EEVblog #215 – Gaussian ResistorsPosted on November 8th, 2011 26 comments
Just how far out is that +/-1% metal film resistor you are using?
Is it just random?
Does it follow the classic bell shaped Gaussian response?
What are the odds of getting one that’s spot on, or right out at the limits?
Dave thought he’d find out, the hard way…
Original Data can be found here, in both Open Office and Excel formats, play around yourself!
See here for more analysis on the data by Bob from Ohio:
That was cool, Dave! A few times, I’ve done studies like this myself to see if I can better understand manufacturing variations, and how things I read in datasheets correspond to real, actual parts. Sometimes I’ve learned some really interesting and quite useful things from doing this.
One trick that could be used is that if you assume that the center of the bell curve is exactly equal to the marked value of the component, then you can use a large sample of a particular part (or better, samples from different manufacturers and/or batches) to calibrate a cheap meter. It’s not an exact method, and it’s not going to make the meter into anything really special, but maybe you can get it to work better than it did before.
One thing that I think really needs to be said is that from the manufacturer’s perspective, the datasheet information is what they “guarantee”, and if you are designing their product into a circuit, you need to respect those numbers, no matter what you actually measure — unless of course you measure something that is OUTSIDE what they give in their data, which IIRC happened to you once!
I have a couple of explanations about why you saw a 0.5% actual variation on a 1% part. Again, look at it from the perspective of the manufacturer. If they say “1%”, then to be good, they need to be as sure as they can that ABSOLUTELY NONE of the devices will be outside of that tolerance. And to do that, it is necessary to maintain a manufacturing line that guarantees LESS THAN 1% variation. Well, _how_much_ less than 1% to maintain becomes a judgement call, and all sorts of factors come into play! So I suspect that one or both of two things were done by that manufacturer:
1. Test all devices, and discard any that test 0.5% or more off the intended value.
2. Adjust and monitor all aspects of the manufacturing process to ensure that devices no more than about 0.5% ever come off the manufacturing line.
Hopefully, no huge mistakes or errors will ever creep in, and the people who work for that company can all sleep easily. If good sleep were not important to them, maybe they could increase the allowed variance to 0.8% or 0.9%, or even more, and increase their profits by selling those extra resistors! But how much extra profit would that create? In the sample you studied, not much.
Although it would take a long time, I think it would be really interesting to compare studies like this one on various manufacturers’ products, from different countries (and engineering cultures). I really wish someone in the electronics industry would do things like that, and publish the results!
What i would do now is go to the shop and buy 500 +/-5% resistors and try to repeat the test.
I bet you will find lots of parts there which are close to +/- 0.5%.
After i saw your results i am sure the manufacturer drops the parts which are between 0.7% 1% into the 5% bin and sells them accordingly.
Maybe we will see a “camel shaped” graph instead of the “bell shaped” one we saw in this test.
All in one, good video
Keep them going
I wouldn’t be surprised if they binned all their resistors in to the 1%, 2% 5% etc and just moved higher tolerance components in to lower tolerance bins to suit demand.
Any reason you didn’t do 4W Kelvin probe measurements given that you have a 4W capable meter, and are trying to do high precision measurements?
Howard Johnson discovered something about resistor tolerance markings and wrote up an interesting article back in June 2010.
This makes me wonder if today’s SMD parts are manufactured, tested, and marked in the same way. It would be very interesting to get a bag of parts at different tolerances from each manufacture and test them to see how they fair.
As i said before, “camel-shaped” graph
I read an article about this one, written (I think) by Bob Pease or Jim Williams. The take-away point was that if you see anything *but* a gaussian distribution, you should change vendors.
The article went on to say that it’s a good idea to test and bin parts as you receive them, because you’ll find incredibly good parts mixed in with the general, run-of-the-mill stuff.
For the distribution above, Phillips probably tuned its process for +/- 1% at six standard deviations.. basically one part per million falling outside of tolerances.
‘Six sigma’ is a fairly common target for quality control purposes, mostly because it makes inspection easy. You don’t have to test every unit (which gets expensive), you just pull small random batches for testing. As long as the average and standard deviation of the sample are where they should be, you can be confident that the whole production run is good.
If we assume +/- 1% is 6-sigma, 1-sigma will be about .166%. For a sample of 400 resistors, you’re not likely to see anything more than 4-sigma away from the average, or about +/- .66%. That’s pretty close to what you saw in the data, though I’d be curious to see the actual standard deviation of your data.
Dave, consider upgrading to the Libre Office fork of OpenOffice.org as that is where the active development is now.
Interesting topic. I’m in the middle of video, but I think you were trying to say at 2.20 that you take 1% res and put them in series and then you have still 1%, but you said 10%. If you put 10 resistors of 100k (10%) it can be 1M +- 100k. Or do I make a mistake?
Of course I understand that when making a long sentence/though it’s easy to loose the track.
It’s nice to see that you have a lot of ideas to make an interesting video that still is totally different then previous ones!
Ît does not matter if you do parallel or series, the resulting resistor has not a better tolerance. Or it has. In fact it depends which theory you consider :
- if you consider just bare tolerance, it does not get better (especially if they are from the same biased batch !)
- if you consider a Gaussian which is centered you will get a better relative variance (in 1/sqrt(n)) http://books.google.com/books?id=E01DvO2nsH0C&pg=PA347&lpg=PA347&dq=gaussian+resistor+series+parallel&source=bl&ots=7ySR9d1HtS&sig=3zkSnAJoh1kApRfkdytTqhaDb9Q&hl=fr&ei=0PC6TrC7DMbMtAb77OzpBg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBwQ6AEwADgK#v=onepage&q=gaussian%20resistor%20series%20parallel&f=false
-For the parallel case, i do not know. let’s try.
assuming two resistors, normalized Ra=Rb=1, variance o for each
variance of 1/Ra : o1= o
variance of 1/Ra+1/Rb : o2= o*sqrt(2)
variance of Rparallel : op = 1/2*o2/2 =o/2/sqrt(2)
normalize that to Rparallel =Ra/2
normalized variance = o/sqrt(2)
same result !
I hope i did not make an error…
- if the gaussian is not biased, you get the same results, with a bias
my conclusion : you could get better precision statistically, but only if you make sure the distribution of your components values are gaussian centered !! parallel or series does not matter.
I always assumed the factory produces some resistors without any expectation of the value (or more like expectation is very broad for example from 1ohm – 100ohm and so on) and only after the process is finished they determine the resistance and put it in proper bin. wouldn’t it give more of a uniform distribution? Or at least gaussian but with bias far away from the value we even consider (thus resembling uniform in our set of resistors). Let me explain by example, as I feel I didn’t express myself too well:
Process in factory produces resistors of values 1k, 10k, 100k etc with broad tolerance of hmm 70% and gausian distribution, then resistors are measured and assigned to proper set. Depending how close we get to some standard value, we determine not only the value, but tolerance as well. It creates a wide set of values and tolerances (with 10% resistors more common, 1% less – thus more expensive). The thing is that it still would generate values that are distributed according to gaussian, but the mean would be far away from the range we even measure. The distribution we would see would be a slight slope into the direction of mean value of the whole batch.
Now when I see the results of measurements it seems a bit silly that the approach I considered the most cost effective is not the case in practice. Or am I missing something?
You need to find out how to get a tour of a passives manufacturing facility and show us
what goes on behind the scenes! That would be a killer vblog. Isn’t anyone close by to entertain an offer of free worldwide exposure? Or has everyone moved to Shanghai?
Great idea, go Dave!
Five minutes! I got five minutes into this video before I was fast asleep, on the first go.
Second go….i got ’bout a third of the way through the video….up to the point where you began to explain how you set up the second column of your Excel spreadsheet, Dave, until my consciousness waned and my head hit the pillow.
One interesting piece of data missing. How long did it take to measure and input the data for the 400 parts?
Cool video. Keep it up.
I’m not sure about the exact syntax of the frequency command, but in the video it seems that you messed it up, at least for the fewer bins column – you forgot to add $ to the classes parameter so down the line you get something like I10:I32 instead of I2:I22
Just tested it with my Excel 2010 – it tells me to put formula in one cell, select whole range where i want output, press F2 and ctrl+shift+enter to get correct results
Great video explanation.
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[...] about the "sample" of (say) 100 consecutive resistors from a reel. If you look at this, and take a look at the data, you can see the issue. 400 1k 1% resistors averaged 999.72462 ohms. [...]
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