Hi welcome to another Fundamentals building-block video today. We're gonna take a look at the capacitance multiplier and it's name is a little bit weird, but we'll get into why it's called that shortly and this is a bit of a follow-on to my previous video which are linking down below and at the end about the Seven Double Six Zero Voltage inverter which we looked at which had we talked about the output ripple of such a voltage inverter. So let's take a look at ripple pattern like typical power supplies and how to get rid of it because using a capacitance multiplier. So what are the ways you can do it that's really effective.

It's better than a voltage regulator. so let's take a look at a couple of scenarios where you might get ripple. Now you might have say a mains transformer like this. You might go into a bridge rectifier like this.

of course you're familiar with this and then you may have an output capacitor like this of course and you're going to get some like ripple on there and this is very common. For example, if you're building an audio amplifier for example, you want to generate you know, positive and negative rails and you want them to be really clean, especially for like class-a amplifiers and stuff like that. So really you know you want to get rid of that sort of repoint. You can increase the capacitance and to do that, but really, you might want to add some post regulation to that, another one might be.

Well, you've just got a DC to DC converter like this, so you've got just a positive voltage in and you might have either a higher if it's a boost converter or a lower voltage output like this. so you know this is like V out. and once again, you may add some more capacitance onto that. but you're gonna get some.

You know, high frequency ripple out because these things typically might be, you know, tens of kilohertz, hundreds of kilohertz, even up into the megahertz region. But you're going to get you know, tens of millions might be typical, or even hundreds of millivolts ripple. Or as per the previous video, the classic Seven Double Six Oh Charge pump. Our converter which basically you know has are some charge which switches in capacitors in there.

And of course you have an output capacitance like this. So you've got V+ going in and you've got V out like this. but once again, it's gonna have some ripple on it and it can be quite high. Commit: Tens of millions might be reasonably low for a charge pump converter like this, for example, or as we saw before, it could even be a couple of hundred millivolts.

You know can really ruin your day, especially if you're actually using this seven Double 600 to go from say, plus 5 volts to minus 5 volts. You're inverting that rail so that you can power your Op amp from plus 5 and minus 5 volts like that, having a 5 volt rail is fine. but if you've got a couple hundred millivolts or even tens and milli volts ripple, It's not very good ripple, but that's ripple on your rail, then that can really ruin your day. So you want to clean up ripple in, you know, any of these sorts of cases, or you know other cases as well.

How do you do that? Well, typically you might just go. Well, that's easy. Dave Oh, just whack in a regulator so you know you might have your minus 5 volts here. and you might say have a minus 4 volt regulator There Just a low dropout regulator that'll be super clean right under your problems.

Ah, as it turns out, your voltage regulators, which are used everywhere to give you what like a supposedly clean regulated hence their name regulated output voltage are actually quite poor at attenuating large amounts of input ripple. Yes, they regulate well. It'll give you your precise minus 4 volts or 3.3 volts or whatever voltage you actually are set your regulator to. But if you've got tens or hundreds of millivolts of input ripple that you're trying to get rid of, how do is can be a poor way to do it because the amount of attenuation of the ripple from input to output depends on not only the type of regulator, it depends on the input to output or the dropout voltage of the regulator.

As you get lower, it can potentially get worse. Here's a graph which can show you a typical of that and it depends on the amount of current on the output as well. The high the output current, the, the less effective in the regulator's going to be and actually attenuating in the ripple. If you don't believe me, if you don't believe it's actually a problem, let's go to the bench.

I'll show you let's have a look at a typical audio regulator. In this case, I've got a little sock 23 microchip MCP 1700 It's a 3.3 volt low dropout regulator. I've just got an input filter cap and input, an output filter cap and no load. But let's actually see what happens if we add some ripple like a lot of ripple to the input here.

Let's actually add a 500 millivolts of ripple, right? Look, what happens to the output? This is 10 millivolts per division. That ripple is coming through to the output like that. But look what happens if we add a little load 270 ohm resister on there. So it's about low.

and what's that about? 13 milliamps or something like that? Look at the amount of ripple on here. Check that out. It's absolutely terrible. We're at 10 millivolts per division.

10 20, 30, 40, 50 60 millivolts peak to peak for 500 millivolts ripple input. It's not doing a very good job is it? And check it out if we AC couple both channels, the regulator's still regulating by the way. Still given 3.3 volts out 50 millivolts per division input ripple. Here at three hundred and thirty-odd milli volts, the output ripple in green is almost the same.

There's virtually no attenuation of that ripple at all. At 10 kilohertz, it's hopeless. So as I demonstrate on the bench. voltage regulators, which are otherwise great for typical applications, are really not very good at getting rid of high amounts of ripple, especially at higher frequencies and high/low Just saw it.

even it like you know the milli amp level tens of million player which is not a very big load if you take the example of the Op Amp that I gave before. Well, they can take a couple of milliamps easily. So just a generating a negative voltage rail for an Op amp, especially from a charge pump like this that can have you know tens or hundreds of millivolts of ripple. and you really want a low amount of ripple on your rail for whatever particular reason it is.

and there's gonna be a whole dozens of different scenarios. Low ripple is good. Like ripples. generally a good thing.

You generally don't want it, but in some cases it's critical. You want to get rid of it. The voltage regulator just doesn't do it. Enter the capacitance multiplier.

So let's just consider all these are scenarios the same. We've just got ripple, and we want to get rid of it. What's the easiest way to get rid of ripple? Well, that's easy. You have a resistor and you have a capacitor like this.

so this is in and this is out. And depending on the value of the R and the C, the larger you make the capacitance, the more ripple rejection you're going to get. It's going to attenuate your ripple even if you take the case of like a low value resistor low ish, like a hundred ohms for example. even with a small amount of current on the output 10 milliamps, you kind of get a 1 volt drop across that resistor.

At 10 milliamps, that's not terrific, especially if you're you know you're generating a negative 5 volt rail. and you need say, a negative. You know, almost near negative 5 volt rail, an output, or even negative 4. You only get a lousy 10 milliamps there.

and even with that low value of resistor, the lower value of resistor you go. So as you decrease the resistor value, you have to increase your capacitance value often to absurdly high values to get the ripple rejection that you actually want. And of course, you can add a second stage on here. For example, you could add another hundred R.

You can add another one, and that works, but you've doubled your amount of voltage drop across there for a given current. And as you can see a typical RC filter, even a multi-stage one is not very effective at all. For anything but ridiculously low currents, Pretty much so. One scenario where an RC filter like this or a two-stage RC filter is fine is if you've got say, a pulse width modulator and your you want to actually generate a DC voltage from that, well this is typically going to go into an Op-amp over here like this and the input impedance.

The Op-amp is very high so you're drawing no occurrence. so it's not really a problem so you can use. You know reasonable values of you know, tens, It, You know, 10 microfarad, a couple of mic in there, and you know hundreds of ohms or 1k resistor or something like that and you can filter out your pulse width modulator down to like bugger-all values. That's fine, but we want to actually do this for you know, tens of millions, hundreds of millions even like in the case of like, several amps for a big audio amplifier for example.

So how do we do this? Yeah, we can lower our resistor value down to one ohm or something like that. but then the capacitor has to be so ridiculously high in value up to the like Farad's range that when you are driving large output currents, that it really becomes completely impractical. So what if we could multiply the capacitance? What if we could use a small capacitor value and somehow multiply it to make it appear bigger? Hmm, we can do that. Let's take a look.

We can actually use the same trick you can use with voltage regulators when your regulator just doesn't have enough current capability, you can put in what's called a series pass transistor on top of that I'm sure I've mentioned that in a video somewhere so we can do the same thing here. We can actually go like this and go into a transistor NPN in this particular case and have it like that and bingo This can be our the out like this and we can get large amounts of current that bypass this resistor like this and we can use a smaller value of capacitor here and you might have noticed this as is a you classic transistor building block circuit. the emitter follower because the output is on the emitter of the transistor like that. So basically what that does is any voltage here is matched on the output.

Here it's an emitter follower. It just follows this value. and because the input current of the transistor like this is relatively small because a transistor has current guy oK you've got a smaller smaller amount of current flowing through this resistor. It's not zero because it's a BJT It's a Bipolar Junction transistor.

It needs some base current, but it has a gain. That transistor has a multiplying gain that multiplies the base current to give you a higher collector current. and that's where the multiplier comes in here. As it turns out, this simple configuration which is basically an RC filter with an emitter follower is what's called a capacitance multiplier and some people don't call it that.

It's just basically an RC filter which is a building block of its own combined with a series pass transistor like this which is again a building block topology circuit of its own. So you combine those two and it in effect the capacitance value see here. It gives you an effective capacitance value of not just the C but C times beta which is the gain of the transistor hence the name multiplier. So the amount of ripple that you get on the output here is equivalent to a capacitance value which is the value you use.

It's let's say it's 1 microfarad times the gain of the transistor, which might be a hundred. So you have an equivalent of a hundred microfarads here. That's not a good example because Haley you can just whack out. A hundred microfarads isn't very big, you could whack it in there, but you can see that when you get to large amounts of current, it can be a really huge benefit.

So if this capacitance multiplier, you can use relatively large values of resistor like this. You can use you know, in the order of kilo ohms, tens of kilo ohms. and you know relatively reasonable values of capacitance. And again, you could actually put in a second stage there too.

if you are really, you know a multiple stage one as well. Now of course you've only got the capacitance times the beta of the transistor. If you use a single bulb bipolar Junction transistor they know particularly have high current gain. So yes, you guessed it, you can actually use once again, another classic building block, which is the Darlington pair.

Whoop like this. There you go. That's a Darlington transistor you could ever use like two separate transistors because you might have your favorite big high current pass transistor here for example, and just a smaller signal one over here to feed in the base. and your Darlington pair actually has a much higher gain.

so your capacitance multiplied effect is even bigger. So you can effectively have you know many Farad's of capacitance here easily. Like, you know, a Darlington pair might have a gain of a thousand or something like that. You can really ramp things up in this sort of scenario so you can really reduce your ripple tip almost negligible levels like half Abby's dick.

But hey, you still might not want to use a BJT because you don't have enough gain. You know you really want a small value of capacitance here. and really, this resistor can't be too high. Otherwise, it can now starve the base current even of a Darlington pair like this.

So you know, if you want really small values of capacitance, large values, a resistor, you guessed it, you can get rid of that and you can use a MOSFET like this. No workers whatsoever, but using a MOSFET you might have like a larger voltage drop or that. It depends on what part you choosing and things like that. But it means because it's a MOSFET There is no gate.

In this particular case, it's not a gate. It's not a base. it's a gate. You've got no I get current here.

So this value of resistor can be as high as you want. And that means you can use really seriously low values of capacitance to get your attenuation. And just like a regular Darlington transistor, you could replace it with a slick high pair. Here it's called which is a compound transistor and I won't go into the advantages and disadvantages between those.

Maybe that could be another video. but basically you can even use a single BJT a Darlington configuration BJT Alaka'i pair or a mosfet configuration transistor. But it works basically the same thing. The capacitance value gets multiplied by the transistor gain and you can reduce your ripple to practically nothing.

It's awesome. So I know what you're thinking. Well, if this capacitance multiplier is so magic, why don't they just build rank voltage regulators like this? Well, you might notice here that there's no regulator element. There's no feedback coming back.

There's no feedback loop which maintains a regulated voltage. so this is not a regulator. The output voltage will change with the input voltage and then I'll change with like temperature of the transistor and or you know sorts of things if you're dealing with high power and stuff like that. Basically it's only use if you want to get rid of Ripple.

It's not good for regulation so you could get could use this circuit to get rid of the ripple and then use a voltage regulator on the output of that. That's a winner, but this to use as a voltage regulator doesn't really work. It's not the job of a capacitance multiplier, so that's pretty cool. Let's go with some fun on the bench, see what happens.

Let's build up our capacitor multiplier. We've got a BD one, three seven power here. fairly typical, sort of, you know, old-school power transistor. not particularly high gain.

anywhere from like 25 up to a hundred ish. I've actually measured it at a hundred and we'll do that in a minute. But there you go. Just an NPN power transistor, a 1k resistor here for our and the C capacitance here is 470 micro farad and we've got our 270 ohm load.

So as before, we've got about four point two ish faults for where three volts our DC in here with a 500 milli volt peak-to-peak 10 kilohertz signal superimposed on that or ripple. So 10 kilohertz ripple at a fairly horrible 500 millivolts. And here's our output. It is supposed to be a green waveform, but it's got cursors on it I'm so it looks yellow, but there's our output.

nice and clean. Look at that. and if we actually go over here and switch it to ACE and we go right down. Oh, we have to 500 micro volts per division.

look at that. it's still there. but Wow it's attenuated a lot. and that's just with a standard non Darlington transistor.

We know we're no chicken dinner, but if we go back to our DC coupling, we're getting about a 3.3 volts output there. You can see that there's roughly about one volt drop due to the pass transistor there, but as I mentioned, it's not regulated. So if we change your offset voltage like this, look our output changes like that. So it is not a regulator.

it's just to get rid of your ripple and the voltage drop here is going to be dependent upon your load that you've got. It's going to be dependent upon your base resistor, the type of transistor that you've got, and the gain as well. So it's you know it just happens to be around about a volt drop in this particular case. And if we change our base resistor here, or a filter resistor from 1k to 10k, for example, we'll find there you go.

We've now got a larger drop like that, but of course, our corresponding AC ripple should go right down like that. but we're basically just down in the noise now. Yeah, there's a lot of noise due to all sorts of crap, but you can see that. there's basically no ripple that we had there when we had our 1k resistor in there.

There you go. There's our 1k resistor and you can see that, so it's a trade off as you increase of the resistor. R Here, it starves the transistor of base current. Therefore, you get a larger voltage drop across the pass transistor.

but you increase the ripple attenuation due to the just the RC filter ratio. And if we go down really wrote low to a hundred Hertz ripple. Here, you see, we're 2 millivolts per division. It's still not much ripple, but of course you can see it actually coming through.

So once again, we're back at the 1k resistor there. So if we really even wanted to knock out the 2 millivolts peak to peak ripple here a hundred Hertz then we could change our single transistor to a Darlington pair for example, that would have higher gain. and then we could use a larger value of resistor for a given capacitance and then filter it out that way. Or we could increase the capacitor value.

But we've already got a pretty large 470 micro farad in there, so you wouldn't want to go much larger than that unless you had like a big audio amplifier. You had plenty of room and all that sort of jazz. But here's a little twist at the end. let's actually confirm that we can actually get a capacitor multiplier in quote marks.

Does it actually multiply this capacitance here C by the gain of this transistor which I'm going to say is a hundred and I've actually measured it as a hundred? Well let's have a look the the free, the cutoff frequency, the minus 3db frequencies should know it's one of the basic Our formulas: 1 over 2 Pi RC that's for your RC filter. So for 1k that we've got in circuit and I've changed the capacitor. Now down to a hundred nano farad here. So for 1k and 100 nano ferrets, our cutoff frequency should be one point Five nine kilohertz so should be 3 DB down at that frequency.

But because we have a beta or gain of this transistor of a hundred, so we should actually get a cutoff frequency of one kilohertz and equivalent to a hundred times that 10 nano farad or 10 microfarads, our cutoff frequency should be fifteen Point Nine Hertz Well what do we get? Let's actually turn it on. Look I've got my input signal here. My input peak to peak ripple is for 70 millivolts. I've got it at 1.59 kilohertz here, so it should be way below that, right? Because if it is actually a multiplier and it's equivalent to 10 microfarads, our cutoff frequency should be fifteen point Nine Hertz So we should get hardly any ripple at all.

What do we get? Turn it on? What? What? What? Wha? about 310 millivolts Or around about that one point three and one point five, nine kilohertz frequency? Our minus three P points. So it's 470 times, not 0.707 which is about 330 going to be near enough because we don't have much resolution in there. so it's the end tolerance in the components. Of course, the minus 3db frequency is not this expected molten capacitor multiplier.

It's exactly the same formula as the RC circuit. Why is it so well? As it turns out, this is why a lot of people don't like the name capacitor Multiplier because it doesn't actually multiply this capacitance. It's not really 10 microfarads in terms of filtering like this. What it does is actually reduce the current through this resistor and hence the current that the capacitor has to smooth out by a hundred times.

So instead of having the the hole low that we got there about 1213 milliamps or whatever it is flowing through this resistor, here, we've got a hundred times less than that. or about, you know, a couple of hundred micro amps flowing through this resistor. But in terms of calculating your cutoff frequency, the formula is actually the same as it is for a normal RC filter. It's just that the currents are reduced.

The capacitor isn't actually multiplied, but I guess it depends on how you want to look at it. Yeah, but as far as calculating the frequency not, it's exactly the same. So capacitor multiplier near you either like that name or you don't. So if we actually measure some of the voltages in here, we can actually find the gain of this transistor.

Let's just you know, not be too precise. But across our 270 ohm load resistor here, we've got about three point four volts or so that's about. You know, twelve and a half millions through this load, and that twelve and a half millions is coming through the series pass transistor here. And if we measure across our 1k resistor there, it was about 0.12 volts are about 100 20 millivolts or thereabouts.

So therefore, our 12 milliamps divided by 120. That gives us a gain of about a hundred on our transistor here, which would be fairly typical. And of course, if we put that into a Darlington pair, we might get you know an order of magnitude increase in that gain. So we might get a thousand times instead of a hundred times for example.

And of course, this is all going to be dependent upon the actual components used and you know, and the output load current as well. It's going to vary. Any datasheet for a power transistor will tell you that the gain varies with your collector currents, but the good thing is is that we can just demonstrate that we can really reduce the ripple to, you know, basically negligible levels using this capacitor multiplier circuit, or an RC filter with a series pass transistor, whatever you want to call it. And just for completeness, there is actually a variation in the capacitance multiplier that actually uses an Op-amp instead of the series pass transistor and it basically works the same way.

But the thing with that is is that the Op-amp can only drive a certain amount of current. There might be more stability like type issues and also you're going to be a game bandwidth limited as well, so it's not a terrific solution. It's not designed for power applications like you get with a series pass transistor, so I hope you found that video interesting. If you did, please give it a big thumbs up.

And as always you can discuss in the comments down below or over on Eevblog Comm and thanks to all my patrons, over on Patreon.com always linked in in the comments down below. They often get to see videos early before everyone else. Thanks! Catch you next time you.