I had a teacher talk about this at uni. He'd bought 10% resistors at some time when he needed a better tolerance, since they were a lot cheaper, and he'd assumed gauss distribution and had planned to measure and select the "good ones". Not a single resistor was closer to nominal than 5%. The production process provided gauss distributed resistances, and they were then measured, sorted and marked by the manufacturer.
Actually, logically, if one thinks about it, if this process were true and they manufactured 5% resistors, but selected the ones within a 1% spec for sale as 1% resistors, if you were to conduct this same test on 5% resistors, there would be a valley from +1% to -1% because all of those values had been extracted. Therefore, if they were doing that, it would make even more sense to extract your 0.5%, 0.1%, and 0.05% resistors from the same pool, because those are even more costly to produce. As there is no valley in this distribution in this video, you know that they didn't do this (to the 1% pool anyway). Thus if they did do this, then you would never see anything with a tolerance of better than |R| = +/-1%, because all of those (presumably) would have been taken out. That in turn would mean unless you're paying top dollar for the most precise resistors they manufacture, you're never going to get the value stated on the tin. So if you buy a 1k 10% resistor, measure it, and find it to be 1000 ohms, you know they aren't doing this. (At least, empirically speaking, to _all_ the resistors, but why would they cherry pick?)
Whiskey Richard Depends, consider if they have to mark in batches, so if one in the batch is out of tolerance they mark it in the next band up, then you would still have Gaussian distributions in each tolerance band. If you manufacture a tape of 1000 resistors all mounted on the tape and then have to mark the whole tape the same for shipping and sale. This would be a lot easier from a process point of view of the whole production line. Fundamentally it would depend on how the production lines are set up as to how they might classify them. Without someone who has setup or works at one of those production lines letting us know, we can't know for sure.
Maybe, but the cost of the testing has to be considered - higher precision resistors might be expensive less because they're incredibly rare, and more because they have to be tested, slowing down the line and raising the cost of regular Resistors, and the higher precision is not needed the vast majority of the time, so say they peel off 10% of the resistors to test and put the rest back into circulation
This is actually very common, I have a large amount of resistors, and you can cherry pick out very good ones (around 0.1% deviation), to terrible ones that fail the 1% spec.
Thanks and thanks to everyone who responded. Just looking back, I wanted to clarify that I think when I said "why would they cherrypick" at the end, I meant why would they take some better tolerance resistors and leave others (amidst lower tolerance resistors). It's possible they do do this, so there isn't a total valley around that tolerance, but I feel if you're going to get some of them you may as well grab 'em all and max your profits. (N/A in the case of batch tolerances as mentioned above) @@mumujibirb
Hi Dave, it would have been good to center the histogram bins symmetrically with respect to the reference value. For example the middle bin between -0.05% and +0.05% instead of 0.0% and 0.1%. I just find it easier to interpret when you refer to the bin for a particular value. Very instructive channel, thanks for the great work!
Nice video! I was wondering about resistors value distribution for a long time (but never get around to actually measure them). Very useful information. Thanks!
I think that's true. You're effectively summing two normal distributions. The standard deviation, and hence the tolerance, goes down with sqrt(x)/x, with x the number of resistors in series or parallel. (this also implies that the 4 resistor example in EEVblog 212 actually has a tolerance of 0.5% if they're normally distributed and the mean is correct)
Excellent video! You asked a very interesting question, came up with a good test, and documented and explained it thoroughly. I'd love to see a similar test of zener diodes. I've heard that those have significant manufacturing variation, so they are sorted and labeled rather than being manufactured to hit a specific voltage.
@allanw Depends how much you pay. Ultra precise $10 resistor would be 100% tested I'm sure. For run of the mill stuff it's likely good enough to batch test to ensure your processors are still tracking ok. The distribution tolerance takes care of the rest.
@rroge5 Any reputable manufacturer would most certainly be measuring and tracking their manufacturing results, to ensure they meet the claimed datasheet specs.
@Desmaad No doubt about that. If they are 100% tested then it would be fully automated as they roll off the line onto the bandoleer, and it probably takes milliseconds each, likely much quicker than the conveyor belt :->
"Boring as batshit"? Those who have a research interest in the digestion in chiroptera must find this pretty rude! :D Nice video. It's always nice to have your expectations confirmed.
@Vlakpage I can't account for meter error because the absolute error of it against a traceable reference standard is not known precisely. But I have good confidence that it is within spec, which is better than the mean difference measured. The absolute mean difference measured could be due to the resistor manufacture, meter accuracy, or drift over time, or likely a combination of all three. Not that it really matters.
Most Interesting Dave and well presented. I wish I'd had you as a teacher. Yes control charts are still used in industry especially where precision components are manufactured. I believe the concept was originally driven by a guy called Walter Shewart who became a buddy of Edwards Deming. Of course this has all been developed into six sigma control where you would only be expected to find one or two components outside a norm in a batch of a million. Remarkable.
@kevinxbuffalo CamStudio It's free. Audio side has a few issues, but works well. I capture a 1280x720 so it's an exact 16:9 ratio with my video. That makes it clear because no pixels get chopped or squished etc.
Manufacturers like to hold tolerances to at least 1/2 the spec value so that all the parts in a run pass inspection. Margin. Every process needs margin.
@nbsr1 I meant to, but forgot. Sorry to those who get a hard-on over such things :-> Trying to explain SD would have made an already long video even longer anyway.
They have an Operating Temperature Range of - 65 to + 165°C; a temperature coefficient of max +-100ppm/°C, and as far as I can see, only the power rating is defined for a specific temperature (70°C), so I assume the 1% tolerance is for the whole temperature range. Maybe that's why they all fall within 0.5% at room temperature?
john Smith 100ppm over 200+ centigrade is 20,000ppm, or 2%. It doesn’t work that way. The tolerance is for the nominal value at room temp. If you get them repeatedly across the temperature extremes and they’ll shift their room-temperature value - sometimes a lot. That’s why tolerance and temperature coefficient are provided separately. And the tempco is almost always under specified: it’s not a constant across temperatures. It often is worse than specified, at some temperatures. The tempco only applies around normal operating temperature. If you need a certain known performance from stock generic parts, you need to qualify them yourself. That’s been true for as long as you could buy passive parts, more or less. I treat both tempco and tolerance as guidance, but if they are critical, there’s nothing to do but qualify the parts, perhaps even test all of them before they get into the product. These days testers can be cheaply made using 3D printed parts, arduinos, stepper motors and drivers, Peltier modules, and off the shelf multimeters. Progress is good :)
@eurokid83 No, not yet. Need the lab to be at 20deg, pretty hot here recently! Did muck around calibrating my Gossen Energy though because it shat itself after a firmware update (see the forum thread) because
Mr. Pedantic here -- the frequency function uses the bin values as *upper limits*, not bin centres. That means that when the bell curve peaked on 0%, that's actually a peak on values between -0.1% and 0%, i.e., demonstrating *a bias* (consistent with the biased average for the data), not a lack of bias. A true Gaussian centered on zero would have two equal-height bars: the -0.1% to 0% bin and the 0% to 0.1% bin.
@HammerFET Designing and building such an automated jig would take MUCH longer than simply doing the work by hand! Unless you had say 40,000 resistors to churn through.
First, a numerical fit of the data to the normal distribution to extract the mean and standard deviation of the distribution would be welcome. Second, 32% of resistors will vary from the mean by more than one standard deviation; 4.6% will vary by more than two sigma; 0.27% will vary by more than three sigma; etc. Given that manufacturers cannot afford for 32% of their sales to be returned for warranty violations, it shouldn't be a surprise that their specifications reflect 5-8 sigma for tolerances. Third, by over-specifying their tolerances, they improve their chances that fresh materials will yield salable resistors before they optimize their process to "zero out" the new mean. Finally, the 1% tolerance is intended as a warranty for all temperatures, humidities, etc. that don't kill the devices.
AFAIK, metal (and carbon) film resistors are always manufactured to a specific value. The distribution seen is very reflective of "six sigma" manufacturing, where you hold the standard deviation of the process to 1/6 of the reject limit. The idea is essentially the reject rate is effective held to zero. When I've heard of binning resistors by value after they were manufactured, it was always in regards to old-school 10% carbon composition resistors. It would be interesting to a get few buckets of those and see if you get something closer to a uniform distribution of values.
Paul Ste. Marie Agreed, this is simple statistics. 400 data points is simply not enough to show a 6sigma distribution. The science of this is the subset of statistics dealing with "confidence intervals". If he measured say 600,000 resistors he would have a decent chance of getting maybe 1 resistor out at the 6sigma limit (at + or - 1%). Unfortunately to fill a gaussian distribution smoothly out to 6sigma requires really millions and millions of samples. His claim that these resistors are really 0.5% tolerance is perfectly valid, in so much that that's probably the 3sigma interval so that anyone buying a moderately sized batch of resistors has a 99.7% chance that all their resistors will lie within the 0.5% tolerance. Had he tested a couple of thousand he likely would have had a couple lie outside the 0.5% tolerance range.
I just designed a voltage divider to narrow the adjustment range of a potentiometer. I wondered how far I could go with narrowing the range before the tolerances of the resistors could possibly push the adjustment range so far to one side that it does not longer include the desired values. I ran a quick Monte Carlo simulation in LTSpice that showed me that the dimensioning was safe. But when specifying the resistor values and tolerance with the directive that uses a uniform distribution within the specified tolerance, I also asked myself if this realistically models the actual distribution of the resistor values. Just as Dave noted, I also did not find related specs from manufacturers. So, this video seems to be one of the rare sources that tackle this issue. From what I learned here, the modeling with the uniform distribution I used for the simulation was most likely conservative.
If you're using two 1k resistors, and one is 995 Ohm and the other is 1005 Ohm, the difference between those two is 10 Ohm, so 1%. When you look at the second histogram, it actually looks like they've cut of at +/- 0.5%. So maybe, you suppose by 1% tolerance, they mean that's the largest possible difference you can get between two (or more) resistors, rather than the maximum possible deviation in just one of them? Very interesting video btw!
@rroge5 You'd probably find they get around it by taking a 10% sample. I don't know how stable the manufacturing process is regarding resistors, as the checks could be 1%, or even 0.1%. I would assume 1 per 1000 is enough - they are just off-the-shelf parts and not milspec
Hi Dave, just to add to my earlier comment. Regarding the standard deviation of the resistance values (an indication of the tightness of the grouping) it would be interesting to see if there are differences to the standard deviation between say 0.1%, 0.5%, 1%, 2%, 5%, and 10% tolerance resistors. This will tell us several things: if we see similar standard deviations across the tolerance bands, then we can expect manufacturers to simply be testing 100% of the resistors as they roll off the line and cherry picking the best resistors to fulfill greater tolerance bands, i.e. I would expect to see truncation in the highest tolerance bands, particularly at 0.1% tolerance. If there are improvements to the standard deviations, then it is possible that manufacturers are doing something to the manufacturing process instead (different manufacturing techniques, feedback control, quality of materials, etc.). Another theory would be that to save cost, 5%, 10% and 20% resistors would not be tested as rigorously (100% testing on every component is expensive) so the manufacturers simply widen the tolerance band as a safety net. In theory, a batch of 5% resistors could be just as good as 1% if they had the same standard deviation. Before the video, I always thought manufacturers would cherry pick resistors to fit within a tolerance band and if they fall outside the band they would be sold to the next band down. For example if I buy a 1k 10% resistor, I would expect the value to be within 900-950 and 1050-1100 ohms with no resistors within the 950-1050 ohm range as these would be reserved for 5% resistors. Perhaps this was the case on carbon resistors which tended to have poorer tolerances, and not on metal film resistors. Either case, this would be interesting to look into.
Well according to Probability, which i have an exam 2days from now, this is not surprising at all. We can assume the resistor values have indepent identical distribution, according to cetral limit theorem, sum of random variables gives you and Gaussian disturbution as number of RV added goes to inf. And there you go! :D
Here's something else to consider. In engineering, one always incorporates a "safety factor" in a design. That's why, say, if there's going to be 15V across a capacitor, you use one rated for 20 or 24V. Perhaps those resistors are produced to + or -- 0.5%, to make sure they're going to be 1%.
I'm not too surprised, actually. If you'd plot the bell curve for the variance, I think you'd find that the expected probability to find a value down in the margins is actually
It's tedious to roach-clip each resistor if on reel package. I've done it, a lot.....lol. Why not build a jig in a small box, with two contact posts at the proper spacing, and those connect to typical banana binding posts or wired directly to the meter ? Then you can quickly test component-to-component while still on the reel/tape package.. There are test jig posts, that "grab" (via tension/compression) the resistor wire, You slip the component into sort of a tightened tweezer. I have some, though they are old stock...1960s I believe. With the popularity of DIY proto boards, I'll bet there's some newer products that are meant as "slip-in" wire-to-wire posts. Another easy option...is to modify some alligator crimps, "filing" a groove at the tip of the clip so that it straddles the component leads. Lay the taped reel on a non-conductive surface, and hand position the two clips (press against the surface) pressing down to make contact, for testing.. Don't forget....to insulate the clips, so you're not touching any metal. This method won't likely work at high accuracy for 1ohm and under....because when your hand gets even close to the leads (or, try grabbing the wire/cable, see what happens) , you become an antenna....and all the other pitfalls of measuring these resistances (stray capacitance, emf, thermal contact, etc....)
@samgab What you're saying would be true if ALL resistors that fit the higher criterion were picked out. If instead the demand was (much) smaller than the actual production of resistors that could be binned for better tolerance, you'd only get a slightly flatter bell curve.
If I remember correctly from the statistics I've studied (I never took a statistics course, but I had to learn some for a lab class I took), the expected average error for a number of individual data is the square-root of the sum of the squares of the individual errors.
Wrong. The square root of the sum of the squares of the individual differences from the average is what is called the variance. And that is a number that comes from an actual measured data set, not a prediction. There are of cause theories that predict what the variation should be depending on what Phillips / NXP did at their factory.
Come on, Dave. They can do way more than plot their process result on a histogram daily or weekly or whatever. They can figure out the maximum frequency of process drift at the magnitude of significance, and sample the product (individual resistors, in this case) at the Nyquist rate of that frequency. Bob's your uncle, they can do real-time binning according to process accuracy at any given point in time, without measuring every resistor after-the-fact. I imagine that a process with 10% cyclic accuracy overall might have 1% cyclic precision over a shorter time interval - since changes take time to accumulate - and that this could be utilized to batch different quality (and possibly even value) resistors from the same continuous production line. Whether they _do_ all that is another matter. But it doesn't seem terribly expensive. I bet it happens. It would explain both your results here, and the common observation that 10% resistors sometimes seem to have long runs where they're -8% ±1% (why not just sell those as 1% or 2% precision resistors at the nearest nominal value of -8%?).
i really liked this video :D you should do one video for how the resistance changes with voltage ( constant current) or how it changes with current (more dificult because of difrent temperatures )
Had a similar example in our Stats unit, except mathematicians tend get these things totally out of context... Pretty interesting results you got though, good to see real data worked with. An interesting idea: Use some kind of jig run by a micro controller to churn through loads of resistors while measuring each one and logging values. I wouldn't have had the patience to get through 400 resistors by hand x_x.
Hi Dave, I've noticed that You did not putted $ sign to the classes (or bin) values, and these values did incremented while dragging. I guess it will make some difference when graphing measurements. Anyway thanks for great video!
A very useful trick is to plot the data on “normal” paper. You can get log-normal or linear-normal. I don’t think Excel can do that. Don’t know about Open office. This shows true Gaussian samples as a straight line. If the line shows two or more slopes then the sample population is probably made up of more than one group mixed together (made on different days maybe). If the curve as “Z” shape (three slopes) then the population started out Gaussian but the manufacturer probably could not make all parts within tolerance and had to cull the outliers.
I extracted some more basic stats from the data. Assuming only initial compliance and at his room temperature, there is a [sample]standard deviation of 1.7 ohms and the probability of a resistor being between 990 and 1010 ohms, is 5.6e-09 or 1/179 500 000 [one in 180 million] (-5.73 to +6.06 standard deviations) If the factory corrects the slight bias so the sample mean exactly equals nominal then it would be 1/270 100 000. Alternately as I don't know the testing temperature or design temperature, raising the temp 5.5k will bring the sample mean to the nominal 1k, assuming exactly 50ppm temperature coefficient. The chi tests are all unity as well so the Gaussian normal curve is a very descriptive model for this data set.
I'd be interested to see what result you would have got from a randomised sample of those resistors. perfect stats to sample all of a population, but I wonder what the smallest randomised sample you could take of a larger population to get a good picture of what is happening, and perhaps give you a general sampling/testing rule for any resistor of that type, as testing every resistor can be time consuming
*Bins don't mean* what Dave thinks it does (look up FREQUENCY spreadsheet function): The *center bin* Dave is referring is not actually it. Speaking of first rougher graph (bins on 0,1% width): What is labeled on a graph as 1.0% is the bin of values 1.0% - 0.9%, so "0.1% bin" is +0.1% to 0.0% and and "0.0% bin" is values 0.0% to -0.1%. Finally, -1.0 % would mean -1% or less. Furthermore, he doesn't have 21 and 41 bins, but 20 and, respectively 40. So there are, actually, *TWO CENTRAL* BINS in both first and second finer bin division (AT 26:30 in video). Look at the graph AT 26:30 : Dave says you see some skew toward negative values looking around the central bin, and he is half right. Actually, you see that bins 0.00%, -0.05% and -0.10% (three bins from 0.00% to -0.15%) have higher individual frequency values than the "0.05% bin" (0.05-0.00%) frequency. Which leads you to the same conclusion.
I'm right at 10:00 and he's been attaching these alligator clips to each other to measure the basic shorted resistance. I think a better way to do this is to connect them both to a single resistor lead (both on the same side of the resistor) - this will account for any contact resistances to the resistor lead. It's surely not much if any different, but I like to be methodical like that.
Excellent! Could it be that the manufacturer's quoted 1% tolerance allows 0.5% across a single batch and 0.5% across different batches? Perhaps Philips could send you 500 batches of 500 x 10k resistors to test. You could do a whole series on it! I can't wait ;)
I wouldn't call a histogram "the frequency domain". When you do an analysis, or convert data between "time domain" and "frequency domain", you preserve all the information, and can go back and forth. If you start with a histogram, you can't go back to your original signal. Alternatively, what you have to begin with isn't in the time domain, since the order of the samples don't really matter* (Not to imply that every frequency domain representation contains all information. a power spectrum density will throw away phase information, for example.) *Well, they might have mattered, if every, say , 5th resistor tended to be a little higher or lower or whatever. To detect that, you can eyeball it, like done in the video, or actually do a frequency domain analysis.
@EEVblog You didn't account for the meter error, is it possible that the shift from center is caused by that? Not long ago I bought nice vintage semi-automatic RLCG bridge Tesla BM 539, it has good basic precision (calibrated 19 years ago). The interesting thing it has is output to electromechanical sorting device BP 5390 (which I've never seen and can't find any info) and many ranges specifically for measuring tolerances. I think it was meant for manufacturer component checking and sorting.
Whoa you actually tested 400 resisters I would probably stop and just a few. xD And thumbs upped for funny bloobers at the end. Were I live I am in the flight path. :)
Hi Dave, I thought I'd leave a comment to say this looks interesting. If you still have the data, I wonder what the standard deviation of your data is. Based on what I see, it looks like those resistors are built to a six sigma manufacturing standard, if this was the case then I expect to see a standard deviation of 1.666... therefore the probability of a 1% resistor being outside 0.5% of stated value is 1 in 370 resistors (0.27%), similar to the odd one or two falling outside this range in your data set. The probability of a resistor being outside of 0.67% of stated value falls to 1/15,787 (0.006%) so you will need to test many many resistors to see this. In short, what this tells us is that if we a have a project that calls for high tolerance resistance say (0.1%) we could buy a set of 1% resisters and be safe in the knowledge that if we were to cherry pick, over 45% will fall in that range (assuming 6 sigma manufacturing standards) - this will save you buying 0.1% resistors at ~20 times the cost.
Do they sell so few precision resistors that they have no choice but to throw them into the 5% bin and sell them for a low price? I really expected a steep dip at spot-on values, caused by binning. Excessive inventory of near-perfect parts would explain the lack of a dip.
I don't know why. but at a glimpse. I thought this was titled as a Caucasian Resistor! what could that even be! I like your channel. I learn something. it makes me think. mostly because some of it is over my head. so it has me googling . researching things. and watching your videos multiple times! oh and Happy New Year. hope all is good!
One thing I would have done with the data is to calculate the standard deviation, and see how it compares to the claimed 1% accuracy. It looks like 1% is at 4 sigmas or so?
actually, this is no surprise, that there is no resistors close to 1% error. 1. If something randomly f up, product is still good. 2. If something regularly f up, you still produce valid product and diagnose what is wrong. 3. You can measure slow changes in distribution while, guess what, producing valid product.
I would think that a manufacturer would save them selves support costs simply by trying to keep these measurements in the middle like this as instrument calibration could easily skew this from side to side. So if I had a meter that was not calibrated properly and say these errors at -1% -0% I would think okay its still within the range but in all actuality my meter could very well be off causing this. So if say they did skew from -1% to +1% and my meter was off I might call and start bitching.
Harry Haefner Quick Google search says red is 50 ppm/K (or ppm/°C) temperature coefficient. (*Sources* at the end.) I don't know what you mean... Like they sell better ones at lower price and label incorrectly?? This would mean that 2 degrees difference offsets ressistance by 0.1 ohm or 0.01% of 1k ohm. Just under measuring accuracy of 4 significant figures. ( *Four sources*: Electronic color code on Wikipedia, 6 Band Resistor Calculator on eeweb.com, Resistor color code on resistorguide.com and Resistor Colour Code on radio-electronics.com )
I had a teacher talk about this at uni. He'd bought 10% resistors at some time when he needed a better tolerance, since they were a lot cheaper, and he'd assumed gauss distribution and had planned to measure and select the "good ones". Not a single resistor was closer to nominal than 5%. The production process provided gauss distributed resistances, and they were then measured, sorted and marked by the manufacturer.
Actually, logically, if one thinks about it, if this process were true and they manufactured 5% resistors, but selected the ones within a 1% spec for sale as 1% resistors, if you were to conduct this same test on 5% resistors, there would be a valley from +1% to -1% because all of those values had been extracted.
Therefore, if they were doing that, it would make even more sense to extract your 0.5%, 0.1%, and 0.05% resistors from the same pool, because those are even more costly to produce. As there is no valley in this distribution in this video, you know that they didn't do this (to the 1% pool anyway).
Thus if they did do this, then you would never see anything with a tolerance of better than |R| = +/-1%, because all of those (presumably) would have been taken out. That in turn would mean unless you're paying top dollar for the most precise resistors they manufacture, you're never going to get the value stated on the tin.
So if you buy a 1k 10% resistor, measure it, and find it to be 1000 ohms, you know they aren't doing this. (At least, empirically speaking, to _all_ the resistors, but why would they cherry pick?)
Whiskey Richard Depends, consider if they have to mark in batches, so if one in the batch is out of tolerance they mark it in the next band up, then you would still have Gaussian distributions in each tolerance band. If you manufacture a tape of 1000 resistors all mounted on the tape and then have to mark the whole tape the same for shipping and sale. This would be a lot easier from a process point of view of the whole production line. Fundamentally it would depend on how the production lines are set up as to how they might classify them. Without someone who has setup or works at one of those production lines letting us know, we can't know for sure.
That is exactly what is done - at least at the fab here (microwave semiconductors).
Maybe, but the cost of the testing has to be considered - higher precision resistors might be expensive less because they're incredibly rare, and more because they have to be tested, slowing down the line and raising the cost of regular Resistors, and the higher precision is not needed the vast majority of the time, so say they peel off 10% of the resistors to test and put the rest back into circulation
This is actually very common, I have a large amount of resistors, and you can cherry pick out very good ones (around 0.1% deviation), to terrible ones that fail the 1% spec.
Thanks and thanks to everyone who responded. Just looking back, I wanted to clarify that I think when I said "why would they cherrypick" at the end, I meant why would they take some better tolerance resistors and leave others (amidst lower tolerance resistors). It's possible they do do this, so there isn't a total valley around that tolerance, but I feel if you're going to get some of them you may as well grab 'em all and max your profits. (N/A in the case of batch tolerances as mentioned above) @@mumujibirb
Aren't 'gaussian resistors' basically inductors? ;)
Hi Dave, it would have been good to center the histogram bins symmetrically with respect to the reference value. For example the middle bin between -0.05% and +0.05% instead of 0.0% and 0.1%. I just find it easier to interpret when you refer to the bin for a particular value. Very instructive channel, thanks for the great work!
Nice video! I was wondering about resistors value distribution for a long time (but never get around to actually measure them). Very useful information. Thanks!
Yes I do. This is my full time job!
I think that's true. You're effectively summing two normal distributions. The standard deviation, and hence the tolerance, goes down with sqrt(x)/x, with x the number of resistors in series or parallel. (this also implies that the 4 resistor example in EEVblog 212 actually has a tolerance of 0.5% if they're normally distributed and the mean is correct)
Excellent video! You asked a very interesting question, came up with a good test, and documented and explained it thoroughly.
I'd love to see a similar test of zener diodes. I've heard that those have significant manufacturing variation, so they are sorted and labeled rather than being manufactured to hit a specific voltage.
@allanw Depends how much you pay. Ultra precise $10 resistor would be 100% tested I'm sure. For run of the mill stuff it's likely good enough to batch test to ensure your processors are still tracking ok. The distribution tolerance takes care of the rest.
@rroge5 Any reputable manufacturer would most certainly be measuring and tracking their manufacturing results, to ensure they meet the claimed datasheet specs.
@Desmaad No doubt about that. If they are 100% tested then it would be fully automated as they roll off the line onto the bandoleer, and it probably takes milliseconds each, likely much quicker than the conveyor belt :->
"Boring as batshit"? Those who have a research interest in the digestion in chiroptera must find this pretty rude! :D
Nice video. It's always nice to have your expectations confirmed.
@Vlakpage I can't account for meter error because the absolute error of it against a traceable reference standard is not known precisely. But I have good confidence that it is within spec, which is better than the mean difference measured. The absolute mean difference measured could be due to the resistor manufacture, meter accuracy, or drift over time, or likely a combination of all three. Not that it really matters.
Most Interesting Dave and well presented. I wish I'd had you as a teacher. Yes control charts are still used in industry especially where precision components are manufactured. I believe the concept was originally driven by a guy called Walter Shewart who became a buddy of Edwards Deming. Of course this has all been developed into six sigma control where you would only be expected to find one or two components outside a norm in a batch of a million. Remarkable.
The simplest explanation for the observed tight packing (sigma
@kevinxbuffalo CamStudio It's free. Audio side has a few issues, but works well. I capture a 1280x720 so it's an exact 16:9 ratio with my video. That makes it clear because no pixels get chopped or squished etc.
@nemoDaedalus It's always implies +/-1% that I have seen. If it was 1% total around the mean, then a couple of them would have been out of spec.
Manufacturers like to hold tolerances to at least 1/2 the spec value so that all the parts in a run pass inspection. Margin. Every process needs margin.
Neat idea for a video!
@nbsr1 I meant to, but forgot. Sorry to those who get a hard-on over such things :-> Trying to explain SD would have made an already long video even longer anyway.
They have an Operating Temperature Range of - 65 to + 165°C; a temperature coefficient of max +-100ppm/°C, and as far as I can see, only the power rating is defined for a specific temperature (70°C), so I assume the 1% tolerance is for the whole temperature range. Maybe that's why they all fall within 0.5% at room temperature?
john Smith 100ppm over 200+ centigrade is 20,000ppm, or 2%. It doesn’t work that way. The tolerance is for the nominal value at room temp. If you get them repeatedly across the temperature extremes and they’ll shift their room-temperature value - sometimes a lot. That’s why tolerance and temperature coefficient are provided separately. And the tempco is almost always under specified: it’s not a constant across temperatures. It often is worse than specified, at some temperatures. The tempco only applies around normal operating temperature. If you need a certain known performance from stock generic parts, you need to qualify them yourself. That’s been true for as long as you could buy passive parts, more or less. I treat both tempco and tolerance as guidance, but if they are critical, there’s nothing to do but qualify the parts, perhaps even test all of them before they get into the product. These days testers can be cheaply made using 3D printed parts, arduinos, stepper motors and drivers, Peltier modules, and off the shelf multimeters. Progress is good :)
@eurokid83 No, not yet. Need the lab to be at 20deg, pretty hot here recently! Did muck around calibrating my Gossen Energy though because it shat itself after a firmware update (see the forum thread) because
Mr. Pedantic here -- the frequency function uses the bin values as *upper limits*, not bin centres. That means that when the bell curve peaked on 0%, that's actually a peak on values between -0.1% and 0%, i.e., demonstrating *a bias* (consistent with the biased average for the data), not a lack of bias. A true Gaussian centered on zero would have two equal-height bars: the -0.1% to 0% bin and the 0% to 0.1% bin.
Is it not common to have an odd number of bins with the center at 0% and limits of say, +- 0.05% ? That would only have one bar in the center.
***** Absolutely, but that's *not* what he did in this video.
TheHue's SciTech I realized that also. Wrote commented that independently just now (in October 2015). You did that more concisely.
@HammerFET Designing and building such an automated jig would take MUCH longer than simply doing the work by hand! Unless you had say 40,000 resistors to churn through.
First, a numerical fit of the data to the normal distribution to extract the mean and standard deviation of the distribution would be welcome. Second, 32% of resistors will vary from the mean by more than one standard deviation; 4.6% will vary by more than two sigma; 0.27% will vary by more than three sigma; etc. Given that manufacturers cannot afford for 32% of their sales to be returned for warranty violations, it shouldn't be a surprise that their specifications reflect 5-8 sigma for tolerances. Third, by over-specifying their tolerances, they improve their chances that fresh materials will yield salable resistors before they optimize their process to "zero out" the new mean. Finally, the 1% tolerance is intended as a warranty for all temperatures, humidities, etc. that don't kill the devices.
AFAIK, metal (and carbon) film resistors are always manufactured to a specific value. The distribution seen is very reflective of "six sigma" manufacturing, where you hold the standard deviation of the process to 1/6 of the reject limit. The idea is essentially the reject rate is effective held to zero.
When I've heard of binning resistors by value after they were manufactured, it was always in regards to old-school 10% carbon composition resistors. It would be interesting to a get few buckets of those and see if you get something closer to a uniform distribution of values.
Paul Ste. Marie Agreed, this is simple statistics. 400 data points is simply not enough to show a 6sigma distribution. The science of this is the subset of statistics dealing with "confidence intervals". If he measured say 600,000 resistors he would have a decent chance of getting maybe 1 resistor out at the 6sigma limit (at + or - 1%). Unfortunately to fill a gaussian distribution smoothly out to 6sigma requires really millions and millions of samples. His claim that these resistors are really 0.5% tolerance is perfectly valid, in so much that that's probably the 3sigma interval so that anyone buying a moderately sized batch of resistors has a 99.7% chance that all their resistors will lie within the 0.5% tolerance. Had he tested a couple of thousand he likely would have had a couple lie outside the 0.5% tolerance range.
hats off for patience. I would start planning on how to do it automatically :)
I just designed a voltage divider to narrow the adjustment range of a potentiometer. I wondered how far I could go with narrowing the range before the tolerances of the resistors could possibly push the adjustment range so far to one side that it does not longer include the desired values.
I ran a quick Monte Carlo simulation in LTSpice that showed me that the dimensioning was safe. But when specifying the resistor values and tolerance with the directive that uses a uniform distribution within the specified tolerance, I also asked myself if this realistically models the actual distribution of the resistor values. Just as Dave noted, I also did not find related specs from manufacturers. So, this video seems to be one of the rare sources that tackle this issue. From what I learned here, the modeling with the uniform distribution I used for the simulation was most likely conservative.
@Chiliyago Sometimes, life ain't easy. You're welcome.
If you're using two 1k resistors, and one is 995 Ohm and the other is 1005 Ohm, the difference between those two is 10 Ohm, so 1%.
When you look at the second histogram, it actually looks like they've cut of at +/- 0.5%. So maybe, you suppose by 1% tolerance, they mean that's the largest possible difference you can get between two (or more) resistors, rather than the maximum possible deviation in just one of them?
Very interesting video btw!
@DaemonPanda But only the stuff I'm interested in, that's the catch!
@rroge5 You'd probably find they get around it by taking a 10% sample. I don't know how stable the manufacturing process is regarding resistors, as the checks could be 1%, or even 0.1%.
I would assume 1 per 1000 is enough - they are just off-the-shelf parts and not milspec
Glad to see 3478A in usage. I am also using this fellow to measure my resistors.
@KeithWasHere1 Ebay, or any decent electronics store all sell them in boxes of 1000
Good job on that lecture. I had similar things in university, except it was awful, yours is awesome.
Hi Dave, just to add to my earlier comment. Regarding the standard deviation of the resistance values (an indication of the tightness of the grouping) it would be interesting to see if there are differences to the standard deviation between say 0.1%, 0.5%, 1%, 2%, 5%, and 10% tolerance resistors. This will tell us several things: if we see similar standard deviations across the tolerance bands, then we can expect manufacturers to simply be testing 100% of the resistors as they roll off the line and cherry picking the best resistors to fulfill greater tolerance bands, i.e. I would expect to see truncation in the highest tolerance bands, particularly at 0.1% tolerance. If there are improvements to the standard deviations, then it is possible that manufacturers are doing something to the manufacturing process instead (different manufacturing techniques, feedback control, quality of materials, etc.). Another theory would be that to save cost, 5%, 10% and 20% resistors would not be tested as rigorously (100% testing on every component is expensive) so the manufacturers simply widen the tolerance band as a safety net. In theory, a batch of 5% resistors could be just as good as 1% if they had the same standard deviation.
Before the video, I always thought manufacturers would cherry pick resistors to fit within a tolerance band and if they fall outside the band they would be sold to the next band down. For example if I buy a 1k 10% resistor, I would expect the value to be within 900-950 and 1050-1100 ohms with no resistors within the 950-1050 ohm range as these would be reserved for 5% resistors. Perhaps this was the case on carbon resistors which tended to have poorer tolerances, and not on metal film resistors. Either case, this would be interesting to look into.
@valajbeg Nah, decided to drop it, at least for a while. New edit software doesn't support it anyway.
Nothing finer than watching full screen - 1080p daves face!
You measured 400 resistors by hand??? That’s why we have interns! :-D
Excellent video Dave!
Well according to Probability, which i have an exam 2days from now, this is not surprising at all. We can assume the resistor values have indepent identical distribution, according to cetral limit theorem, sum of random variables gives you and Gaussian disturbution as number of RV added goes to inf. And there you go! :D
Here's something else to consider. In engineering, one always incorporates a "safety factor" in a design. That's why, say, if there's going to be 15V across a capacitor, you use one rated for 20 or 24V. Perhaps those resistors are produced to + or -- 0.5%, to make sure they're going to be 1%.
Still statistical analysis is important: if I use 10 x 1 Ohm 1% resistors in series will it be equivalent to 10 Ohm 0.33% or 10Ohm 1% ?
I'm not too surprised, actually. If you'd plot the bell curve for the variance, I think you'd find that the expected probability to find a value down in the margins is actually
It's tedious to roach-clip each resistor if on reel package. I've done it, a lot.....lol.
Why not build a jig in a small box, with two contact posts at the proper spacing, and those connect to typical banana binding posts or wired directly to the meter ? Then you can quickly test component-to-component while still on the reel/tape package..
There are test jig posts, that "grab" (via tension/compression) the resistor wire, You slip the component into sort of a tightened tweezer.
I have some, though they are old stock...1960s I believe. With the popularity of DIY proto boards, I'll bet there's some newer products that are meant as "slip-in" wire-to-wire posts.
Another easy option...is to modify some alligator crimps, "filing" a groove at the tip of the clip so that it straddles the component leads. Lay the taped reel on a non-conductive surface, and hand position the two clips (press against the surface) pressing down to make contact, for testing.. Don't forget....to insulate the clips, so you're not touching any metal.
This method won't likely work at high accuracy for 1ohm and under....because when your hand gets even close to the leads (or, try grabbing the wire/cable, see what happens) , you become an antenna....and all the other pitfalls of measuring these resistances (stray capacitance, emf, thermal contact, etc....)
@riktw There is no need to in this instance.
Interesting video and very thorough. This is why I like EEVblog :)
@samgab What you're saying would be true if ALL resistors that fit the higher criterion were picked out. If instead the demand was (much) smaller than the actual production of resistors that could be binned for better tolerance, you'd only get a slightly flatter bell curve.
If I remember correctly from the statistics I've studied (I never took a statistics course, but I had to learn some for a lab class I took), the expected average error for a number of individual data is the square-root of the sum of the squares of the individual errors.
Wrong. The square root of the sum of the squares of the individual differences from the average is what is called the variance. And that is a number that comes from an actual measured data set, not a prediction. There are of cause theories that predict what the variation should be depending on what Phillips / NXP did at their factory.
Come on, Dave. They can do way more than plot their process result on a histogram daily or weekly or whatever.
They can figure out the maximum frequency of process drift at the magnitude of significance, and sample the product (individual resistors, in this case) at the Nyquist rate of that frequency. Bob's your uncle, they can do real-time binning according to process accuracy at any given point in time, without measuring every resistor after-the-fact. I imagine that a process with 10% cyclic accuracy overall might have 1% cyclic precision over a shorter time interval - since changes take time to accumulate - and that this could be utilized to batch different quality (and possibly even value) resistors from the same continuous production line.
Whether they _do_ all that is another matter. But it doesn't seem terribly expensive. I bet it happens. It would explain both your results here, and the common observation that 10% resistors sometimes seem to have long runs where they're -8% ±1% (why not just sell those as 1% or 2% precision resistors at the nearest nominal value of -8%?).
i really liked this video :D
you should do one video for how the resistance changes with voltage ( constant current) or how it changes with current (more dificult because of difrent temperatures
)
Had a similar example in our Stats unit, except mathematicians tend get these things totally out of context... Pretty interesting results you got though, good to see real data worked with.
An interesting idea: Use some kind of jig run by a micro controller to churn through loads of resistors while measuring each one and logging values. I wouldn't have had the patience to get through 400 resistors by hand x_x.
Hi Dave,
I've noticed that You did not putted $ sign to the classes (or bin) values, and these values did incremented while dragging. I guess it will make some difference when graphing measurements.
Anyway thanks for great video!
Thanks for sharing!
I used to take my DMM to the elec shop and choose G.P transistors with good hfe to buy, I guess I could do the same with resistors ;)
@soolevi I doesn't work if you put the $ sign in the 2nd parameter.
A very useful trick is to plot the data on “normal” paper. You can get log-normal or linear-normal. I don’t think Excel can do that. Don’t know about Open office. This shows true Gaussian samples as a straight line. If the line shows two or more slopes then the sample population is probably made up of more than one group mixed together (made on different days maybe). If the curve as “Z” shape (three slopes) then the population started out Gaussian but the manufacturer probably could not make all parts within tolerance and had to cull the outliers.
Worst case, you can always take the log or exponential of the values and graph that on a regular lin-lin scale :)
still kicking ass dave
Well... 10 points for effort. :)
Very interesting video. Makes math a lot more interesting when you can apply it like this.
I extracted some more basic stats from the data. Assuming only initial compliance and at his room temperature, there is a [sample]standard deviation of 1.7 ohms and the probability of a resistor being between 990 and 1010 ohms, is 5.6e-09 or 1/179 500 000 [one in 180 million] (-5.73 to +6.06 standard deviations)
If the factory corrects the slight bias so the sample mean exactly equals nominal then it would be 1/270 100 000. Alternately as I don't know the testing temperature or design temperature, raising the temp 5.5k will bring the sample mean to the nominal 1k, assuming exactly 50ppm temperature coefficient.
The chi tests are all unity as well so the Gaussian normal curve is a very descriptive model for this data set.
There can be zero probability, if they reject any too far out.
I'd be interested to see what result you would have got from a randomised sample of those resistors. perfect stats to sample all of a population, but I wonder what the smallest randomised sample you could take of a larger population to get a good picture of what is happening, and perhaps give you a general sampling/testing rule for any resistor of that type, as testing every resistor can be time consuming
*Bins don't mean* what Dave thinks it does (look up FREQUENCY spreadsheet function):
The *center bin* Dave is referring is not actually it. Speaking of first rougher graph (bins on 0,1% width): What is labeled on a graph as 1.0% is the bin of values 1.0% - 0.9%, so "0.1% bin" is +0.1% to 0.0% and and "0.0% bin" is values 0.0% to -0.1%. Finally, -1.0 % would mean -1% or less.
Furthermore, he doesn't have 21 and 41 bins, but 20 and, respectively 40.
So there are, actually, *TWO CENTRAL* BINS in both first and second finer bin division (AT 26:30 in video).
Look at the graph AT 26:30 :
Dave says you see some skew toward negative values looking around the central bin, and he is half right. Actually, you see that bins 0.00%, -0.05% and -0.10% (three bins from 0.00% to -0.15%) have higher individual frequency values than the "0.05% bin" (0.05-0.00%) frequency. Which leads you to the same conclusion.
I'm right at 10:00 and he's been attaching these alligator clips to each other to measure the basic shorted resistance. I think a better way to do this is to connect them both to a single resistor lead (both on the same side of the resistor) - this will account for any contact resistances to the resistor lead. It's surely not much if any different, but I like to be methodical like that.
Obviously, I stopped the video 30 seconds too soon...
Excellent! Could it be that the manufacturer's quoted 1% tolerance allows 0.5% across a single batch and 0.5% across different batches? Perhaps Philips could send you 500 batches of 500 x 10k resistors to test. You could do a whole series on it! I can't wait ;)
I wouldn't call a histogram "the frequency domain". When you do an analysis, or convert data between "time domain" and "frequency domain", you preserve all the information, and can go back and forth. If you start with a histogram, you can't go back to your original signal. Alternatively, what you have to begin with isn't in the time domain, since the order of the samples don't really matter* (Not to imply that every frequency domain representation contains all information. a power spectrum density will throw away phase information, for example.)
*Well, they might have mattered, if every, say , 5th resistor tended to be a little higher or lower or whatever. To detect that, you can eyeball it, like done in the video, or actually do a frequency domain analysis.
Aaaaah it's engineering 103 and stochastic processes, all over again! :0
j/k Good work Dave, and great explanations.
I once special ordered 5% resistors, because that's what was on the drawing. Turns out, the manufacturer did 1% as standard 😅
They probably don't have the time to test every single resistor but they at least test a few per batch.
A few years ago I tested 100 20k 1% resistors. About half were within 0.25%. (This was for project using A/D converter)
Fantastic, well done bro
@EEVblog You didn't account for the meter error, is it possible that the shift from center is caused by that?
Not long ago I bought nice vintage semi-automatic RLCG bridge Tesla BM 539, it has good basic precision (calibrated 19 years ago). The interesting thing it has is output to electromechanical sorting device BP 5390 (which I've never seen and can't find any info) and many ranges specifically for measuring tolerances. I think it was meant for manufacturer component checking and sorting.
and why they are called gaussian resistors?
isnt gauss the unit for magnetic field or is this name related with the german mathematician
+Alex Verias the title refers to the gaussian or normal distribution. Those resistors are just resistors ..
Whoa you actually tested 400 resisters I would probably stop and just a few. xD
And thumbs upped for funny bloobers at the end.
Were I live I am in the flight path. :)
Hi Dave, I thought I'd leave a comment to say this looks interesting. If you still have the data, I wonder what the standard deviation of your data is. Based on what I see, it looks like those resistors are built to a six sigma manufacturing standard, if this was the case then I expect to see a standard deviation of 1.666... therefore the probability of a 1% resistor being outside 0.5% of stated value is 1 in 370 resistors (0.27%), similar to the odd one or two falling outside this range in your data set. The probability of a resistor being outside of 0.67% of stated value falls to 1/15,787 (0.006%) so you will need to test many many resistors to see this. In short, what this tells us is that if we a have a project that calls for high tolerance resistance say (0.1%) we could buy a set of 1% resisters and be safe in the knowledge that if we were to cherry pick, over 45% will fall in that range (assuming 6 sigma manufacturing standards) - this will save you buying 0.1% resistors at ~20 times the cost.
I'm surprised no one mentioned the central limit theorem
Do they sell so few precision resistors that they have no choice but to throw them into the 5% bin and sell them for a low price? I really expected a steep dip at spot-on values, caused by binning. Excessive inventory of near-perfect parts would explain the lack of a dip.
I am no expert with statistics, but the distribution looked more like a Poisson than a Gaussian.
I'm surprised you used two-terminal sensing and not a the HP's 4 wire measurement for the resistors.
I don't know why. but at a glimpse. I thought this was titled as a Caucasian Resistor! what could that even be! I like your channel. I learn something. it makes me think. mostly because some of it is over my head. so it has me googling . researching things. and watching your videos multiple times! oh and Happy New Year. hope all is good!
One thing I would have done with the data is to calculate the standard deviation, and see how it compares to the claimed 1% accuracy. It looks like 1% is at 4 sigmas or so?
Suburbs ARE in the flight path usually :)
actually, this is no surprise, that there is no resistors close to 1% error.
1. If something randomly f up, product is still good.
2. If something regularly f up, you still produce valid product and diagnose what is wrong.
3. You can measure slow changes in distribution while, guess what, producing valid product.
@Manekinen Umm what? I'm pretty sure that 10^3 = 1000, not 1024. You're speaking in binary.
@xmlisnotaprotocol Hey, why not!
@Chiliyago No problem here!
Excellent excellent video as always Dave. More of the same please.
If one of these resistors was 1.1% out and it caused an accident, would the manufacturer be liable?
At 12:23 this isn't a perfect 1k resistor because the cables have 0.00016 ohms resistance.
@kiyotewolf It would have jinxed EVERYTHING! 400 is good karma!
Hi there great videos on the EEVBlog regarding electronics. Can you measure the resistors by using only a xmultimeter without a oscolloscope?
Dave where do you get all of those toys?! Throughout the videos I've seen there has been like tens of thousands of dollars of equipment in them!
I would think that a manufacturer would save them selves support costs simply by trying to keep these measurements in the middle like this as instrument calibration could easily skew this from side to side. So if I had a meter that was not calibrated properly and say these errors at -1% -0% I would think okay its still within the range but in all actuality my meter could very well be off causing this. So if say they did skew from -1% to +1% and my meter was off I might call and start bitching.
Hello Mr Dave
as you said the yellow is 25ppm and orange 15ppm
isnt yellow the 15ppm or am i wrong
red is 2 ppm anyway, nothing like over complication on the simple.
Harry Haefner Quick Google search says red is 50 ppm/K (or ppm/°C) temperature coefficient. (*Sources* at the end.)
I don't know what you mean... Like they sell better ones at lower price and label incorrectly?? This would mean that 2 degrees difference offsets ressistance by 0.1 ohm or 0.01% of 1k ohm. Just under measuring accuracy of 4 significant figures.
( *Four sources*: Electronic color code on Wikipedia, 6 Band Resistor Calculator on eeweb.com, Resistor color code on resistorguide.com and Resistor Colour Code on radio-electronics.com )
so you got a 4 wire multimeter, why didn't you use a 4 wire measurement?
riktw No need for it: the offset was immaterial.
If you put 10 10k 1% resistors in parallel you end up with 1 1k 1% resistor. Yeap 1%!!! You can't change accuracy that way.
Don't component manufacturers automate testing these days?
Hey Dave, What software do you use to capture your desktop?
could that bell shape there come from the measure instrument at the factory when they sort the higher tolerance Rs for the 1% ones? ;)
one percent is one per cent and that's the way it is