Hi welcome to Fundamentals Friday What if I told you that this piece of one-ounce copper clad board was exactly the same end-to-end resistance as this piece here. or I can go one further and say that this monster sheet of copper clad once again, one ounce. it's green because it's got a positive pre photo resist coated on it. But what if I said that's exactly the same resistance as this tiny little piece.

Exactly the same one ounce copper. It called me crazy, right? But no, not, really. hang around and I'll explain what I'm talking about why this is true and I'll demonstrate it now. This topic comes up because of a previous video I did on precision thin film resistor networks, which I'll link in down below if you haven't seen it.

I Sort of made the throwaway comment in that video that one piece of resistive material bit copper or nichrome or anything else which I'll explain is exactly the same resistance. it might be one milli ohm for example as a much larger piece if they're both squares like this, and this confused a lot of people. So what they do with these precision thin film resistor networks? they've got a ceramic base and they might coat them with, say, a Nichrome material which has a relatively high resistance per area. It might be 100 ohms per square for example, and this is how they create them.

They put the a film of the material on there and then they might laser cut like that certain areas out to increase the resistance and trim it to the exact resistance and that you require. and this is actually the same method that they use to make your thin film. Oh 805 you know Oh 603 resistors The SMD resistors that you're familiar with and exactly the same property regardless of whether or not it's Nichrome or whether it's just a regular copper clad. PCB It's exactly the same in that no matter how big the square of copper or nichrome is, it's going to be exactly the same resistance regardless of the size.

So this brings up a really interest property called sheet resistance. And it's units are Ohms per square knot, Ohms per square meter, or Ohms per square centimetre or other area. There is no area unit on it, it's just ohms per square and copper clad PCB will have a figure four Ohms per square. Your Nichrome will have a figure 4.

Ohm is per square and pretty much any material which has a uniform thickness like this. be a copper clad or whether or not it's a 3d solid body. It can also have that so it's just as long as you got a uniform thickness on the material. You can talk in terms of sheet resistance.

So if we take a look at a piece of resistive material in this case copper clad which we'll work with, then of course we have a length, a width, and a thickness. It's one ounce copper, about 35 microns or there abouts universal thickness. Now the resistance of this piece of copper, or whatever material it is, is the resistivity. Which is that's not a P.

it's the symbol Rho and that's the material resistivity. Each material will have its own resistivity figure and we'll take a look at that and then it's multiplied by the length divided by the area. Now, of course, the area is length on width times thickness. That's the area.

Now if we take that formula and we just rearrange it a little bit, but it's still exactly the same just to make it a little bit clearer, you'll see why in a second. So it's ro on thickness times the length, on the width and you'll notice this here because now it's now separate term. What is the length and the width are the same ie. a square that we were talking about here.

Well, that becomes 1. so it's multiplied by 1. So all we're left with in the case of a square and the resistance is only determined by Rho on the thickness. It's got nothing to do with how big this square is.

Doesn't matter if it's that big or if it's that big like that, it's still one. The only thing that matters is the thickness. And it's not just a square either. If you had a small rectangle like that which was say, like two squares joined and you had another one there which was exactly the same, it's the same thing.

It's just a different ratio there, instead of being one, it's something else. No matter how big the rectangle is, the resistance is gonna stay exactly the same. But I know what you're thinking. Dave That doesn't make sense I Know for a fact that if I have a longer trace, I'm gonna get more resistance.

What the hell's going on here? And well I haven't lied to you. This is actually true. The resistance of this smaller one is exactly the same resistance of this bigger one, but there's a catch. It all has to do with how you connect to it.

Now in this case, sheet resistance and the examples we're talking about here assume that you connect across the entire length light of the end like that, from one side to the other. If you just solder a wire on there and a wire on there like that, all bets are off. This theory does well. it.

the theory still works, but it's You have to calculate it differently. So if you physically connect, like have one big long contact strip across there and across there, then and here and here, then trust me and we'll measure it in a minute. This resistance of this bigger one will be exactly the same as that one. That's what sheet resistance is all about and why.

it's a unit without a dimensional area. It's just units our owns per square. It doesn't matter how big the square is, and that's why it's actually quite relevant to these thin-film resistor networks here. Because if you've seen the previous video, take a look.

I might include a photo a screenshot. Here they'll have like a big conductive piece on there that connects to the pin, which overlays onto the much higher resistance resistive nichrome material so that you do effectively yet. I You know, a big connection point on the one end. It's not just like a single wire point connecting usually, and it's even more appropriate with your standard thin film resistor networks as well because they'll have like a bulk connection on one end like that.

and then you might have your little laser trim cut in there something like that to trim the value. but you're connecting across. you know, the entire end piece of that resistive material. So what door comes down to, and how you can analyze sheet resistances like this and think about it is in terms of squares.

So if you just got a single square like this, then our ratio is 1 here that. but if you put two squares like this in series effectively, then of course you've got to double your resistance. Put a third square over here. make your trace, making a copper PCB trace longer then you get a longer resistance again and again.

If we were just adding things up like that, it's all about the connection point. Remember, a solid connection point at the end, but what if it was just a single connection point like this? Well, then, yeah. then you start getting into the fact that okay, you got a square here, a square here, and all the way along there. But then you've got squares in parallel up here like this and you can can kind of divide it up Or you can say okay, I've got a big square like this and then I've got other ones and it gets a bit tricky.

So yes, if you've got a just a single connection, a point like that instead of the entire edge, then of course, yes, you're going to have all those extra little squares. However, you want to sort of break it up and figure it out and sort of guesstimate it based on square areas. Then yeah, of course your resistance is going to lower because you've got all these extra squares in parallel, and it just becomes a different geometrical problem than the one of that we've been talking about about a single square piece of copper. But that's really essentially how it works with.

you know your SMD resistors, how they trim them, and your thin film resistor networks. You know you can say okay, we've got a big square there, and we might say we're going to square there and a square there and it just becomes a real difficult geometrical problem based on squares and things like that. But that's generally how you can think about it and the whole aspect why it's called ohms per Square. So you'll analyze this based on a square, which is a dimensionless quantity.

It's just a square, doesn't matter how big or how small it is. So just to complete this, what is the sheet resistance of typical one ounce copper clad PCB material? I'm glad you asked. Let's take a quick look at it. It is row on the thickness.

Remember so our sheet resistance of typical one ounce copper is the mid row. The material resistivity of copper is 1.7 times 10 to the minus 8 Ohm Meters. That's Ohm Meters, not owns per meter. Ohm Meters is the units of resistivity of a material, whether copper or anything else.

and we divide that by a 1 ounce. Copper clad board is around about 35 microns thickness and that comes out to 0.5 milliampere. not per square meter, Not per square centimeter per square like that. Doesn't matter how big it is, remember, But there's one very important point to be made here is that this sheet resistance.

Ohms per square does not change. It never changes. regardless of what shape. You can have a weird and wonderful shape.

No matter how many laser cuts you put in there in your fin field, it doesn't matter. The sheet resistance is a constant for that particular material and thickness and everything else. It doesn't change. All you're doing is changing your electrical resistance between one end and the other for your practical purpose.

And the mathematicians out there can get really excited about this sort of stuff. and you can prove that how you add up the squares and everything and it's always going to come back to the exact same ohms per square figure. And there's all sorts of mathematical proofs. Go for your life! So I know what you're thinking.

Dave I Still don't believe it. Show us some measurements. Ok, let's go to the bench and prove that this theory is actually true now. I would love to show you how this works on a piece of copper-clad board, but unfortunately that's not going to be easy.

because as you saw, 0.5 millions are you. 500 micro ohms per square and trying to get a some sort of contact probe which probes along all the ends like that of the thing are down in the micro ohm region is just. it's just not practical. So unfortunately we're going to have to use something else now.

I'd love to use like a sheet of Nichrome for example. what they're using those thin film resistor networks at like a hundred ohms per square that'd be really controlled and that would be really nice. unfortunately. I don't have something like that, but what I do have is today a conductive anesthetic mat.

You've seen these you plug your eye see is this high-density foam that you can get and these. It's not going to be a hugely controlled resistance across here across the material. this is. You know it's reasonably thick, but as I said, it doesn't matter about the thickness, as long as it's a uniform thickness across there.

Anyway, this will have a much higher resistance. you know, tens of K hundreds of K that sort of thing. So we should be older. Use this as to get some ballpark measurements and prove this thing.

So to do this experiment, what I've got is some conductive foam I got from JK I Have no idea what the sheet resistance of this stuff is. don't have a datasheet forward or anything I cut these from exactly the same larger sheet so they're all identical. and I've got two copper clad plates which allow me to get the contact along the full edge like that. And of course, it doesn't matter if it's longer than that, it's no problem.

You just have to contact along the entire edge like that as I as we saw on the white board. and then we just kind of measure the resistance. Let's try it now. the size of these squares doesn't really matter, but hey, each one is about a quarter of the size than the one before it, so let's give that a bill.

Okay, I've got my meter on a fixed range here the 50 K ohm range and let's put these plates on now. Unfortunately, the resistance is going to vary depending on the amount of pressure I put on. That's just a function of the you know, the material and the contact area and things like that. and no, my hands aren't touching sorry I'll get out of shot there.

and basically what I'll do is I'll apply a large amount of pressure on there and get sort of a minimum value. So I'll put like maximum pressure on all of them and I'm getting around about five K there. I'm going to take that as safe five K right? So that's about as higher pressure as I can get. I'll get my smaller one here and let's see if it's the same it should be if I apply even pressure because you've got to have that even contact.

Bingo There it is. There's yeah, there's your five odd they should. five odd K I know it's bouncing around and I people will complain that Art's not control test. It's as good as I can do here.

Now let's put in the smaller one and oh, because we've got to make contact over the whole area. Bingo, look at that. Where are still around about that five K figure with even pressure on all those. So today, we've essentially proven and demonstrated there that the sheet resistance the Ohms per square knot, square millimetre knot, square metre knot, square furlong ohms per square of this material is you're not determined by the site, they're physical size, and of course, you'd get exactly the same result will be at a copper clad board regardless of how thick it is, a solid piece of copper or some other metal or anything else.

And of course, you have to contact the entire edge of that thing you can't just like, like go on there, like at an angle on the top, like that. it's not going to work. so you have to get the entire if it's a bulk material like that on the entire thing. So the thinner it gets, down to the level where it's you know, like 35 microns thick on a PCB copper clad like this? Then basically you can just put like a contact on the edge, but of course copper.

This is so incredibly low resistance and then you have to do proper four-term on a measurement across the entire edge. Oh, it's just a nice, but this conductive foam demonstrates it rather nicely. And it it's not like a close analogy or anything like that. It is exactly the same thing as copper clad on Nichrome or any other material whatsoever.

It's just that. Yeah, this is not hugely controlled, but it was good enough to see that you know if you expect something higher. if I chop that in 1/4 again, we'll get exactly the same result. Heck, let's do that.

Here we go. We got a tiny tiny little piece in there like that, and let's there we go. It's still around about that 5k figure depends on the pressure and things like that, so you would expect that to increase Based on, you know, before you knew about sheet resistance, you would think this would be much larger resistance then this massive sheet here. But it's not.

It's ohms per square and if you don't believe me that it adds up well. I've cut that square in half with slightly wonky. but anyway, it's good enough. This should only give us 10.

There we go, got ourselves 10 I can get it I can't get it much lower than that. Look, it's double it is. It has increased double or an ounce starting to bend and it's getting a bit tricky. but you saw it and if we do three times the length there we go, there's that.

Well, there's our 15 odd K So just think about the sheet resistance next time you're calculating the resistance of a PCB trace. For example, because this is not just theoretical mumbo-jumbo it has real-world practical applications. If you've got a PCB trace like this, you are actually going to have pretty much an end-to-end connection. like the entire edge on here in the entire edge.

Over here because imagine this is a little tiny. You know, tenth hour trace or whatever going into a surface mount components in a surface mount component that end. Then you you know you're basically touching the entire edge. so you can divide this up into squares 1, 2, 3, 4, or however many squares lengths.

So you know the sheet resistance of 1 ounce copper. you can say it's like a rule of thumb, it's gonna be pretty darn precisely close to it. Actually a point 5 million per square. Just count up the number of squares you got.

You can calculate the length of your trace brilliant And that will apply to copper or any other material which has its sheet resistance if I'd So I hope you found that Fundamentals Friday useful. A lot of people don't know about she resisting because it's a little bit counterintuitive to what they're used to. but it's a real thing and it's how materials like the nichrome forms and and copper clad PCB and other stuff actually are specified. So there you go.

If you liked it, please give it a big thumbs up because that always helps a lot. And if you want discuss it, jumping over to the EEV blog forum or leave Youtube or blog comments. Catch you next time you.