Useful Noise? or just Statistics?

Oh you little tinker!
I used to know this stuff.... but seeing as how I rarely use it.

I shall fudge the issue by saying it depends on how you define tolerance.

Have you heard the theory that 5% resistors will be 5% out because the 'better' ones are taken out to be higher tolerance ?
Are they all from the same batch...do batches come out randomly or are they going to tend to be all 'out' in the same direction.

They will be 1% or maybe better...but then a single resistor may be better...
On the other hand....oh you little tinker...

Del (PS This could run and run.... you mentioned Bell shaped curves...just don't mention Bath tub curves )

I will wait for a few more replies before stating whether its true, by how much etc... or whether its a load of cobblers...

John

By the way folks, this assumes the resistors are randomly selected and follow the Gaussian bell shaped curve with 3 sigma as the limits of +/- 1%

Think of it.... as the resistors average out against each other the sigma reduces and the bell shape curve peaks... ???

Your problem is a "limited sample "one. The normal (Gaussian) distribution is valid for a BIG number of samples. The case you mention should be analysed with the Student- Distribution which has as limit the Gaussian.

For samples under 30 the differences between Gauss and Student are quite important. They depend on the required degree of confidence.

If one assumes that all resistors have same IT and are placed in series then the PROBABLE IT of the resulting resistor will be IT(N)=IT(1)*N^0.5.

For the parallel connection it is more complex. There is an algebra of probabilistic numbers which allows to compute it.

The backwards computation is less easy. Better is to measure the ten one by one and analyse the 10 values as a sample.

Well okay then let's take 100 resistors and apply them in this example then...

John.

1 resistor or 10 ???

Depends on what you want to do !

If you want to build one or only few devices then it would be easier or more reliable to select the best resistors out of a lot of cheap ones and use these.

If you go into volume production then the selection costs may be too high relative to the devices manufacturing costs. In this case you would pick and place 10 cheap resistors with 1% tolerance limit and increase the limit by a factor of xxx and for the price of 9 cheap resistors.

Regards Uwe

... sorry ... of course you DEcrease the limit !

As the resistors must be within the bell curve to give the manufacturer the confidence to claim they are 1% tolerance

I think they measure them.

As Del said you certainly used to get batches of say 5% resistors: with none within the 2% band. And the 2% ones had none in the 1% band.

In the past when I've been trying to select similar values then there seems to be a close correlation between adjacent components on a bandolier.

However if you had a selection which did meet the Bell curve (up to the cut off/ given tolerance), and selected batches of 10 at random then you'd expect a smaller standard deviation than you'd get from individual components.

As in post #3 assume they are randomly picked and meet the gaussian distribution shape...