INA827: error caculation of noise

Hi,

If you are unfamiliar with noise analysis, then you may want to take a look at the TI precision labs on noise, which can be found here: training.ti.com/ti-precision-labs-op-amps-noise-1

The equation adds the noise of the input stage and output stage and refers them to the input. Remember when adding uncorrelated noise sources they sum as vectors, or the square root of the sum of the squares. The output noise term is divided by the gain to refer this noise to the input. The noise term under the radical effectively gives you the input referred voltage noise density. To get the rms noise you multiply this term by the square root of the noise bandwidth (which is the 3db bandwidth times the 1st order correction factor of 1.57). Multiplying this term by 6 roughly gives the peak to peak noise, and dividing by the input signal expresses this peak noise as a percentage of your input.

That being said, I believe the 6ppm given in the table is just a conservative estimate of the worst case noise error you can expect, it is not clear from the table what conditions this figure assumes, but if you apply the equation you can work out the noise error for your application.

Thanks for such a detailed explaination from you. By your instuction, it is as follows:
sqrt(1000*1.57)*sqrt((17e-9)^2+(250e-9/10)^2)*6/1=7.1874e-06=7.1874 ppm when G=10
sqrt(1000*1.57)*sqrt((17e-9)^2+(250e-9)^2)*6/1=5.9572e-05=59.72ppm when G=1
why they are all 6ppm whether G=1or10?

Hi,

Your calculations look correct to me. The table in the datasheet has a few errors in it, for one the INA827 has a minimum gain of 5, so the table specifying gain = 1 should actually say gain = 5. One thing to mention is that the gain and bandwidth of the INA are directly related so your bandwidth for a gain of 5 and gain of 10 for the calculation should actually be different. you can apply filtering before and after the INA but if you are just looking at the input referred error without filtering you should go by the bandwidth of the INA in whatever gain you are configured in.

You are absolutely right though, with different gains the error should not be the same, I'm not sure where the 6ppm figure came from.