Why Do Electronic Components Have Such Odd Values?

Discussion in 'General Electronics Chat' started by Engr Tech, Jul 17, 2017 at 6:11 AM.

  1. Engr Tech

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    Like Resistors , Capacitors, Zener diodes etc... why ?
     
  2. OBW0549

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  3. WBahn

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    One thing I (and several others I know) have tried to track down is exactly how a few of the specific preferred values were chosen, because they aren't the rounded values that adhere most closely to the geometric progression. I've got lots of speculation about it, from bending to industry pressure to use a close value that was already extremely common, to trying to minimize possible confusion based on the color bands, to a handful of others. But who knows, since most standards-setting processes have a lot in common with sausage making, only bloodier. Unfortunately, I've never found anything that even discusses it, let alone references contemporary sources. I suspect that this is something that is simply lost to history.
     
  4. crutschow

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    I know that the E96 ( 1%) values are a geometric (log) progression because I wrote a simple program for my calculator that generated the closest 1% value to any value I input, and it used an exponential function (answer rounded to the closed 3rd digit) to calculate the 1% resistor value.
    I suspect the other tolerance values follow a similar progression.

    Basically the progression is such that each value's tolerance band is close to the tolerance band of the next value.
    Thus for E96 1% it goes 1, 1.02. 1.05. 1.07, etc.
    The tolerance band for these is (approximately) .99-1.01, 1.01-1.03, 1.04-1.06, 1.06-1.08, etc.
     
    Last edited: Jul 19, 2017 at 1:12 PM
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  5. KeepItSimpleStupid

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  6. dl324

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    They seem to use the same formula, but there are a couple mismatches for E96, exact match for E48, and more mismatches for E24 and E12.
    upload_2017-7-17_10-19-23.png
     
  7. crutschow

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    This formula supposedly properly calculates all 1% resistor values.
     
  8. dl324

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    That's the formula I used for calculating all E series above. There are two mismatches for E96.

    It also works for E6 and E3, with some exceptions...
     
  9. crutschow

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    Why is 21.5 in red?
    That is not a mismatch as it's a standard 1% value.
    Its also the value from the formula R = 10 * 10^i/96 (rounded to one decimal places).

    What's the other supposed E96 mismatch you found?
     
    Last edited: Jul 17, 2017 at 4:58 PM
  10. dl324

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    It should be 21.6. To two decimal places, that cell is 21.54.

    EDIT: Guess I have to take that back; 21.5 is the correct value. Don't know where I got 21.6. E96 and E48 are exact matches. The rest have discrepancies.
     
  11. The Electrician

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    There is in fact an error in the E192 series. Using the formula 10^(185/192) we get an exact value of 9.19478686. This should become a 3 digit value of 9.19, but the value found in a table of commercially available E192 resistors is 9.20

    Somebody made a slide rule error way back then.
     
  12. shortbus

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    Not a EE but a die maker/machinist. But the way I was taught to round up machining dimensions, the 9.19478686 would be rounded up to 9.20. In machining dimensions you go back a few places, so 9.19478686 the ''78686" would cause the "4" to be a "5", and then the "5" would cause the "19" to become a "20". Guess I don't understand why it would be different in the EE world. :) Or maybe I was taught wrong? :(
     
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  13. dl324

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    It's an EE thing.

    For E192, E96, and E48 we use 3 digits and a multiplier. For lower precision resistors, we use 2 digits and a multiplier.
     
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  14. shortbus

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    I guess. This whole wide tolerance of values thing EE is still hard for me to get over. Metal isn't so forgiving, you can't force a 20% oversize part into most things, even with a big hammer. :D
     
  15. The Electrician

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    Have a look at the absolute value of the difference between the exact value and each of the two approximations:

    Abs( 9.19478686 - 9.19) = .00478686

    Abs( 9.19478686 - 9.20) = .00521314

    The numerical "distance" from 9.19 to the true value is smaller.

    One of the things to be learned in numerical analysis is that rounding in multiple steps can give a different result than doing it in one step.
     
  16. WBahn

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    I would imagine that in mechanical assemblies it would be common to decide whether a given dimension should be rounded up or rounded down based on the particular goal and I would expect those considerations to require dimensions be rounded up most of the time. If you are designing a shear pin to have a safety factor of two and the needed diameter comes out to be 9.014 inches and your final part dimension is to be dimensioned to a tenth of an inch, then you would dimension it as 9.1 inches because 9.0 inches doesn't have the required safety factor. The same thing CAN happen in circuit design, but the natural tolerances of the parts generally swamps this so that, when needed, you use a larger margin and then round normally. It's also usually very application specific whether a value should be rounded up or rounded down to achieve a particular constraint, so having the component standards adopt one or the other makes little sense.

    That really doesn't make any sense. Which value is closer to 9.19478686, 9.19 or 9.20? If your intent is to choose the dimension that is closest to the ideal one, then you would choose 9.19.

    According to your approach, you would round 9.19444445 upward.
     
  17. shortbus

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    No because the number of "4's" in that number don't approach the higher numbers in the original example. It's not a statisical thing at all. But you guy's also come from a different back round than I do.
     
  18. WBahn

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    Where's any statistics?

    So when DO the number of 4's approach a high enough number to justify rounding 0.4xxx up to 1.0 ?
     
  19. dl324

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    We use the same rules for rounding that other disciplines use.
     
  20. GopherT

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    @WBahn
    The value 9.19478686 would not have existed in any reasonable engineers notebook back when resistor values were set. The log tables would usually have been 4 digits, or, 9.195 - especially if they were only looking for 1% accuracy.

    Now, round that one = 9.20
     
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