OT-ish: resistor value solver

[The Natural Philosopher]

that being the sort of tolerance on them anyway, when first introduced.

Its a log scale.

[Dave A]

Salmon coloured band for 20%?

[Andy Dingley]

Works for film resistors too, you just need a triangular needle file and work along the spiral groove (one slip and it's open circuit though!).

[Man at B&Q]

te:

I think there's more than that missing here.

Eh? 2% is 2%, whether it's (A + B) + 2% or ((A + 2%) + (B + 2%)).

MBQ

[Andy Dingley]

Is this one-off or production? Can you afford the time to measure individuals.

You've already quoted a value to 1% precision, so this is either excessive for the accuracy you need or else you can accept a rather wider range of target values than simply 5250 alone. If you really must have that, then you're looking at hand-selecting resistors from a batch to get that close. Unless you really are going that close and testing individual examples, there's just no point in serial connection of 4700 and 47 resistors together: one's lost in the tolerance of the other.

AFAIR, tolerances of cheap resistors are also non-Gaussian (owing to sampling and sorting artefacts during manufacture), particularly so for E12s and the higher tolerance bands. Otherwise it's a reasonable assumption that tolerances add according to the classic Einsteinian drunkard's walk rule of sqrt(n), i.e. two 2% resistors should be treated as a tolerance of 1.414 x 2% or about 3%

[Fredxx]

I'd use 5.6k and a 82k in parallel. It's 8 ohms out!

1/5600 + 1/8200 = 1/5242

You should be able to get 1% resistors as well. Even with 1% the tolerance would be 53 ohms.

QED

[Gordon Henderson]

You're right. Brain not in gear.

Gordon

[Fredxx]

The tolerance of a resistor is the maximum extreme of measured resistance. 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%. As you suggest, the way resistors are selected means that the statistical shape of the error is likely to be non-gaussian.

[Andy Dingley]

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.

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)

[The Natural Philosopher]

Actually, if the tolerances are randomly distributed , ten 10k 10% resistors in parallel is actually a 1k 1% resistor. See monte carlo analysis.

[Frank Erskine]

On Wed, 09 Sep 2009 14:51:49 +0100, Dave A had this to say:

ISTR that a salmon band indicated High Stability.

[NT]

no band for 20%, silver 10%, gold 5%, red 2%. Other tolerance bands are tighter spec.

NT

[bof]

In message , Dave Baker writes

Well, 2% of 4700 is 94, which puts both 68 and 12 'within the noise' of the 4700 resistor. The preferred way to do it used to be to use a number of similar, but different, values of resistor to make up the value, hoping that the tolerances of the different batches would even out in opposite directions. I remember writing a program for the BBC computer to do this, that gave recommended serial and parallel combinations.

[Fredxx]

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

[Man at B&Q]

Maybe to a mathematician, but you can't rely on that kind of analysis in the real world of engineering.

If they're from the same production lot then the actual values are unlikely to be distributed randomly. ten 10k - 10% resistors still make a 1k - 10% resistor.

MBQ

[The Natural Philosopher]

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.

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

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

[The Natural Philosopher]

Oh dear. You had better tell Boeing, NASA, IMB, INTEL and everyone else who uses it all the time.

worst case perhaps, bit in practice its likely to be a lot closer.

The chances of getting 10 resistors ALL out by the same maximum tolerance is the tenth power of the chances of geting one out that far, given *uniform* distribution.

Given Gaussian, its *even smaller*.

In real life. engineering design consists in reducing the probability of failure to below the probability of failure of the leasts reducible other issue, and provided that is acceptable, building it. The improbable failures are tested for, and if tests are passed, then the subassembly is fit for purpose.

At least one piece of Acorn hardware is known to have a bug that will cause it to crash every ten years or so of continuous use, on average.

However, that is insignificant compared with the software that would run on it, or in fact its power supply and hard drives. Or indeed, its estimated service life.

[Dave Plowman (News)]

Can you give details out of interest?

Loads and loads of mid '90s RPCs still in use. I've got two. HDs replaced because of limited size - they didn't envisage how many pics etc we'd store. But both the original Connors still work. One has a modified PC PS because it was cheaper than buying the alternative larger Acorn one - but the original didn't fail. They are built like tanks. ;-)

[Man at B&Q]

You also have to account for process and voltage variation. Then you test. then you "speed bin" the parts sorting thise that can be sold as meeting varying specifications.

The crucial point is your admition that those rthat fail the grade are thrown away. Thus in the customers hands the parts have a guaranteed absolute tolerance that can be relied upon by the design engineers.

The implication from previous posts was that components that didn't make the grade were still sold and the customer could not rely on absolute tolerance.

Bollocks. When did you last do timing analysis on a multi-million gate ASIC?

Bollocks again.

MBQ

[Man at B&Q]

A little knowledge is dangerous. I would put it out of your mind before you hurt yourself.

I could show you lots of examples of such hardware.

Any hardware that requires data to be synchronised between two different clocks will have a finite Mean Time Between Failures. There are well understood design practices to cope with this that do indeed rely on statitics.

It has nothing, however, to do with calculating worst case propogation delays through a logic path. When analysing a digital circuit for performance worst case figures are used for max and min delay over Process, Voltage and temperature. These figures are *always* used cummulatively. A chain of 10 AND gates each with a max delay of 500ps has a total delay of 5ns (ignoring routing delays for the purpose of clarity).

You would not get very far in a job interview by trying to claim it's anything less.

MBQ