[HN Gopher] Why does the E12 resistor sequence use 27 and 33 ins...
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Why does the E12 resistor sequence use 27 and 33 instead of 26 and
32?
Author : mhh__
Score : 191 points
Date : 2022-11-20 02:06 UTC (1 days ago)
(HTM) web link (electronics.stackexchange.com)
(TXT) w3m dump (electronics.stackexchange.com)
| londons_explore wrote:
| When were the resistor series' first invented?
|
| Is it possible that calculating the logarithmic scale numerically
| was quite a lot of effort, so instead a graphical approach, using
| a slide rule, was used? If so, small errors of a couple of
| percent could be expected in the results, especially if the rule
| wasn't precisely made?
| [deleted]
| Someone wrote:
| We had good logarithm tables in the 1620's.
| http://www2.cfcc.edu/faculty/cmoore/LogarithmInfo.htm: _"Napier
| died in 1617. Briggs published a table of logarithms to 14
| places of numbers from 1 to 20,000 and from 90,000 to 100,000
| in 1624. Adriaan Vlacq published a 10-place table for values
| from 1 to 100,000 in 1628, adding the 70,000 values"_
|
| These will have had errors, but I doubt they had them in the
| first 4 digits and if they had them, they would be easily
| spotted. (Edit:
| https://adsabs.harvard.edu/full/1872MNRAS..32..255G says there
| were errors)
|
| (https://en.wikipedia.org/wiki/Adriaan_Vlacq)
| pyinstallwoes wrote:
| > One of the modern applications of Egyptian fractions is the
| request of a specific resistance value needed in the design of
| an electrical circuit, a problem called in the literature the
| 2- Ohm problem. College students know well from their physics
| class, that the equivalent resistance R of two parallel
| resistances and is given from a law very easy to deduce, based
| on equating the current passing through the fictitious
| equivalent resistance R with the two currents passing through
| both resistances while maintaining same potential. One direct
| application of this, suppose an engineer wishes to incorporate
| in one of his designs a resistor of so many ohms which the
| manufacturer does not produce; for it is impossible that the
| latter displays in the market all possible ohm-values for his
| resistors. First, the market cannot possibly sustain it, but
| more important, one cannot feasibly produce resistors with
| values as elements of a dense subset of the real line, being,
| as analysis taught us, an uncountable set. Rather,
| manufacturers display only in the market what they call an "E12
| series", i.e. resistors in sets of 12 different values, namely
|
| > 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 ......
|
| > 100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680,
| 820......
|
| > 1000, 1200.......... Ohms, etc.....
|
| > Now suppose an engineer needs in one of his designs a
| resistor of 7 ohms, then he would resort to a parallel
| combination from the fraction 1/7=1/10+1/56+1/100+1/120+1/150
| in which all the resistors belong to the E12 series, i.e. he
| will replace his 7 ohms resistor with 5 parallel resistors;
| this he reaches using a special software (computer programmes
| exist for such designs, yet the exact solution is by no means
| trivial). What I did myself instead, is to resort to Ahmes 2/n
| table and wrote 2/7=1/4+1/28 or that 1/7=1/8+1/56. Decomposing
| further 1/8 into 1/12+1/24=1/12+1/48+1/48, but then I shall
| have to use instead of the 48 ohms resistor a resistor of 47
| ohms from the E12 table. My final fraction is 1/7=1/12+1/
| 47+1/47+1/56, i.e. my resistor of 7 ohms will be simulated by 4
| parallel resistors instead of 5 (I am accepting equal
| fractions). My solution is both minimal and optimal based on
| Ahmes table. The relative error of my design will not exceed
| 0.6 per cent, being negligible; especially that any
| manufactured resistor will itself be subject to some allowed
| tolerance of the same order.
|
| https://web.archive.org/web/20130625181118/http://weekly.ahr...
|
| So, a thousands of years ago? Ancient Egypt and before? :)
|
| Also:
|
| > The measured values of voltages and currents in the infinite
| resistor chain circuit (also called the resistor ladder or
| infinite series-parallel circuit) follow the Fibonacci
| sequence. The intermediate results of adding the alternating
| series and parallel resistances yields fractions composed of
| consecutive Fibonacci numbers. The equivalent resistance of the
| entire circuit equals the golden ratio.
| mlyle wrote:
| > then he would resort to a parallel combination from the
| fraction
|
| Easier to find series combinations and then maybe clean them
| up with one parallel resistor. e.g. 4.7 + 2.2 ohms = 6.9
| ohms; if you want better, 3.9+3.9 =7.8, and a 68 ohm resistor
| in parallel yields 6.997 ohms, an error of .04%.
|
| Often that parallel resistor will be a trimpot or other
| adjustable means.
| snarkconjecture wrote:
| Or the greedy approach: 6.8+.22 in parallel with 2700 gives
| you 7.0018 with .026% error.
| adql wrote:
| >my resistor of 7 ohms will be simulated by 4 parallel
| resistors instead of 5 (I am accepting equal fractions).
|
| If we had just 1,2,5 series that would just be 2 resistors
| tho ? 3 resistors to get 9,8; 2 to get 6,4,3
|
| The whole thing seems to be not that practical for
| electronics where you don't aim your amplifier to have
| amplification of "golden ratio" but in most cases some
| integer like x5 or x100
| snarkconjecture wrote:
| 1/7 [?] 1/8.2 + 1/47 gives about half the error (<.3%) with
| half the resistor count.
| snarkconjecture wrote:
| > one cannot feasibly produce resistors with values as
| elements of a dense subset of the real line, being, as
| analysis taught us, an uncountable set
|
| The rational numbers are an example of a countable dense set.
|
| Unfortunately, countably-infinite product catalogs are still
| a bit unwieldy.
| fuzzfactor wrote:
| Something else to think about is the way different resistors and
| other components have been graded over the decades.
|
| For instance there were manufacturing approaches where a target
| value was produced for a large number of components, but the
| manufacturing tolerance was a very wide +/- 20%.
|
| The parts were then graded individually into the 1%, 5%, 10% and
| 20% bins, marked and priced accordingly.
|
| If you then specified the lowest-cost 20% parts, _none of them_
| were actually any closer than 10% to their nominal value.
| sbf501 wrote:
| Its funny how the comments section of this question on
| stackexchange.com are people complaining to @jonk that his answer
| is irrational when he's just reciting material, yet they double
| down on their position despite his objection. Doesn't help that
| @jonk is kind of arrogant, but my point is... people.
| Dylan16807 wrote:
| "Your document is at least 40 years younger than E-series
| components and all the odd/even numerology was not an issue."
| is a pretty strong criticism! It doesn't matter if jonk is
| reciting material if he's citing _the wrong material_.
| sbf501 wrote:
| Huh. Did I not expand a comment somewhere? Because I didn't
| see anyone citing the _correct_ material.
| Dylan16807 wrote:
| Neither do I. I'm not sure if that claim is right or wrong
| but it doesn't seem properly resolved.
| NohatCoder wrote:
| Pretty much all the numbers can be explained as being the closest
| number to the geometric mean of the previous and following
| number. Once you have chosen to round the second number in E3 to
| 22, 47 is the closest to splitting 22 and 100 evenly. The
| exception is 33 in the E6 series, that should be 32 when
| splitting 22 and 47, most of the other "errors" in E12 and E24
| are there because 33 pushes the other numbers upwards.
| fuzzfactor wrote:
| Three of the 33's in series also add up to 100 better than
| three having a value of 32 each.
| explodingwaffle wrote:
| I do wish someone would put up the paid for magic documents that
| allegedly contain the actual reasoning behind the choice of the
| E-series. I think this SE answer coould be true, but it feels a
| little contrived- and, at least to me, this is one of electronics
| history's greatest mysteries.
| duped wrote:
| The standards docs don't give you the reasoning behind
| decisions, that's all in the closed door meetings. And most of
| the time it's "because that's the way it is."
| TheRealPomax wrote:
| except in this case, given its title, the document almost
| certainly does exactly that: "ISO 497:1973, Guide to the
| choice of series of preferred numbers and of series
| containing more rounded values of preferred numbers"
| (mentioned in the answer on the post that was used to close
| the one HN links to).
|
| The fact that ISO documents aren't just free PDF files with
| all rights past "viewing" locked down, charging businesses
| money for hard copies, is still one of the most blatant ways
| in which the ISO has held, and continues to hold back the
| world.
| duped wrote:
| I'm not saying that standards shouldn't be freely viewable,
| but this isn't that big of a problem or unique to the ISO.
| There are hundreds of standards for manufacturing split
| across dozens of publishers and industry organizations
| (just for electronics you have JEDEC, IPC, ISO, and then
| 2-3 more depending on specific application domains).
|
| If you're working in industry your company pays the
| pittance for membership as an organization then you pay the
| (relative) pittance for the doc and shove the PDF into your
| company's network store (unless they're jerks and lock it
| to a device).
| TheRealPomax wrote:
| Are you responding to something completely different? I
| was remarking on the "The standards docs don't give you
| the reasoning behind decisions" claim, which is almost
| always true, but in this case seems incorrect, given that
| there is a standards whose sole purpose is to give the
| reasoning behind the decisions.
| duped wrote:
| I was commenting on your last sentence
| fqrley wrote:
| The reason is likely because discrete resistor values are trimmed
| in circuit by placing a much larger value in parallel to bring
| the overall value down.
| Cerium wrote:
| Those values make the E24 sequence evenly spaced with adjacent
| values. Since the other series are more course, any error is less
| important than manufacturing practicalities.
| JoeAltmaier wrote:
| And why does American coinage and currency not observe the 2-3-5
| rule?
|
| We have $1, $2 but it's obsolete, $5, $10, $20, $50, $100 but no
| $200, $500, $1000 but no $2000 and so on.
|
| Worse yet, coinage! 1 cent, 5, 10, 25(!), 50, 100 and we're done.
| ElevenLathe wrote:
| Now that some ATMs let you choose your denominations, I get all
| my cash in fives. Even $300 (pretty much the outer limit of
| what I ever want to carry in cash) in fives comfortably fits in
| my wallet, and you avoid most of the headaches of trying to
| make change for larger bills.
| meatmanek wrote:
| You can fit a stack of 60 bills in your wallet comfortably!?
| The internet says a bill is 0.0043 inches thick, so 60 bills
| would be roughly a quarter inch thick. Folded in half, that's
| over half an inch just for your cash.
| ElevenLathe wrote:
| ah, sorry. My "wallet" is one of those folio type things
| that doubles as a phone case. I don't keep it in my back
| pocket like a traditional Costanza-style wallet.
| OJFord wrote:
| Do people keep wallets in their back pockets outside of
| cartoons and 20th century pickpocket victims in films? I
| prefer it separate to my phone, but always front pocket,
| I don't want to sit (lop-sided?!) on it.
| ElevenLathe wrote:
| I used a regular back-pocket wallet until 2020 when I
| didn't use it for a few months except to enter my credit
| card number online. I'm in the Midwest and it seems that
| this is still the norm. Maybe things are different on the
| coasts?
| Dylan16807 wrote:
| Because currency isn't trying to fill out the spectrum. We want
| to have as few different values as possible, focused on a
| certain range. And really big bills are rare.
|
| So looking at 1-100, 20 vs. 25 doesn't really matter, people
| won't bother to carry 50s, and people won't bother to carry 2s.
| 3s wouldn't help at all.
|
| We barely even need the 10 either. 1,5,20/25,100 works fine.
|
| And above 100 you can use powers of 10 and nobody will really
| care.
| eurasiantiger wrote:
| The reason is clearly outlined on the wikipedia page:
| https://en.wikipedia.org/wiki/E_series_of_preferred_numbers
|
| > Since the electronic component industry established component
| values before standards discussions in the late-1940s, they
| decided that it wasn't practical to change the former established
| values. These older values were used to create the E6, E12, E24
| series standard that was accepted in Paris in 1950 then published
| as IEC 63 in 1952.
| jefftk wrote:
| That's not much of a reason: why were the older values chosen?
| The article looks back and argues that it was to make more
| unique values possible.
| svnt wrote:
| They were probably chosen because the decision was made in
| concert with manufacturers who wanted to be able to continue
| to buy/build with the values they had before.
|
| I'm surprised so many here are taking issue with the answer
| on the page. It's a reasonable answer reflecting a pragmatic
| process. Just don't rug-pull our existing components and give
| us more variation.
|
| And don't give me "you can get odd numbers with two
| resistors" -- at the time this was done, these things were
| not cheap, they were not small, and doubling your component
| count and increasing your product size because of a new
| government standard would not have gone over well.
| [deleted]
| adql wrote:
| That seems the same problem of "why train track spacing is
| like it is" and the answer is "nothing actually technical".
|
| 1,2,5 series woud've been much more useful considering how
| often in electronics you need integer ratio of some 2 values
| ted_dunning wrote:
| Well, the 1, 2.2, 4.7 E3 sequence that is embedded in the
| E12 sequence is plenty close enough for almost all
| applications. The successive ratios are noticeably more
| consistent than for the 1,2,5,10 sequence (2.2, 2.14, 2.13
| versus 2, 2.5, 2)
| threatripper wrote:
| You can ask that question, too - but it's irrelevant to the
| question why the E12 series was changed in this way.
| hgsgm wrote:
| simne wrote:
| I'm electric engineer by first education, and have more than ten
| years exp in field.
|
| Must say, in many cases, these numbers are not important, in good
| schemes acceptable +-10%, so 26 could be 23.4-28.6.
|
| Even more, cheap resistors marks have accuracy +-5%.
|
| Exists precision resistors with accuracy +-0.5%, or even 0.1%,
| but high precision applications, typically used some very
| different technologies. For example, are high quality multi-turn
| variable resistors, laser cut resistivity pads, created with high
| cost materials or even rare-earth materials.
|
| And many current applications use some sort of very high quality
| reference, in many cases, based on totally different physical
| principle, and scheme constantly adjusted with closed loop.
| simne wrote:
| What really need, is to put analog parts into right mode, and
| to make it stable, for example vs temperature changes.
|
| As electrical contact points and traces could add up to few
| Ohms, so resistors need not be exact numbers, but few different
| from range of planned +-these few Ohms.
| LeifCarrotson wrote:
| > Exists precision resistors with accuracy +-0.5%, or even
| 0.1%, but high precision applications, typically used some very
| different technologies. For example, are high quality multi-
| turn variable resistors, laser cut resistivity pads, created
| with high cost materials or even rare-earth materials.
|
| Most modern resistors are of either a thin-film type, with sub-
| micron-thin layers of nickel directly sputtered and onto a
| ceramic body, or a thick-film type, with a metal oxide/ceramic
| paste applied and baked onto the ceramic body.
|
| The process window is aimed at a target, but binning operations
| after production are all that separate precision resistors from
| cheap resistors.
|
| If you sputter on a little too much nickel, or your paste isn't
| quite as conductive after baking as you hoped, you just sell
| that one as a 10% or 5% resistor.
|
| If you get lucky, and produce one that is within 0.01% of an
| E96 resistor (which might even happen while aiming for an E12
| resistance!), you sell it as a precision unit.
|
| Agreed that these aren't that important in most modern designs.
| bsder wrote:
| > binning operations after production are all that separate
| precision resistors from cheap resistors.
|
| Really? I would have assumed that resistors are so cheap that
| testing them is more expensive than designing the process up
| front around the tolerance.
| negative_zero wrote:
| Yup really. Grab some 5% and 1% resistors and measure them
| with decent multimeter.
|
| You'll find that their values are almost exactly:
| stated_value+/-tolerance rather than a range of values.
|
| i.e a 100k 5% resistor will be almost exactly either 105k
| or 95k not some number in between.
| bsder wrote:
| Nope. Not buying it. Just pulled a couple of bog standard
| thick film 100K 1% 1206s and they are measuring at 99.94,
| 99.96, 100.02, 99.93 kiloohms.
|
| They're probably batch controlled. There is no way every
| resistor is being tested for compliance given how cheap
| SMT resistors are.
| russdill wrote:
| A single measurement does not a 0.01% resistor make. When you
| want that kind of tolerance, drift and aging properties are
| hugely important and the resistor is not going to be
| constructed the same way as your bog standard $5/reel 1%
| resistors.
| simne wrote:
| Are you miss (one time) programmable resistors? They appear
| in 2000s and where available to by, but expensive.
|
| I have not tried myself, just don't found case to use them.
|
| And I have few high precision resistors, and even microwave
| resistors, they very different from cheap film resistors.
|
| Technologies exists different, for different cases, for
| different pockets.
| codeflo wrote:
| The "coverage" explanation given by the top answer doesn't make a
| whole lot of sense. With the manufacturing tolerances involved
| (especially historically when those values were chosen!) the idea
| that 22 and 47 gives more useful combinations than 22 and 46 is
| numerology, not engineering.
|
| Wikipedia only says that the deviation is for "unknown historical
| reasons". Maybe a deep explanation doesn't exist, and it's a
| simple historical error that was propagated?
| simne wrote:
| Main reason are costs for mass production, and nuances of
| technology, that electronic components usually made in very
| huge batches, then distributed to distribution network and lie
| on storage up to tens years.
|
| So manufacturers made series of agreements, like "in 2020-2025
| make e3; in 2025-2030 make e12".
| simne wrote:
| Expensive high precision parts, are not in this scheme, they
| allocated by direct requests, like Toshiba manufacture high-
| end transistors, and order for them high-end resistors with
| some exact value.
| csours wrote:
| As I read it, rationalization is one of the core reasons.
| danbruc wrote:
| Similarly I find the no odd numbers argument unconvincing,
| again because of the tolerances and also because placing two of
| the resistors in parallel yields odd values for 10 and 22 and
| almost 15 (14.9855) for 22 and 47.
| adql wrote:
| Also you can just use one magnitude lower resistor... 10
| isn't odd but 1 is.
|
| Honestly the explanation looks like someone tried to reverse-
| engineer a mistake into logic.
| layer8 wrote:
| Note that the linked document
| https://www.govinfo.gov/content/pkg/GOVPUB-C13-f5fea679df4c3...
| doesn't just apply to resistors or electrical components. It is
| a general framework for deriving "preferred" numbers.
| YetAnotherNick wrote:
| But there is no reason why 0 tolerance resistor couldn't exist
| or even being very useful for certain application like
| voltmeter.
| deelowe wrote:
| > But there is no reason why 0 tolerance resistor couldn't
| exist
|
| I think the laws of physics is a pretty good reason.
| Melkman wrote:
| The reason you can not build a 0% tolerance resistor is the
| laws of physics. A very high precision resistor can certainly
| be build but it will never be perfect. Increasing precision
| has a cost to it. For normal resistors the shape and
| thickness of the film of resisting material is calculated and
| the tolerance is mainly dictated by the precision of the
| manufacturing process. Increasing this precision of the
| process adds cost. High precision resistors can be trimmed to
| specification. When you manufacture the resistor with a lower
| resistance you can use a laser to trim some of the resistive
| material away. This is an extra step and adds extra cost.
| While this can be very precise you are limited to what you
| can measure and there is a limit to that. Also precision is
| limited by environmental factors like heat, humidity and
| aging.
| adql wrote:
| That's also how many higher end analog chips are made, just
| blast it with laser till it fits tolerance. Making a bunch
| of chips in less precise process then trimming them chip by
| chip ends up cheaper than going to more expensive
| processes.
| YetAnotherNick wrote:
| We are saying the same thing. For most applications, 5%
| tolerance is fine if could be cheaper. But for some
| applications it is worth the extra cost.
| klodolph wrote:
| It sounded like you were saying that a 0 tolerance
| resistor would be worth the extra cost, and the reply is
| pointing out that a 0 tolerance resistor is not actually
| possible anyway, and as you approach 0, the cost
| increases beyond whatever your limit is.
| JKCalhoun wrote:
| It would seem pretty pointless to try to nail the
| resistor to within 0% tolerance when the solder bridges,
| wire that connects them to the circuit will have
| resistance.
| [deleted]
| Gordonjcp wrote:
| If you want 0% tolerance, you can hand-match.
|
| No-one needs 0% tolerance.
| atoav wrote:
| Sure, you can handmatch. If the thermal radiation of your
| hands wouldn't affect the measurement.
| Gordonjcp wrote:
| This is actually a real problem with semiconductors. I
| often need carefully matched sets of transistors and
| diodes, and a quick and easy way to get them "good
| enough" is just to measure either a diode or the B-E
| junction of the transistor with a multimeter in "diode
| check" mode. I pin the paper strip to a piece of wood and
| let the temperature stabilise for about half an hour
| before I start, and only touch the component with the
| meter probes.
|
| You can try this yourself. With any given 1N4148 you'll
| see the Vf indication on the meter change as the
| microscopic current warms the junction up a tiny bit. If
| the room (and thus the diode) is fairly cold, it can
| detect the heat from your finger at about 1cm away.
| pclmulqdq wrote:
| Ultra-precise resistor values have been possible for as long as
| there have been good meters. It turns out that's a very long
| time ago.
|
| The numerology makes a lot of sense if you are working with
| 0.1% tolerance parts. Lower tolerances have actually gotten
| more popular as electronics have become more cost-sensitive.
| michaelt wrote:
| Possible, sure, but isn't the origin of the E12 series, as
| opposed to using e.g. the Renard R10 series, for specifying
| +-10% precision parts?
|
| 1 +-10% is 0.9 to 1.1
|
| 1.2 +-10% is 1.08 to 1.32
|
| 1.5 +-10% is 1.35 to 1.65
|
| 1.8 +-10% is 1.62 to 1.98
|
| 2.2 +-10% is 1.98 to 2.42
|
| And so on.
| adql wrote:
| > Ultra-precise resistor values have been possible for as
| long as there have been good meters. It turns out that's a
| very long time ago.
|
| It's not about metering but stability of the resulting value.
| 1% or 0.1% doesn't do you much good if few degree temperature
| change gets it out of spec. Now temperature coefficent is an
| additional spec on the spec sheet but by definition you kinda
| need low drift to go in pair with high precision
|
| > The numerology makes a lot of sense if you are working with
| 0.1% tolerance parts. Lower tolerances have actually gotten
| more popular as electronics have become more cost-sensitive.
|
| Lower tolerances have just become cheap. Back when I was a
| kid there was significant difference in price between 1% and
| 5% resistors. Now they cost basically same (for low power
| ones at least) so why not ? [1]
|
| You also don't really need that many precision parts in the
| first palce.
|
| Where before in say a power amplifier you had say an analog
| preamp driving power IC (or outright discrete power
| amplifier) you had to have a bunch of precise resistors (or
| someone tweaking a pot on the production line) to keep the
| gain same in both tracks. Now you just slap a D-class chip
| that takes line in and outputs power and you're done, and the
| few % variance in power supply caps or output filter doesn't
| matter much.
|
| * [1] https://eu.mouser.com/c/passive-
| components/resistors/?case%2...
| Scoundreller wrote:
| > you had to have a bunch of precise resistors (or someone
| tweaking a pot on the production line) to keep the gain
| same in both tracks
|
| Or match them by hand before they're placed.
| pclmulqdq wrote:
| On price - you are looking at low quantity. Buy a few
| million of them from a manufacturer, and you will find the
| 5% ones still significantly cheaper (even at standard temp
| coefficients and power levels). That's why new 5% and 10%
| resistor products are still sold.
| couchand wrote:
| Note that the second part of the argument was that the
| quantities needed are low. I'd go even further than the
| GP: even in the "old days" my understanding is that the
| number of precision parts needed was very low. Most
| circuitry is of the "pick a component value in this order
| of magnitude" variety, even on sensitive hardware. Only
| the handful of parts where it really matters need
| precision.
|
| But, whereas previously you might spec 5% for a few
| resistors and 10% for the bulk, now it's no longer worth
| the added line on your BOM.
| yongjik wrote:
| But if you need 0.1% tolerance resistors and the circuit
| diagram requires a 13.3 (+-0.1%) kO resistor, you can just
| order one ...?
|
| I have a hard time imagining situations like "We need a very
| precise 57kO (+-0.5kO or about 1%) resistance but we can only
| get three precise resistors: 10kO, 22kO, and 47kO! Oh thank
| god we can connect 10kO and 47kO, if the last one was 46kO we
| would have been in trouble."
| posterboy wrote:
| In terms of scale, you cannot simply order a larger
| factory. It has opportunity cost.
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