Distribution of component values with a given tolerance?

Question

Suppose I have a collection of parts with the same nominal value and some tolerance, say 50 Ohm 1% tolerance resistors. What distribution of actual component values can I expect? I can imagine several definitions:

• The parts follow a normal distribution with standard deviation 0.5 Ohms
• 95% of parts will be within 0.5 Ohms of the nominal value
• 100% of parts will be within 0.5 Ohms of the nominal value
• ...

What is the actual technical definition of component tolerance?

My reason for asking is that I wish to simulate many instances of a particular circuit, each time selecting 'realistic' component values, to determine what variation in the final circuit performance I can expect, based on the tolerances of the underlying passive components.

Answer 1

You can make no assumptions about distribution within the specified range. 50 Ω ±1% means exactly that. Since 1% of 50 Ω is 500 mΩ, the manufacturer is saying that any one resistor you get will be from 49.5 Ω to 50.5 Ω. You can't read into it or assume more than that.

Added:

Some people have pointed out that they have gotten tightly clumped values from a batch. I have seen that too. However, that changes nothing.

Depending on the type of part and the manufacturing, testing, and binning processes, you might get a tight distribution within a batch. But the most important word is "might". There is no guarantee, and just because one batch was tight you can't make assumptions about the next batch.

Consider a few different manufacturing scenarios:

• The production process has good tolerance, so parts are made to specific values. Each part is tested, and the rare outlyer is discarded. In this case you probably do get something like a normal distribution. The center might not be in the center of the range though, depending on the temperature, phase of moon, and species of dead fish waved over the equipment during the run.

• The manufacturer sells different tolerance grades, with the high tolerance having a higher price. Let's say the equipment can make 1% resistors reliably enough, but not as tight as .1% reliably. In this case the manufacturer measures each unit and the ones within .1% are labeled and sold as such and the rest are labeled and sold as 1%.

  In this scenario, the .1% parts probably have a fairly even distribution accross their range. The 1% parts have more of a normal distribution, except that there is a gap within .1% of the ideal value.

• The production process has wide variation. Each part is tested and sold as the value it happens to fall within. In this case you'd get a fairly even distribution within each tolerance band, but it may take a large number of parts to see that distribution.

When you don't know anything about the manufacturing process, there is nothing you can assume other than each part will be somewhere within the specified range. You have to consider the value of each part as a separate uncorrellated random event. Sometimes there might in fact be some correlation between sequential parts, but since you don't know when that is, you're still back to having to assume there isn't. Even if you measure one batch and find a correlation, the next batch is a separate random event for which the data from the previous batch is unrelated. Again you can't assume anything.

In summary, if you need to know more than the accuracy specified by the manufacturer, you have to measure each part individually.

Each time you flip a coin the result is random and uncorrelated to other times, but you can still get 3 heads in a row often enough to look like a pattern if you don't think about it carefully.

 

Answer 2

• You probably have to characterise distributions based on real world products of the type you are dealing with.

• Brand matters.

• Industry norms may be greatly improved on by competent manufacturers.

• Never rely on all items clustering as tightly as most do.

Olin is correct (of course) but some field experience and general comment may be of interest and possibly of value.

You can probably expect a processs like setting resistor values to cluster normally about the nominal value BUT you have no certainty of this.

I had a largish number of through hole metal film resistors from Philips in the days when through hole was almost current and Philips had not sold the machinery that made them to somebody in South america (I think it was).

These were5% rated but being metal film and being Philips the real accuracy was usually much better. In ye good olde days you used to be able to select a resistor of choice by measurement - they spread fairly well across the nominal range or beyond. But these resistors were almost all about +/-1%or thereabouts. Finding a resistor in betyween was hard to do.

One gets blase. One day I lashed up a circuit and used resistor vales where 1% was OK. I had problems with accuracy and it took some while to find that I'd chosen a resistor that was well off centre value. Veru unusual but ... .

BUT

LEDS usually have a very wide s[read of Vf (forward voltage). So much so that thse are binned but are still very wide. Maybe overall an LED may be rated as 2.9 - 3.7V Vf. Few at the extremes but probably a wider and flatter distribution than normal. In recent years I have had a lot of LEDs from Nichia and have tested LEDs from numerous manufacturers - name brand well known and never heards of. The never heard ofs you largely don't want to hear of!. We ened up using a a Nichia "Raijin" LED in reasonable volume = NSPWR70CSS-K1. Nichia were cooperative at supplying more than usual data. One sheet showed Vf distributions for several hundred thousand LEDs taken from ongoing production. As I recall they cluster at 2.95 +/- 0.05V for about 99% of production. There are a few outliers but they are very few and far beyween. Such tight Vf clustering is very very unusual. It also happens o be the best LED in its class efficiency wise that I have seen, There are now better but for several years this was the best It's only 50 mA rated alas.

SO:

• You probably have to characterise distributions based on real world products of the type yu are dealing with.

• Brand matters.

• Industry norms may be utterly ignored by competent manufacturers.

• Never rely on all items clustering as tightly as most do.

Answer 3

It depends on who you buy your components from. If a manufacturer quotes their parts to have a tolerance of 1% then you can expect that practically all of their parts are within that spec. It might be possible that a part is out of spec but it would be a lot less than 5%, probably more like one in a few million and it's unlikely to be out by much.

Generally you need to go by the datasheet. If the particular part's datasheet specifies that the tolerance of the parts follow a Gaussian distribution then you could assume that. Otherwise it could still be the case, but it's not guaranteed.

Also, think about how manufacturers might produce resistors. For example, a manufacturer may have separate production lines for identical valued parts with different tolerances say a 1kOhm 1% line, a 1kOhm 5% line and a 1kOhm 0.1%. Alternatively, they may produce all same-valued parts in a single run and use some automated procedure to extract the better spec'd parts to be sold as higher tolerance parts. For example, all parts could be created as 1kOhm 5% resistors. Then the ones that fall within 1% spec might be labelled and sold as 1% resistors while the rest are sold as 5% resistors. This would lead to their 5% resistors being very unlikely to coincide with a resistance close to the target value (1kOhm). I'm not saying that this is how manufacturer's actually do it, I'm not sure, but it's possible.

Dave Jones did a great video blog on this topic, it's a great watch.. here's the link(s):

Part 1 - eevblog-215-gaussian-resistors

Part 2 - eevblog-216-gaussian-resistor-redux

Answer 4

Adding to the already great answers here. If you do a tolerance analysis of your design, and you have the same part number multiple times in your design, you need to assume that all are correlated as these part are likely from the some batch and the same manufacturing run.