The proliferation of hybrid electric vehicles (HEVs) and electric vehicles (EVs) has created a new dynamic in automotive designs. HEVs and EVs no longer operate off a traditional 12-V lead-acid battery—primarily used to generate enough spark to get the engine started—but instead implement solid-state batteries, similar to smartphone batteries but on a much larger scale. These new battery management systems (BMSs) require high-precision current measurement to meet a variety of operating modes. Vehicle propulsion and battery charging are examples of the high end of the operating current range, while vehicle-off communication is an example of a low-current operating mode.

Solving this bidirectional challenge requires a very precise current-measurement solution with a wide operating range. This article shows how to determine the shunt resistor value to handle the high operating current required for vehicle motion or battery charging. It also examines how various alternatives will affect accurate measuring of the minimum current.

**Current sensing in automotive BMS**

**Figure 1** illustrates the placement of the current-measurement solution as either top of stack or bottom of stack in a BMS, depending on where the shunt resistor is located relative to the battery output and battery ground. For EVs, bottom of stack is the most popular implementation because of the high voltage at the top of the stack. For 48- and 12-V BMS implementations, either location works. The main benefit that top of stack offers over bottom of stack is the direct connection of the battery stack to the system ground.

**Figure 1** Simplified automotive BMS current-measurement locations identified as top of stack or bottom of stack. Source: Texas Instruments

High-current operating modes—such as the engagement of the traction motors during vehicle motion or battery charging—may exceed 1,000 A. Low-current operating modes—such as vehicle-off communications and system monitoring—can be as low as sub-1 A. In addition to the wide dynamic range, a BMS requires bidirectional current measurement, sinking current during battery charging versus sourcing current for vehicle operation.

A wide dynamic range creates a challenge when determining the value of the shunt resistor. The maximum current—typically in excess of 1,000 A—combined with the full-scale input range of the measurement system will determine the largest shunt value possible. At the other end of the current range, sub-1 A, there are potentially two challenges to overcome: the error induced by the amplifier’s offset (V_{OFFSET}) and the error induced by the amplifier’s bias current (I_{BIAS}), which is the current that the input pins pull off the signal. The simplest way to deliberate the second error is the ratio of I_{BIAS} to measured current. For most current-sense amplifiers, I_{BIAS} is well under 100 µA. So, as long as the current range is at least 100 mA, the bias current error contribution should be negligible.

**Calculating the shunt resistor value**

As mentioned earlier, a BMS will require a device capable of bidirectional current measurement; so, let’s assume a symmetrical bidirectional maximum current of ±1,000 A when determining the respective shunt values. To measure bidirectional current with an analog output current-sense amplifier, use a reference voltage (V_{REF}) to set the output level when the differential input is zero. For a symmetrical operation, this is normally set to 50% of the supply voltage. Now that you know the supply voltage, you can determine the full-scale input voltage for an analog output current-sense amplifier using Equation 1:

V_{Full-scale input }= (V_{Supply}-V_{Swing-to-supply}-V_{REF}) / Gain (1)

Using the maximum gain—including the gain error and temperature drift for the amplifier—will result in the “minimum” expected unidirectional full-scale input voltage. Dividing the unidirectional full-scale input range by the maximum unidirectional current (1,000 A) results in the maximum shunt resistor value.

As an alternative to an analog current-sense amplifier, let’s consider TI’s digital power monitor INA229-Q1. Digital power monitors are specialized analog-to-digital converters (ADCs) dedicated to measuring current. With digital power monitors, the full-scale input range of the ADC scales from that of a typical ADC to accommodate the small-signal voltage drop across a shunt resistor. The INA229-Q1 power monitor has a full-scale input range of ±163.84 mV, which makes calculating the maximum shunt resistor value fairly straightforward because you simply divide the full-scale input by the unidirectional maximum current.

**Table 1** summarizes the key specifications and calculations in determining the maximum shunt resistor value capable of measuring ±1,000 A for three different device options. We will use the two gain options (25 V/V and 500 V/V) of the INA190-Q1 chip as the analog options in making the calculations.

Device option |
INA190A1 |
INA190A5 |
INA229-Q1 |

V_{S} |
5 V | ||

Swing to supply | 40 mV | ||

V_{REF} |
2.5 V | ||

Maximum unidirectional output voltage | 2.46 V | ||

Nominal gain option | 25 V/V | 500 V/V | Unity |

Gain error at 25°C | 0.2% | 0.4% | 0.1% |

Gain drift | 7 ppm/°C | 20 ppm/°C | |

Maximum gain error at 125°C | 0.27% | 0.47% | 0.3% |

Maximum gain at 125°C | 25.07 V/V | 502.35 V/V | |

Maximum unidirectional input voltage | 98.1 mV | 4.9 mV | 163.84 mV |

Maximum unidirectional current | 1,000 A | ||

Maximum shunt value | 98.1 µΩ | 4.9 µΩ | 163.8 µΩ |

**Table 1** Key specifications and calculations that help determine the maximum shunt resistor value capable of measuring ±1,000 A for the INA190A1, INA190A5 and INA229-Q1. Source: Texas Instruments

To ensure full linear operation at the maximum current, the actual shunt resistor value chosen will need to be a lower ohmic value than the calculation in order to factor in tolerance variations of the shunt resistor as well as the supply voltage and reference voltage for the INA190-Q1 analog output options. Therefore, we will use 90 µΩ for the INA190A1, 4.5 µΩ for the INA190A5, and both 100 µΩ and 50 µΩ for the INA229-Q1 in the remaining calculations.

**Calculating the effect of V _{OFFSET} on error**

Using the chosen shunt resistor values, it’s time to determine the lowest current you can accurately measure. The TI Precision Labs training series on current-sense amplifiers provides a method to determine the error that you can expect under various operating conditions. From this, you know that the error is dominated by offset error as the load current decreases. To simplify the calculations, we will only use amplifier offset error and gain error along with the root-sum-square methodology expressed by Equation 2:

e = √ (e^{2}_{OFFSET} + e^{2}_{GAIN}) (2)

where e_{OFFSET} = V_{OFFSET } / (I_{INPUT} × R_{SHUNT}).

The total error will rise exponentially as the current approaches 0 A (Table 2).

Device option |
INA190A1 |
INA190A5 |
INA229-Q1 |
INA229-Q1 |

Chosen shunt resistor value | 90 µΩ | 4.5 µΩ | 100 µΩ | 50 µΩ |

INA190 V_{OFFSET} at 25°C |
15 µV | 1 µV | ||

INA190 V_{OFFSET} drift |
80 nV/°C | 10 nV/°C | ||

INA190 V_{OFFSET} at 125°C |
23 µV | 2 µV | ||

INA190 gain error at 125°C | 0.27% | 0.47% | 0.30% | |

Error at 125°C: |
||||

1,000 A | 0.27% | 0.69% | 0.25% | 0.25% |

100 A | 0.37% | 5.1% | 0.30% | 0.30% |

10 A | 2.6% | 51.1% | 0.36% | 0.50% |

1 A | 25.6% | 511.1% | 2.02% | 4.01% |

0.1 A | 255.6% | 5111.1% | 20.00% | 40.00% |

**Table 2** Error calculations at selected input currents with chosen shunt resistor values for the INA190A1, INA190A5 and INA229-Q1. Source: Texas Instruments

**A low V _{OFFSET} solution enables five decades of measurement**

The error calculations in Table 1 show that the 500-V/V option will provide little dynamic range because the value of the shunt resistor is too low to measure low currents, even with a very low offset amplifier. The gain of 25 option could enable four decades of capability if 25% error is acceptable in the application. The INA229-Q1’s offset of 1 µV and 10 nV/°C drift enable five decades of measurement dynamic range with either of the two shunt resistor values chosen. Engineers would need to trade off the peak I^{2}R power dissipation versus the system’s low-current accuracy requirements to determine whether they can implement the actual shunt resistor.

Because INA229-Q1 is a specialized ADC, it’s important to understand if it is capable of resolving this low level of signal as well. The INA229-Q1 is a 20-bit delta-sigma ADC with one bit as the sign bit. Dividing the full-scale input by 19 bits gives you 312.5 nV per least significant bit, which corresponds to 2.9 µA on a 100-µΩ shunt resistor or 5.8 µA on a 50-µΩ shunt resistor. Both levels are well below the offset error level, meaning that the ADC capability is not the limitation in the measurement.

These calculations will work out similarly to enable five decades of measurement, whether the maximum current is 1,000 A used for the automotive BMS application in this article or 1 A for an industrial application such as test and measurement or optical networking modules. The shunt resistor value will scale down by the same factor of 1,000, which results in a thousand-fold increase in the minimum current to achieve the same error level. As mentioned at the beginning of the article, when the current range extends under the milliampere range, you will need to account for the potential I_{BIAS} error. The INA229-Q1’s ultra-low I_{BIAS} of 2.5 nA enables precise measurements down into the microampere range.

Measuring up to five decades of current—which the latest automotive BMSs require—is a challenge that has not had a simple answer until now. The combination of a 1-µV maximum V_{OFFSET}, 10-nV/°C offset drift, 154-dB common-mode rejection ratio and 2.5-nA I_{BIAS} offers a maximum offset of 2.02 µV at 125°C. This performance enables engineers to measure up to five decades, whether the application requires a maximum current of 1 A or 1,000 A.

*Dan Harmon**, author of Signal Chain Basics blog # 167 for Planet Analog, **is **automotive marketing manager for the current and position sensing product line at Texas Instruments (TI).*

**Related Content**

- Temperature sensing for Battery Management Systems
- Current Sensing Considerations in Li-ion Battery Management
- Battery management systems for electric vehicles: The crucial role of the current sensor interface
- Battery Management Systems for Electric Scooters
- High-Performance Electromobility Solutions with Battery Management and Embedded Technology
- Maximizing cell monitoring accuracy and data integrity in energy storage Battery Management Systems

## 0 comments on “How to precisely measure current in EV/HEV battery management systems”