Standard Resistor Values: Why not a true geometric series?

[Tom Bruhns]

It seems to me that one would want the tolerance ranges to overlap. That
way, any resistance value you calculate analytically will be within the
tolerance band of a commercially available resistor.

The value of resistance which is midway between a pair of resistors on a
percent tolerance basis is the harmonic mean of the values; this is 2 times
the parallel equivalent of the two values. For example, given a 12 ohm and
a 15 ohm resistor, the value 2(12*15)/(12+15) = 13.333333 ohms. This is
11.1111111% less than 15 ohms, and 11.1111111% more than 12 ohms.

The amount (on a percentage basis) by which this middle value differs
from each of the bounding values is given by 100*(R2 - R1)/(R1 + R2). In
the example just above, this gives 100*(15 - 12)/(15 + 12) = 11.1111111%.

So, to find out if an adjacent pair of resistors have tolerance bands
which overlap, just calculate 100*(R2 - R1)/(R1 + R2) and compare it to the
tolerance of the E series you're investigating. If it's bigger than the
series tolerance, they don't overlap.

If the previous 12 and 15 ohm resistors are taken to be members of the
E12 series, then we see that since 11.1111111% > 10%, their tolerance bands
don't overlap.

If their tolerance bands don't overlap, this means that there is a zone
of values between the two nominal resistance values which are not within
rated tolerance for either of the two nominal values of that E series.

I find that for the E12 series, the following pairs have a zone of
no-overlap between them:

12 and 15
22 and 27

the tolerance zones for the pairs:

18 and 22
27 and 33

just touch.

For the E24 series, these pairs have a zone of no-overlap:

13 and 15
16 and 18
18 and 20
24 and 27
27 and 30
56 and 62
82 and 91

The E48, E96 and E192 series are rife with no-overlap zones. This is to
be expected, since the exact values in the logarithmic sequence are rounded
to 3 digits, and sometimes we round up, sometimes down.

I noticed on the Wikipedia pagehttp://en.wikipedia.org/wiki/Preferred_number
that on the discussion tab, somebody noticed that in the E192 series, there
is one value that doesn't fit the expected logarithmic sequence, namely
920, a fact I first became aware of about 15 years ago. It should be 919;
if one uses the formula for the 185th member of the sequence:

Value = 100 * 10^(185/192) one gets 919.478686+ which should be rounded to
919, not 920.

However, I discovered that a very simple change will correctly give all the
values in the commercial E192 series, including the oddball 920:

Value = 100 * 10^(185/191.9977), with the 185 replaced with the ordinal
member number for other values. This small change allows a simple formula
to be used in a program, giving ALL the correct commercially available
values.

Why did "they" pick 920? I assume that they made an error. Since the
digits after the decimal point are near .5000000, which would be the value
above or below which one rounds up or down, maybe their calculation was a
little off. Perhaps they used a slide rule!

All this still fails to answer the OP's question, a question I've long
wondered about. I'm afraid that the people who made the choices are
probably no longer with us.

There was a guest editorial, "Preferred Numbers", published in the
Proceedings of the IRE, p. 115 in 1951. There were a couple more items in
that year on page 467 and page 1572 in answer. Unfortunately, they don't
answer the OP's question.

All interesting comments, and I thank you for them, but I do want to
say I don't immediately agree with the premise that I want the 10%
bands to overlap. Well, OK, I don't use 10% resistors, or even 5%
resistors, but same applies to the 1% parts. I assume that the 1%
parts I use will very seldom be close to the edge of their tolerance
band. Measurement of lots of parts tells me that _usually_ they are
within half a percent, and if my design doesn't stress them they'll
stay put pretty darned well for a long time. I'm pretty careful to
design things so that parts that are anywhere within their 1% band
will work correctly, but if I really want a value that's different
from the nominal value, I'll either pick a different part that
guarantees to be close enough to the value I really want, or I trim
using series or parallel combinations. My first preference, though,
is to design the circuit so it works properly with E12 values, and
trims are unnecessary. We do a lot with calibration of one sort or
another, almost all run under processor control these days.

In general, though, I don't see that overlap of the n% bands makes a
whole lot of difference; if I need to have a component be within some
specific tolerance of a particular value, that defines what I need to
do. I either use a part (or combination of parts) that gives the
desired result, or I re-design for a different value and/or
tolerance. Especially given that we don't find it economical to
design using the full E96 range, but use only the "E24" set out of the
E96 values (except in very rare instances), we are quite used to
having desired values fall outside the tolerance range of the
available parts.

In any event, this is a pretty minor point. We have what we have to
work with, and it's pretty unlikely that our discussion here will
alter the accepted set of E6, E12, ... E192 values. If you're willing
to pay enough for a custom value, you can get it.

Cheers,
Tom

 

[ªºª rrock]

WrongAgain, twice this time!

The total error can't be more than 5%.

And most "5%" resistors these days are much closer than 5%. In fact,
the total will NEVER be off more than 5%, and will usually be within
1%. That's why 1% and 5% resistors cost about the same.

Long ago, moulded carbon resistors had a huge production spread, and
were culled into 20%, 10% and 5% categories. Nowadays, nearly all
resistors are production trimmed to value, by spiral cutting or laser
trimming, so they tend to be very close. 5% resistors are usually
within a few tenths of a per cent these days. Measure some and see.

John

Save your breath. He lives in a smaller universe than the rest of us,
one that has only existed for twenty years and where he reigns supreme
as the most ancient and wise. A universe where he has experienced all
there is to experience and therefore knows all there is to know. He
can no longer learn anything and is doomed to cursing at people that
confound his reasoning with simple things like logic or examples of
reality that are beyond his universe in either space or time. To him,
those things simply do not exist and any whom would believe in such
things make statements that are "shit" and ask questions that "do not
warrant" an answer. lololol

 

[Fred Bloggs]

This isn't strictly true. When filling in the values from E6 to E12, the
value between 47 and 68 should be 57 if you use the geometric mean method,
but the actual value is 56. The E12 to E24 transformation works ok with
the geometric mean method.

The calculation of the E96 series from the E48 series using the geometric
mean method gives 7 values that do not match the actual E96 series, whereas
using the 96th root of 10 method gets them all correctly.

The E96 to E192 transformation by the geometric mean method gets 33 wrong
values, whereas the 192nd root of 10 method gets them all right, except for
that pesky 920 value.

As I told you before, you don't take the geometric mean of the actual E
series values, you take it from the exact values they are rounded from.
My statements are exactly right.

 

[ChairmanOfTheBored]

WrongAgain, twice this time!

The total error can't be more than 5%.

And most "5%" resistors these days are much closer than 5%. In fact,
the total will NEVER be off more than 5%, and will usually be within
1%. That's why 1% and 5% resistors cost about the same.

Long ago, moulded carbon resistors had a huge production spread, and
were culled into 20%, 10% and 5% categories. Nowadays, nearly all
resistors are production trimmed to value, by spiral cutting or laser
trimming, so they tend to be very close. 5% resistors are usually
within a few tenths of a per cent these days. Measure some and see.

John

Actually. SMT resistors are trimmed at production run time.

Axial TH std resistors are still mass produced, and culled by automated
measuring machinery, and seldom get sent through trimming processes.

 

[ChairmanOfTheBored]

Save your breath.

You're a goddamned idiot. This is a written forum, dumbfuck. There is
no breath involved, dipshit.

He lives in a smaller universe than the rest of us,

Actually, retards that cannot even draft a correctly formatted
paragraph do.

one that has only existed for twenty years and where he reigns supreme
as the most ancient and wise.

I am wiser than a retarded , illiterate dumb **** like you will ever
be.

A universe where he has experienced all
there is to experience

I never said that, you retarded ****. Dumbfucks like you that spout
baseless horseshit like this should be removed form the face of the earth
by those of us that are real men.

and therefore knows all there is to know. He
can no longer learn anything and is doomed to cursing at people that
confound his reasoning with simple things like logic or examples of
reality that are beyond his universe in either space or time.

Said the total twit that doesn't even know how to write correctly?
Sure, bub.

To him,
those things simply do not exist and any whom would believe in such
things make statements that are "shit" and ask questions that "do not
warrant" an answer. lololol

lololol? Know we KNOW that you are a mere gang boy retard.

The ten blank lines after your retarded posts tells a lot as well. You
are a total idiot, boy. Your mental age approaches, but does not surpass
eleven years.

 

[Spehro Pefhany]

Actually. SMT resistors are trimmed at production run time.

Axial TH std resistors are still mass produced, and culled by automated
measuring machinery, and seldom get sent through trimming processes.

Leaded *film* resistors are helically cut to value using a simple
mechanical (diamond tipped cutter) or laser process. Often they just
set the value on the controller to the nominal so the resistors tend
to end up a bit higher than the nominal value.

Film SMT resistors are laser trimmed with much better equipment.


Best regards,
Spehro Pefhany

 

[Robert Adsett]

Nonsense. They're PUNCHED. All in one bang, with the outline. They
warm the paper-based phenolic to make it easier to punch without
cracking. That's how you get a PCB for 20 cents. More tooling cost.

Do they punch out the CU traces as well?

Robert

 

[The Phantom]

As I told you before, you don't take the geometric mean of the actual E
series values, you take it from the exact values they are rounded from.

When did you tell me this before?

My statements are exactly right.

That's because if "you don't take the geometric mean of the actual E series
values, you take it from the exact values they are rounded from.", it is a
mathematical tautology. The results from taking the geometric mean of the exact
values of two adjacent elements of an E series and making that the exact value
of the intermediate value of the next series (and then rounding), is
mathematically identical to just using the root of 10 method to compute the
exact values (before rounding) of intermediate values in the next series.

For example, in the E48 series, the exact values of the 2nd and 3rd members
would be:

104.913972914 and 110.069417125

the geometric mean of these two is:

107.460782832

Using the root of 10 method, we would get as an E96 value intermediate between
the same two E48 members:

100 * 10^(3/96) = 107.460782832, exactly the same.

There's no need to even consider the geometric mean method if you use exact
values, because it gives no different results than the root of 10 method.

If you apply the geometric mean method to the rounded values, it might explain
some things in the E6, E12 and E24 series, but not in the higher series.

Unlike the values in the lower series, the values in the higher (E48, E96,
E192) are the properly rounded values from the root of 10 method (except for
920), so there's no question where they came from.

 

[ªºª rrock]

You're a goddamned idiot. This is a written forum, dumbfuck. There is
no breath involved, dipshit.




Actually, retards that cannot even draft a correctly formatted
paragraph do.




I am wiser than a retarded , illiterate dumb **** like you will ever
be.




I never said that, you retarded ****. Dumbfucks like you that spout
baseless horseshit like this should be removed form the face of the earth
by those of us that are real men.




Said the total twit that doesn't even know how to write correctly?
Sure, bub.




lololol? Know we KNOW that you are a mere gang boy retard.

"Know we KNOW"? And you give advice on paragraphs? lololol Hey!
You didn't draft any correctly formatted paragraphs in your reply!
Maybe if you'd breathe while tapping on your keyboard your brain
would get more oxygen. lololol Oh, but "real men" in your tiny
universe don't require oxygen, do they? lolololol

 

[The Phantom]

All interesting comments, and I thank you for them, but I do want to
say I don't immediately agree with the premise that I want the 10%
bands to overlap. Well, OK, I don't use 10% resistors, or even 5%
resistors, but same applies to the 1% parts. I assume that the 1%
parts I use will very seldom be close to the edge of their tolerance
band. Measurement of lots of parts tells me that _usually_ they are
within half a percent, and if my design doesn't stress them they'll
stay put pretty darned well for a long time. I'm pretty careful to
design things so that parts that are anywhere within their 1% band
will work correctly, but if I really want a value that's different
from the nominal value, I'll either pick a different part that
guarantees to be close enough to the value I really want, or I trim
using series or parallel combinations. My first preference, though,
is to design the circuit so it works properly with E12 values, and
trims are unnecessary. We do a lot with calibration of one sort or
another, almost all run under processor control these days.

In general, though, I don't see that overlap of the n% bands makes a
whole lot of difference; if I need to have a component be within some
specific tolerance of a particular value, that defines what I need to
do. I either use a part (or combination of parts) that gives the
desired result, or I re-design for a different value and/or
tolerance. Especially given that we don't find it economical to
design using the full E96 range, but use only the "E24" set out of the
E96 values

Yes, I understand this philosophy. Some years ago when the good quality 5%
film resistors started showing up from Japan, I noticed that, without fail, they
were within 1% of the nominal E24 value. This meant that if I designed some
filters, for example, that needed just those values, I could count on the
performance 1% resistors would give, for less money.

But, when a committee selects the values for an E series, I think one would
like to get "full coverage". Say you need a single resistor for a series
dropping resistor, perhaps. Now, you can't play with ratios, you just have to
have that value, within 5%, say. One would like almost every possible
resistance value to be within 5% (or 10%, or whatever) of a commercially
available value in an E series .But this just isn't going to happen in a series
like the E96 because there are so many values to round that sometimes the
rounding goes up, sometimes down, giving either a little overlap or a llitle
underlap (is that a word?). But the coverage is good enough.

As you say, it's a small point.

I still wonder what the answer is to the OP's question. There's a lot of
speculation and reverse engineering, but I've never found an authoritative
answer.

 

[John Larkin]

Actually, retards that cannot even draft a correctly formatted
paragraph do.


I am wiser than a retarded , illiterate dumb **** like you will ever
be.


I never said that, you retarded ****. Dumbfucks like you that spout
baseless horseshit like this should be removed form the face of the earth ^^^^

by those of us that are real men.


Said the total twit that doesn't even know how to write correctly?

Amazing. Whan people criticize other people's writing, they usually
mess up something themselves. That's somebody's law or something.

John

 

[John Larkin]

Leaded *film* resistors are helically cut to value using a simple
mechanical (diamond tipped cutter) or laser process. Often they just
set the value on the controller to the nominal so the resistors tend
to end up a bit higher than the nominal value.

Film SMT resistors are laser trimmed with much better equipment.

I got a call last month from a guy at United Airlines who tests jet
engines and APUs. He needed some 1000:1 current transformer burden
resistors so he could read APU power output, using one of our VME
boards. We have a bunch of Dale 1 ohm, 3 watt, 5% ww resistors in
stock, so I measured them, 4-wire, at the standard 3/8 inch lead
length. They were all within 0.3%. So they must wind them to the exact
resistance somehow.

We delivered the resistors by hand and got the tour. In one of his
"shops" he had a 757 with both engines pulled out. He has five
full-size engine test cells, with *big* exhaust fans, load cells, the
whole bit. And he has several smaller, bedroom-size, cells for testing
APUs. Impressive. Aircraft MRO is an enormous and practically
invisible business.

John

 

[ªºª rrock]

Amazing. Whan people criticize other people's writing, they usually
mess up something themselves. That's somebody's law or something.

John

Pretty sure i tried finding it a couple years or so back and never did turn
up with anything. Maybe you should just call it Larkin's Law and be done with it.
There's another one about the intelligence of the troll being inversely proportional
to the number of expletives he uses. That one is supposedly based on some other
arcane law about selectivity and vocabulary.

 

[Fred Bloggs]

When did you tell me this before?




That's because if "you don't take the geometric mean of the actual E series
values, you take it from the exact values they are rounded from.", it is a
mathematical tautology. The results from taking the geometric mean of the exact
values of two adjacent elements of an E series and making that the exact value
of the intermediate value of the next series (and then rounding), is
mathematically identical to just using the root of 10 method to compute the
exact values (before rounding) of intermediate values in the next series.

For example, in the E48 series, the exact values of the 2nd and 3rd members
would be:

104.913972914 and 110.069417125

the geometric mean of these two is:

107.460782832

Using the root of 10 method, we would get as an E96 value intermediate between
the same two E48 members:

100 * 10^(3/96) = 107.460782832, exactly the same.

There's no need to even consider the geometric mean method if you use exact
values, because it gives no different results than the root of 10 method.

If you apply the geometric mean method to the rounded values, it might explain
some things in the E6, E12 and E24 series, but not in the higher series.

Unlike the values in the lower series, the values in the higher (E48, E96,
E192) are the properly rounded values from the root of 10 method (except for
920), so there's no question where they came from.

You appear to be suffering from memory loss and possibly other
disabilities since I already covered all this in a previous post. The
dumb geometric series approach is not useful in the most common scenario
of the application engineer requiring an E-series value closest to the
result of theoretical calculation, and this only necessary for 1% or
better tolerance. That is where the viewpoint of successive geometric
means results a simple algorithm for the calculation, which I presented
in that same post. Any idiot who can't recall 5% or more is not an
electronics engineer. The 920 is an erroneous arithmetic mean and not a
geometric mean.

 

[Spehro Pefhany]

Amazing. Whan people criticize other people's writing, they usually
mess up something themselves. That's somebody's law or something.

John

Skitt's law.

Best regards,
Spehro Pefhany

 

[Tom Bruhns]

I still wonder what the answer is to the OP's question. There's a lot of
speculation and reverse engineering, but I've never found an authoritative
answer.

Yeah, it frustrates me that my memory isn't quite good enough to pull
out this piece of trivia. I do remember reading long ago about it, in
a place I trusted. The history behind some of the developments in
electronics can be quite interesting.

Cheers,
Tom

 

[The Phantom]

You appear to be suffering from memory loss and possibly other
disabilities since I already covered all this in a previous post.

So you say. I asked you to tell me when you covered it, and you don't
seem to be able to answer the question. You just repeated your assertion
that you did cover it. If you can't give me a link to a google archive of
the post where you covered it, I'll assume you're the one suffering from
memory loss.

The
dumb geometric series approach is not useful in the most common scenario
of the application engineer requiring an E-series value closest to the
result of theoretical calculation, and this only necessary for 1% or
better tolerance. That is where the viewpoint of successive geometric
means results a simple algorithm for the calculation, which I presented
in that same post. Any idiot who can't recall 5% or more is not an
electronics engineer. The 920 is an erroneous arithmetic mean and not a
geometric mean.

Were you a member of the committee that made these decisions about what
values to include in each E series? Can you provide a copy of the minutes?

You don't know that for a fact; you're just guessing, like the rest of us.

 

[ChairmanOfTheBored]

Maybe if you'd breathe while tapping on your keyboard your brain
would get more oxygen. lololol Oh, but "real men" in your tiny
universe don't require oxygen, do they? lolololol

Grow up, you little illiterate retard.

 

[ChairmanOfTheBored]

I got a call last month from a guy at United Airlines who tests jet
engines and APUs. He needed some 1000:1 current transformer burden
resistors so he could read APU power output, using one of our VME
boards. We have a bunch of Dale 1 ohm, 3 watt, 5% ww resistors in
stock, so I measured them, 4-wire, at the standard 3/8 inch lead
length. They were all within 0.3%. So they must wind them to the exact
resistance somehow.

Now heat them up and watch that specified derating curve fall right in.

We delivered the resistors by hand and got the tour. In one of his
"shops" he had a 757 with both engines pulled out. He has five
full-size engine test cells, with *big* exhaust fans, load cells, the
whole bit. And he has several smaller, bedroom-size, cells for testing
APUs. Impressive. Aircraft MRO is an enormous and practically
invisible business.

You should see the units at MCAS Miramar.

 

[ChairmanOfTheBored]

Pretty sure i tried finding it a couple years or so back and never did turn
up with anything. Maybe you should just call it Larkin's Law and be done with it.
There's another one about the intelligence of the troll being inversely proportional
to the number of expletives he uses. That one is supposedly based on some other
arcane law about selectivity and vocabulary.

You're STILL a goddamned illiterate retard. Hell, you're worse than
Rosie O'Retard.