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user16324
user16324

I have usually followed the "random walk" (described at a certain Scottish university in terms of the progress of a drunken man!) so I would note that the RMS sum of two 1% errors is neither 0.7% nor 2% but 1.4%

That is, there is a slow sqrt(N) growth in error with increasing number N of uncorrelated error sources, not a reduction in error.

Note this is the opposite of the statistical process you describe, which I think you are applying incorrectly : if you applied increasing numbers N of components to the same error source - e.g. forming a precision resistor from N resistors in series or parallel - you would reduce the error by sqrt(N).

More careful reading of the question : the specific case of splitting the input resistor into two series components falls into the latter case, so the input resistor could be modelled as a 0.7% error source (but see Oleg's answer : the errors are probably correlated).

However the amplifier's gain is still subject to the sum of two independent error sources R1,R2 or (R3+R4), R5.

I have usually followed the "random walk" (described at a certain Scottish university in terms of the progress of a drunken man!) so I would note that the RMS sum of two 1% errors is neither 0.7% nor 2% but 1.4%

That is, there is a slow sqrt(N) growth in error with increasing number N of uncorrelated error sources, not a reduction in error.

Note this is the opposite of the statistical process you describe, which I think you are applying incorrectly : if you applied increasing numbers N of components to the same error source - e.g. forming a precision resistor from N resistors in series or parallel - you would reduce the error by sqrt(N).

I have usually followed the "random walk" (described at a certain Scottish university in terms of the progress of a drunken man!) so I would note that the RMS sum of two 1% errors is neither 0.7% nor 2% but 1.4%

That is, there is a slow sqrt(N) growth in error with increasing number N of uncorrelated error sources, not a reduction in error.

Note this is the opposite of the statistical process you describe, which I think you are applying incorrectly : if you applied increasing numbers N of components to the same error source - e.g. forming a precision resistor from N resistors in series or parallel - you would reduce the error by sqrt(N).

More careful reading of the question : the specific case of splitting the input resistor into two series components falls into the latter case, so the input resistor could be modelled as a 0.7% error source (but see Oleg's answer : the errors are probably correlated).

However the amplifier's gain is still subject to the sum of two independent error sources R1,R2 or (R3+R4), R5.

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user16324
user16324

I have usually followed the "random walk" (described at a certain Scottish university in terms of the progress of a drunken man!) so I would note that the RMS sum of two 1% errors is neither 0.7% nor 2% but 1.4%

That is, there is a slow sqrt(N) growth in error with increasing number N of uncorrelated error sources, not a reduction in error.

Note this is the opposite of the statistical process you describe, which I think you are applying incorrectly : if you applied increasing numbers N of components to the same error source - e.g. forming a precision resistor from N resistors in series or parallel - you would reduce the error by sqrt(N).