E12/E24 series for components and geometric series

I wrote some code to find the nearest E12 (or E24) resistor value recently and I was surprised during testing when it didn't quite work for all values. I was using the mathmatically determined values and hadn't realised there's some tiny deviations from the calculated values.

Anyway, I ended up making some graphs to show how the values look for an article I was writing. The main thing I wanted to show was the use of a geometric as opposed to an arithmetic series. The deviations are rather minor but are marked up. I thought I'd share these in case anyone else wants to use them to show why common resistors are seen in 330 and 470 ohms rather than 300 (this one is in E24), 400 and 500 ohms.

E12 preferred values - linear view
e12-lingraph-v2-g1.png (32.4 KiB) Viewed 3001 times

E12 preferred values - logarithmic relationship and deviation from calculate values
e12-loggraph-v2-g2.png (42.11 KiB) Viewed 3001 times

kevinjwalters

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Re: E12/E24 series for components and geometric series

I'm a bit leery of the second graph.

The math is good, but the deviation assumes the values are mathematically precise. Try plotting the series value and ideal value between +/-5% and +/-1% tolerance bars.

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Re: E12/E24 series for components and geometric series

I was aiming to use them as part of explanation of why the numbers aren't 100, 200, 300. There are graphs on https://electronics.stackexchange.com/q ... 7984#67984 but they looked a bit dull to me. I then added in the thing that surprised me, 316.2 somehow got rounded up to 330 and not 320. I thought I'd make them more visually relevant to the real world with the example resistor pictures (without tolerance bands) showing the values.

I agree it would be nice to show that component values have tolerances too. I'll see if I can do that and still keep it "legible" when the image is small.

kevinjwalters

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Re: E12/E24 series for components and geometric series

The first image is great.. it shows the exponential nature of the curve nicely. Adding the color bands is a nice touch.

Tolerance bands add some more useful infomation. Almost every value between 10 and 100 is within 10% of a nominal E12 value, for instance:

10pct-tolerance.png (250.32 KiB) Viewed 2823 times

(there's a small gap between 110% of 12 (13.2) and 90% of 15 (13.5))

The theoretical value of 31.6 is just within the 5% tolerance of 33:

5pct-tolerance.png (235.37 KiB) Viewed 2823 times

and 33 is convenient for calculations involving thirds. It's close to 1/3 of 100, and if you want a resistor value of 30, you can put a 33R in parallel with a 330R.

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Re: E12/E24 series for components and geometric series

I tweaked log version and I've made an animated one to show tolerance values.

E12 preferred values - logarithmic relationship and deviation from calculated values (v4 re-arranged)
e12-prefvalues-v4-g2.png (37.8 KiB) Viewed 2525 times

E12 preferred values - logarithmic relationship and deviation from calculated values with tolerances (animated gif)
e12-prefvalues-v4-tolerances.gif (120.19 KiB) Viewed 2525 times

kevinjwalters

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Re: E12/E24 series for components and geometric series

Nice!

At this point I have to acknowledge being a Tufte junkie (Edward Tufte, MIT professor and author of “The visual Display of Quantitative Information”, known somewhat less formally as ‘the god of graphs’). One of his central ideas is that every visible element of a graph should convey useful meaning.

With that in mind, what are you using for the shape of the tolerance region? Are those circles on a logarithmic scale?

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Re: E12/E24 series for components and geometric series

They are violin plots showing the distribution. I was going to put in a notched version showing the removal of the higher tolerance components from the selection process but I had a quick look around t'Internet and it seems that doesn't appear to happen anymore plus there's something going on with resistors where they appear to bias them to lower values. I just timmed a normal distribution which is used to multiply the component's actual E value, a snippet from my hastily written R code:

Code: Select all | TOGGLE FULL SIZE
`toldist <- function (n, tol) {  set.seed(220330470)  return(discard(rnorm(n, mean=1, sd=tol/100/1.24), c(1.0-tol/100, 1.0+tol/100)))}for (tol in c(1,2,5,10,20)) {  tol_data <- do.call(rbind,                      apply(data[,c("raw_sequence", "actual")], 1,                            function(x) { return(data.frame(x=x[1],                                                            y=x[2] * toldist(100000, tol),                                                            fill=paste0("tol",                                                                        as.character(tol)),                                                            row.names=NULL)) }))`

I spotted the visual asymmetry of the splodges but haven't checked or pondered that too closely... got a few other things on my plate at the moment.

kevinjwalters

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Re: E12/E24 series for components and geometric series

kevinjwalters wrote:I spotted the visual asymmetry of the splodges but haven't checked or pondered that too closely

The asymmetry makes sense for a log plot.. large numbers are closer together than smaller ones.

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Re: E12/E24 series for components and geometric series

I found a real example of some analysis of components where the central section of the distribution was missing. The initial choice of +/- 10% resistors for the rebuild of the Atanasoff-Berry Computer had this feature, see Figure 3 in John Gustafson: Reconstruction of the Atanasoff-Berry Computer. It's not stated but perhaps they were using some old stock to try and get a closer match for what was originally used in the 1940s.

kevinjwalters

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Joined: Sun Oct 01, 2017 3:15 pm

Re: E12/E24 series for components and geometric series

Yep, that's what binning looks like. Some vendors used to do their tolerances that way: if you bought 10% resistors, you could assume the values would be between 5% and 10% away from nominal.

It's still a valid practice when you're doing one-off construction and need especially good matching.

Fortunately the philosophy of manufacturing has changed since then. The standard practice now is to tune the manufacturing process for a standard deviation between 1/3rd and 1/6th of the tolerance. That puts the chance of getting an out-of-spec part between 1-in-300 and 1-in-500-million. For small and inexpensive parts like resistors, it's actually cheaper to use tight control.. automatic testing is measured in cents per second, which is proportionally expensive for parts that sell for less than 1c. It costs less to be statistically confident that only one in [some large number] will be outside the expected range.