[SOTGO]

Can someone explain the last paragraph? The author gives the example of trying to find a 70 Ohm resistor and how the 68 Ohm and 75 Ohm are a little off. They conclude by saying you should just use 33 and 47 Ohm resistors, but wouldn't that give an resistance of 80, not 70?

[dbcurtis]

I think the author maybe doesn’t know how to order 1% resistors from Digi-Key??

My intro circuit analysis prof gave these wise words to live by: “If you need more than one significant digit, it isn’t electrical engineering, its physics”

[xxs]

Even ordering from China the 1% are perfectly fine. E96 resistors are ubiquitous and cheap.

[rexer]

I think that was a typo and they meant 22 + 47, which equals ~70 Ohms

[rylittle]

I also thought that was interesting. Also, wouldn't the tolerance be doubled when you add them in series? Or does it still average out to +/- 5%?

[riedel]

Fun fact is that afaik component values are often distributed in a bi-modal way because actually +-5% often means that they sorted out already the +-1% to sell as a different more expensive batch. At least it used to be that way. Wonder if it is still worth doing this in production. So I guess one could also measure to average things out otherwise the errors will stay the same relatively.

[dmurray]

If you can measure them with that precision, would it make sense to sell them with that accuracy too? So if you tried to manufacture a resistor at 68kΩ +/- 20%, and it actually ended up at 66kΩ +/- 1%, couldn't you now sell it as an E192 product which according to TFA are more expensive?

Selling with different tolerances only makes sense to me if the product can't be reliably measured to have a tighter tolerance, perhaps if the low- quality ones are expected to vary over their life or if it's too expensive to test each one individually and you have to rely on sampling the manufacturing process to guess what the tolerances in each batch should be.

[retrac]

Resistors with worse tolerances may be made out of cheaper, less refined wire, which will vary resistance more by temperature. The tolerance and resistance is good over a temperature range. For more reading looking up "constantan".

[RetroTechie]

Most resistors don't use wire, but some film of carbon (cheaper, usually the E12 / 5% tolerance parts) or metal (E24, or 1% and tighter tolerances) onto a non-conducting body. Wires mean winding into a coil, which means increased inductance.

I suspect in most cases the tolerances are a direct result from the fabrication process. That is: process X, within such & such parameters, produces parts with Y tolerance. But there could be some trimming involved (like a laser burning off material until component has correct value). Or the parts are measured & then binned / marked accordingly.

Actual wire is used for power resistors, like rated for 5W+ dissipation. Inductance rarely matters for their applications.

[Gibbon1]

Accuracy depends on the technology used. Carbon comp tends have less accuracy then carbon film. And it's not true that higher accuracy is always better.

Some accurate resisters are essentially wound coils and have high inductance and will also induce and pick up magnetic interference. Stuff like that matters often a lot.

[projektfu]

Thanks, always good to remember that the tolerance of a resistor is not just a manufacturing number but also defined over the specified temperature range.

[dylan604]

Depends on where in the production line they are being tested. If they are tested after they've had their color bands applied, then you wouldn't be able to sell it as a 66kH since the markings would for a 68kH

[wongarsu]

The issue is probably volume. Very few applications need a resistor that's exactly 66kΩ, but a lot of applications need resistors that are in the ballpark of 68kΩ (but nobody would really notice if some 56kΩ resistors slipped in there).

For every finely tuned resonance circuit there are a thousand status LEDs where nobody cares if one product ships with a brighter or dimmer LED.

[projektfu]

Unless the components are expensive, that proposition seems dubious. It's much more economical to take a process that produces everything within 12% centered on the desired value and sell it as ±20%. 100% inspection is generally to be avoided in mass production, except in cases where the process cannot reach that capability, chip manufacturing being the classic example. For parts that cost a fraction of a penny, nobody is inspecting to find the jewels in the rough.

[riedel]

Actually it seems to be really the case that multimodal distribution are rather the result of batches not having a mean. So it is rather the effect of systematic error [1]. I guess it is really a myth (we did low cost RF designs back in 2005 and had some real issues with frequencies not aligning die to component spread and I really remember that bi modality problem, but I guess okhams razor should have told me that it makes no economical sense)

[1] https://www.eevblog.com/2011/11/14/eevblog-216-gaussian-resi...

[projektfu]

Yup, forever the reason for the trim pot.

[bluGill]

I'm not sure where the line is, but at some point things like temperature a matter and so a low % resister cannot be high % that passes tests.

[aleph_minus_one]

> Also, wouldn't the tolerance be doubled when you add them in series? Or does it still average out to +/- 5%?

Neither.

Let R_{1, ideal}, R_{2, ideal} be the "ideal" resistances; both with the same tolerance t (in your example t = 0.05).

This means that the real resistances R_{1, real}, R_{2, real} satisfy

(1-t) R_{1, ideal} ≤ R_{1, real} ≤ (1+t) R_{1, ideal}

(1-t) R_{2, ideal} ≤ R_{2, real} ≤ (1+t) R_{2, ideal}

Adding these inequalities yields

(1-t) (R_{1, ideal} + R_{2, ideal}) ≤ R_{1, real} + R_{2, real} ≤ (1+t) (R_{1, ideal} + R_{2, ideal})

So connecting two resistors with identical tolerance in series simply keeps the tolerance identical.

[thornewolf]

tolerance should actually go down since the errors help cancel each other out.

reference: https://people.umass.edu/phys286/Propagating_uncertainty.pdf

disclaimer: it will be a relatively small effect for just two resitors

aleph's comment is also correct. the bounds they quote are a "wost-case" bound that is useful enough for real world applications. typically, you won't be connecting a sufficiently large number of resistors in series for this technicality to be useful enough for the additional work it causes.

[rexer]

Note that tolerance and uncertainty are different. Tolerance is a contract provided by the seller that a given resistor is within a specific range. Uncertainty is due to your imprecise measuring device (as they all are in practice).

You could take a 33k Ohm resister with 5% tolerance, and measure it at 33,100 +/- 200 Ohm. At that point, the tolerance provides no further value to you.

[MobiusHorizons]

It’s not nearly that simple:) Component values change with environmental factors like temperature and humidity. Resistors that have a 1% rating don’t change as much over a range of temperatures as 5% or 10% components do. This is typically accomplished by making the 1% resistors using different materials and construction techniques than the lower tolerance parts. Just taking a single measurement is not enough.

[immibis]

If values are normally distributed, random errors accumulate with the square root of the number of components. Four components in series have 2x the uncertainty over all, etc, but if you divide that double uncertainty by four times the resistance, it's half the percentage uncertainty as before. (I avoid using the word "tolerance" because someone will argue whether it really works this way)

In reality, some manufacturers may measure some components, and the ones within 1% get labeled as 1%, then it may be that when you're buying 5% components that all of them are at least 1% off, and the math goes out the window since it isn't a normal distribution.

[afiori]

I wonder about the effect of different wiring patterns. For example you can can combine N^2 resistors in N parallel strips of N resistors in serie.

I expect that in this case the uncertainty would decrease

[RetroTechie]

In the article's example, I'd prefer 2 resistors in parallel. That way result is less dramatic if 1 resistor were to be knocked off the board / fail.

Eg. 1 resistor slightly above desired value, and a much higher value in parallel to fine-tune the combination. Or ~210% and ~190% of desired value in parallel.

That said: it's been a long time since I used a 10% tolerance resistor. Or where a 1% tolerance part didn't suffice. And 1% tolerance SMT resistors cost almost nothing these days.

[bombela]

This might be why pretty much all LED lightbulbs/fixtures have two resistors in parallel. Used for the driver chip control pin, that sets the current to deliver via some specific resistance value.

It's always a small and a large resistor. The higher this control resistance, and the lower the driving current.

Cut off the high value resistor to increase the resistance a bit. In my experience this often almost halves the driving current, and up to 30% of the light output (yes, I measured).

Not only most modern lights are too brights to start with anyways, this fixes the intentional overdriving of the LEDs for planned obsolescence. The light will last pretty much forever now.

[afiori]

Iterating either of

f(x) = 3/(1/x + 1/110 + 1/90)

g(x) = 1/(1/(3x) + 1/(3110) + 1/(3*90))

Seems to show that 100 is a stable attractor.

So I will postulate without much evidence that if you link N^2 resistors with average resistance h in a way that would theoretically give you a resistor with resistance h you get an error that is O(1/N)

[nomel]

> tolerance should actually go down since the errors help cancel each other out.

Complete nonsense. The tolerance doesn't go down, it's now +/- 2x, because component tolerance is the allowed variability, by definition, worst case, not some distribution you have to rely on luck for.

Why do they use allowed variability? Because determinism is the whole point of engineering, and no EE will rely on luck for their design to work or not. They'll understand that, during a production run, they will see the combinations of the worst case value, and they will make sure their design can tolerate it, regardless.

Statistically you're correct, but statistics don't come into play for individual devices, which need to work, or they cost more to debug than produce.

[tempestn]

The total tolerance is not +/- 2x, because the denominator of the calculation also increases. You can add as many 5% resistors in series as you want and the worst case tolerance will remain 5%. (Though the likely result will improve due to errors canceling.)

For example, say you're adding two 10k resistors in series to get 20k, and both are in fact 5% over, so 10,500 each. The sum is then 21000, which is 5% over 20k.

[jjmarr]

> Statistically you're correct,

The Central Limit Theorem (which says if we add a bunch of random numbers together they'll converge on a bell curve) only guarantees that you'll get a normal distribution. It doesn't say where the mean of the distribution will be.

Correct me if I'm wrong, but if your resistor factory has a constant skew making all the resistances higher than their nominal value, a bunch of 6.8K + 6.8K resistors will not on average approximate a 13.6K resistor. It will start converging on something much higher than that.

Tolerances don't guarantee any properties of the statistical distribution of parts. As others have said, oftentimes it can even be a bimodal distribution because of product binning; one production line can be made to make different tolerances of resistors. An exactly 6.8K resistor gets sold as 1% tolerance while a 7K gets sold as 5%.

[nomel]

> Tolerances don't guarantee any properties of the statistical distribution of parts.

That's incorrect. They, by definition, guarantee the maximum deviation from nominal. That is a property of the distribution. Zero "good" parts will be outside of the tolerance.

> It will start converging on something much higher than that.

Yes' and that's why tolerance is used, and manufacturer distributions are ignored. Nobody designs circuits around a distribution, which requires luck. You guarantee functionality by a tolerance, worst case, not a part distribution.

[Dylan16807]

> The Central Limit Theorem (which says if we add a bunch of random numbers together they'll converge on a bell curve) only guarantees that you'll get a normal distribution. It doesn't say where the mean of the distribution will be.

That's kind of overstating and understating the issue at the same time. If you have a skewed distribution you might not be able to use the central limit theorem at all.

[_dain_]

>If you have a skewed distribution you might not be able to use the central limit theorem at all.

The CLT only requires finite variance. Skew can be infinite and you still get convergence to normality ... eventually. Finite skew gives you 1/sqrt(N) convergence.

[Dylan16807]

If you're going to say "Complete nonsense." you shouldn't get the calculation wrong in your next sentence.

[nomel]

Very true, I was writing as absolute value, not % (magnitude is where my day job is). My point still stands: it is complete nonsense that tolerance goes down.

[Dylan16807]

They said it "should" go down, but that another comment saying the worst case is the same is "also correct".

I do not see any "complete nonsense" here. I suppose they should have used a different word from "tolerance" for the expected value, but that's pretty nitpicky!

[Sohcahtoa82]

Nope, still averages to +/- 5%.

To give an example, let's say you've got two resistors of 100 Ohm +/- 5%. That means each is actually 95-105 Ohm. Two of them is 190-210 Ohm. Still only a 5% variance from 200 Ohm.

[sram1337]

Can you assume that +/-5% isn't linearly distributed? If so, the tolerance in practice may likely end up even smaller.

[sophacles]

There's a fundamental misunderstanding here.

Tolerance is a specification/contractual value - it's the "maximum allowable error". It's not the error of a specific part, it's the "good enough" value. If you need 100 +/- 5%, any value between 95 and 105 is good enough.

Using two components to maybe cancel out the error as you describe. On average, most of the widgets you make by using 2 resistors instead of one may be closer to nominal, but any total value between 95 and 105 would still be acceptable, since the tolerance is specified at 5%.

To change the tolerance you need to have the engineer(s) change the spec.

[renewiltord]

But 80 is within 20% of 70 so we're fine ;)

[phkahler]

>> But 80 is within 20% of 70 so we're fine ;)

So are the 68 Ohm and 75 Ohm.

[Stratoscope]

You are correct. Two of the comments on the article itself also mention this error.

[LeifCarrotson]

Brilliant, informative writing, and yet people will jump to nit-pick the arithmetic.

I'd better spell-check this comment before clicking reply...