6 ms·

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,

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.

Denvercoder9 2y ago
I feel like the author conflates tolerance in component value choice and fabrication tolerance. The E-series were chosen so that if you have perfect resistors (no fabrication tolerance) of only their values available, you can replace any resistor value you need with one from the series, and you'll never be more off than a fixed error (e.g. 20% for the E6 series). This only works with perfect resistors, though. If your actual resistors have a fabrication tolerance, you might be more off. For example, if you need a 41 Ohm resistor, you can use a perfect 47 Ohm resistor from the E6-series, and you'll be within 20% error. However, if that 47 Ohm resistor has a 10% fabrication tolerance, in reality it might be 51 Ohm, and that's more than 20% off from the 41 Ohm you needed. To take the example from the author's last paragraph, if you need a 70 Ohm resistor, the idea is not that you could be lucky and find an exact 70 Ohm in your E24 resistor set, but that you change the design to use a 68 Ohm instead, and don't introduce more than 5% off by doing so (regardless of the resistor value you needed).
- xw390112 2y ago
  In 2024, if your resistor vendor has even 5% tolerance, you need to find another vendor.
  - rchowe 2y ago
    Thin-film resistor design engineer here! It's dependent on value and geometry -- if you order a 0.5 ohm resistor the meters on our trimming lasers only go down to 20 mΩ and you're getting a 5% part at best.
    - alright2565 2y ago
      What about shunt resistors? I can pretty easily get a 1% 5mΩ resistor, but they don't look to me like they are constructed in the same way as a generic resistor.
      - KennyBlanken 2y ago
        They're made in a bunch of ways but the general principle is "the stuff inside is much lower resistance than what's normally used."
    - SAI_Peregrinus 2y ago
      And that's why the really precise resistors are so damn expensive. E.g. VPG makes a 10k 1/5W 0.001% tolerance ±0.2ppm/°C, but they're $116 each with a minimum order quantity of 25 on DigiKey (so $2900 minimum purchase). They've got a really expensive meter for their trimming setup!
      - galaxyLogic 2y ago
        I see. I guess that's why high-end audio is so expensive
        atoav 2y ago
xw390112 2y ago
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- deleted 2y ago
  [deleted]
- neuralRiot 2y ago
  And before digital circuits. All I see now is 10k, 1k and 100 Ohm resistors.
  - xxs 2y ago
    Most resistor in power supplies would be different values. For digital stuff and low current applications (along with designated FET drivers) you dont need too much.
- deleted 2y ago
  [deleted]
- mb_72 2y ago
  'Laser-trimmed resistors' will be the next selling point on a boutique guitar FX company's 57th clone of a Tubescreamer.
- analog31 2y ago
  Factored into the tolerance is the temperature coefficient, because the tolerance is specified over the operating range. There are also 3 basic temperature ranges: Industrial, automotive, and military. I've used this to my advantage by spec'ing automotive capacitors when I needed tighter tolerances for my normally room temperature applications. They also laser-trim IC's.
jessriedel 2y ago
Seems easier to me to say they are logarithmically distributed, rounded to 2 digits. Like yes, this means that if your manufacturing tolerances are typically some percentage of the amount (more natural than an additive error) then the overlaps are nicely spaced. But a log scale means that's true for any relative allowance (manufacturing or otherwise), which is the much more natural sort. It doesn't matter if your 100-foot house is off by 1mm, but it does matter if your 1mm-thickness fork is.
- throw0101d 2y ago
  > Seems easier to me to say they are logarithmically distributed, rounded to 2 digits. Except that it is the tolerance overlap that allows for that specific distribution to work.
  - jessriedel 2y ago
    I can’t tell what you mean.
SamBam 2y ago
I still don't really get the overlapping tolerances, though, because each resistor is not a range, it's a single value that's somewhere in that tolerance. He says about the cables: > Each size of cable had a max/min rating that just overlapped it’s neighbor above and below, so every required value was covered by one or more cable. So that means if you needed a "size 12" cable you could pick a size 10 OR a size 15, and they would both work. But if you need a 12ohm resistor, it's possible that neither the 10 nor the 15 might work, because the 10 could be a 9 and the 15 could be a 17. So I don't really see how it connects. To put it another way, what if we had 1000% error tolerances? Could we then get away with just a 1ohm. 1000ohm and 1Mohm resistors, because their tolerances overlap? Obviously not, so I don't see how it relates.
- deleted 2y ago
  [deleted]
- SAI_Peregrinus 2y ago
  Each resistor in the design is a range. The designer picks the tolerance to use, some resistors will be fine with a 10% tolerance, others only with a 2% or 1% tolerance. Also each resistor is a range, not a single value, since each resistor changes value with temperature & other environmental factors (though temperature is the biggest). That variation is (for normal resistors) less than the tolerance range.
ChrisRR 2y ago
The image it what made it clear to me. https://digilent.com/blog/wp-content/uploads/2015/01/E12_series_tolerance.svg_.png https://digilent.com/blog/wp-content/uploads/2015/01/E12_ser...

Denvercoder9 2y ago

I feel like the author conflates tolerance in component value choice and fabrication tolerance. The E-series were chosen so that if you have perfect resistors (no fabrication tolerance) of only their values available, you can replace any resistor value you need with one from the series, and you'll never be more off than a fixed error (e.g. 20% for the E6 series). This only works with perfect resistors, though. If your actual resistors have a fabrication tolerance, you might be more off. For example, if you need a 41 Ohm resistor, you can use a perfect 47 Ohm resistor from the E6-series, and you'll be within 20% error. However, if that 47 Ohm resistor has a 10% fabrication tolerance, in reality it might be 51 Ohm, and that's more than 20% off from the 41 Ohm you needed. To take the example from the author's last paragraph, if you need a 70 Ohm resistor, the idea is not that you could be lucky and find an exact 70 Ohm in your E24 resistor set, but that you change the design to use a 68 Ohm instead, and don't introduce more than 5% off by doing so (regardless of the resistor value you needed).

xw390112 2y ago
In 2024, if your resistor vendor has even 5% tolerance, you need to find another vendor.
- rchowe 2y ago
  Thin-film resistor design engineer here! It's dependent on value and geometry -- if you order a 0.5 ohm resistor the meters on our trimming lasers only go down to 20 mΩ and you're getting a 5% part at best.
  - alright2565 2y ago
    What about shunt resistors? I can pretty easily get a 1% 5mΩ resistor, but they don't look to me like they are constructed in the same way as a generic resistor.
    - KennyBlanken 2y ago
      They're made in a bunch of ways but the general principle is "the stuff inside is much lower resistance than what's normally used."
  - SAI_Peregrinus 2y ago
    And that's why the really precise resistors are so damn expensive. E.g. VPG makes a 10k 1/5W 0.001% tolerance ±0.2ppm/°C, but they're $116 each with a minimum order quantity of 25 on DigiKey (so $2900 minimum purchase). They've got a really expensive meter for their trimming setup!
    - galaxyLogic 2y ago
      I see. I guess that's why high-end audio is so expensive
      - atoav 2y ago

xw390112 2y ago

[dead]

deleted 2y ago
[deleted]
neuralRiot 2y ago
And before digital circuits. All I see now is 10k, 1k and 100 Ohm resistors.
- xxs 2y ago
  Most resistor in power supplies would be different values. For digital stuff and low current applications (along with designated FET drivers) you dont need too much.
deleted 2y ago
[deleted]
mb_72 2y ago
'Laser-trimmed resistors' will be the next selling point on a boutique guitar FX company's 57th clone of a Tubescreamer.
analog31 2y ago
Factored into the tolerance is the temperature coefficient, because the tolerance is specified over the operating range. There are also 3 basic temperature ranges: Industrial, automotive, and military. I've used this to my advantage by spec'ing automotive capacitors when I needed tighter tolerances for my normally room temperature applications. They also laser-trim IC's.

jessriedel 2y ago

Seems easier to me to say they are logarithmically distributed, rounded to 2 digits. Like yes, this means that if your manufacturing tolerances are typically some percentage of the amount (more natural than an additive error) then the overlaps are nicely spaced. But a log scale means that's true for any relative allowance (manufacturing or otherwise), which is the much more natural sort. It doesn't matter if your 100-foot house is off by 1mm, but it does matter if your 1mm-thickness fork is.

throw0101d 2y ago
> Seems easier to me to say they are logarithmically distributed, rounded to 2 digits. Except that it is the tolerance overlap that allows for that specific distribution to work.
- jessriedel 2y ago
  I can’t tell what you mean.

SamBam 2y ago

I still don't really get the overlapping tolerances, though, because each resistor is not a range, it's a single value that's somewhere in that tolerance. He says about the cables: > Each size of cable had a max/min rating that just overlapped it’s neighbor above and below, so every required value was covered by one or more cable. So that means if you needed a "size 12" cable you could pick a size 10 OR a size 15, and they would both work. But if you need a 12ohm resistor, it's possible that neither the 10 nor the 15 might work, because the 10 could be a 9 and the 15 could be a 17. So I don't really see how it connects. To put it another way, what if we had 1000% error tolerances? Could we then get away with just a 1ohm. 1000ohm and 1Mohm resistors, because their tolerances overlap? Obviously not, so I don't see how it relates.

deleted 2y ago
[deleted]
SAI_Peregrinus 2y ago
Each resistor in the design is a range. The designer picks the tolerance to use, some resistors will be fine with a 10% tolerance, others only with a 2% or 1% tolerance. Also each resistor is a range, not a single value, since each resistor changes value with temperature & other environmental factors (though temperature is the biggest). That variation is (for normal resistors) less than the tolerance range.

ChrisRR 2y ago

The image it what made it clear to me. https://digilent.com/blog/wp-content/uploads/2015/01/E12_series_tolerance.svg_.png https://digilent.com/blog/wp-content/uploads/2015/01/E12_ser...