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Resistor mismatch hand calculation and simulation

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ashrafsazid

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I would like to discuss about resistor mismatch citing a very old post, even when I was not a student of Electronics. The post link is here: Resistor matching calculation

Let's say, I have two equal Resistor (R1, R2), 10k each, having a standard deviation (sigma ) is around 20. Therefore, the mismatch percentage we can say 0.2%. (sigma divided by mean, 20/10k).

What will be the sigma for the sum (R1+R2)?
What will be the sigma for the ratio (R1/R2)?
What will be the sigma for the resistive divider (R1/(R1+R2))?

as the variance are added, therefore the deviation of the sum is sqrt(20² +20²) = 28.28. in percentage 0.14%, (sigma divided by mean 28.28/20k)

The variances also add during the calculation of ratio. Therefore, I can expect same 28.28 for (R1/R2). But in this case I get from simulation that it is valid for the percentage. that means sqrt(0.2² + 0.2²) = 0.28

Selection_003.jpg


Therefore, it is unclear, when to calculate variance ( hence standard deviation) with percentage and when dirctly with the absolute number.
Could somebody please explain it to make me understand? Thanks in advance.
 

standard deviation is not tolerance

two resistors in series add
the appropriate way to add the tolerance, or standard deviation is square root of sum of squares of (tolerance or standard dev) in ohms divided by value in ohms
therefore you need to convert tolerance to resistance (percent to value)

it gets more complicated if you do more complicated things

what is it that you really need? why are you concerned about the variance in a combination of resistors?

if you want two equal valued, matched resistors, you need to buy them that way
if you want two resistors to provide a specific voltage division you need to buy them that way

we did that for many projects using Caddock resistor
they make high quality resistors to very tight tolerances
they can track over temperature.

if you need two identical resistors (value, tolerance, temp coefficient, etc) this is the place to get them

http://www.caddock.com/
 

standard deviation is not tolerance

if you want two equal valued, matched resistors, you need to buy them that way
if you want two resistors to provide a specific voltage division you need to buy them that way

we did that for many projects using Caddock resistor
they make high quality resistors to very tight tolerances
they can track over temperature.

if you need two identical resistors (value, tolerance, temp coefficient, etc) this is the place to get them

http://www.caddock.com/

I expected a statistical answer. And sorry, I do not work with discrete elements.
 

There is something called "error propagation law". This should be teacher at every school during laboratory measurement, so you should be able to find a lot of materials on it.
 

There are several different ways to propagate error (uncertainty)
This is one:

For f(x,y,z), the uncertainty in f(x,y,z) is given by: ∆f(x,y,z)=f√((∂f/∂x)^2+(∂f/∂y)^2+(∂f/∂z)^2 )

that is, the value of the function times the square root of the sum of squares of the partial derivative of the function with regard to each variable.
this assumes the variables are independent.

if the variables are not independent, it gets more complicated
 

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