# Standard Resistor Values: Why not a true geometric series?

Discussion in 'Electronic Design' started by Rick Nungester, Oct 15, 2007.

1. ### Rick NungesterGuest

10% standard resistor values are close to a geometric series with
multiplier 10^(1/12), but not exactly. 1 decade of standard values,
followed by the rounded 10^(1/12) series values follows. (To generate
the 2nd column set a hand calculator to round to the nearest integer,
and multiply repeatedly by 10^(1/12).)

Why were the 5 "off by one" values chosen as standard?

10 10
12 12
15 15
18 18
22 22
27 26 <<<
33 32 <<<
39 38 <<<
47 46 <<<
56 56
68 68
82 83 <<<
100 100

2. ### Phil AllisonGuest

"Rick Bungester"

** What values are in the 20% tolerance ( E6 ) group - eh ???

Wanker.

........ Phil

3. ### John LarkinGuest

It's a shame the ratios are nearly geometric. It means that the
ability to design voltage divider ratios is severely restricted.

John

4. ### Rick NungesterGuest

** What values are in the 20% tolerance ( E6 ) group - eh ???

The 20% (E6) group has the same issue, deviating from a 10^(1/6)
multiplier. Standard versus geometric series follows.

10 10
15 15
22 22
33 32 <<<
47 46 <<<
68 68

http://en.wikipedia.org/wiki/Preferred_number includes history of when/
who picked the values, and a discussion of the "odd values" issue
under its "Discussion" page. But it doesn't answer the "Why?"

5. ### Richard HenryGuest

Maybe use 1% resistors?

6. ### John LarkinGuest

We use 0.1% resistors, and sometimes 0.05%. But they are still nailed
to the 1% values, which are geometrically spaced. So if you have some
assortment of resistors in stock, various combinations tend to keep
hitting the same ratios, and some ratios can't be done.

John

7. ### Richard HenryGuest

Ummmm, gee... how close do you need to be?

8. ### Simon S AysdieGuest

Exactly, and the "standard 1%" family is always "correctly" rounded,
unlike the "standard 5%" family.

It is perhaps ironic, but the skewing of the "standard 5%" family
values often serendipitously provides a better ratio match than
correctly rounded "standard 1%" family values will. I've encountered
that many times. So is it really serendipitous? I've wondered if
"they" skewed them for exactly that reason.

There are 8 skewed values (82 is unique too,as it is a skew down
rather than up):

10 18 33 56
11 20 36 62
12 22 39 68
13 24 43 75
15 27 47 82
16 30 51 91

10 18 32 56
11 20 35 62
12 22 38 68
13 24 42 75
15 26 46 83
16 29 51 91

100 147 215 316 464 681
102 150 221 324 475 698
105 154 226 332 487 715
107 158 232 340 499 732
110 162 237 348 511 750
113 165 243 357 523 768
115 169 249 365 536 787
118 174 255 374 549 806
121 178 261 383 562 825
124 182 267 392 576 845
127 187 274 402 590 866
130 191 280 412 604 887
133 196 287 422 619 909
137 200 294 432 634 931
140 205 301 442 649 953
143 210 309 453 665 976

9. ### Guest

As to 'cannot be done', that does not always have to be a problem.
computer),
it needed a 5.00V reference.
Now I had a LM317 with 2 resistors that gave anywhere near 5.xx.
Measured it, made a #define in the program, and: any accuracy you
want.
Same with PICs, just calibrate in the software, set value in its
EEprom.

10. ### Spehro PefhanyGuest

Nominally perfect would be nice; failing that at least 10-20x better
than the resistor tolerances. But I don't mind much putting a much
smaller value 1% resistor in series (or a much larger value in
parallel) with a 0.1% resistor if it's that kind of deal.

Best regards,
Spehro Pefhany

11. ### Tom BruhnsGuest

Ah, but for small quantities, it's much cheaper to buy standard
values. You _can_ get any value you want, if you pay enough; but if
your volume isn't great enough, it's much more economical to do series
and/or parallel combinations. With an E24 set of high accuracy
values, two in parallel or two in series will always get you within
0.23% of a desired value, and if you're stuck trying to get to a low
value where series won't work, or a high value where parallel won't
work, you still can get within 0.45%. And that's without being very
creative about picking values (just one closest to the desired and one
to trim it). For ratiometric stuff, it generally gets even better:
with one "stock" value and one trimmed value, you get to 0.23%, but
add a trim to the stock value and you get much finer ratio adjustment.

I have some very low TC matched resistor sets in my junque box, from
HP voltmeter scrap, that have "weird" values. Given the needed
precision and the relatively high volume in the voltmeter market, the
custom values made sense for HP. For the work I do, trimming as
needed with series and/or parallel is fine: I do need 0.1% parts at
times, but never in high volume.

Also, it helps a lot to design systems in such a way that really close
arbitrary ratios aren't necessary. For practically everything we do,
stability is far more important than absolute accuracy; the accuracy
is obtained by calibration. Calibration used to involve adjusting
pots and possibly variable capacitances and inductances; that's
practically all been replaced with processor-based calibration. I
realize that on rare occasion, there's no good way around some
precision ratio, but at least in what I've seen for quite a few years
now, those occasions are pretty rare.

Cheers,
Tom

12. ### Tom BruhnsGuest

This may be a good question for a different group. Someone that
checks into rec.radio.amateur.boatanchors may have a reasonable
answer, or there may be some other group that delves into history
more.

Of course, when the values were standardized (some time around WWII, I
believe), people didn't use pocket calculators or Excel or Matlab to
easily calculate a set of values, with rounding applied. One may
forgive them for rounding incorrectly. But some of the values are off
worse than that: 33 ohms "should be" 31.6.

Before that time, the "standard" values were even crazier. Count your
blessings??

Cheers,
Tom

13. ### ªºª rrockGuest

It's far cheaper to sell resistors that either do not meet mil-spec or
have been over-produced relative to the military customer's consumption
rate, to the commercial market rather than make them separately.
See MIL-PRF-39005 for an example of the resistance values.

14. ### John DevereuxGuest

I wrote a program to calculate the optimum combination of 3 resistors
to get a given ratio. Yes, I know there are lots of these about - but
mine only uses the values I carry in stock!

I started out thinking how to write it efficiently, then realised I
could simply try all possible combinations and pick the closest...

15. ### Tim WilliamsGuest

Micromicrofarads ("mmf") and that's the way I likes it! :^)

Tim

16. ### Phil AllisonGuest

"Rick Bungester"

** Not the point at all - you SNIPPING cretin.

........ Phil

18. ### ChairmanOfTheBoredGuest

Repeatability in a production setting is always an issue, and should be
of somewhat serious import to a designer. 1% (E96) using two in series
or parallel will nearly ALWAYS result in a combination that requires ZERO
matching or culling in a batch. Using a five percent mix can result in
"chaining errors" that are worse than the original tolerance, even WITH
matching and culling procedures in place.

Yet, it all depends on the application. Precision, instrumentation op
amp circuit where you want the entire production lot to have the same
gain ratio, or a simple current limit value for an LED driver circuit.

Application is everything, particularly if large volumes are involved.

One penny savings over a ten Million piece run is:

\$100,000.00

There is typically far more than one penny difference between 5% and 1%
values.

19. ### ChairmanOfTheBoredGuest

Did you know that Joe Walsh is a big Ham Radio relic collector?

20. ### ChairmanOfTheBoredGuest

It isn't the values. Mil spec resistors are produced in an entirely
different manner, and the process controls are much tighter. They have
to be or else they will only succeed in getting a 3% yield.

3 out of every 100 parts made is not very profitable. Better to make a
process that guarantees a more promising production yield, and yes, that
IS why they also have a higher attached price.

Where do you people get this shit from?