Error margins

[born2laser]

(10-28-2024 03:33 PM)Albert Chan Wrote:  

(10-27-2024 02:51 PM)Thomas Klemm Wrote:  You might consider dual numbers:
Automatic differentiation using dual numbers
Here's an example on how this could be used for a circuit of two parallel resistors.

FYI, this only work with + * (parallel resistance intervals work due to luck)
For - /, we need to flip the sign of 2nd number, to maximize intervals
Other changes may need to adapt to other functions.

If you calculate a value based on measured parameters that are known with uncertainty (error), the canonical way of estimating the uncertainty of the calculated value is to multiply each error by the partial derivative respect to each parameter and then add them all in quadrature (square root of the sum of the squares). This of course assumes small errors as it is a Taylor expansion and statistical independence of the parameters.
Back in college I wrote a program for my 41 that calculated the derivatives numerically and used it to estimate the propagated error.
Funnily enough that lead to the only time in 40 years that I used my 41 for work. I needed to come up with an alternative resistor bridge design using the AD5254 digital pot (30% unit to unit tolerance!) that would not be hopelessly inaccurate. I used the 41 program to quickly evaluate alternatives.