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Why do electronic components have such odd values? (2021)

digilent.com

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Re: Why do electronic components have such odd values? (2021)

#31

Post by nomel »

thornewolf wrote: post #8
rylittle wrote: post #5

Earlier quoted context omitted.

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%?

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 re…

> 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.

Re: Why do electronic components have such odd values? (2021)

#32

Post by tempestn »

nomel wrote: post #31
thornewolf wrote: post #8

Earlier quoted context omitted.

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 re…

> 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…

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.

Re: Why do electronic components have such odd values? (2021)

#33

Post by afiori »

afiori wrote: post #30
immibis wrote: post #14

Earlier quoted context omitted.

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 manufactur…

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

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)

Re: Why do electronic components have such odd values? (2021)

#34

Post by throw0101d »

This part is the thing that made me understand the numbering series:

> […] Continuing this trend, rounding as needed, and we end up with the series 10, 15, 22, 33, 47, and 68. Components built to the E6 standard have a 20% relative error tolerance, and if we look at the values again we’ll see a trend. Starting with 10 again and adding 20% error we end up with 12. Moving to 15 and subtracting 20% we get… wait for it… 12. Moving up from 15 we get 15 + 20% = 18 and 22 – 20% = 17.6. This trend repeats no matter what range of powers of 10 you use, as long as they are consecutive. So 47kΩ + 20% = 56400, while 68kΩ – 20% = 54400.

> Look again at the values 47 and 68. The max/min values overlap right about 56, don’t they? That sounds familiar. The E12 standard uses all of the same values as E6, but with 6 more values mixed in. These 6 additional values are roughly where the E6 values overlap, and now in order to cover the entire range our %-error is reduced to 10%. Starting again at 10, we have 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, and 82. The math holds true here as well, with the error values just slightly overlapping.

It's the 'tolerance overlap' concept that makes the numbers work, but I don't think I've ever seen it explained so clearly before.

Re: Why do electronic components have such odd values? (2021)

#36

Post by perlgeek »

csours wrote: post #15
rylittle wrote: post #4

Insightful article. Not something I had considered before, but also...isn't this just a fancy way of defining a geometric sequence thats convenient for values in base-10?

do geometric sequences care about the base?

The ones mentioned in the article return to powers of 10.

In contrast, musical notes don't, their frequencies return to powers of 2.

Re: Why do electronic components have such odd values? (2021)

#37

Post by RetroTechie »

afiori wrote: post #30
immibis wrote: post #14

Earlier quoted context omitted.

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 manufactur…

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

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.

Re: Why do electronic components have such odd values? (2021)

#38

Post by timerol »

rylittle wrote: post #4

Insightful article. Not something I had considered before, but also...isn't this just a fancy way of defining a geometric sequence thats convenient for values in base-10?

It's not just a geometric sequence that's convenient for base 10, it's the standard set of geometric sequences (that was chosen because they're convenient for base 10).

The caption on the graph (and the paragraph before the graph) directly addresses this: "This graph shows how any value between 1 and 10 is within ±10% of an E12 series value, and its difference from the ideal value in a geometric sequence."

Re: Why do electronic components have such odd values? (2021)

#40

Post by phkahler »

renewiltord wrote: post #23
SOTGO wrote: post #2

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?

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

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

So are the 68 Ohm and 75 Ohm.

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