EEVBlog #212 - resistors in series/parallel

[alexwhittemore]

I agree that, assuming the limits of the resistor tolerance, you proved that the end series equivalent resistor tolerance will definitely be within the same tolerance. However, you didn't note that you'll statistically improve tolerance by using a bunch of resistors in series. I'm not sure that there's anywhere that it's practically applicable, but imagine that I have 1 million 1ohm 1% resistors, and one 5% 1Mohm resistor. It's certainly possible that the 5% resistor will be spot on, but given that you've effectively averaged a million 1% resistors which are, on average, perfectly spot on accurate, the chain has better tolerance!

Of course, a million 1ohm resistors is a bad example, since contact/joint/lead resistance will begin to dominate the error.

[slateraptor]

...but imagine that I have 1 million 1ohm 1% resistors, and one 5% 1Mohm resistor.

There appears to be a bit of cheating going on here.

[ejeffrey]

Also, as dave showed, the mean error is not necessarily zero.  This is to be expected -- when you build a setup for manufacturing and testing 1% resistors, you are going to specify that the meter used to measure them is calibrated to 0.1%.  There are other systematic errors both fixed and temperature/time dependent that may also be another 0.1% (or so).  This means that every resistor from a batch, the same factory, or even the same manufacturer will have a slight average bias.  Furthermore, someone pointed out in the other thread that the manufacturer may deliberately target a point slightly below the nominal value to keep the resistor as accurate as possible accounting for aging and operating at elevated temperature.

So 1 million resistors in series will average out the statistical errors in manufacturing, but it won't necessarily converge on the nominal value.  The compound resistor will also be just as drifty as a single resistor made by the same technique. Real precision resistors need to be designed as such. 

[slateraptor]

The compound resistor will also be just as drifty as a single resistor made by the same technique. Real precision resistors need to be designed as such.

Oh, how we so often fail to acknowledge our friend tempco. *Bows to ejeffrey*