Fredxx wrote:
"Andy Dingley" wrote in message
...
On 9 Sep, 16:14, "Fredxx" wrote:

The tolerance of a resistor is the maximum extreme of measured
resistance.
AIUI, it isn't - although this depends on the resistor technology.

Cheap resistors (carbon rod) were made by little more than the "bake &
sort" approach, so were individually measured and sorted. Tolerance
(which was pretty broad then) was an absolute limit, but the
distribution was sufficiently broad that you would frequently
encounter resistors close to the limits of this band.

High quality resistors are also measured and so have some hard cut-off
for tolerance.

For most modern resistors though (i.e. 1% & 2% films) production
process quality is such that they're now made "to spec" and the
resistors are made in separate batches for each value without needing
to be tested or sorted afterwards. Tolerance is however now based on a
Gaussian distribution (or close to it). It's also possible that a
resistor from the batch could be out of spec, but it's unlikely to be
so (some accepted large proportion of the batch will be). The 2%
figure is set at some number of standard deviations away from the
mean, such that 9*.*% of the resistors will be within that band.

So if you combine 2% resistors, where in series or in parallel, the
maximum
deviation of actual resistance either singly or combined is still only
2%.
That only holds if the tolerance is an absolute. If it's a Gaussian,
it doesn't hold (but is still predictable, with a bit more maths)

This is a definition of tolerance as applied to resistors from the Vishay
website


Tolerance: The tolerance on delivery is the range within
which the resistor can deviate percentually from the value at
the time of delivery.

Electrical and electronic design rely upon absolute tolerances.

They do not. I could cite you a hundred examples of how and why nearly
all digital electronics is actually made to a monte carlo statistical
model of tolerances. The aim is that, given Gaussian distribution of
(mostly time delays through the kit) 99.9% of the units will work within
the specified temperature range, and the 0.5% that do not are thrown
away, or sold off to cowboy board makers.

If cumulative worst case delays were used it would result in about 10
times more expensive kit. Or about 1/4 the current clocking speeds.
Whatever. Statistical analysis is THE way most large designs are done.
Most small designs do NO analysis for tolerance at all, until a batch of
semiconductors 'doesn't work'

The ONLY time I was required to do worst case analysis was in military
and avionic equipment, and even there, only for the most critical
elements. For the rest, it was simply tested over the temperature range,
and if it failed, it was fixed till it did not, by replacing parts.


For any
component where there is a gaussian tolerance, the datasheet would include
the standard deviations so the user could determine the probability that
99.9999% of resistors were within tolerance when they left the factory.

They would not, and they do not. I know. I spent a day measuring 1500
phototransistors. The spread was beautifully gaussian., with the top and
the bottom tails chopped off. Except for two, which had either slipped
through the manufacturers selection, or had in fact been thrown in to
'make up the numbers' since the manufacturer did specify 'no more than
tow parts per thousand out of spec' Hmm.

I did this because I needed to establish whether or not a particular
circuit could be produced without recourse to setting up
potentiometers, and whether or not any in spec transistor would work.,
Fortunately the answer was yes to both.

That's semiconductors, where you get pretty much perfect gaussian
distribution.

Resisrorors are a different kettle of fish. Currently resistors are made
on machines that actually cut a spiral groove in a carbon film on a
ceramic substrate. You set the desired resistance on the machine and it
simply makes them up to as near an exact figure as the machine is
capable of. In general that's better than 1%, so although you do get a
gaussian distribution, its a very narrow one. It seldom exctends over
the full range allowed by the tolerance. In fact ion a givenm batch of
say 1000 resistors, its likely that e.g. a 1k will all be 1.03k or
something, plus minus a shade, that being the way the machine spat them
out. With the occasional odd one out, that clearly slipped into the bin
during manufacture from somewhere else ;-)

None of this is mentioned on any data sheet, because to do so would pin
the manufacturer down to a tighter spec than is needed in most cases.

With resitosrs, apart from a few instances, they can vary enormously
without affecting the circuits final performance. Only in a few cases do
you need precision, and those few case are catered for by specially
selected precision resistors, or setting up with a trim pot.




Can
you cite any manufacturers datasheet, where they don't specify tolleance in
an absolute percentage form, but in a gaussian form?



Of course not. But that means nothing. Beyond the fact that they have
selected examples OUTSIDE tolerance and called them something else.