on page 20). For example, with the arrangement shown in Figure 24, the field along the sensor Y direction is tangential and weaker, so the X-axis should be reduced (ETX = 1 and ETY = 0). If both ETX and ETY are set to 1, the current bias is reduced in both directions the same way (i.e. without side-shaft correction) (see Table 15). MGLT or MGHT (8) 000 001 010 011 100 101 110 111 Table 15: Trimming Direction Parameters ETX Enable Trimming of the X-Axis 0 1 ETY Disabled Enabled Enable Trimming of the Y-Axis 0 1 Disabled Enabled Magnetic Field Thresholds The magnetic flags (MGL and MGH) indicate that the magnetic field at the sensor position is out of the range defined by the lower (MGLT) and upper magnetic field thresholds (MGHT) (see Figure 25). Field Threshold in mT From Low to High Magnetic Field 26 41 56 70 84 98 112 126 (7) From High to Low Magnetic Field 20 35 50 64 78 92 106 120 Notes: 7) 8) Valid for VDD = 3.3V. If different, then the field threshold is scaled by the factor VDD / 3.3V. MGLT can have a larger value than MGHT. The MGL and MGH alarm flags are available to be read in register 27 (bit[6] and bit[7], respectively), and their logic state is also given at digital output pins 11 and 16. To read the MGL and MGH flags via the SPI, send the 16-bit read command for register 27: Command 0 1 0 Reg. Address 1 1 0 1 1 Value LSB 0 0 0 0 0 0 0 0 MSB The MAQ473 responds with the register 27 content in the next transmission: MGH MGL Register 27 [7:0] x x MG1L MG2L x x The MGL and MGH flags’ logic state has no effect on the angle output. Figure 25: MGH and MGL Signals as a Function of the Field Strength MAQ473 Rev. 1.1 8/8/2022 MGL Application Note Pulses with a duration of about 1.3μs to 1.5μs appear randomly in the MGL signal. They appear on both the pin and register values (Register 27, bit 6). MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 22 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS These pulses appear around angle values of 44, 138, 224, and 318 degrees (sensor output) or in an interval of ±1.5 degrees around these values. These pulses have an amplitude of 3.3V (VDD). The minimum interval between two pulses is 100μs. MGL Workarounds 1. Invert the MGH signal to replace MGL. The MGL and MGH magnetic thresholds only differ by a small hysteresis (see Table 17 on page 22). An inverted MGH signal can be used to replace the MGL output in the application. 2. Read the MGL signal level twice. Using two readings, which must be between 2µs and 100µs apart, allows the user to distinguish erroneous from real transitions. Table 18 shows examples of different cases. 3. Read register 27 with the SPI and compute a corrected MGL value using MG1L and MG2L. The corrected MGL signal = not (MG1L OR MG2L). This means that the corrected MGL must be set to 1 only when both MG1L and MG2L are equal to 0. See the C implementation below: correctedMGL = !(MG1L | MG2L) Table 18: MGL Multiple Reading Workaround MGL First Reading Case 1 0 Case 2 Case 3 1 1 MGL Second Reading (e.g. 20μs After the First Reading) Second reading is not needed 1 0 True MGL Value FW[7:0] τ (µs) 51 68 85 102 119 (default) 136 153 170 187 64 128 256 512 Effective Resolution at 45mT (Bits) 9.5 10 10.5 11 1024 2048 4096 8192 16384 1 0 The filter window (FW) affects the effective resolution (defined as the ±3σ noise interval) and the output bandwidth, which is characterized by fCUTOFF. Table 19 gives the resulting resolution and bandwidth for each window. 6000 3000 1500 740 StartUp Time (ms) 0.5 1.1 2.5 5.5 11.5 370 12 12 12.5 13 13.5 185 93 46 23 26 57 123 264 fCUTOFF (Hz) The time constant (τ) is the parameter entered in the transfer function (1). This allows the user to accurately model the system and analyze the stability of a control loop. ABZ Incremental Encoder Output The MAQ473 ABZ output emulates a 12-bit incremental encoder (such as an optical encoder), providing logic pulses in quadrature (see Figure 26). Compared to signal A, signal B is shifted by a quarter of the pulse period. During one revolution, signal A pulses n times, where n is programmable from 1 to 1024 pulses per revolution. The number of pulses per channel per revolution is programmed by setting parameter PPT, which consists of 10 bits split between registers 0x4 and 0x5 (see Table 8 on page 18). The factory default value is 1023. Table 20 describes how to program PPT[9:0] to set the required resolution. 0 Filter Window (FW) MAQ473 Rev. 1.1 8/8/2022 Table 19: FW Table 20: PPT PPT[9:0] 0000000000 0000000001 0000000010 0000000011 … 1111111100 1111111101 1111111110 1111111111 Pulses per Revolution 1 (min) 2 3 4 … 1021 1022 1023 1024 (max) Edges per Revolution 4 (min) 8 12 16 … 4084 4088 4092 4096 (max) MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 23 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS For example, to set 120 pulses per revolution (i.e. 480 edges), set PPT to 120 - 1 = 119 (binary: 0001110111). Table 21 shows how to set registers 4 and 5. Table 21: Example PPT Setting for 120 Pulses R4 R5 Bit[7] Bit[6] Bit[5] Bit[4] Bit[3] Bit[2] Bit[1] Bit[0] 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 Table 22: HYS HYS[7:0] 200 188 148 152 156 (default) 116 120 124 84 Hysteresis (deg) 0.08 0.14 0.18 0.36 0.52 0.70 1.4 2.1 2.8 Table 23: RMS Noise FW(7:0) Figure 26: ABZ Output Timing Signal Z (zero or index) rises only once per turn at the zero-angle position. 51 68 85 102 119 (default) 136 153 170 187 Effective Resolution at 45mT (Bits) 9.5 10 10.5 11 11.5 12 12.5 13 13.5 1σ Noise (deg) 0.08 0.06 0.04 0.03 0.02 0.015 0.01 0.007 0.005 The position and length of the Z pulse is programmable via bits ILIP[3:0] in register 0x4 (see Figure 27). Figure 28: Hysteresis of the Incremental Output Figure 27: ILIP Parameter Effect on Index Shape By default, the ILIP parameter is 0000. The index rising edge is aligned with the channel B falling edge. The index length is half of the A or B pulse length, depending on the user’s selection. ABZ Hysteresis The hysteresis is set by the parameter HYS (see Table 22 on page 24). To avoid spurious transitions (see Figure 28 on page 24), it is recommended that the hysteresis be 12 times greater than the output root mean square (RMS) noise (1σ). Table 23 on page 24 shows indications of the 1σ noise MAQ473 Rev. 1.1 8/8/2022 ABZ Jitter The ABZ state is updated at a frequency of 16MHz, enabling accurate operation up to a very high rpm (above 105rpm). The jitter characterizes how far a particular ABZ edge can occur at an angular position different from the ideal position (see Figure 29). Figure 29: ABZ Jitter MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 24 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS The measurable jitter is composed by a systematic jitter (i.e. always the same deviation at a given angle, and given in the General Characteristics section on page 5) and a random jitter. The random jitter reflects the sensor noise. Therefore, the edge distribution is the same as the SPI output noise. The random jitter is a function of the rotation speed. At lower speeds, the random jitter is less than the sensor noise. This is a result of the fact that the probability of measuring an edge at a certain distance from the ideal position depends on the number of ABZ updates at this position. PWM Absolute Output This output provides a logic signal with a duty cycle proportional to the angle of the magnetic field. For the PWM frequency (fPWM), see the General Characteristics section on page 5. The duty cycle is bound by a minimum value (1/514 of the period) and a maximum value (513/514 of the period), so it varies from 1/514 to 513/514 with a resolution of 14 bits (see Figure 30). The angle can be obtained by measuring the on time. Since the absolute fPWM can vary from chip to chip or with the temperature, accurate angle detection requires measuring the duty cycle (i.e. measuring both the on time (tON) and the off time (tOFF)). The angle can be calculated with Equation (8): angle (in ) =  t ON 360  -1 (8)  514 512  t ON + t OFF  Figure 30 shows one period of the PWM signal. The period (t) is 1 / fPWM. MAQ473 Rev. 1.1 8/8/2022 Figure 30: PWM Output Timing, Top Signal = 0°; Bottom Signal = Full Scale (i.e. 360° (1 - 1/16384)) Diagnostic Features The following features can be used to determine correct operation: 1. Parity bit on the angle (see the Parity Bit section on page 16). 2. Magnetic field in range via MIR[3:0] (see below). Magnetic Field in Range Bits MIR[3:0] in register 27 can be used to verify that the magnetic field is between the thresholds set by MGLT[2:0] and MGHT[2:0] in register 6. The value of MIR[3:0] is 0011 when the field is between these thresholds. This also indicates that the Hall sensor front end is functioning correctly and acquiring angle samples. For example, assuming MGLT[2:0] is at its default value of 00 (15mT), and the MGHT[2:0] is at 111 (126mT), then if the field strength is between these values, the MIR[3:0] value is 0011. Table 24 shows the MIR[3:0] values for the default threshold settings described above. MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 25 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS Table 24: MIR[3:0] Logic States MIR[3:0] Conditions MGLT[2:0] at default 15mT, MGHT[2:0] at default 126mT 0011 1111 0000 0001 0010 0100 1000 1001 1010 1011 1100 1101 Field in range and Hall sensor array operational Field above MAGH and MAGL threshold (magnet too close to sensor) Field below MAGH and MAGL threshold (magnet too far away/missing) Invalid state: Hall array sensor functional error Invalid state: Hall array sensor functional error Invalid state: Hall array sensor functional error Invalid state: Hall array sensor functional error Invalid state: Hall array sensor functional error Invalid state: Hall array sensor functional error Invalid state: Hall array sensor functional error Invalid state: Hall array sensor functional error Invalid state: Hall array sensor functional error MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 26 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS TYPICAL APPLICATION CIRCUITS Figure 31: Typical Configurations Using SPI Interface and MGH/MGL Signals Figure 32: Typical Configuration Using ABZ Interface MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 27 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS PACKAGE INFORMATION QFN-16 (3mmx3mm) MAQ473 Rev. 1.1 8/8/2022 MonolithicPower.com MPS Proprietary Information. Patent Protected. Unauthorized Photocopy and Duplication Prohibited. © 2022 MPS. All Rights Reserved. 28 MAQ473 – 9-BIT TO 14-BIT, AUTOMOTIVE ANGLE SENSOR W/ ABZ & PWM OUTPUTS APPENDIX A: DEFINITIONS Effective Resolution (3σ noise level) The smallest angle increment distinguishable from the noise. The resolution is measured by computing three times σ (the standard deviation in degrees) taken across 1,000 data points at a constant position. The resolution in bits is obtained with: log2(360 / 6σ). Refresh Rate The rate at which new data points are stored in the output buffer. ABZ Update Rate The rate at which a new ABZ state is computed. The inverse of this rate is the minimum time between two ABZ edges. Latency The time elapsed between the instant when the data is ready to be read and the instant at which the shaft passes that position. The lag in degrees is lag = latency x v, where v is the angular velocity in deg/s. Start-Up Time The time until the sensor delivers valid data beginning at start-up. Maximum deviation between the average sensor output (at a fixed position) and the true mechanical angle (see Figure A1). Integral Nonlinearity (INL) Figure A1: Resolution, INL, Lag INL can be obtained from the error curve err(a) = out(a) - a, where out(a) is the average across 1,000 sensor outputs and a is the mechanical angle indicated by a highprecision encoder (
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