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 19-5223; Rev 1; 4/10
Stand-Alone OCV-Based Fuel Gauge
General Description
The DS2786B estimates available capacity for rechargeable Li-ion (Li+) and Li+ polymer batteries based on the cell voltage in the open-circuit state following a relaxation period. The open-circuit voltage (OCV) is used to determine relative cell capacity based on a lookup table stored in the IC. This capability makes accurate capacity information available immediately after a battery pack is inserted. During periods of moderate to high rate discharging, which preclude OCV measurements, the DS2786B uses coulomb counting as a secondary means of estimating relative capacity. Remaining capacity is reported in percent, along with cell voltage, current, and temperature information. Cell characteristics and application parameters used in the calculations are stored in on-chip EEPROM. The DS2786B is intended for use on the host side of portable devices, though it can also be mounted within a battery pack. Measurement and estimated capacity data are accessed through an I2C interface. Temperature data is available from an on-die sensor. Resistance measurements of a pack identification resistor and pack thermistor are supported by ratiometric measurements on two auxiliary inputs. The DS2786B comes in a 10-pin, lead-free, TDFN 3mm x 3mm package with an exposed pad (EP).
Features
Relative Capacity Calculated from Combination Coulomb Counter and Open-Circuit Cell Voltage (OCV) Battery Model Accurate Warning of Low-Battery Conditions Even on First Cycle (No Learn Cycle Needed) 12-Bit Battery Voltage Measurement 10mV Accuracy 1.22mV LSB, 0V to 4.5V Input Range 11-Bit Bidirectional Current Measurement 25V LSB, 51.2mV Dynamic Range 1.67mA LSB, 3.4A (RSNS = 15m) Current Accumulation Measurement Resolution 204.8mVh Range 13.65Ah (RSNS = 15m) Internal Temperature Measurement 0.125C LSB, 3C Accuracy Two 11-Bit Auxiliary Input-Voltage Measurements 8 LSB Accuracy, Ratiometric Inputs Eliminate Supply Accuracy Issues VOUT Pin Drives Resistive Dividers, Reduces Current Consumption 2-Wire Interface Low Power Consumption Active Current: 50A (typ), 80A (max) Sleep Current: 1A (typ), 3A (max)
DS2786B
Applications
3G Multimedia Wireless Handsets Digital Still Cameras Digital Audio (MP3) Players
PART DS2786BG+
Ordering Information
TEMP RANGE -20C to +70C PIN-PACKAGE 10 TDFN-EP*
DS2786BG+T&R -20C to +70C 10 TDFN-EP* +Denotes a lead(Pb)-free/RoHS-compliant package. *EP = Exposed pad. T&R = Tape and reel.
Operating Diagram
VOUT
VIN
SYSTEM P
DS2786B
Li+ PROTECTION CIRCUIT THERMISTOR PACKID AIN0 AIN1 VSS SDA SCL SNS I2C INTERFACE
RSNS (EEPROM PROGRAMMING TEST POINT NOT SHOWN)
________________________________________________________________ Maxim Integrated Products
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For pricing, delivery, and ordering information, please contact Maxim Direct at 1-888-629-4642, or visit Maxim's website at www.maxim-ic.com.
Stand-Alone OCV-Based Fuel Gauge DS2786B
ABSOLUTE MAXIMUM RATINGS
Voltage on All Pins Except VPROG Relative to VSS ...-0.3V to +6V Voltage on VPROG Relative to VSS ..........................-0.3V to +18V Operating Temperature Range ...........................-40C to +85C Storage Temperature Range .............................-55C to +125C Lead Temperature (soldering, 10s) .................................+300C Soldering Temperature (reflow) .......................................+260C
Stresses beyond those listed under "Absolute Maximum Ratings" may cause permanent damage to the device. These are stress ratings only, and functional operation of the device at these or any other conditions beyond those indicated in the operational sections of the specifications is not implied. Exposure to absolute maximum rating conditions for extended periods may affect device reliability.
RECOMMENDED DC OPERATING PROCEDURE
(2.5V VDD 4.5V, TA = -20C to +70C.)
PARAMETER Supply Voltage Data I/O Pins Programming Pin VIN, AIN0, AIN1 Pin SYMBOL VDD SCL, SDA VPROG VIN, AIN0, AIN1 (Note 1) (Note 1) (Note 1) (Note 1) CONDITIONS MIN +2.5 -0.3 -0.3 -0.3 TYP MAX +4.5 +4.5 +15.5 VDD + 0.3 UNITS V V V V
DC ELECTRICAL CHARACTERISTICS
(2.5V VDD 4.5V, TA = -20C to +70C, unless otherwise noted.)
PARAMETER Active Current Sleep-Mode Current Current-Measurement Resolution Current-Measurement Full-Scale Magnitude Current-Measurement Offset Error Current-Measurement Gain Error SYMBOL IACTIVE ISLEEP ILSB IFS IOERR IGERR VDD = 3.6V at +25C Timebase Accuracy tERR TA = 0C to +70C TA = -20C to +70C Voltage Error Input Resistance VIN, AIN0, AIN1 AIN0, AIN1 Error VOUT Output Drive VOUT Precharge Time Temperature Error tPRE TERR IO = 1mA 13.2 -3 VGERR RIN VDD = VIN = 3.6V, TA = 0C to +50C TA = -20C to +70C (Note 1) (Note 2) -50 -1.5 -1 -2 -3 -10 -20 15 -8 VDD 0.5 13.7 14.2 +3 +8 VDD = 2.0V, SCL, SDA = VSS SCL, SDA = VSS CONDITIONS MIN TYP 50 0.3 1 25 51.2 +50 +1.5 +1 +2 +3 +10 +20 mV M LSB V ms C % MAX 75 1.0 3 UNITS A A V mV V % of reading
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Stand-Alone OCV-Based Fuel Gauge
DC ELECTRICAL CHARACTERISTICS (continued)
(2.5V VDD 4.5V, TA = -20C to +70C, unless otherwise noted.)
PARAMETER Input Logic-High: SCL, SDA Input Logic-Low: SCL, SDA Output Logic-Low: SDA Pulldown Current: SCL, SDA VPROG Pulldown Input Capacitance: SCL, SDA Bus Low Timeout EEPROM Programming Voltage EEPROM Programming Current EEPROM Programming Time EEPROM Copy Endurance SYMBOL VIH VIL VOL IPD RVPROG CBUS tSLEEP VPROG IPROG tPROG 3.1 100 (Note 3) 1.5 14 (Note 1) (Note 1) IOL = 4mA (Note 1) VDD = 4.2V, VPIN = 0.4V 0.2 20 50 2.2 15 2 14 CONDITIONS MIN 1.4 0.6 0.4 1.0 TYP MAX UNITS V V V A k pF s V mA ms Writes
DS2786B
ELECTRICAL CHARACTERISTICS: 2-WIRE INTERFACE
(2.5V VDD 4.5V, TA = -20C to +70C.)
PARAMETER SCL Clock Frequency Bus Free Time Between a STOP and START Condition Hold Time (Repeated) START Condition Low Period of SCL Clock High Period of SCL Clock Setup Time for a Repeated START Condition Data Hold Time Data Setup Time Rise Time of Both SDA and SCL Signals Fall Time of Both SDA and SCL Signals Setup Time for STOP Condition Spike Pulse Widths Suppressed by Input Filter Capacitive Load for Each Bus Line SCL, SDA Input Capacitance SYMBOL fSCL tBUF tHD:STA tLOW tHIGH tSU:STA tHD:DAT tSU:DAT tR tF tSU:STO tSP CB CBIN (Note 8) (Note 9) (Notes 6, 7) (Note 6) (Note 5) (Note 4) CONDITIONS MIN 0 1.3 0.6 1.3 0.6 0.6 0 100 20 + 0.1CB 20 + 0.1CB 0.6 0 50 400 60 300 300 0.9 TYP MAX 400 UNITS kHz s s s s s s ns ns ns s ns pF pF
Note 1: All voltages are referenced to VSS. Note 2: Offset specified after autocalibration cycle and Current Offset Bias Register = 00h. Note 3: The DS2786B enters the sleep mode 1.5s to 2.2s after (SCL < VIL) and (SDA < VIL). Note 4: Timing must be fast enough to prevent the DS2786B from entering sleep mode due to bus low for period > tSLEEP. Note 5: fSCL must meet the minimum clock low time plus the rise/fall times. _______________________________________________________________________________________ 3
Stand-Alone OCV-Based Fuel Gauge DS2786B
ELECTRICAL CHARACTERISTICS: 2-WIRE INTERFACE (continued)
(2.5V VDD 4.5V, TA = -20C to +70C.) Note 6: The maximum tHD:DAT has only to be met if the device does not stretch the low period (tLOW) of the SCL signal. Note 7: This device internally provides a hold time of at least 100ns for the SDA signal (referred to the VIHMIN of the SCL signal) to bridge the undefined region of the falling edge of SCL. Note 8: Filters on SDA and SCL suppress noise spikes at the input buffers and delay the sampling instant. Note 9: CB--total capacitance of one bus line in pF.
SDA
tF tLOW tR tSU;DAT
tF tHD;STA
tSP
tR
tBUF
SCL
tHD;STA S tHD;DAT
tSU;STA Sr
tSU;STO P S
Figure 1. 2-Wire Bus Timing Diagram
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Stand-Alone OCV-Based Fuel Gauge
Pin Configuration
TOP VIEW
DS2786B
AIN1 AIN0 SCL SDA SNS
1 2 3
10 9 8
VDD VIN VOUT VPROG VSS
DS2786B
4 5 EP 7 6
TDFN (3mm x 3mm)
Pin Description
PIN 1 2 3 4 5 6 7 8 9 10 -- NAME AIN1 AIN0 SCL SDA SNS VSS VPROG VOUT VIN VDD EP Auxiliary Voltage Input Number 1 Auxiliary Voltage Input Number 0 Serial Clock Input. Input only 2-wire clock line. Connect this pin to the clock signal of the 2-wire interface. This pin has a 0.2A typical pulldown to sense disconnection. Serial Data Input/Output. Open-drain 2-wire data line. Connect this pin to the clock signal of the 2wire interface. This pin has a 0.2A typical pulldown to sense disconnection. Current-Sense Input. Connect to the handset side of the sense resistor. Device Ground. Connect to the battery side of the sense resistor. EEPROM Programming Voltage Input. Connect to external supply for production programming. Connect to VSS during normal operation. Voltage Out. Supply for auxiliary input voltage measurement dividers. Connect to high side of resistor-divider circuits. Battery Voltage Input. The voltage of the cell pack is measured through this pin. Power-Supply Input. 2.5V to 4.5V Input Range. Connect to system power through a decoupling network. Exposed Pad. Connect to VSS. FUNCTION
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Stand-Alone OCV-Based Fuel Gauge DS2786B
Detailed Description
The DS2786B provides current-flow, voltage, and temperature-measurement data to support batterycapacity monitoring in cost-sensitive applications. Current is measured bidirectionally over a dynamic range of 51.2mV with a resolution of 25V. Assuming a 15m sense resistor, the current-sense range is 3.4A, with a 1 least significant bit (LSB) resolution of 1.667mA. Current measurements are performed at regular intervals and each measurement is accumulated internally to coulomb count host power consumption. Each current measurement is reported with sign and magnitude in the 2-byte Current Register. Batteryvoltage measurements are reported in the 2-byte Voltage Register with 12-bit (1.22mV) resolution, and auxiliary voltage measurements are reported in the 2byte Aux Volt Registers with 11-bit resolution. Additionally, the Temperature Register reports temperature with 0.125C resolution and 3C accuracy from the on-chip sensor. The on-chip temperature measurement is optional and replaces auxiliary voltage channel AIN1. Figure 1 is the 2-wire bus timing diagram; Figure 2 is the DS2786B block diagram. Figure 3 is an application example.
SWITCH IS ON WHEN AIN0 OR AIN1 IS BEING MEASURED. VOUT BIAS TIMEBASE VDD
VOLTAGE REFERENCE
EEPROM STATE MACHINE 2-WIRE INTERFACE 1k
VPROG
TEMPERATURE MEASUREMENT
ADC
SDA SCL
SNS
AIN1 1k VSS VIN AIN0
IC GROUND
Figure 2. Block Diagram
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Stand-Alone OCV-Based Fuel Gauge DS2786B
BATTERY PACK+ 150
SYSTEM
SYSTEM VDD 1k VIN VPROG PROGRAMMING TEST POINT
VOUT VDD 1k PACKID AIN1 THERM PROTECTION IC (Li+/POLYMER) 1k VSS 10nF (1) 5.6V
AIN0
DS2786B
SDA SCL SNS
SYSTEM SERIAL BUS
RSNS PACK-
SYSTEM VSS (1)
(1) OPTIONAL FOR 8kV/15kV ESD
2.5V
1nF
1nF
Figure 3. Application Example
The DS2786B provides accurate relative capacity measurements during periods of host system inactivity by looking at cell open-circuit voltage. Cell capacity is calculated using an OCV voltage profile and a 1-byte scale factor to weight-accumulated current. The OCV voltage profile and scale factor are stored in EEPROM memory. The EEPROM memory is constructed with a SRAM shadow so that the OCV voltage profile and scale factor can be overwritten by the host to accommodate a variety of cell types and capacities from multiple-cell vendors. The I 2 C interface also allows read/write access to the Status, Configuration, and Measurement Registers.
Power Modes
The DS2786B operates in one of two power modes: Active and Sleep. While in Active Mode, the DS2786B operates as a high-precision battery monitor with temperature, voltage, auxiliary inputs, current, and accumulated current measurements acquired continuously and the
resulting values updated in the measurement registers. In Sleep Mode, the DS2786B operates in a low-power mode with no measurement activity. Read-and-write access is allowed to all registers in either mode. The DS2786B operating mode transitions from sleep to active when: (SCL > VIH) or (SDA > VIH) The DS2786B operating mode transitions from Active to Sleep when: SMOD = 1 and (SCL < VIL) and (SDA < VIL) for tSLEEP Caution: If SMOD = 1, a pullup resistor is required on SCL and SDA in order to ensure that the DS2786B transitions from Sleep to Active Mode when the battery is charged. If the bus is not pulled up, the DS2786B remains in Sleep and cannot accumulate the charge current. This caution statement applies particularly to a battery that is charged on a standalone charger.
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Stand-Alone OCV-Based Fuel Gauge DS2786B
Parameter Measurement
The DS2786B uses a sigma-delta A/D converter to make measurements. The measurement sequence shown in Figure 4 repeats continuously while the DS2786B is in Active Mode. The VOUT pin is activated tPRE before the AIN0 and AIN1 conversion to allow for the VOUT output voltage to settle. The DS2786B can be configured to measure temperature using its on-chip sensor instead of the AIN1 input. When the internal temperature measurement uses the AIN1 conversion timeslot, VOUT is not activated. A full sequence of voltage measurements nominally takes 1760ms to complete.
VIN PIN MEASUREMENT VOLTAGE REGISTER
AVERAGE OVER 440ms 0.86ms DELAY
NEW REGISTER VALUE
VOUT PIN
INACTIVE tPRE
ACTIVE (INACTIVE FOR TEMPERATURE MEASUREMENT)
INACTIVE
ALTERNATING AIN0 OR AIN1/TEMPERATURE MEASUREMENT
AVERAGE OVER 220ms 0.86ms DELAY NEW REGISTER VALUE
AIN0 OR AIN1/ TEMPERATURE REGISTER
DIFFERENTIAL CURRENT MEASUREMENT
AVERAGE OVER 220ms 0.86ms DELAY 0.86ms DELAY
CURRENT REGISTER
NEW REGISTER VALUE
440ms
220ms CYCLE OF MEASUREMENTS REPEATS EVERY 880ms.
220ms
Figure 4. Measurement Sequence
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Stand-Alone OCV-Based Fuel Gauge
Voltage Measurement
Battery voltage is measured at the VIN input with respect to VSS over a 0 to 4.999V range and with a resolution of 1.22mV. The result is updated every 880ms and placed in the Voltage Register in two's-complement form. Voltages above the maximum register value are reported as 7FFFh. Figure 5 is the Voltage Register format. The input impedance of V IN is sufficiently large (> 15M) to be connected to a high-impedance voltage-divider in order to support multiple-cell applications. The pack voltage should be divided by the number of series cells to present a single-cell average voltage to the VIN input. Every 1024th conversion, the ADC measures its input offset to facilitate offset correction to improve voltage accuracy. Offset correction occurs approximately every 15min. The resulting correction factor is applied to the subsequent 1023 measurements. During the offset-correction conversion, the ADC does not measure the VIN signal. The voltage measurement just prior to the offset conversion is displayed in the Voltage Register. The OCV algorithm automatically adjusts for the effects of the offset-correction cycle.
DS2786B
Auxilary Input Measurements
The DS2786B has two auxiliary voltage-measurement inputs, AIN0 and AIN1. Both are measured with respect to VSS. These inputs are designed for measuring resistor ratios, particularly useful for measuring thermistor or pack identification resistors. Prior to the beginning of a measurement cycle on AIN0 or AIN1, the VOUT pin outputs a reference voltage in order to drive a resistive divider formed by a known resistor value, and the unknown resistance to be measured. This technique delivers good accuracy at a reasonable cost, as it removes reference tolerance from the error calculations. Measurements alternate between each input. Each auxiliary measurement is therefore updated every 1760ms and placed in the corresponding AIN0 or AIN1 Register in two's-complement form. Figure 6 shows the Auxiliary Input Registers format.
MSB--ADDRESS 0Ch S MSB "S": SIGN BIT(S), "X": RESERVED 211 210 29 28 27 26 25 LSB 24 MSB 23 22
LSB--ADDRESS 0Dh 21 20 X X X LSB UNITS: 1.22mV
Figure 5. Voltage Register Format
AIN0 S MSB 210 29
MSB--ADDRESS 08h 28 27 26 25 24 LSB 23 MSB 22 21
LSB--ADDRESS 09h 20 X X X X LSB UNITS: VOUT x 1/2047
"S": SIGN BIT, "X": RESERVED
AIN1 S MSB 210 29
MSB--ADDRESS 0Ah 28 27 26 25 24 LSB 23 MSB 22 21
LSB--ADDRESS 0Bh 20 X X X X LSB UNITS: VOUT x 1/2047
"S": SIGN BIT, "X": RESERVED
Figure 6. Auxiliary Input Registers Format
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Stand-Alone OCV-Based Fuel Gauge DS2786B
Temperature Measurement
The DS2786B uses an integrated temperature sensor to measure battery temperature with a resolution of 0.125C. Temperature measurements are updated every 1760ms and placed in the Temperature Register in two's-complement form. The format of the Temperature Register is shown in Figure 7. The ITEMP bit in the Status/Configuration Register must be set to enable the internal temperature measurement instead of the AIN1 measurement. input as long as the continuous or average signal level does not exceed 51.2mV over the conversion-cycle period. The ADC samples the input differentially and updates the Current Register every 880ms at the completion of each conversion cycle. Figure 8 describes the Current Measurement Register format and resolution for each option. Charge currents above the maximum register value are reported at the maximum value (7FFFh = +51.2mV). Discharge currents below the minimum register value are reported at the minimum value (8000h = -51.2mV). Every 1024th conversion, the ADC measures its input offset to facilitate offset correction to improve current accuracy. Offset correction occurs approximately every 15min. The resulting correction factor is applied to the subsequent 1023 measurements. During the offset correction conversion, the ADC does not make a measurement. The current measurement just prior to the offset conversion is displayed in the Current Register. See Table 1 for current range and resolution for various RSNS values.
LSB--ADDRESS 0Bh 24 23 LSB 22 MSB 21 20 X X X X X LSB UNITS: 0.125C
Current Measurement
In the Active Mode of operation, the DS2786B continually measures the current flow into and out of the battery by measuring the voltage drop across a low-value current-sense resistor, RSNS, connected between the SNS and VSS pins. The voltage-sense range between SNS and VSS is 51.2mV. Note that positive current values occur when VSNS is less than VSS, and negative current values occur when VSNS is greater than VSS. Peak signal amplitudes up to 102mV are allowed at the
MSB--ADDRESS 0Ah S MSB "S": SIGN BIT(S), "X": RESERVED 29 28 27 26 25
Figure 7. Temperature Register Format
MSB--ADDRESS 0Eh S MSB "S": SIGN BIT 210 29 28 27 26 25 24 LSB 23 MSB 22 21
LSB--ADDRESS 0Fh 20 X X X X LSB UNITS: 25V/RSNS
Figure 8. Current Register Formats
Table 1. Current Range and Resolution for Various RSNS Values
CURRENT RESOLUTION (1 LSB) |V SS - VSNS| 25V RSNS 20m 1.25mA 15m 1.667mA 10m 2.5mA 5m 5mA VSS - VSNS 51.2mV CURRENT INPUT RANGE RSNS 20m 2.56A 15m 3.41A 10m 5.12A 5m 10.24A
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Stand-Alone OCV-Based Fuel Gauge
Current Offset Bias
The Current Offset Bias Register (COBR) allows a programmable offset value to be added to raw current measurements. The result of the raw current measurement plus the COBR value is displayed as the current measurement result in the Current Register, and is used for current accumulation and detection of an OCV condition. The COBR value can be used to correct for a static offset error, or can be used to intentionally skew the current results and therefore the current accumulation. Read and write access is allowed to COBR. Whenever the COBR is written, the new value is applied to all subsequent current measurements. COBR can be programmed in 25V steps to any value between +3.175mV and -3.2mV. The COBR value is stored as a two's-complement value in nonvolatile (NV) memory. The COBR factory default value is 00h. Figure 9 shows the Current Offset Bias Register format.
DS2786B
Table 2. Accumulated Current Range for Various RSNS Values
IACR RANGE VSS - VSNS 204.8mVh RSNS 20m 10.24Ah 15m 13.65Ah 10m 20.48Ah 5m 40.96Ah
Cell-Capacity Estimation
The DS2786B uses a hybrid OCV measurement and coulomb-counting algorithm to estimate remaining cell capacity. During periods of charging or discharging the cell, the DS2786B counts charge flow into and out of the cell. When the application becomes inactive, the DS2786B waits for the cell voltage to relax and then adjusts the coulomb count based on an open-circuit voltage cell model stored in device EEPROM. The resulting calculation is reported to the system as a percentage value between 0 and 100%. As the cell ages, a learn feature adjusts for changes in capacity. The Relative Capacity Register reports remaining cell charge as a percentage of full. Relative capacity is reported with a resolution of 0.5% and is limited to a value between 0% and 100%. The Relative Capacity Register is updated each time the IC performs a current measurement or open-circuit cell-voltage measurement. See Figure 10.
ADDRESS 02h 27 MSB 26 25 24 23 22 21 20 LSB UNITS: 0.5%
Current Accumulation
An Internal Accumulated Current Register (IACR) serves as an up/down counter holding a running count of charge since the last OCV condition. Current measurement results, plus a programmable bias value are internally summed, or accumulated, at the completion of each current measurement-conversion period. The IACR has a range of 204.8mVh. The IACR uses the Initial or Learned Cell Capacity Registers to increment or decrement the Relative Capacity Register as current flows into or out of the battery. In this way, the fuel gauge is accurate even when an OCV condition does not occur for an extended time period. See Table 2 for the accumulated current range for various RSNS values.
ADDRESS 60h S MSB "S": SIGN BIT 26 25 24 23 22 21 20 LSB UNITS: 25V/RSNS
Figure 10. Relative Capacity Register Format
Figure 9. Current Offset Bias Register Format
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Stand-Alone OCV-Based Fuel Gauge DS2786B
Prior to the first learn operation, the relative capacity value is calculated by adding the IACR multiplied by the initial capacity scaling factor (7Ah) to the last OCV relative capacity (16h). After the first learn operation, the relative capacity value is calculated by adding the IACR multiplied by the learned capacity scaling factor (17h) to the last OCV relative capacity (16h). Each Capacity Scaling Factor Register has a resolution of 78.125%/Vh and a maximum range of 0 to 19921.875%/Vh. During assembly, the Initial Capacity Register should be programmed to the capacity of the cell. For example, an application using a 1Ah cell and 0.015 sense resistor would set the Initial Capacity Register to a value of (100%/(1Ah x 0.015))/ 78.125%/Vh = 55h. The Learned Capacity Scaling Factor Register is controlled by the DS2786B. The power-up value is 00h, and the register is updated with the calculated new cell capacity value after every learn operation. See Figures 11 and 12. operational current, but above the maximum idle current of the application should be selected. The OCV Threshold Register has a resolution of 25V/RSNS, and a range from 0mV/RSNS to 6.375mV/RSNS. The factory default value is 28h. See Figure 13 for the OCV threshold register format. While the measured current is below the OCV threshold level, the DS2786B actively searches for a relaxed cell by calculating the change in cell voltage as reported in the Voltage Register over 7.5min intervals (dV/dt). If the 7.5min dV/dt change of an average of four Voltage Register readings is less than the value stored in the OCV dV/dt Threshold Register, the DS2786B determines that the cell is now in a relaxed state and the Relative Capacity Register is adjusted based on the OCV cell model stored in parameter EEPROM. This operation occurs repeatedly every 7.5min up to 1hr after the cell enters a relaxed state. The OCV dV/dt Threshold Register has a resolution of 0.61mV/7.5min and a range from 0mV/7.5min to 9.15mV/7.5min. The factory default value is 2.44mV/7.5min. Note that the upper 4 bits of the OCV dV/dt Threshold Register are used to EEPROM back bits from the Status/Configuration Register. Figure 14 shows the OCV dV/dt threshold register format.
OCV Detection
When the magnitude of the measured current (after COBR is applied) is less than the value defined by the OCV Threshold Register, the DS2786B begins dV/dt measurement evaluation to detect an OCV voltage condition. A threshold value that is below the minimum
ADDRESS 7Ah 27 MSB 26 25 24 23 22 21 20 LSB UNITS: 78.125%/Vh
ADDRESS 7Bh 27 MSB 26 25 24 23 22 21 20 LSB UNITS: 25V/RSNS
Figure 11. Initial Capacity Scaling Factor Register Format
Figure 13. OCV Threshold Register Format
ADDRESS 17h 27 MSB 26 25 24 23 22 21 20 LSB UNITS: 78.125%/Vh SMOD MSB
ADDRESS 7Ch LDIS VODIS ITEMP 23 22 21 20 LSB UNITS: 0.61mV/7.5min
Figure 12. Learned Capacity Scaling Factor Register Format
Figure 14. OCV dV/dt Threshold Register Format
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Stand-Alone OCV-Based Fuel Gauge
OCV Cell Model
The OCV cell model is a 9-point piece-wise linear approximation of open-circuit cell voltage vs. the remaining capacity of the cell. Whenever an OCV update occurs, the Relative Capacity Register is adjusted to a new value based on the OCV voltage reading and a linear approximation of the table values. Figure 15 shows the factory-default cell model stored in EEPROM. The OCV cell model can be modified by changing the Capacity and Voltage Breakpoint Registers in EEPROM. Capacity 0 is fixed at 0% and cannot be changed. Capacity 1 through Capacity 7 are stored with 0.5% resolution at addresses 61h through 67h, respectively. Capacity values must be monotonic (Capacity 1 > Capacity 0, Capacity 2 > Capacity 1, etc.), but otherwise can be written to any value between 0.5% to 99.5%. Capacity 8 is fixed at a value of 100% and cannot be changed. See Figure 16. Voltage breakpoints require 2 bytes per breakpoint, but are otherwise stored in a similar manner: voltage breakpoint 0: MSB stored at address 68h, LSB stored at address 69h. Other voltage breakpoints are stored sequentially through address location 79h. Each voltage breakpoint has a resolution of 1.22mV, and a range from 0.0V to 4.996V. Voltage breakpoint values must also be monotonic. Figure 17 is the Voltage Breakpoint Register format.
DS2786B
4.2 BREAKPOINT 7 4.087V 90.5% BREAKPOINT 4 3.831V 52.5% BREAKPOINT 8 4.171V 100% BREAKPOINT 6 4.042V 85% BREAKPOINT 5 4.005V 80%
4.0 BREAKPOINT 2 3.673V 10%
3.8
3.6 BREAKPOINT 3 3.752V 25%
BREAKPOINT 1 3.619V 5%
3.4
BREAKPOINT 0 3.186V 0%
3.2
3.0 100% 80% 60% 40% 20% 0%
Figure 15. DS2786BG-C3 OCV Cell Model
ADDRESS 61h-67h 27 MSB 26 25 24 23 22 21 20 LSB UNITS: 0.5%
Figure 16. Capacity 1 to Capacity 7 Registers Format
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Stand-Alone OCV-Based Fuel Gauge DS2786B
MSB--EVEN ADDRESSES 68h-78h 211 MSB "X": RESERVED 210 29 28 27 26 25 24 LSB 23 MSB 22 LSB--ODD ADDRESS 69h-79h 21 20 X X X X LSB UNITS: 1.22mV
Figure 17. Voltage Breakpoint Register Format
Initial Capacity Estimation
The DS2786B calculates relative capacity immediately upon power-up. During initialization, the DS2786B makes a voltage measurement and uses the OCV cell model data to determine a starting point for the Relative Capacity Register. This estimation occurs regardless of the load on the cell. Any error induced from cell loading is removed at the next OCV adjustment. The initial voltage measurement used in determining the starting point is stored in the Initial Voltage Register until the IC is power cycled. See Figure 18.
New Capacity Learning
As the cell ages, the Initial Capacity Scaling Factor Register value might no longer accurately reflect the true capacity of the cell, causing error in relative capacity calculation while in coulomb-counting mode of operation. The DS2786B has a learn feature that allows the IC to remain accurate as the cell changes. The DS2786B
compares the percent relative capacity difference between the last two OCV updates to the change in the coulomb count to learn the new cell capacity. The Last OCV Register maintains the relative capacity percentage at the previous OCV adjustment point used for learning the new cell capacity. The last OCV is updated with a new value at each OCV adjustment. Figure 19 shows the Last OCV Register format. Example: Assuming a 15m sense resistor, the DS2786B adjusts the relative capacity of a 1000mAh cell to 10% based on an OCV measurement during an idle period of the application. The cell is then charged by 500mAh (to 60% expected) based on the internal coulomb count multiplied by the learned capacity scaling factor value of 55h. The next OCV adjustment determines the relative capacity should actually be at 65%, not 60%. The DS2786B then adjusts the learned capacity scaling factor value upward to (65% - 10%)/(500mAh x 0.015) = 5Eh, lowering the expected cell capacity by approximately 10%.
MSB--ADDRESS 14h S MSB "S": SIGN BIT(S), "X": RESERVED 211 210 29 28 27 26 25 LSB 24 MSB 23 22
LSB--ADDRESS 15h 21 20 X X X LSB UNITS: 1.22mV
Figure 18. Initial Voltage Register Format
ADDRESS 16h 27 MSB 26 25 24 23 22 21 20 LSB UNITS: 0.5%
Figure 19. Last OCV Register Format
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Stand-Alone OCV-Based Fuel Gauge
ADDRESS 7Eh 27 MSB 26 25 24 23 22 21 20 LSB UNITS: 0.5%
Figure 20. Learn Delta Percent Threshold
The learn delta percent threshold allows the application to select how large a cell capacity change is required before the new cell-capacity value is learned. The difference between the present OCV measurement and the last OCV measurement must be greater than the learn delta percent threshold value for a learn to occur. This prevents IC measurement resolution from adding error to the learned cell-capacity value. It is recommended this register be set to a value of at least 50%. Figure 20 shows the learn delta percent threshold.
Memory Map
The DS2786B has memory space with registers for instrumentation, status, and control. When the MSB of a 2-byte register is read, both the MSB and LSB are latched and held for the duration of the read data command to prevent updates during the read and ensure synchronization between the 2 register bytes. For consistent results,
always read the MSB and the LSB of a 2-byte register during the same read data command sequence. Memory locations 60h through 7Fh are EEPROM storage locations. EEPROM memory is shadowed by RAM to eliminate programming delays between writes and to allow the data to be verified by the host system before being copied to EEPROM. The read data and write data protocols to/from EEPROM memory addresses access the shadow RAM. Setting the RCALL bit in the Command Register (FEh) initiates data transfer from the EEPROM to the shadow RAM. See Figure 21. Setting the COPY bit in the Command Register initiates data transfer from the shadow RAM to the EEPROM. An external voltage supply must be provided on the VPROG pin prior to writing the COPY bit. The DS2786B requires the COPY bit be reset to zero within the tPROG time window to properly program EEPROM. Resetting COPY too soon might prevent a proper write of the cells. Resetting COPY too late might degrade EEPROM copy endurance. The DS2786B uses shadow RAM data for fuel-gauge calculations. Fuel-gauge information can be changed in the application by writing the shadow RAM locations. Afterwards, the SOCV bit should be written to reset the fuel gauge. Note that any reset of the IC causes the shadow RAM data to be restored from EEPROM.
DS2786B
COPY
EEPROM
WRITE SERIAL INTERFACE READ SHADOW RECALL
Figure 21. EEPROM Access Through Shadow RAM
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Stand-Alone OCV-Based Fuel Gauge DS2786B
Table 3. Memory Map
ADDRESS 00h 01h 02h 03h to 07h 08h 09h 0Ah 0Bh 0Ch 0Dh 0Eh DESCRIPTION Reserved Status/Config Register Relative Capacity Reserved Auxiliary Input 0 MSB Auxiliary Input 0 LSB Auxiliary Input 1/ Temperature MSB Auxiliary Input 1/ Temperature LSB Voltage Register MSB Voltage Register LSB Current Register MSB READ/WRITE -- R/W R -- R R R R R R R ADDRESS 0Fh 10h to 13h 14h 15h 16h 17h 18h to 5Fh 60h to 7Fh 80h to FDh FEh FFh DESCRIPTION Current Register LSB Reserved Initial Voltage MSB Initial Voltage LSB Last OCV Relative Capacity Learned Capacity Scaling Factor Reserved Parameter EEPROM Reserved Command Reserved READ/WRITE R -- R R R R -- R/W -- R/W --
Table 4. Parameter EEPROM Memory Block
ADDRESSS 60h 61h 62h 63h 64h 65h 66h 67h 68h 69h 6Ah 6Bh 6Ch 6Dh 6Eh 6Fh DESCRIPTION Current Offset Bias Register Capacity 1 Capacity 2 Capacity 3 Capacity 4 Capacity 5 Capacity 6 Capacity 7 Voltage Breakpoint 0 MSB Voltage Breakpoint 0 LSB Voltage Breakpoint 1 MSB Voltage Breakpoint 1 LSB Voltage Breakpoint 2 MSB Voltage Breakpoint 2 LSB Voltage Breakpoint 3 MSB Voltage Breakpoint 3 LSB FACTORY VALUE 00h 0Ah 14h 32h 69h A0h AAh B5h A3h 20h B9h 50h BCh 10h C0h 20h ADDRESS 70h 71h 72h 73h 74h 75h 76h 77h 78h 79h 7Ah 7Bh 7Ch 7Dh 7Eh 7Fh DESCRIPTION Voltage Breakpoint 4 MSB Voltage Breakpoint 4 LSB Voltage Breakpoint 5 MSB Voltage Breakpoint 5 LSB Voltage Breakpoint 6 MSB Voltage Breakpoint 6 LSB Voltage Breakpoint 7 MSB Voltage Breakpoint 7 LSB Voltage Breakpoint 8 MSB Voltage Breakpoint 8 LSB Initial Capacity Scaling OCV Current Threshold OCV dV/dt Threshold I2C Address Configuration* Learn Threshold User EEPROM FACTORY VALUE C4h 20h CDh 10h CEh F0h D1h 40h D5h 90h 80h 06h 94h 60h* 78h 00h
*The factory default 7-bit slave address is 0110110. The upper 3 bits are fixed at 011; the lower 4 bits can be changed by writing the I2C Address Configuration Register as illustrated in Figures 24 and 25.
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Stand-Alone OCV-Based Fuel Gauge
Status/Config Register
The Status/Config Register is read/write with individual bits designated as read only. Bit values indicate status as well as program or select device functionality. Bits 3 though 6 are EEPROM backed at memory location 7Ch. Note that their bit positions differ between these locations. See Figure 22: * PORF--The power-on-reset flag is set to indicate initial power-up. PORF is not cleared internally. The user must write this flag value to a zero in order to use it to indicate subsequent power-up events. POR event causes a reset of the fuel gauge. PORF is read/write-to-zero. * SMOD--Sleep Mode enable. A value of 1 allows the IC to enter Sleep Mode when SCL and SDA are low for tSLEEP. A value of zero disables the transition to Sleep Mode. This bit is EEPROM backed by bit 7 of memory location 7Ch. The factory-programmed value is 1. Caution: SMOD sleep feature must be disabled when a battery is charged on an external charger that does not connect to the SDA or SCL pins. SMOD sleep can be used if the charger pulls SDA or SCL high. The IC remains in sleep on a charger that fails to properly drive SDA or SCL and therefore does not adjust relative capacity when a battery is charged. * LDIS--Learn disable. A value of 1 disables cellcapacity learning by the IC. A value of zero allows cell-capacity learning to occur normally. This bit is EEPROM backed by bit 6 of memory location 7Ch. The factory-programmed value is zero. * VODIS--VOUT disable. A value of 1 disables the VOUT output. When set to zero, this output is driven tPRE before the AIN0 conversion begins, and disabled after the AIN1 conversion ends. This bit is EEPROM backed by bit 5 of memory location 7Ch. The factory-programmed value is zero. ITEMP--ITEMP. A value of 1 enables measurement of temperature using the internal sensor during the AIN1 conversion timeslot. The AIN1 input is not selected and VOUT is not enabled during the AIN1 timeslot. A value of zero restores the measurement of AIN1 and enables VOUT during the AIN1 timeslot. This bit is EEPROM backed by bit 4 of memory location 7Ch. The factory-programmed value is 1. AIN1--AIN1 conversion valid. This read-only bit indicates that the VOUT output was enabled and a conversion has occurred on the AIN1 pin. When using the VODIS bit, before reading the AIN1 Registers, read the AIN1 bit. Only once the AIN1 bit is set should the AIN1 Register be read. AIN0--AIN0 conversion valid. This read-only bit indicates that the VOUT output was enabled and a conversion has occurred on the AIN0 pin. When using the VODIS bit, before reading the AIN0 Registers, read the AIN0 bit. Only once the AIN0 bit is set should the AIN0 Register be read.
DS2786B
*
*
*
Command Register
The Command Register is read/write accessible. Bit values indicate operations requested to be performed by the device. See Figure 23 for the Command Register format.
ADDRESS 01h BIT 7 X X--Reserved. BIT 6 PORF BIT 5 SMOD BIT 4 LDIS BIT 3 VODIS BIT 2 ITEMP BIT 1 AIN1 BIT 0 AIN0
Figure 22. Status/Config Register Format
ADDRESS FEh BIT 7 POR X--Reserved. BIT 6 1 BIT 5 X BIT 4 X BIT 3 POCV BIT 2 SOCV BIT 1 RCALL BIT 0 COPY
1--Bit always reads logic 1.
Figure 23. Command Register Format
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Stand-Alone OCV-Based Fuel Gauge DS2786B
* COPY--The Copy bit is set to start a copy command of the scratchpad to EEPROM. A programming voltage must be present on the VPROG pin prior for the copy to be successful. The Copy bit must be cleared by software within the tPROG time window. RCALL--The Recall bit is set to recall the contents of EEPROM into the scratchpad. SOCV--Stored OCV calculation. This command can be used to reset the relative capacity calculation after updating OCV cell model data in the scratchpad. When set to 1, the part is performing an OCV calculation based on the voltage stored in the Initial Voltage Register and the OCV lookup table values present in the scratchpad. Writing the bit to 1 forces a calculation. Forcing an OCV calculation creates capacity-estimation error. The bit is cleared when the hardware completes the calculation. POCV--Present OCV calculation. When set to 1, the part is performing an OCV calculation based on the voltage stored in the Voltage Register and the OCV lookup table values present in the scratchpad. Writing the bit to 1 forces a calculation. This function should be used for test purposes only. Forcing an OCV calculation creates capacity-estimation error. The bit is cleared when the hardware completes the calculation. POR--Power-on reset. A value of 1 starts a poweron reset event. The bit is cleared on the next start or stop on the 2-wire bus, exiting the reset state.
Bit Transfer
One data bit is transferred during each SCL clock cycle, with the cycle defined by SCL transitioning low to high and then high to low. The SDA logic level must remain stable during the high period of the SCL clock pulse. Any change in SDA when SCL is high is interpreted as a START or STOP control signal.
* *
Bus Idle
The bus is defined to be idle, or not busy, when no master device has control. Both SDA and SCL remain high when the bus is idle. The STOP condition is the proper method to return the bus to the idle state.
START and STOP Conditions
The master initiates transactions with a START condition (S) by forcing a high-to-low transition on SDA while SCL is high. The master terminates a transaction with a STOP condition (P), a low-to-high transition on SDA while SCL is high. A Repeated START condition (Sr) can be used in place of a STOP then START sequence to terminate one transaction and begin another without returning the bus to the idle state. In multimaster systems, a Repeated START allows the master to retain control of the bus. The START and STOP conditions are the only bus activities in which the SDA transitions when SCL is high.
*
*
Acknowledge Bits
Each byte of a data transfer is acknowledged with an Acknowledge bit (A) or a No Acknowledge bit (N). Both the master and the DS2786B slave generate Acknowledge bits. To generate an acknowledge, the receiving device must pull SDA low before the rising edge of the acknowledge-related clock pulse (ninth pulse) and keep it low until SCL returns low. To generate a no acknowledge (also called NAK), the receiver releases SDA before the rising edge of the acknowledge-related clock pulse and leaves SDA high until SCL returns low. Monitoring the Acknowledge bits allows for detection of unsuccessful data transfers. An unsuccessful data transfer can occur if a receiving device is busy or if a system fault has occurred. In the event of an unsuccessful data transfer, the bus master should reattempt communication.
User EEPROM
Location 7Fh provides 1 byte available for storage of user-defined information. This byte does not affect operation of the fuel gauge. Factory default is 00h.
2-Wire Bus System
The 2-wire bus system supports operation as a slaveonly device in a single or multislave, and single or multimaster system. The 2-wire interface consists of a serial data line (SDA) and serial clock line (SCL). SDA and SCL provide bidirectional communication between the DS2786B slave device and a master device at speeds up to 400kHz. The DS2786B's SDA pin operates bidirectionally; that is, when the DS2786B receives data, SDA operates as an input, and when the DS2786B returns data, SDA operates as an open-drain output, with the host system providing a resistive pullup. The DS2786B always operates as a slave device, receiving and transmitting data under the control of a master device. The master initiates all transactions on the bus and generates the SCL signal, as well as the START and STOP bits, which begin and end each transaction.
18
Data Order
A byte of data consists of 8 bits ordered MSB first. The LSB of each byte is followed by the Acknowledge bit. The DS2786B registers composed of multibyte values are ordered MSB first. The MSB of multibyte registers is stored on even data memory addresses.
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Stand-Alone OCV-Based Fuel Gauge
Slave Address
A bus master initiates communication with a slave device by issuing a START condition followed by a slave address (SAddr) and the read/write (R/W) bit. When the bus is idle, the DS2786B continuously monitors for a START condition followed by its slave address. When the IC receives an address that matches its slave address, it responds with an Acknowledge bit during the clock period following the R/W bit. The DS2786BG-C3 7-bit slave address is 0110110. The upper 3 bits are fixed at 011; the lower 4 bits can be changed by writing the I 2 C Address Configuration Register at location 7Dh.
Bus Timing
The DS2786B is compatible with any bus timing up to 400kHz. No special configuration is required to operate at any speed.
DS2786B
2-Wire Command Protocols
The command protocols involve several transaction formats. The simplest format consists of the master writing the START bit, slave address, and R/W bit, and then monitoring the Acknowledge bit for presence of the DS2786B. More complex formats such as the write data, read data, and function command protocols write data, read data, and execute device-specific operations. All bytes in each command format require the slave or host to return an Acknowledge bit before continuing with the next byte. Each function command definition outlines the required transaction format. Table 5 applies to the transaction formats.
Read/Write Bit
The R/W bit following the slave address determines the data direction of subsequent bytes in the transfer. R/W = 0 selects a write transaction, with the following bytes being written by the master to the slave. R/W = 1 selects a read transaction, with the following bytes being read from the slave by the master. With the ADDR3-ADDR0 bits at their default of 0110, writes occur using address 0x6Ch, while reads occur at 0x6Dh.
ADDRESS 7Dh BIT 7 ADDR3 X--RESERVED. ADDR3:0--USER-ADJUSTABLE BITS OF THE DS2786BG-C3'S I2C ADDRESS. FACTORY DEFAULT IS 0110. BIT 6 ADDR2 BIT 5 ADDR1 BIT 4 ADDR0 BIT 3 X BIT 2 X BIT 1 X BIT 0 X
Figure 24. I2C Address Configuration Register Format
BIT 7 0
BIT 6 1
BIT 5 1
BIT 4 ADDR3
BIT 3 ADDR2
BIT 2 ADDR1
BIT 1 ADDR0
BIT 0 R/W
Figure 25. DS2786B I2C Address Byte Format
Table 5. 2-Wire Protocol Key
KEY S SAddr FCmd MAddr Data A N START bit Slave address (7 bit) Function command byte Memory address byte Data byte written by master Acknowledge bit--master No acknowledge--master DESCRIPTION KEY Sr W R P Data A N R/W bit = 0 R/W bit = 1 STOP bit Data byte returned by slave Acknowledge bit--slave No acknowledge--slave DESCRIPTION Repeated START
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Stand-Alone OCV-Based Fuel Gauge DS2786B
Basic Transaction Formats
Write: S SAddr W A MAddr A Data0 A P A write transaction transfers 1 or more data bytes to the DS2786B. The data transfer begins at the memory address supplied in the MAddr byte. Control of the SDA signal is retained by the master throughout the transaction, except for the acknowledge cycles.
Read: SAddr W A MAddr A Sr SAddr R A Data0 N P Write Portion Read Portion
1 can be written immediately after the acknowledgment of the data at address MAddr. If the bus master continues an autoincremented write transaction beyond address 4Fh, the DS2786B ignores the data. Data is also ignored on writes to read-only addresses and reserved addresses, as well as a write that autoincrements to the Function Command Register (address FEh). Incomplete bytes and bytes that are not acknowledged by the DS2786B are not written to memory. As noted in the Memory Map section, writes to EEPROM locations modify the shadow RAM only.
A read transaction transfers 1 or more bytes from the DS2786B. Read transactions are composed of two parts--a write portion followed by a read portion--and are therefore inherently longer than a write transaction. The write portion communicates the starting point for the read operation. The read portion follows immediately, beginning with a Repeated START, Slave Address with R/W set to 1. Control of SDA is assumed by the DS2786B beginning with the Slave Address Acknowledge cycle. Control of the SDA signal is retained by the DS2786B throughout the transaction, except for the acknowledge cycles. The master indicates the end of a read transaction by responding to the last byte it requires with a no acknowledge. This signals the DS2786B that control of SDA is to remain with the master following the acknowledge clock.
Read Data Protocol
The read data protocol is used to read register and shadow RAM data from the DS2786B starting at memory address specified by MAddr. Data0 represents the data byte in memory location MAddr, Data1 represents the data from MAddr + 1, and DataN represents the last byte read by the master: S SAddr W A MAddr A Sr SAddr R A Data0 A Data1 ...DataN N P Data is returned beginning with the MSB of the data in MAddr. Because the address is automatically incremented after the LSB of each byte is returned, the MSB of the data at address MAddr + 1 is available to the host immediately after the acknowledgment of the data at address MAddr. If the bus master continues to read beyond address FFh, the DS2786B outputs data values of FFh. Addresses labeled Reserved in the memory map (Table 3) return undefined data. The bus master terminates the read transaction at any byte boundary by issuing a no acknowledge followed by a STOP or Repeated START.
Write Data Protocol
The write data protocol is used to write to register and shadow RAM data to the DS2786B starting at memory address MAddr. Data0 represents the data written to MAddr, Data1 represents the data written to MAddr + 1, and DataN represents the last data byte, written to MAddr + N. The master indicates the end of a write transaction by sending a STOP or Repeated START after receiving the last acknowledge bit: S SAddr W A MAddr A Data0 A Data1 A ... DataN A P The MSB of the data to be stored at address MAddr can be written immediately after the MAddr byte is acknowledged. Because the address is automatically incremented after the LSB of each byte is received by the DS2786B, the MSB of the data at address MAddr +
Package Information
For the latest package outline information and land patterns, go to www.maxim-ic.com/packages. Note that a "+", "#", or "-" in the package code indicates RoHS status only. Package drawings may show a different suffix character, but the drawing pertains to the package regardless of RoHS status. PACKAGE TYPE 10 TDFN PACKAGE CODE T1033+1 DOCUMENT NO. 21-0137
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Stand-Alone OCV-Based Fuel Gauge
Revision History
REVISION NUMBER 0 1 REVISION DATE 7/08 4/10 Initial release Changed the maximum operating voltage on VDD to 4.5V in the Features, Electrical Characteristics, and Pin Description sections DESCRIPTION PAGES CHANGED -- 1-4
DS2786B
Maxim cannot assume responsibility for use of any circuitry other than circuitry entirely embodied in a Maxim product. No circuit patent licenses are implied. Maxim reserves the right to change the circuitry and specifications without notice at any time.
Maxim Integrated Products, 120 San Gabriel Drive, Sunnyvale, CA 94086 408-737-7600 ____________________ 21
(c) 2010 Maxim Integrated Products Maxim is a registered trademark of Maxim Integrated Products, Inc.


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