Hi. We've talked about the Humble Resistor on here a fair bit. uh, over the time and I've done the recent blogs on the decade resistance, uh, boxes and how you can build your own and we've talked about tolerance a fair bit. But what exactly is the tolerance? and how does it vary in your typical metal film resistor like this? And it's a good question.

and it's something you can't really find in the data sheet. CU You read the data sheet for one of the these things and it says you know it's plusus 1% metal film resistor? Well, okay, where is that actual value of this resistor going to fall within that 1% Is it completely random? Is it shifted towards one end? Do they manufacture uh, 10% tolerance resistors and measure them? and uh, and then Mark these ones and sell these ones as 1% and sell the other ones as 5% sell the other ones as 10% Etc How do they do it? They don't really tell you on the data sheets and getting info on that sort of thing is hard. So just what is the probability distribution? That's the technical term of the values of a typical resistor like this? Damn well can't really find it in the data sheets. and is it I've always assumed I've never actually measured it I've always assumed and you know from industry knowledge it's just assumed to be a typical bell-shaped uh or what's called a normal distribution or Gausian distribution response.

But is it I Don't know. I've never actually seen the manufacturing graph for a resistor or not that I can recall. Maybe I have. but I Don't know if you can find one somewhere from a manufacturer.

Point it out. but I thought what bug of that? It'd be interesting to actually measure it. What are these resistors and what is their probability distribution? Well, it's easy to find out. You get a whole bunch of resistors and you measure them.

Let's go as you saw in the decade resistance Box: Uh, video. If you take a bunch of 1% resistors and you put them in series, then your total as what. That's how a decade resistance box works. put them in series and you end up with the same tolerance as the single resistor.

So if you got a 1% tolerance resistor, you put 10 in series. it's 10% But if you put them in uh, in parallel uh, combinations you can actually end up with are better like if you put if you want 1K and better than 1% but you've only got 1% resistors. If you put 10 10K resistors in parallel, you should end up with a better tolerance resistor than that 1% if it is actually a true uh, bell-shaped Giian normal distribution around that Center mean value if it's not around the center, mean value. If that Center mean value is shifted to one side or the other as it could be, then you you're not going to end up with that 1K You're going to end up with something shifted down the side and it all gets quite complex.

If you want to actually do the math behind it, can, that can actually get quite complex too. So anyway, I Thought we'd measure them and see what we get. Now there's actually two sides to this issue. One is the case where you've got all of these resistors and they're manufactured from the same batch because they're on the same bandier.

You can, uh, pretty much be assured that were manufactured at the same time, on the same bit of equipment, on the same day, by the same operator, with the same materials, etc, etc, etc at the same temperature. yada yada yada. So there are quite a lot of Uh process variations. So um, but because these are all from the same batch, That's one uh issue in itself.

What is? That's one thing we want to find out. We want to know what is the probability distribution of the resistors in a same production batch and then the second Uh issue is if okay, if you take 10 resistors and put them in parallel, but they're from if you get one resistor from separate batches that are all a year apart, well, is that distribution going to be the same as what you get from a one manufacturing batch distribution? It sounds complicated, but they are two separate issues. But because I don't have um, you know, no one separate resistors from separate batches, you know, and all that sort of stuff. We'll just look at this case today, but this should reveal hopefully something interesting cuz when you measure and plot data, you'd be surprised at what can come out of the end of it.

I Don't know what we're going to find? could be boring as bad. And as always with electronics, you find some real interesting stuff when you start measuring things, collecting data, and just a simple aspect of graphing it. In this case, we're going to get a probability distribution and we may or may not find something really interesting, but we don't know unless we actually try it. Take those measurements, go to the effort to do it, see what pops out the other end? I Have no idea, but it's going to be fun.

Let's find out now. the resistors we're going to use today are, um, some I've had uh in my possession for quite some time. They're a Philips brand I don't know the exact uh part number might be it's it's torn off as you can see there. but um, I believe they are 1% metal film resistors now.

um, this uh will probably only be valid for this particular uh type metal film cuz there are many different types of resistors there's you know, Carbon composition resistors. and there's thick film, um, resistors, thin film and there's wire wound and all sorts of things. so you know we're only going to do metal film today now just because we don't know the uh exact part number for this resistor doesn't mean we can't figure out what it is based on the colorcoded bands. Now just so happens, this is one of these six banded resistors.

Now in this case um, it's got uh brown, black, black, brown, brown, red, and uh, this red one. This s this sixth band on the end here indicates the temperature coefficient and uh, that can vary. If if this last band here if the six sixth band was actually uh Brown, it would mean 100, uh PPM. But because it's uh, red, it's actually 50 PPM And if it was orange would be uh 15 PPM and yellow would be uh 25, um 25 PPM So you can actually work out the temperature coefficient of that resistor.

Now of course if this was a regular three band resistor, um, you know a 5% tolerance one or whatever. If it only had three Bands then it would of course for 1K it would be brown, black, red and if it was a four band resistor, it would actually have uh, brown, black, black, brown. Now the fifth band actually uh, indic indates the Uh tolerance. In this case it is brown and that's indicates plus - 1% If it was red, it would be plus - 2% if it was Green Plus - half a% blue .25 Violet uh or purple would be .1% and if it was gray it can go down to 0.05% Now I Know that this is probably enough because uh 1K um plus - 1% is at 10 ohms so it's it's going to be plusus this second digit here.

but you know I I Just want extra resolution and this is where resolution counts. and uh, also, with this sort of test, you're going to want stability. and once again, the Fluke 87 is more than stable enough for a measurement like this. But hey, I've got a HP 3478 bench meter with an extra digit of resolution and better stability.

so hey, why not? let's use it. So let's Guild the Lily Shall we and uh, use the five-digit mode I Mean you know the 3478a has got uh, a four-digit mode to mimic the Uh Fluke 87 or even a three-digit mode if you're that way. inclin. but uh, we'll use the five-digit mode.

it's warmed up so it's nice and stable. and the other thing which can affect uh, this sort of measurement is the change in temperature over time. so we'll just uh, monitor that uh as well. but I you know I wouldn't expect a major change.

these are fairly low PPM value resistors. they're probably 50 PPM or something like that. So I but I'll just monitor the temperature change over the span of like I Don't know what an hour it's going to take me to actually measure these things or something. The temperature shouldn't change that much so, but if you're doing, you know this sort of stuff.

Seriously, then uh, you have to take those sort of things into consideration. The you know, any changes in uh, temperature, just physically, even just physically handling a single resistor like that can actually heat it up and change its temperature. Even touching the Lea you're actually heating up that resistor so you know you've got a handling can be important. Those sort of things.

And of course, the other thing you have to consider is the uh repeatability of your probing system. Now in this case, we've just got these regular 4 mm banana plug to alligator clip. uh leads. you know, fairly cheap ones, but uh, they they should do a fairly decent um uh job of actually biting through any oxidization on the leads.

And but and because got 1K it's not going to be a huge uh differential. If we were measuring like a 100 ohm resistor or something, it might matter or a 10 Ohm resistor would be worse Then the contact resistance could vary a bit, but on 1K it's pretty good. and if we short them out, let's have a look and there we go. It's 160 Milli 150 milliamps.

take it apart, put it back together. There you go, it's it's going to be within plus minus. You know, one uh, leas significant digit there. and if we just disconnect there, wiggle these around.

all that sort of thing. Just make sure you test the repeatability of your system. I'm fairly happy with that. now.

let's actually put it when you short the uh things out, but let's actually put it on a resistor leg, shall we? And no, yeah, there we go. it's the same. So we're obviously you know we're biting through any contact resistance there. Wiggle those around and that looks pretty repeatable to me.

And you know, down to um, uh, the order of, you know, 100, uh, 100 milliom. And there's our first resistor in this uh batch here. And really, I've left it for a while and it really hasn't uh, varied? uh, much at all you know, plus minus at most? uh, two, uh, least significant digits so you know I'm I'm fairly happy with that and I've played around with the probing and I've swapped it around and I've also got it on fixed manual range here so it won't Auto Range or anything like that. and I'm I'm fairly happy that this will give us consistent results.

So I'm going to go through measure each one of these resistors one by one. Maybe I won't do the two the whole lot. I'll do it until I get bored and um, enter the values into an Excel spreadsheet so we can do some analysis wo data analysis. Great fun and just to make sure that there's no funny business with this uh, bandier and the GL Well, there's there's a little bit of glue that's uh, actually used inside there and you know there could be some contamin.

You know, some uh, impedance across there between resistors, so they might be a little bit in parallel. Who knows? Well, let's uh, check that here. 99.51 Ohms. Let's uh, take it off, pull it out and 99.52% actually get through all the resistors and it, uh, I stopped at 400.

There were like 402, but there you go. 400. Nice round number. lots of data to work with I really like it.

The temperature only changed 0.1 de over that time. not that it really matters, but uh, we've got a lot of data to work with. Now it's time to graph it, play around with it and see what pops out because often you can get some mysterious results pop out, but only if you try it. Okay, here we go.

We've got our data and let's do some analysis, shall we? Now Column A Here is the all the 400 measured values which I entered directly from the meter, but I didn't The meter didn't zero out the lead resistance. so I've done that here in Uh, column B Here as you can see, I've actually subtracted 0.15 there, which was the constant lead resistance and contact resistance. We had I subtracted those and so they Column B is the true measured value of the resist. Now Uh, Column C here I've calculated the variation from a nominal in percentage from a nominal 1K uh value.

So that gives us our plus minus deviation, which we're interested in because the resistor obviously has a claim spec of plus - 1% so it's better if we easier for us and clearer if we work in a percentage uh based value. So that's exactly what I've got. So Column C Here is the data we're actually going to Uh plot and work from now. If you go down here and you plot column C there on a regular XY graph here, you'll see on the X- Axxis.

Here are all of our 400 Uh values and uh, you'll notice that they're scattered pretty much as you'd expect. Uh, no surprises in the actual scattering and the mean is pretty close to spot on Zero. There, you know if you just do it by I close one eye and squint a bit and uh, you can see that the nominal is going to be. you know, reasonably close to zero.

So no surprise there at all. But one of the big surprises I found is that no value went over plus6 or Min -.6 Actually, it's about plus .5 no value went over that, so that was a surprising result. I Expected to get values very close to the nominal Uh to the Uh claimed spec of plus - 1% but it turns out these resistors seem to be much tighter tolerance. I mean out of 400 resists I expected at least a few outlier ones to be right out near that.

you know, 0.98% at least uh variation. but we didn't see that. it's uh, the uh. The biggest values are uh, plus half a per and minus 6.

Very surprising. And if you're curious to know what the actual uh nominal average value is, it's 99.72% randomly, uh, scattered. So I think if you mixed up those resistors and measured them all again or or just unsorted them, you know just uh, did a different sort on on that and just randomized it, you'd get the same result. So that brings up another interesting point.

What do we get if we actually sort all of the values from lowest to highest or highest to lowest? It doesn't really matter. Uh, So we're going to select these columns over here. We sort ascending and as you can see the values in column C there are now sorted. What does that give us on the graph? Bingo There it is and no surprises for me at all.

This is exactly I've seen this countless times. This is exactly what I expect from a bunch of uh random data and a Gan distribution at that, which we'll get on to uh uh, sorted. um graph of just uh, random uh data because if it's a bell shaped ging distribution, you'd expect to sort of get most of your values like this. So the slope in the middle here, um to be quite shallow and the slope just gets steeper and steeper at the ends where the outliers are because there's fewer outline values.

So that's a very typical uh Gan type uh response for random data and this uh particular method is useful for showing Uh offsets better and uh, things like that I Ideally you would, um, if you had Z you'd expect it to be right smack in the center of the graph there, but you can see there is a little uh, tiny offset in there and uh, this is just a useful another useful way to interpret the data, but no surprises there at all. So I think we're going to get our Gan uh bell-shaped response when we do our frequency analysis. Now what we want to do is some frequency analysis. Now it's similar to the difference between time domain and frequency uh domain that that you're probably used to.

in this case, this uh data over here. uh, it can be considered the time domain data and this and the data we're now going to analyze to get our histogram is the frequency domain data and the way this works is uh, you create uh, different bins. In this case, um I've got uh 21 bins ranging from 1% uh, down in .1% uh, increments down to minus 1% and we would find out uh, how many of uh, these particular values appear in each one of those bins. So we're doing a frequency uh sort here.

So we're going to use um, the frequency command which is available in Excel or open Office which is what we're uh using here and um, it it uh, takes all of this input data in column C here and uh it it uh, analyzes all these start and counts how many of a particular um, uh, how many items actually fall within each one of these bins over here. And the way you do this is you use the frequency command. It accepts two input parameters here and uh, as you can see in the help, uh, popup here it's got um, data. So the first uh part of this is the data set in this case C We want column C here and we want all of the data now.

A little trap here is you got to put in the dollar signs there and there, there and there. Now the reason you have to do that is because when you uh, when you actually create this thing and then drag it down like this, you want all of um, other it will actually uh, increment, um that C value unless you put the dollars in there and for each one of these, you want to sort through all of the data. So putting the dollars in there ensures that you actually, uh, do that. Now the second um one up here is actually called classes but it's uh, it's bins is the other name for it which we're going to use here.

So these bins are in Colum I I2 to I22 down here as you can see and we've got those 21 bins and the frequency command is just magic. It just goes through and C and counts the data in those bins and converts it effectively into the frequency domain. So then once we've got the data here in column H in the frequency domain, we can just plot it at exactly the same as we did before. Exactly the same plot except we're doing a column uh graph and bingo, This is the response we get out of this and that is our histogram.

and as you can see, it does show that normal distribution exactly as we were expecting. No surprises there at all. It's centered. uh, prec.

It's centered on zero there around about zero and it. But the big surprise of course is that it only extends to Plus plusus half a perc. There are no outlying values uh out, right out here as we saw in our other graph. but it's clearer here that the uh Um because this effectively represents this gra.

This Uh distribution normal Orian uh, bell-shaped distribution uh effectively represents the Uh probability of one of these resistors actually being manufactured out here. in the outli, you can see most of them are going to be within the you know tight 0% bin. there a good lot of them are going to be, you know, Plus -1% either side of that, and you know, a fair number. Uh, plus -2% And then you start getting into the outliers out here.

and once you get to 0.5% well, there's just almost nothing left. There's only a couple of items down in, you know, five or under in these sort of bins. Now it's not a perfectly shaped, uh uh, bell shaped curve there, or gsy in response. You' got to use your imagination a bit.

Um, like this one here in the 0.3% It you know should have been up a bit and this one should have. You know, these should have been down. This one should have been up a bit here and up a bit. and well, you know, in an ideal world, that would be an ideal shaped curve.

And really, with a random, A true random set of data. Um, as you'll get with a manufacturing, uh, process. Uh, like this, you will, ultimately, um, get that provided two things. Uh, provided a that you have enough data Now in this case, we've only got 400 Now 400 sounds like a lot.

Um, when you're and and it is a lot when you're plotting just, uh, the data like this. That's an awful lot of uh, you know, data. More data than you can poke a stick at. But when you're doing frequency analysis like this, you're left with uh, fewer and fewer, uh uh, actual uh items in each bin.

Uh, when you actually convert it into the frequency domain like that Now, um, we can, uh, change. We can, uh, change this by increasing the number of bins we've got And that's what I'll do over here. But um, then you effectively have your number of data in that particular bin. So when you're doing frequency analysis like this, the more data you have, the better.

It's very important and in theory, if we had an infinite number of, uh, infinite amount of data to work with and we did a large enough number of bins, then we would find ultimately that it would average out and we would get our perfect, uh, normal distribution. Gan response curve. So as you can see, this one's a bit Rough and Ready Here, it's a, you know it. It really is a rough as guts kind of thing.

but you can still see because we are expecting uh, that Gan response. You can actually see it and uh, and it is there. But uh, what happens if we increase our number of bins now I've done exactly the same uh thing here. except I've got 41 bins instead of 21.

I've actually uh, doubled the number of bins here. And as I said, you have the number of items when you do that, so you need, so you can't just, uh, you know, increase the number of bins to an infinite amount because then you'll end up with no data at all. Um, in each bin or one item in randomly space bins and it'll be useless. So um, but the more data you have the uh it.

It's beneficial to, uh, have a higher number of bins like this and you know our highest number here is uh, 61. That's not too bad, but uh, you know when you start getting to the outliers down here, you know this one's zero and this one's one and you know it's a bit. It's a bit over the shop there, but anyway, I've done exactly the same uh thing. Exactly the same formulas here except I've got twice as many bins and when you plot that and you go over here, here it is, There is your response.

and uh, as you can see, it's a bit more fine detail because we've doubled our number of bins. Uh, and as you can see, there's probably a slight offset there on the negative, uh, side of things. as you'd expect when because we've got a slight negative offset. If you look down here, you remember we had a slight negative offset in our average value and also, you saw that on our sorted graph and uh, that manifests itself on the histogram here by having a slight offset.

and if you're not centered around the mean, this histogram will actually, uh, move either side like this. But I'm very impressed and not really surprised that the manufacturing tolerance for these good quality Phillips resistors are actually, uh, right on that. 0% Now the really interesting uh thing though is that as we've said before, it sort of peed us out at 0.5 plus - 0.5% not the uh plus uh, minus 1% which we were expecting. So this kind of, uh, well, it doesn't really Bust The Myth but it does in this case.

in for this particular Uh batch from uh Phillips the metal film resistors at this particular time manufactured in this Factory they clearly weren't targeting as a lot of people uh, claim that they manufacture say 5% resistors and then they, uh, test them all and the ones that um, pass to plus - 1% they sell them as Mark them and sell them as plus - 1% and the others they sell as plus- 5% Well, that's clearly not the case because if that was the case, uh, you would expect well I would expect a response which is much shallower. It would still kind of be like the peak, the top sort of peak of that gsy response. So I would have because imagine if this is plus - 5% here. Okay, and then we're getting the plus- 1% bin.

so we'd only be seeing that little bit over there like that. So that would manifest itself. maybe in a graph which started out say at 30 here and oh, let's say 20 down at 20 here and sort of went up and peaked like that pretty quick and then roll off sort of. You know, once again, down at say, around about 20 here for argument sake.

So it would have been much flatter and we would have seen a a you know, a reasonbly large number of resistors out here at the 1% limits and that if you get the cheap one hung low resistors or something like that you buy them from, you know, off eBay and you measure them then they could very well be uh, 5% resistors tested as 1% Who knows I Don't know. maybe they don't do that anymore. Maybe it's a maybe it's a myth these days. Maybe they did it in the old days, but these days they would have targeted they.

They could Target their manufacturing processes. As you tweak them, they can get better and better. and that's what Phillips have clearly done here with these resistors. Their manufacturing processes and tolerances are obviously geared around a plus minus 5, uh, 0.5% uh, manufacturing tolerance.

So maybe they sell these resistors they target and Market them as 0.5% resistors and uh, they uh, sell those as plus - 1% because they know they're going to be well within plus - 1% And maybe when they sell them and mark them as 0.5% resistors. possibly they? you know they they lose a few, you know, percent. They might be losing 5% of their resistors out here and out here, but there you go. I I You know they're clearly targeting 0.5 per resistors.

So ultimately, what? These kind of uh manufacturing? uh, normal Gan uh response curves show it. just. it's typical, not only for resistors, but uh, you know most other components as well. You're going to get uh, this sort of manufacturing uh response.

If you know you've got a a a uh, noise floor of an opamp or something, it's going to have this same type of uh, Gausian response and what it basically represents is a probability or the probability of, uh, a particular device you buy. In this case, it's a resistor, but it could be an IC or an LED with its brightness or whatever. Um, where it's going to fall uh, within. uh, this the probability of you getting a device which Falls within this range and as you can see, the highest probability is going to be smack on zero like this and the next highest, you know, and you got a fairly good chance that you're going to fall within that, uh, plusus .1% range at least for these Phillips resistors.

Remember, this may not be the case for some cheap one hung low brand resistors or something like that. So, but your odds of getting a resistor, that's you know right out here in this case. For this particular batch, the odds of getting like a .8% resistor out here are almost bordering on zero. I'm not going to say it's not possible, but it's very, very unlikely and getting one right at the 1% limit in this particular case.

well, you know it's pretty rare. I mean we had 400 resistors? That's I Guess that's not a huge number, but uh, you know, if you maybe if you got 40,000 resistors or something, you might see a few that sort of, you know, poke their head out just just like this one did at. you know, 0.55 out here, given ultimately given enough time, Anything Uh is given enough numbers. Any probability there's no such thing as a zero probability out here, they can actually appear, but it's very unlikely.

And the other thing to remember with these Um responses is that they can shift like this and this will be in in the manufacturing environment. They will actually, uh, do plots like this. you know, either daily or weekly to track their Uh manufacturing and how it's drifting and you might see the peak actually drift back and forth as you change. Uh man, you know, various uh, you know, change materials.

You've got suppliers, you change workers who are operating the Machinery perhaps? Um, you know if it, if it requires some sort of manual process or manual intervention or something like that and you can watch your uh, you can watch your processors drift or if your temperatures changing in your manufacturing environment that can alter things and all sorts of things. So you can get really some good insights into manufacturing. uh, whether components or products or whatever it is you're manufacturing Using this frequency and analysis, it's a really good tool. So I hope you found that interesting.

There are a couple of surprises in there, but there you go. We got our Gan response exactly as we expected. and if you've got more uh, data on how they actually manufacture these things, um, these days anyway. Um, then yeah, send us the information.

I'll catch you next time. Probability distri brute. So just what is the probability? Distribute probability distribution Planes flying over got to stop filming. go figure.

Jeez you think I'm in the flight path or something instead out here in the suburbs.