Hi. I recently shot this video as part of another video, which I'll link in up here and down below if you haven't seen it. where I do, uh, in-circuit capacitance measurements with an Lcr meter and I thought I'd do an interlude of how Lcr meters work. so I go through the whole theory of it ended up being 20 minutes long, so I decided to split it out as a second video and that's what you're seeing now, but it's related to the other bench video so you really have to watch them both anyway.

just pretend this is a standalone video and then go watch the other one. Let's go for a brief interlude to the whiteboard to see how Lcr meters actually work, because this will explain everything that we're seeing here and it's really cool to know and really to properly, uh, use your Lcr meter. You really should understand the fundamental concepts of how they work. So your Lcr meter is nothing more than an Ac signal source.

Here, that's the test frequency We've got usually 100 hertz, 120 hertz because that weird American rubbish. One kilohertz, 10 kilohertz, 100 kilohertz. they can go higher, but they're the general steps in any sort of Lcr meter that you're typically, uh, going to use and then that will have a particular test voltage. It could be like one volt Rms, for example.

We'll get into this later because that's also one of the traps for young players. Stick around so that say, 1 volt Rms signal at whatever frequency you select goes through a series range resistor like this and of course that goes off and they measure the voltage and current across that range resistor. And that you saw how just before how our capacitance meter actually changed ranges gave us less resolution, less digits when we actually switched frequency. that's because of range resistor limitations and then it goes directly on the test terminals.

and then we've got our device under test. So we're going to call that X dot. there dot is the industry term for device under test, And then of course, the instrument can measure the voltage across the load as well as the voltage across the range resistor. and it can also measure the current I as well, which will be the same for both.

Now here's the trick. We have to start talking about phase angles and complex numbers, which we've coincidentally just looked at in the recent Ac Fundamentals tutorial series linked up here and down below. If you haven't seen it, highly recommend it. Otherwise, you may not understand what we're talking about when we start talking about Js down here.

So the sneaky thing your Lcr meter does is it measures both the voltage and current at zero degrees phase angle and 90 degrees phase angle like this with reference to your reference waveform, which is your signal generator over here. So if you've got your signal gen like this, so the signal generator is the reference and then you'll measure it at this point here and also this point here as well on the waveform. So what they do is they measure the voltage and current at this reference point, time here, on the waveform, and then at 90 degrees here as well. So this is a kind of a weird graph because we've got voltage on this axis and also voltage on this axis.

But you can see that it's a phasor diagram in that it has a phase angle in there. so this just represents that voltage that you're measuring at 90 degrees there. And by measuring the voltage, of course, you can also measure the current because you've got a pure range resistor. And as we've talked about in previous videos, if you're just measuring a resistor a pure resistor, then your phase angles are all going to be zero Like this because there's no reactive components at all.

A resistor. A pure resistor is not reactive, but then you might have some inductance in the test leads as we saw before, but when we actually switched those test leads over, it made a difference. But in theory, if you're measuring a pure resistive load here, then you wouldn't have any phase angle on your voltages and your currents. They'd all be in phase.

so we just have to apply some arbitrary labels here. Uh, our voltage. Uh, Phasor Like this. You drop it down like this and this gives you.

you will call it Vp. That's your voltage at zero degrees phase angle. You could call it V0 if you wanted and then likewise with your current. Here you measure the current, which is the voltage across the range resistor there.

Then you drop that down and that will be your current at zero degrees phase angle. We'll call that Ip and then we'll do the same at 90 degrees. We'll take a measurement at 90 and instantaneous measurement at 90 degrees and that will give us our voltage in at 90 degrees, which we'll call Vq and the current. Iq and I have that arrow back to front.

and then we can use these two equations here, which you don't have to know. Don't bother remembering, it doesn't matter, I'm just putting there. For completeness, we can get values for the equivalent circuit which we're going to turn our device into. Our device becomes an equivalent circuit with a series resistor we'll call Rs and a series reactance, which is why we have to call it x X is reactants.

Remember, we have no idea whether this is a pure capacitor, a pure inductor, a dodgy capacitor, a dodgy inductor, or a pure resistor or whatever. We don't know. It depends on the phase angles that we've actually got here for the voltage and current. So we're now talking about.

instead of capacitance and inductors, we're talking about reactances. So these two formulas here will give you the value for Rs, which is your pure resistance. You always have a resistance in series with any Uh component. It can be zero, ideally, but uh, right.

it's we have a series resistance and then a reactance value. And that's they're calculated slightly differently. You'll see that these are slightly swapped around here, but as I said, doesn't matter. We measure these things and we calculate an equivalent circuit.

And the cool thing is from that equivalent circuit, we can calculate everything else that our Lcr meter measures. Now, if you watch my Ac Fundamentals series, you'll know all about complex planes and complex numbers and reactances. In fact, I have to do another video on just reactances and Ac components and stuff like that. Actually, this video probably should have came after those videos, but I don't plan ahead anyway.

We've now got a complex plane. So we've got J. That's our imaginary operator J, which tells us that we're using complex numbers in the complex plane. So we've got J X, which is our reactant.

So our reactants is an imaginary component, and by imaginary, I mean it's the imaginary plane. Now, you have to watch my previous videos if you don't know what this is. Sorry, go and watch them. So we've got our complex reactive component Jx here and we've got our real component of course on our real line down the bottom here and this represents our equivalent circuit.

So Xs, which is the series component in here will have a phase angle in the complex plane and we'll call that phase angle Phi down. here. it's different to Theta as I've talked about in a previous video. and if you actually drop that vector down like this, then you get the real value for Rs here.

and then there'll be another angle in here, Which that symbol there you might. It's a bit weird, that's actually a Delta, which is another lowercase Greek letter. And so with Uh Phi and Delta here these two angles and these values, we can calculate the quality factor, the Q of the component, the Q of the capacitor. As you see on an Lcr meter, you'll see Q quality factor, and also D, which is your dissipation factor.

Have I done a video on capacitors that explains that? Probably. So you can calculate your quality factor. Q is just equal to 10 phi. here.

this phase angle and that's actually equal to the absolute magnitude of Xs on Rs. So the absolute value of series reactance, reactance, on the value of your series resistance, and likewise dissipation factor is 10 delta. Here, this angle in here and that's equal to your absolute value. That's what those little bars there that just means take out the sign.

They're absolute divided by x s here. which is your Uh series reactance. You'll notice that they're actually opposite. And of course, one on Q is D and one on D is Q Easy.

And if you've watched my previous Ac Fundamentals series videos, this should probably be up in your head or it's already popped out that if it's a positive angle. If Xs is series, reactance is a positive angle like this on the complex plane, then it's inductive. And if it happens to go negative like that, then it's capacitive. And this is how your Lcr meter can detect whether or not you've got a in auto mode, whether or not you've got an inductor or a capacitor by knowing what this phase angle Xs is here by doing these measurements at different angles.

Cool huh? And we can measure a lot more than quality factor and dissipation factor by just having these two values. Here, we can measure everything that your Lcr meter can measure is calculated from these, this equivalent circuit, and these two components. So we've got quality factor, dissipation factor. They're the formulas we just took from there.

D is one on Q, and then we've got Rp, which is your parallel resistance and you'll see uh, the symbols on the Lcr meter. depending on what mode you're in, stick around and I'll show you this graphically in a second, but you can see the parallel uh resistance. for example, one on Q plus plus times Rs doesn't. You don't have to remember these formulas, just know that everything is calculated from this simple equivalent circuit like this.

And then your impedance is the square root of uh, your series resistance. plus your series reactants are squared in there. and then Cp, that's your parallel. uh, capacitance.

If you're in parallel uh mode or series mode, for example. this is this parallel resistance you'll get in parallel with your parallel, uh, capacitance. There's the formula up there. and then your parallel inductance.

Um, it has that formula. Remember, this is not W, It's Omega, which is two Pi F you should know that from my previous video. so it takes into account the frequency when you're calculating the capacitance and the inductance values. And then in series mode on your Lcr meter, which can never be automatically or manually selected.

there's usually a series parallel button on there. Then series capacitance will be one on omega. Absolute value of your series reactants down here. and Ls is just pretty much the opposite of that.

So you can calculate all these things. Everything you see on there by simply measuring at 0 degrees and 90 degrees like that with a simple range resistor. Now, not every Lcr meter goes to this amount of effort to do this. There are various ways that you can, you know, do this, you know, sort of like cheating.

Uh, a bit. uh, brute force. But you know, if you want to do this properly and your high-end Lcr meters, you know you get one of your real high-end bench ones and stuff like that, Then yeah, they'll be measuring these until the cows come home and calculating all this stuff. I just find it amazing that from these two simple values here, and from simple measurements, all of this just comes out in the wash.

So how does your Lcr meter determine in auto mode? Whether or not it's inductor or a capacitor, Or whether or not you know what are the series? Uh, what are the dominant values? Whether it's a dominant resistor, you saw it in the measurements before it thought the capacitor was a resistor. Um, in auto mode, It's not that it didn't know any better. it's that's what came out of the dominant thing. So um, what we've got here is our once again our complex plane.

Positive J Operator Positive reactance. This is our reactants. Whether or not it's positive like this, or whether or not it's negative like this. As I said, if it's positive in relation to the real resistance value, Rs remember that this is the real resistance component.

It has no reactants whatsoever. Zero, uh, phase angle. If you're measuring Um, Lcr meters can actually measure they can measure resistance as well hence the R in the Lcr name, then yeah, it'll be like a real resistance Like that. there will be.

For an ideal component, there will be no other capacitance or inductance. but in practice there always is. If you're measuring a real resistor like this with your Lcr meter, there's going to be a small amount of capacitance in parallel with it. That's going to be uh C P that we looked at before and then you're going to have L S like this and they're going to be your components.

You'll have tiny little phase angles in there, and if you're lucky, your Lcr meter can just measure a smidgen of these parasitic values. So anyway, where the measurement ends up if it goes negative like this, and the Lcr medium goes aha. I know this is a capacitive component, and if it goes positive, it knows. Aha.

this has an inductive component, but how much inductance? How much capacitance in relation to, say, a capacitor? For example, this is the equivalent circuit. the real equivalent circuit of a capacitor. It's got some Esr, some equivalent series resistance in here. It's got some lead inductance, and you know, an internal inductance of the package and all that sort of stuff.

And then you've got the capacitance, which is the factor that's going to dominate, of course. and but then it's also got some parallel resistance. Some leakage in here as well. So how ideal this capacitor is depends on how close it gets to minus 90 degrees.

Like this, if it gets right down to minus 90 degrees, it's practically a perfect capacitor. Well, that's the definition of a perfect capacitor is this will be completely 90 degrees. There's no series resistance when you run those. Do these measurements, uh, cycle thing here.

And then we spit out all plug the numbers into those equations and it pops out that, well, no, there's no series resistance at all. There's no series inductance at all, and there's no parallel resistance at all. It's a perfect capacitor, but in practice, that doesn't really happen. And likewise, for inductors, if it's purely positive 90 degrees like this, then it's a pure inductor.

There is going to be no series resistance. There's going to be no any parallel winding capacitance. It's going to be nothing. It's an ideal inductor, but usually somewhere you know your component's going to be like somewhere like that, or it's going to be somewhere like that.

Now, the interesting thing is is that at this angle like this, your quality factor and your dissipation factor which is just one on Q and vice versa is equal to one. So you'll have that at an angle for the inductive part, and you'll have that at an angle for the capacitive part. and whether or not it's uh, sort of like below. I guess we could call it or above that quality factor.

The quality factor actually determines everything for both your capacitor and your inductor. It determines whether or not the capacitance is dominating over your parallel resistance. So in the case of the inductor up here, I've actually drawn like a large inductor here and a small resistor to show that the inductance if it's if it has a quality factor greater than one. So if it goes in this direction, the quality factor q goes greater than one.

It can go up to hundreds, thousands or whatever depending on how perfect uh your inductor is. And if it's under, if you have a quality factor under one, it means that the resistance is dominating. It means that your component is mostly a resistor with a little amount of series inductance in there. So if the quality factor is less than one, then the Lcr meter goes aha.

I know this is basically a resistor with a little bit of inductance, so it will switch to displaying the resistance as the primary component. but if the quality factor is above one, it'll think oh, this is mostly an inductor and it will show the inductance on the primary display instead of the resistance. So obviously that measurement that we did before of that capacitor in circuit because there's other components in there as we'll talk about in a minute. That means that there was something else in circuit at frequency.

Remember, we have a frequency component in here and these values are going to be dependent upon the test frequency because your component and your test leads and everything else as we uh, saw Teslas had series resistance and they have series inductance. It upsets the Apple cart and the Lcr meter thought, oh, it's dominant resistor like this because it was measuring that capacitance at a high frequency. Remember the capacitive reactance is one on J Omega C Omega is that two Pi F component. It has that frequency component.

So the Lsr meter is going to try and figure out based on the value that's spat out with the equivalent circuit down here of the quality factor, or whether or not it's a resistor down here with maybe a little bit of parallel capacitance and stuff like that. So likewise, down for the capacitor. If the capacitor has a quality factor greater than one, then of course it's going to be more towards an ideal capacitance and it'll have a small amount of parallel resistance or leakage like that. So that's how Lcr meters work.

And the takeaway from this is that the test frequency matters. It matters a lot. Basically, if you're measuring large values of capacitance, you want a lower test frequency because then it's not going to think that the resistor is dominating like this. It's not at a high test frequency.

Your capacitance is going to measure close to a zero relative to the range resistor. So and of course the other thing is is that it has to know which range you're on and you can auto range arms some Lcr meters, but generally they'll do it like automatically based on you know they'll just like scan through and figure out you know whether or not it's a dominant capacitor or whether or not it's a dominant resistor. And if you choose a high frequency, well, it doesn't matter which range resistor you get, it's just gonna think it's a resistor most of the time. And likewise for inductors, you want to have as high a frequency as possible so that it appears more like a dominant inductor than it does a dominant resistor.

So hopefully I didn't put you off Lcr meters there. But this is the fundamental concepts of how they work. As I said, some, you know, lower end Lcr meters might do it like cheating different ways to actually get these values. But any good quality Lcr meter in theory, this is how it's going to measure it and calculate all of those values and what things dominate based on your reference waveform here, and your frequency and your range resistor matters.

And it can matter a lot when you measure trying to measure components in circuit as we're doing in this video. because, um, all those extra components. It's not just the capacitor there, there's all these other components that are in parallel with it. whether or not it's part of a power supply.

Whether or not it's a, you know, a reset cap on a digital logic gate for a reset pin or something, there's all these log. There's all these other circuit elements surrounding the capacitor when you try and measure it in circuit, and that makes it really hard. That's why it's easy to confuse your Lcr meter depending upon what other circuit configuration is around it. But as you saw, you can actually do a reasonable job of measuring uh, capacitors in circuit if you choose, uh, force it, into the capacitance range so it knows.

Aha Okay, it's definitely a uh, you know, I'm telling you, this is a capacitor so you damn well do your best with this range resistor up here to try and measure it as a capacitor, you.