Hi. Time for another fundamentals video. And I know I said in the previous one that it doesn't get much more fundamental than voltage and current sources. Well, it does.

I'm going back. Even more fundamental than this: Resistive voltage dividers, and series and parallel resistors. I know it's incredibly simple stuff, but it's important. Trust me.

If there's one bit of theory you're guaranteed to use in electronics in some form or another, it's voltage dividers, resistive voltage dividers, and there's more complex voltage dividers. When you start, you can get capacitive voltage dividers, and non-linear voltage dividers, and all sorts of stuff. Now, we're only talking about in this video: resistive voltage dividers. But they're absolutely everywhere.

So what is a resistive voltage divider? Well, in its most basic form, It's only two resistors like this. We've got an input voltage here, and an output voltage. And as per regular convention in in electronics, the input or the input voltage in this case, is on the left hand side. the output voltage is on the right.

That's just how you draw and conceive. things in electronics. stick to it. Trust me.

Anyway, it's a resistive voltage divider where the output is always some voltage less than the input, and that's it. It's incredibly simple because you're dropping voltage across this top resistor and tapping off the voltage from the lower resistor, so it's always going to be less. There is no gain in this at all, so V out has to be less than V In. So what use is that? Well, it's used in practically every aspect of electronics.

It's even on my t-shirt for goodness sake. It's used in amplifiers. It's used in, uh, attenuators. It's used in every form of voltage regulation.

and it even appears in circuits where you don't think, oh, that's not a voltage divider because it's not drawn like a voltage divider like we had our in a previous video which is actually the following video to this. I should have done the videos in order, but you know how we had our voltage source like this with our you know Rs over here and this is vs. our voltage source. This is our battery or whatever.

Well, once you go and put a load on here, it's exactly the same thing that is a voltage divider. The output is going to be less than the voltage source. So it's any sort of battery or power supply or feedback for a regulation circuit or feedback for amplifiers. And you'll find voltage dividers embedded in all sorts of chips.

Uh, to actually get a feedback signal. Because what it's used for is it to get a known precise fraction of, say, And it can be like in this case, it's an output of an amplifier here. and you can feed that back in feedback. A known fraction of that's used in comparators and all sorts of analog circuits.

It's everywhere. But first, absolutely fundamental electronics. I mean, I guarantee apart from what is a voltage and what is a resistor, I am pretty sure it's as much unless you want to get into electron current flow and all that sort of crap. It doesn't get much more simple than basic series and parallel resistors and some basic formulas you need to know.

And we've got some basic formulas for the voltage divider as well. But let's just recap because I don't think I've ever done it. Series and parallel resistors. If you've got two or more resistors in series like this, the total resistance is just all of them added up.

So it's r1 plus r2 plus R3 or however many you've got in series. that is the total resistance. Simple parallel resistors like this where they're across each other a little bit more complicated. Uh, the total resistance here is 1 over r1 plus 1 over R2 plus 1 over R3 and then one over all of that.

And then you've got a special case where you've only got two resistors, so there's no R3 like that. Okay, then you can actually use a different formula and sometimes that's some people just prefer to use this one. It's r1 times r2 over r1 plus r2 that gives your total resistance for two resistors in parallel. So that's absolutely fundamental.

And of course, V out is never going to be no load. There's no such thing as a no load source, so you're going to have another resistor across here like this. So this one's in parallel with this one, and you need to know your parallel resistance formulas to be able to then calculate voltage dividers and do other things. So yeah, learn that.

and very often you're going to use parallel resistors to actually trim resistor values because you can't always get the exact value you need in your E12 range, your E24, your E48, your E96 range, or whatever a preferred resistor value you want. You have to tweak it a little bit by putting more one or more resistors in parallel. And that brings us to some rules of thumb for parallel resistors. Uh, if you want to lower the value because putting a resistor in parallel always lowers the value, then if you want to lower the value by, say, 10 roughly.

Rule a thumb. then you use a value that's 10 times higher than uh, the one that you're using. So if you've got a 10k resistor there, then if you want to change, lower that value by about 10, you put 100k in parallel with it, and likewise for one percent and same thing for 0.1 percent. it's a thousand times, etc.

Next rule of thumb is that if you want to, uh, halve the value of your resistance, then you simply put two resistors in parallel. That's what this little Uh symbol. If you ever see these two parallel lines like that that are, usually they'll have them sloping a bit like that, then that means parallel. and even some calculators have that.

And if you want to drop your resistance value by three times, you put three of the same value in parallel, etc, etc. etc. And you can also do the inverse of this for the series as well. If you've got a value that you want to increase by say, ten percent value, then you put one tenth of the value in series with it instead of, uh, ten perce instead of ten times, you put one tenth.

And likewise, if you got, say, a 10k resistor here and you want to increase it roughly rule of thumb by one percent, then you put a 100 of the value in parallel. So if you've got 100k there and you want to increase that value by 0.1 percent, you would whack a 1k in series with and so on. Getcha Like these aren't exact values because you know, plug these numbers into these formulas and you'll find that they don't precisely work out. That's why they're called Rules of Thumb Good enough for Australia, and as is common in electronics, you often don't need to be precise.

You just need to be near enough. Even sometimes within an order of magnitude is good enough. Anyway, we're here to talk about resistive voltage dividers because they're so darn useful. I keep saying it, and trust me, they are now another formula you absolutely have to remember because I guarantee you're going to use this in all aspects of electronics.

V out here equals R2, which is the resistor that's across the V out doesn't have to be labeled r2. I'm just labeling them R1 and R2 here, so don't take that religiously. Somebody may. This one may be labeled R2 and this may be labeled R1 In that case, you need to swap them around.

Okay, so it's the output resistor here: r2 over r1 plus r2 or the total resistance here times the input voltage like this. So this actually applies to any arbitrary size network. So if you've got any arbitrarily long voltage divider like this, and you want to know, the tap across any one of these resistors doesn't have to be the bottom one down here like this Here, I've got an example of four resistors like this: If we want to know what the output voltage here is across, just R2 and you may want to do this, There's circuit configurations where this might be like you might have positive and negative supplies and you may have like a split thing happening, or you may just be tapping off some sort of differential thing or something like that. There's many reasons why you might want to do this.

Then the formula is exactly the same. It's actually R2 just so happens to be the same. But anyway, it's it's the resistor you're interested in that you're getting the output voltage across divided by the total resistance. So just add up r1 plus r2 plus R3 plus R4 That gives you r total times V in and that will give you your output voltage.

It's exactly the same for any sort of scenario, and likewise, it doesn't have to be across this bottom resistor. It can be across this top resistor up here like this. So in this case, it'll be r1 over r1 plus r2 times Vn Got it? And just so I don't have to do another video that leads us also into current dividers. Not nearly as common, but you should know this and this formula applies itself again, although with a sneaky little reversal now.

Uh, we've got our current source here and we've got I, which is I total Okay. And then we've got two different current branches like this with two resistors like this which is labeled I1 and I2. Let's say, you want to find what the current is down I1 here and you've got resistor 1 and resistor 2 here. What is the formula? Well, it looks very familiar like this: I one here equals r2 over r1 plus r2 times the total current over here.

Now you might think this looks identical, but aha, there's a sneaky difference. That's why I've put it in red. If it was exactly the same, this would be R1 on top over the total resistance here, but it's actually not. It's actually the opposite value.

So it's R2. So if you want to calculate I one down here, it's R2 and so forth. Anyway, there's some really nice uh derivations of uh, these formulas. Um, actually, and I won't bog down this video with those.

But anyway, and yes, it's not parallel because these resistors are in parallel. but it's actually plus. Hmm, that's interesting, isn't it? I'll leave that to those playing along at home to figure out why. Now, unfortunately, this current divider formula.

It only applies for the case of two parallel resistors like this. You can't extend it by. uh, like we saw before. Like being r total like this, you can't just add them up.

It's uh, it doesn't work the same way. So if you want to extend that to more resistors in parallel, then you need to go to Kirchhoff's current Laws it. This formula no longer applies like it does up here. it's just a little sneaky coincidence.

and voltage dividers actually brings us nicely back to a previous video. or is that forward because technically this is after voltage dividers in terms of theory. Anyway, brings us back to our previous video about voltage and current sources and Thevenin and Norton equivalent circuits. and I never did Actually show you how to calculate the Thevenin voltage and the thethen and the resistance here thin and say that three times quickly.

So once again, we've got some formulas to remember. so we're going to take the voltage divider here as the example. We've got a 10 volt voltage source and we've just got two 10k resistors. The voltage is the output is across The bottom resistor here.

So what is that In terms of the Thevenin equivalent circuit? In terms of just a voltage and a resistor here? Because if you remember from this previous video which I'll link in, if you haven't seen it, any combination of linear resistors and voltages and current sources can be replaced with a single voltage source and a single resistor. So that's what we can do here. This voltage divider here is going to have an equivalent circuit. as in it's a voltage source with a series resistance like this.

In this case, it's going to be a pretty poor voltage source, because ideally, of course, an ideal voltage source is the voltage source with zero series resistance. So regardless of what load you put on there, it'll always give you that voltage. But there's no such thing as an ideal voltage source. But let's calculate it.

How do you do it? It's easy. There's two simple formulas. One's not even a formula really. it's just equals the uh, feathers and voltage here is equal to V.

Open. What that means is open circuit. So the circuit here. This is our output.

So we open circuit our output so we've got no load on there. What is the voltage across there? Well, it's easy. From your voltage divider, it's obviously 5 volts, although we could go through the formula. So of course, using your standard voltage divider formula, it's r2 over r1 plus r2 times 10 volts, here, which is our source.

And of course, that gives you 0.5 times 10 which is 5 volts. So Vth our Theta then and resistance is 5 volts. What's Rth Our third and equivalent resistance. Series resistance.

Well, it's actually equal to the V open circuit that we had before. So that could be Vth divided by the short circuit current. So we take our circuit again. and we actually short circuit it like that.

So we short circuit that and calculate the current through there like that. What is it? Well, what's a short circuit across 10k? Well, it's zero. So all the current is now going to flow through the short circuit like this. and it's simply 10 volts on 10k? That's it.

Which is one milliamp. This is all just Ohm's law stuff. and Ohm's laws everywhere. So Rth equals Vth on I short circuit current.

So we've got our 5 volts here. Vth divided by our short circuit current which is 1 milliamp equals 5k. So Rth is 5k here. So our voltage divider here is equivalent to having a battery or a voltage source with a 5k series resistance.

It's absolutely equivalent. This is just not theoretical nonsense. This, This is what it would be like if you had a 5 volt battery. If you get it like seriously, go do it.

Get a 5 volt battery or a 5 volt voltage source. Uh, regular 5 volts, You've got them everywhere. And put a 5k resistor in series with it and have an experiment. And that's exactly what you'll get with a 10 volt voltage source and two 10k resistor voltage divider like this.

And of course, that's a pretty piss-poor voltage source Because as I said, you, ideally you want zero ohms in there. So really, it can only power like really high impedance, really high resistance loads like say, an Op-amp for example, which has Nafl getting towards Nafl input current. So 5k series resistance in. you know, even like a bipolar Op Amp input.

Not a problem whatsoever. This is why you'll find voltage dividers like this in all sorts of regulator circuits, switching regulators, linear regulators, and stuff like that in the feedback circuit for those circuits. I've done lots of power supply videos and you've seen that before and they can be up in you know, the hundreds of K's and things like that. Because Point: You don't want to piss away your power, do you? So you want to use particularly high value resistances, but then it can only drive really high value loads as a rule of thumb.

basically an order of magnitude or more. So if your load is like 50k for example, then you're only going to get like a 10 ish error. If it's 500k, Boom, you're only going to get a 1 error if it's 5 meg. point one percent et cetera.

And from the previous video on this, how do we actually convert from a thevenin voltage source into a Norton equivalent current source? Well, I'm glad you asked. Once again, a real simple formula. based on Ohm's law. the Norton current here I N is just equal to V T H divided by R T H.

Once again, you just short circuit that like that and calculate the current just like we did down here. We short circuited you, short circuit this like this, so it'll in this particular case, it'll be uh, 5 volts divided by 5k. so that once again, it'll be 1 milliamp. So it'll be a 1 milliamp current source here.

and Rn is equal to Rth, They're just equivalent. And likewise, if you want to go from a Norton equivalent current source back to a seven and voltage source, you just use Ohm's law in reverse. It's too easy. in this case.

Vth. Ohm's law equals in times Rn Boring, huh? But this is really powerful stuff. Feathers, and equivalent circuits and voltage dividers like this. They're used everywhere.

and you've got to be aware that they're equivalent to a like, a relatively high impedance voltage source. And if you think voltage dividers are only used for analog circuits, well think again. Although, technically all your analog fan boys are going to say digital is just like analog anyway. But anyway, in digital systems, uh, termination is a big deal in very fast memory.

like a Ddr memory. For example, you might have mid-point termination that's using voltage dividers and stuff like that. So even in the digital realm, you know you can still use these analog voltage dividers. They're everywhere.

Another place you're using voltage dividers every time you use that times: 10 oscilloscope probe. It's a voltage divider. It's quick experiment and trap for young players. Time: I've got a voltage divider.

We've got a 10k voltage source here. Power supply. We've got two One Meg resistors like this. and we've got a voltmeter over here.

And there's my one Meg resistor on the top. There's one Meg resistor on the bottom that we're measuring. It's a decade box so that I can just, you know. trim precisely.

Uh, half value. And you can go through the formula on the white board just for, uh, some practice. But of course, because they're the same value. It's of course.

uh, the. it's just 10 volts divided by two. It's half. so it's five volts.

And that's exactly what we measure. Winner, winner chicken dinner. So let's just double check that with another meter because you know you never know. Measure twice.

Cut once, is that it? Um, for what? what? 4.785 volts? What the hell is going on? I think we're going to have to use the third meter to measure it. Um, let's go like old school. Come on. This will always work.

Old school meters. Analog meters. They always work. We're on 10 volt voltage range.

Um, uh uh. that's actually just a smidgen over 1.4 volts bit of parallax error there on the mirror. What the hell's going on? Let's go back over here just to verify. And yet sure enough, Five volts.

Oh oops. If you're wondering what button I pushed there, there it is input Z, which is input impedance or input resistance. 10 meg or auto auto means basically there's no input resistance. It's really, really high.

It's Gig Ohms and you know that order of magnitude thing I was talking about on the whiteboard where if you had like one order of magnitude greater in this case 10 meg ohms input impedance of the meter, then it causes like roughly that, uh, 10 error where you have to go through the calculation, we'll go through that in a second. But and then if you have two orders of magnitude, or in this case that would be a hundred meg input impedance so you get one percent error. Or if you go up to like Gig Ohms and you have several orders of magnitude, um, then it's not really going to affect it at all. And that's why I measured 5 volts.

Because when we had that meter set to effectively infinite input impedance, it's almost as if like it's an ideal uh, multimeter, and like there's just no load on there at all. So that's why we measured precisely 5 volts. But once we switched to that 10 mega Ohm input impedance, we've now got another 10 Meg resistor across here like this. and that's what's called your meter.

Loading down is circuit under test. and for really high impedance stuff like a one mega and voltage divider, even your 10 mega ohm input resistance of your standard multimeter. Sometimes it's 11, but you know it's around about that. Then yeah, up, you can get like a like an order of like 10 percent error.

You've changed that value by 10. That's pretty huge. And when you're multimeters, you know you've got your 0.05 and accuracy multimeter. Well, it's no good when it's causing a 10 error on your circuit.

You've Kamagatsa. You might be asking why is our old-school analog meter reading so low? I mean, yeah, we've got 10 volts full scale at the moment. So 8642, it's just a smidgen over 1.4 volts there. And the interesting thing is, watch this.

If I change it from 10 volt range to 2.5 you might think it'll jump up to uh, you know, to 1.4 but it doesn't. And if we go to 1 volt range, so this is 1 volt full scale, it's now about 0.2 volts. What the? It's because of this little itty bitty thing down here. 20 000 ohms per volt Dc.

Because this is not a fixed input resistance like your regular multimeter is it's not just 10 meg Ohms. It varies with the range and it's ohms per volt. This is a trap with old-school analog meters and one of the huge reasons why digital meters took over. But of course, you can actually get uh fed analog meters that actually have active circuitry just like a digital meter.

And there it is. 10 meg. Ohms. Uh, because yeah, it's got little fets in it.

So yeah, but this needs batteries. It doesn't rely on the 50 microamps to move the meter anymore. Well, it does. But it comes from the batteries inside, not from your circuit under test.

So what? This 20 K ohms per volt means. it means that it actually takes 50 microamps of current to move that needle over full scale. And you can think of it in the current terms. But we'll think of it in terms of resistance like this.

So 20 kilos per volt? You've actually got to multiply that by the range you're on. So that's uh, 10 volts. So that's actually 200k. So effectively, we've got a 200k input resistance on this multimeter instead of 10 meg.

That's why it's reading low. So how do we measure 1.4 volts on our analog meter here? Well, it's easy. at 20 kms per volt on the 10 volt range, it's equivalent to a 200k resistor. So a 200k resistor is now in parallel with our one Meg.

There's various ways you can solve this as we've looked at in other videos, but we're going to use the formulas that we did today. First of all, we work out the parallel resistance values. So using our parallel resistance formula we saw earlier, we'll use the one over version instead of the other one. Then we've got 200k invert plus one meg invert equals and then invert all of that 166.6 k.

So that's the bottom resistor. Now we have to work out our voltage divider. It's one meg and 166.6 k. So remember our voltage divider formula.

so 166.6 k divided by one. I can add these up here: 1.1666 meg. Like that times 10 tada 1.428 volts. We measured just a smidgen over 1.4 because the analog meter is not that precise.

There you go. That's why we measured 1.4 circuit loading of your test instrument. Classic trap for young players, especially in high impedance circuits. And you can actually use a second meter to measure the input impedance of our Bm786 over here.

And you can see it's about 11.1 meg and that changes depending on the circuit design of the meter. but they're all you know roughly around that 10 11 meg. Uh, value for a standard digital meter. Unless you've got a high input impedance meter Uh, which.

Usually you'll only get that on like the millivolt, the lower ranges like the millivolts, and maybe if you're lucky in into the lower voltage ranges. So there you go as some homework. I want you to repeat that for 11.1 meg, input impedance, and of the Bm-786 I guarantee you'll work out roughly 4.78 volts. So there you have it.

that's voltage dividers. And I know this is normally like one page in a textbook. They'll just throw these formulas at you and that's it. But they're important to know because they're in practically every aspect of electronics.

I guarantee there's a lot of stuff a lot of theory you learn in electronics that you may not touch for your entire career. In fact, probably like the majority of it, you may not touch. But like, voltage dividers are there absolutely everywhere. Yeah, just try and use your oscilloscope with your Times 10 probe without knowing about voltage dividers.

Anyway, I hope you enjoyed that video and found it useful. If you did, please give it a big thumbs up. As always, Discuss down below. catch you next time you.