Welcome back, this is Dr. Ferri. In this lesson, we will look at another lab demo, this one on RLC circuits. Just to remind you where we are in this module, we've looked at the analysis of an RLC circuit, and now we're going to look at a demonstration of it. We would like to measure the response of this circuit. Now this circuit, we would like to have a voltage source right here. But there's a bit of a problem with this. The problem is that if I want to give this a square wave input, so I want to trigger the transient, I've got sharp and abrupt changes in the voltage. Well, sharp and abrupt changes in the voltage here are going to require sharp and abrupt changes in the voltage over here. And because the current is equal to c times dvcdt, I'm looking at the derivative of something that changes very quickly. So that means it's going to require large currents. And this is a problem when you're trying to build a circuit. A lot of times this causes problems. If I'm going to require a lot of current here, my source has to be able to give a lot of current, have a high current limit, and a lot of sources function generators don't. It's equivalent to having a AAA battery. You're trying to power a circuit with a AAA battery. Well, a AAA battery has 1.5 volt value to it, but it's very current limited, very power limited. Compared to D-sized battery, which is also 1.5 volt, but it can pack a lot more power to it. So what we have to do is get a circuit, put some sort of conditioner on this so that we can give the power that we need. And the particular circuit we are going to build is it's going to be what I would call a buffer circuit built out of an op amp. This will be the output of my function generator here. And I'm going to put it through a buffer circuit that amplifies the power, so that V sub s right here is the very same voltage level as it is here, but it's able to draw more current. And in case you're interested, the actual circuit that I built is an op amp. It's a common device and it has its own power supply. Because of that, it's able to provide more power than the function generator. So that's just a common problem that you sometimes have when building a regular circuit. So the Lab Demo is on RLC circuits. We are going to be building an RLC circuit on this protoboard and demonstrating its response. Now notice I've already got something hooked up here. This is our op amp circuit. Remember that the op amp helps us to boost the power. So we've got the input to the op amp circuit from the function generator, and the op amp itself is inside this integrated chip. And it's got metal pins out the side of the integrated chip that allow us to hook up to the internal components. The output of the op amp goes here, and that's going to be the input to my RLC circuit. Now, here's our schematic here. The function generator is hooked up here and I've got a common ground. My voltage source to my circuit, I'm going to define as being right here V sub s. Recall that it has the same waveform as a function generator waveform, the same voltage level, but it's able to provide more current. So I'm going to hook this up to my oscilloscope to display it, and that's going to be channel 0. And I'm also interested in the voltage for classic capacitor and I'm going to hook that up to the oscilloscope channel 1. Nathan has already examined this circuit and shown the equations for this circuit, and they're given here. If we want to find what sort of response it is, we have to find the roots of this polynomial right here. For these values of L, R, and C, I get real roots, these are the roots right here, the real and distinct roots. That means this is an overdamped system. And just as a, sort of beyond the scope of this particular course, but if you understood about differential equations, you could write down what that response looked like. And with an overdamped system, it would look like these. The two roots show up as exponentials, and notice that one of them is very, very negative. And if I were to plot this, it decays so quickly that it becomes negligible very quickly, and the response looks more like a first order exponential response. So that's what we predict will happen here, that we're going to get an overdamped system that looks more or less like this one right here. Now let's go back and build our actual circuit. This comes from my op amp, and that's V sub s. I connect that to this inductor. Remember, that inductor is just a coil of wires. In series with that inductor, I put a 20K resistor. In series with that resistor along the same row, I'm going to insert a capacitor. Okay, so I've got those three in series now, and I have to finish my circuit by connecting it to ground. So that's my ground wire. Now I want to hook up the oscilloscope channels. I'm going to zero out, Channel 0 that I connected to ground, and the low side of channel 1, again to ground. Remember, along the side rails of a protoboard they're all connected, so everything along here connected together. So all these wires are connected. The plus side of channel 0, I want to hook up to V sub s. The plus side of channel 1, I want to hook up to V sub c. So now I have my circuit hooked up the way I showed in the schematic. Let's go to the, Function generator and oscilloscope panels. And I've got my function generator set to a square wave at 700 hertz. Let me start that running and let me run the oscilloscope. And I see that my response looks this way that the, let me go ahead and change that so, there it is. I'm displaying channel 1 and channel 0. So channel 0's in green, channel 1's in blue. Channel green is my voltage source and channel blue is my capacitor voltage. So you see, I predicted that it would look exponential, and it does because my roots are, it's an overdamped system with my two roots that are very different in magnitude with respect to another. And so, the result looks like a first order system and I can actually come up with a time constant here. So this is an overdamped response. Going back to this slide, this schematic, if I changed my 20k resistor to a 100 ohm resistor and recalculate what the roots are, I now find that the roots are imaginary, they're complex, where j is the square root of -1. So this is the imaginary part versus the real part. The smaller the value of R, then this gets to be low damping. So as R is decreased, it's decreased to some value at which I have complex roots, and then if I continue decreasing R, then my system has lower and lower damping. So right here looking at the roots, complex roots means it's underdamped, low values of R means that the imaginary part becomes large with respect to the real part. What is that happened with regard to the response that I see? So what I want to do is take out the 20k resistor. So you're seeing what the 20k resistor is, that's the overdamped case. Let me take that out and put in a 100 ohm resistor, And you see that response. That's an underdamped response. You see that oscillations? Let me expand the time scale here so you see a little bit better. You see the oscillatory behavior. The smaller the value of R in the circuit, the smaller the resistance, the higher peaks I have, the more oscillatory that behavior is, and it's also known as lower damping in my system. So, overdamped system comes from real roots, underdamped system comes from complex roots. Thank you. So in summary, we've seen that an underdamped RLC circuit has a small R value and results in large peaks. An overdamped RLC circuit has a large R value and doesn't have any peaks to it, no oscillatory behavior. In the next lesson, we will look at applications in inductors and capacitors that exploit mechanical components. Thank you.