INA851: Gain error

HI Pascal,

Yes, the INA851 offers the lowest gain error at G=1 since there are no external resistors involved, no external connections involved, and the internal resistors of the INA851 are ratiometrically matched. Therefore, at G=1 the error is ±0.02% maximum with ±5ppm/°C drift.

- On the G=0.2V/V configuration, the internal 1.25kΩ is connected in parallel with the internal 5kΩ resistor via an external connection, by connecting the G02+ to OUT+, and  G02- to OUT- as shown below. 

As you have mentioned, the specified gain error in this configuration is ±0.1%.  Although the 1.25kΩ and 5kΩ internal resistors are carefully and ratiometrically matched in the IC internal layout to provide the lower gain error, since this configuration involves an external connection routed through the package wire bond connections, the package pins, and the external PCB connections, these additional connections add some variation on the series resistance producing a small error. Therefore, the gain error at G=0.2 configuration is a conservative ±0.1% max specified on the datasheet.

 - Adding the Gain errors directly tends to provide a very conservative estimate of gain error. The compounded probability of the input stage, output stage and resistor tolerance all being near their worst tolerance at the same time is very small.  Keep in mind, the compounded probability that all three sources of error are near the max tolerance, is the product of the three small probabilities, resulting in a very small compounded probability.    

The root-sum-of-squares is an operation commonly used in industry when combining errors from uncorrelated sources to obtain an estimate of error. When estimating the gain error accounting for the external resistor tolerance, the input stage gain error, and the output stage gain error, you may consider using the root-sum-of-squares. The root-sum-of-squares tends to provide a more realistic estimate of error. Rather than adding the maximum values, the standard deviation of uncorrelated Gaussian distributions can are combined as the square root sum of the squares. 

On your example, you could use the below to estimate Gain error, when the input stage is set on GIN=10, GOUT=0.2, and accounting for the resistor tolerance. Assuming the RG resistor has a  ±0.1% tolerance, the estimated gain error calculated from the maximum specs using the RSS is ~0.224%.  See calculation below.  

Edit 4/9/2024: Corrected calculation, input stage gain error is ±0.2% at G=10 per INA851 data sheet

Also, on the estimate above, we used the maximum data sheet specifications to estimate the maximum overall gain error.  The INA851 typical performance gain error is much smaller.

Thank you and Regards,

Luis   

Thanks Luis for the extensive answer.  

I missed the uncertainty in the 1.25k external connection. I will then also compute an uncertainty estimate for the input gain when G is between 1 and 10 to not overestimate the error.

Pascal