How to Calculate Current Measurement Accuracy for Improved Functional Safety

【Introduction】As functional safety requirements are increasingly valued, it is imperative to improve system diagnostic capabilities. Among them, current measurement is an important part of diagnostic evaluation. To determine the measurement accuracy of the design, it is important to understand the error sources.

As previously discussed in Signal Chain Basics #141, knowing how to interpret the datasheet is important for calculating the accuracy of high-side current measurements. Additionally, understanding the effects of external components is critical to obtaining correct current measurements.

High-side current sensing implementation

In a high-side configuration, there are two common methods for current measurement:

● Use a differential operational amplifier as shown in Figure 1.

Figure 1. Operational amplifier circuit for high-side current measurement.

Use a current sense amplifier as shown in Figure 2.

Figure 2 Current sense amplifier circuit for high-side current measurement

There are some fundamental differences between the two approaches, primarily in that the current sense amplifier integrates the gain resistor network, while the op amp uses external discrete resistors as its gain network. Regardless of which approach you use, the basic system transfer function applies, as shown in Equation 1:

   Formula 1

in

● y is the output voltage (VOUT).

● m is the system gain, which for this system is RSHUNT×G. G is predefined for most current sense amplifiers and for op amps it is RF/RI.

● x is the input current (I).

● b is the offset voltage of the system. If the system measures bidirectional current, b is the output voltage when the input current is zero. If measuring unidirectionally, b is ideally 0V at 0A, but it may be limited by the amplifier output swing specification. For op amps and current sense amplifiers, VOFFSET is usually specified with reference to the input. Therefore, b actually needs to consider the gain of the system as well.

The transfer equation for current measurement can be rewritten as Equation 2:

   Formula 2

Based on this basic transfer function, there are two types of errors: gain and offset voltage.

Gain Error

There are two main sources of system gain error: shunt resistor and amplifier gain. Shunt resistor error is common to op amps or current sense amplifiers and is easily determined by looking at the resistor specification sheet, while amplifier gain error depends on the amplifier solution chosen.

For the differential op amp solution, as mentioned previously, the gain is the ratio of the two resistors, RF/RI. To calculate the error, look at the resistors’ datasheets. Typical discrete gain network resistors have a tolerance of 0.5%, 100ppm/°C. To calculate the maximum error in this ratio, assume that one resistor is at its maximum value and the other is at its minimum value. This gives a 1% error at room temperature, and 3% at 125°C because reverse drift is assumed.

For current sense amplifiers, the gain error is usually listed in the datasheet. Figure 3 shows the gain error of the Texas Instruments (TI) INA186-Q1. As can be seen, the gain error is 1.0% at room temperature. With a temperature drift of 10ppm/°C, the gain error is 1.1% at 125°C.

Figure 3. INA186-Q1 gain error and gain error drift specifications datasheet

This is a key advantage of TI's current sense amplifiers: precision-matched integrated gain networks minimize temperature drift effects. For op amp circuits, you can use precision-matched resistor networks, but they significantly increase solution cost.

Offset Error

As mentioned above, the output offset voltage must include the gain. Since the offset voltage is usually specified as referenced to the input, Equation 3 calculates the offset voltage error as follows:

   Formula 3

From Equation 3, we can see that the offset voltage error is significant when VSHUNT (IxRSHUNT) is close to the offset voltage value and approaches infinity as the current goes to 0. Conversely, if VSHUNT >> VTOTAL OFFSET, then this error term approaches 0.

The total input referred offset voltage has three main components:

Amplifier VOFFSET Specification and Drift.

Common-mode rejection ratio (CMRR).

Power supply rejection ratio (PSRR).

Since the VOFFSET of an amplifier is usually specified at fixed common-mode voltage and supply voltage, CMRR and PSRR also contribute to offset voltage errors. Figure 4 shows the fixed values ​​for the INA186-Q1, and Figure 5 shows the fixed values ​​for the popular op amp TI TLV2186.

Figure 4 INA186-Q1 CMRR and PSRR datasheet for fixed common-mode voltage and supply voltage specifications

Figure 5 CMRR and PSRR datasheet of TLV2186 at fixed common-mode voltage and supply voltage specifications

As mentioned in Signal Chain Basics #141, the VOFFSET of current sense amplifiers is specified differently in the datasheet than op amps. Specifically, the current sense amplifier offset voltage includes the effects of the integrated resistor network, while the op amp VOFFSET is specific to the device only. The total offset voltage in the op amp solution needs to account for the effects of the external resistors.

Since current flows through the external resistors from the common-mode voltage, the external resistors can be considered the cause of common-mode rejection errors. Assuming all four gain resistors have the same tolerance, the gain of the circuit and the tolerance of the resistors will determine the “resistor CMRR” according to Equation 4:

   Formula 4

Figure 6 shows the calculated resistor CMRR (in decibels) for different gains and resistor tolerances, where you can see the impact of different gains and resistor tolerances.

Figure 6 Calculated CMRR values ​​for three different gain configurations and different resistor tolerances

For current sense amplifiers, the total input offset voltage can be calculated by simply adding the effects of CMRR and PSRR to the device’s offset voltage specification. CMRR and PSRR are usually specified over the entire temperature range; therefore, any drift effects are already accounted for. However, temperature drift must be considered when calculating the error at different temperatures.

Total error

In theory, the worst-case total error is simply the sum of the individual error terms. It is statistically unlikely that all errors will occur at the same time. Therefore, the first-order total error is calculated using the root sum of squares method (Equation 5):

   Formula 5

Figure 7 lists the key performance metrics for a gain of 20 using the INA186-Q1 and TLV2186.

Figure 7 Key performance indicators for high-side current measurement applications using INA186-Q1 or TLV2186

Figure 8 shows the following error curves calculated using Equation 5 for the two solutions using 10mΩ, 0.5%, and 50ppm/°C RSHUNT at room temperature and 125°C, respectively.

Figure 8. Root sum square error curves for high-side current measurement using INA186-Q1 or TLV2186 with 10mΩ, 0.5%, and 50ppm/°C RSHUNT

As can be seen in Figure 7 and Figure 8, the external gain resistors are the dominant error source for the discrete solution, especially over temperature. Calibration can minimize the offset voltage error at room temperature, but temperature drift is not easily calibrated out.

Summarize

Improving the accuracy of the current sensing scheme can improve the diagnostic capabilities of the system by increasing the achievable design margin. But as with any electronic system, improved accuracy usually comes at the cost of the system. By understanding the error sources and their impact under different operating conditions, you can make the appropriate trade-off between cost and accuracy.

references

● Download the INA186-Q1 data sheet.

● Download the TLV2186 data sheet.