# Signal Chain Basics #155: Calculate current measurement accuracy to improve functional safety

An increased focus on functional safety requirements is driving demand for improved system diagnostics. One of the key inputs for these diagnostic assessments is current measurement. To determine your design’s measurement accuracy, make sure you understand the error sources.

As discussed previously in Signal Chain Basics #141, it is important to understand how to interpret data sheets in order to calculate the accuracy of your high-side implementation. In addition, understanding the impact of the external components is critical to arriving at the correct current measurement.

High-side current-measurement implementations

There are two common methods for measuring current in a high-side configuration:

• Use an operational amplifier (op amp) configured differentially, as shown in Figure 1. Figure 1 Operational amplifier circuit used for high-side current measurement

Use a current-sense amplifier as shown in Figure 2. Figure 2 Current-sense amplifier circuit used for high-side current measurement

While there are a few fundamental differences between the two methods, the main difference is that current-sense amplifiers integrate the gain resistor network, while op amps use external discrete resistors for their gain network. Whichever implementation is you use, the basic system-transfer function applies, expressed as Equation 1:

Where

• y is the output voltage (VOUT).
• m is the gain of the system, which for this system is RSHUNT × G. G is pre-defined for most current-sense amplifiers, while for the op amp it is RF/RI.
• x is the input current (I).
• b is the offset of the system. If the system is measuring bidirectional current, b is the output voltage when the input current is zero. If measuring unidirectionally, b ideally would be 0 V at 0 A, but it will likely be limited by the amplifier’s output swing specification. For both op amps and current-sense amplifiers, VOFFSET is normally a referred-to input specification. Therefore, b would actually need to factor in the gain of the system as well.

You can rewrite the transfer equation for current measurement as Equation 2:

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

Gain error

The system gain error has two primary sources: the shunt resistor and the amplifier gain. The shunt error is common to either the op amp or current-sense amplifier implementation and is easily determined by looking at the resistor specification sheet. The amplifier gain error determination is based which of the two implementations you choose.

For a differential op amp implementation, as I previously stated, the gain is the ratio of two resistors, RF/RI. To calculate the error, you’ll need to look at the resistor data sheets. The tolerance of a typical discrete gain network resistor is 0.5%, 100 ppm/°C. To calculate the maximum error for this ratio, you need to assume that one resistor is at its maximum value while the other is at its minimum value. This results in a 1% error at room temperature, and since you have to assume that they drift opposite as well, 3% at 125°C.

For the current-sense amplifier, the gain error is normally listed in the data sheet. Figure 3 shows how the gain error is listed for the Texas Instruments (TI) INA186-Q1. As you can see, the gain error is 1.0% at room temperature. With a drift of 10 ppm/°C, you get a gain error of 1.1% at 125°C. Figure 3 INA186-Q1 data sheet showing the gain error and gain error drift specifications

This is one of the key differentiators for TI’s current-sense amplifiers: an integrated, precision-matched gain network that minimizes the temperature drift effect. For the op amp circuit, you could use precision, matched resistor networks, but they significantly drive up the cost of the implementation.

Offset errors

As discussed above, the output offset has to include the gain. Since offset is normally specified as the referred-to input, Equation 3 calculates the offset error as:

As you can see from Equation 3, offset error matters as VSHUNT (I x RSHUNT) approaches the offset value, and will approach infinity as current goes to 0. Conversely, if VSHUNT >> VTOTAL OFFSET, then this error term will approach 0.

The total input referred offset voltage has three primary components:

• The amplifier VOFFSET specification and drift.
• The common-mode rejection ratio (CMRR).
• The power-supply rejection ratio (PSRR).

CMRR and PSRR are included as part of the offset error since the VOFFSET of amplifiers is normally specified at a fixed common-mode voltage and power-supply value. Figure 4 shows these fixed values for the INA186-Q1, while Figure 5 shows the fixed values for a common op amp, the TI TLV2186. Figure 4 INA186-Q1 data sheet showing the fixed specifications used for CMRR and PSRR Figure 5 TLV2186 data sheet showing the fixed specifications used for CMRR and PSRR

As discussed in Signal Chain Basics #141, the VOFFSET for a current-sense amplifier is specified differently in a data sheet versus an op amp. Specifically, the current-sense amplifier offset includes the effect of the integrated resistor network, while the op-amp VOFFSET applies only to the device. The total offset of the op amp implementation requires that you include the effect of the external resistors.

You can consider these external resistors as contributing to the common-mode ejection error due to the current flowing through them from the common-mode voltage. The circuit’s gain and the resistors’ tolerances will determine the “resistor CMRR” based on Equation 4, assuming that all four gain resistors have the same tolerance:

You can see the effect in Figure 6, which shows the calculated resistor CMRR (in decibels) for varying gains and resistor tolerances. Figure 6 Calculated CMRR values for various resistor tolerance values in three different gain configurations

For the current-sense amplifier, the total input offset is calculated simply by adding the effect of the CMRR and PSRR to the device’s offset specification. CMRR and PSRR are normally specified over the full temperature range; therefore, any drift affects are already included. You must include offset drift to calculate error at different temperatures, however.Total error

In theory, the worst-case total error is simply the summation of the individual error terms. Statistically speaking, this scenario where all errors are simultaneously at their worst is unlikely. Therefore, a root-sum-square method (Equation 5) calculates a first-order total error:

If you use the INA186-Q1 and TLV2186 and choose a gain of 20, Figure 7 lists the key performance metrics. Figure 7 Key performance metrics for high-side current measurement applications implemented using either the INA186-Q1 or the TLV2186

Using Equation 5 for the two implementations and a 10-mΩ, 0.5%, 50-ppm/°C RSHUNT, Figure 8 shows the following error curves at room temperature as well as at 125°C. Figure 8 Root-sum-square error curves for high-side current measurement implementations using either the INA186-Q1 and TLV2186 with a 10-mΩ, 0.5%, 50-ppm/°C RSHUNT

As you can see from Figures 7 and 8, the external gain resistors are the primary error source for a discrete implementation, especially over temperature. It is possible for calibration to minimize the offset error at room temperature, but the over temperature drift is not as easily calibrated.

Summary

Increasing the accuracy of your current-sensing implementation can improve a system’s diagnostic capability by increasing the achievable design margins. As with any electronic system, though, increasing precision typically requires an increase in system cost. Understanding the error sources and their effects under different operating conditions will enable you to make the appropriate trade-off between cost and precision.

References