1 00:00:00,640 --> 00:00:05,500 Welcome back, this is Dr Ferri. In this lesson we will look at another 2 00:00:05,500 --> 00:00:13,370 lab demo, this one on RLC circuits. Just to remind you where we are in this 3 00:00:13,370 --> 00:00:17,560 module, we've looked at the analysis of an RLC circuit, now we are going to look 4 00:00:17,560 --> 00:00:25,170 at a demonstration of it. We would like to measure the response of 5 00:00:25,170 --> 00:00:29,870 this circuit. Now this circuit, we would like to have a 6 00:00:29,870 --> 00:00:33,835 voltage source right here, but there's a bit of a problem with this. 7 00:00:33,835 --> 00:00:41,690 The problem is that if I want to give this a square wave input, So, I want to 8 00:00:41,690 --> 00:00:46,710 trigger the transient. I've got sharp and abrupt changes in the 9 00:00:46,710 --> 00:00:48,940 voltage. Well, sharp and abrupt changes in the 10 00:00:48,940 --> 00:00:55,270 voltage here are going to require sharp and abrupt changes in the voltage over 11 00:00:55,270 --> 00:01:00,930 here. And, because the current is equal to c 12 00:01:00,930 --> 00:01:04,290 times DVCDT. I'm looking at the derivative of 13 00:01:04,290 --> 00:01:08,230 something that changes very quickly. So that means it's going to require large 14 00:01:08,230 --> 00:01:11,720 currents. And this is a problem when you're trying 15 00:01:11,720 --> 00:01:15,400 to build a circuit. A lot of times this causes problems. 16 00:01:15,400 --> 00:01:21,500 If I'm going to require a lot of current here, my source Has to be able to give a 17 00:01:21,500 --> 00:01:24,450 lot of current, have the high current limit. 18 00:01:24,450 --> 00:01:27,520 And a lot of sources function generators don't. 19 00:01:27,520 --> 00:01:30,170 It, it's equivalent to having a, a triple a battery. 20 00:01:30,170 --> 00:01:34,290 You're trying to, to power a circuit with a triple a battery. 21 00:01:34,290 --> 00:01:40,380 Well, triple a battery has 1.5 volt value to it, but it's very current limited, 22 00:01:40,380 --> 00:01:46,390 very power limited compared to a D size battery, which is also 1.5 volt, but it 23 00:01:46,390 --> 00:01:52,920 can pack a lot more power to it. So what we have to do is get a circuit, 24 00:01:52,920 --> 00:01:57,870 you know, put a, some sort of conditioner on this, so that we can give the power 25 00:01:57,870 --> 00:02:02,620 that we need. And the particular circuit we're going to 26 00:02:02,620 --> 00:02:06,569 build is, it's going to be what I would call a buffer circuit built out of an op 27 00:02:06,569 --> 00:02:09,370 amp. This will be the output of my function 28 00:02:09,370 --> 00:02:14,200 generator here, and I'm going to put it through a buffer circuit that amplifies 29 00:02:14,200 --> 00:02:19,700 the power, so that V sub S right here is the very same voltage level as it is 30 00:02:19,700 --> 00:02:26,230 here, but it's able to draw more current. And in case you're interested, the actual 31 00:02:26,230 --> 00:02:30,660 circuit that I built is an up amp, it's a common device. 32 00:02:30,660 --> 00:02:35,040 And it has it's own power supply, and because of that it's able to provide more 33 00:02:35,040 --> 00:02:39,270 power than the function generator. So that's just a common problem that you 34 00:02:39,270 --> 00:02:41,460 sometimes have in building a regular circuit. 35 00:02:45,520 --> 00:02:53,219 So the lab demo is on RLC circuits. We're going to be building an RLC circuit 36 00:02:53,219 --> 00:02:56,630 on this proto-board. And demonstrating its response. 37 00:02:56,630 --> 00:02:58,860 And I notice that I've already got something hooked up here. 38 00:02:58,860 --> 00:03:03,450 This is our op amp circuit. Remember that the op amp helps us to 39 00:03:03,450 --> 00:03:06,590 boost the power. So I've got the input to the op amp 40 00:03:06,590 --> 00:03:11,590 circuit from the function generator. And the op amp itself is inside this 41 00:03:11,590 --> 00:03:14,950 integrated chip. And it's got metal pins out the side of 42 00:03:14,950 --> 00:03:19,196 the integrated chip that allow us to hook up to the internal components. 43 00:03:19,196 --> 00:03:23,814 The output the op amp goes here, and that's going to be the input to my ROC 44 00:03:23,814 --> 00:03:33,524 circuit. Here's our schematic here. 45 00:03:33,524 --> 00:03:37,839 The function generator is hooked up here. And I've got a common ground. 46 00:03:39,420 --> 00:03:44,095 My voltage source to my circuit I'm going to define as being right here, V sub S. 47 00:03:44,095 --> 00:03:49,280 Recall that has the same waveform as function generator waveform, the same 48 00:03:49,280 --> 00:03:52,990 voltage level, but it's able to provide more current. 49 00:03:52,990 --> 00:03:56,890 So I'm going to hook this up as, to my oscilloscope to display it, and it's 50 00:03:56,890 --> 00:04:01,230 going to be channel zero. And I'm also interested in the voltage 51 00:04:01,230 --> 00:04:05,395 across the capacitor, and I'm going to hook that up to the oscilloscope channel 52 00:04:05,395 --> 00:04:11,070 1. Nathan has already examined this circuit 53 00:04:11,070 --> 00:04:14,032 and shown the equations for the circuit, and they're given here. 54 00:04:14,032 --> 00:04:20,470 If we want to find what sort of response it is, we have to find the roots of this 55 00:04:20,470 --> 00:04:27,640 polynomial right here. For these values of L, R, and C, I get 56 00:04:27,640 --> 00:04:30,430 real roots. These are the roots right here, the real 57 00:04:30,430 --> 00:04:37,290 and distinct roots. That means that this is an overdamped 58 00:04:37,290 --> 00:04:39,150 system. And just as a, sort of beyond the scope 59 00:04:39,150 --> 00:04:42,940 of this particular course, but, if you understood about differential equations, 60 00:04:42,940 --> 00:04:47,150 you could write down what that response looked like. 61 00:04:47,150 --> 00:04:49,510 And with an overdamped system, it would look like these. 62 00:04:49,510 --> 00:04:54,790 The 2 roots show up as exponentials. And notice, that one of them is very, 63 00:04:54,790 --> 00:04:58,340 very negative. And if I were to plot this, it decays so 64 00:04:58,340 --> 00:05:01,530 quickly that it becomes negligible very quickly. 65 00:05:01,530 --> 00:05:06,610 And the response looks more like a first-order exponential response. 66 00:05:06,610 --> 00:05:09,755 So that's what we predict will happen here, that we're going to get an 67 00:05:09,755 --> 00:05:14,020 overdamped system that looks more or less Like this one right here. 68 00:05:14,020 --> 00:05:19,849 Now let's go back and build our actual circuit. 69 00:05:19,849 --> 00:05:25,827 This comes from my op amp, and that's [INAUDIBLE]. 70 00:05:25,827 --> 00:05:34,820 I connect that to this Inductor, remember that inductor is just a coil of wires. 71 00:05:34,820 --> 00:05:37,780 In series with that inductor, I put a 20 k resistor. 72 00:05:37,780 --> 00:05:50,490 In series with that resistor, along this same row, I'm going to insert a 73 00:05:50,490 --> 00:06:03,150 capacitor. Ok, so I've got those three in series 74 00:06:03,150 --> 00:06:07,065 now, and I have to finish my circuit by connecting it to ground. 75 00:06:07,065 --> 00:06:12,180 So that's my ground wire. Now I want to hook up the oscilloscope 76 00:06:12,180 --> 00:06:15,807 channels. I'm going to zero out channel zero that I 77 00:06:15,807 --> 00:06:23,610 connected to ground and the low side of channel one, again, to ground. 78 00:06:23,610 --> 00:06:28,020 Remember, along the rails of a, side rails of a Try to avoid the raw 79 00:06:28,020 --> 00:06:29,870 connectors. Everything all in here are connected 80 00:06:29,870 --> 00:06:33,570 together, so all these wires are connected. 81 00:06:33,570 --> 00:06:38,045 The plus side of channel zero, I want to hoook up to [UNKNOWN] s. 82 00:06:38,045 --> 00:06:50,230 Plus side of channel one I want to hook up to [UNKNOWN] c. 83 00:06:50,230 --> 00:06:57,100 So now I have my circuit hooked the way I showed in the schematic. 84 00:06:57,100 --> 00:07:05,440 Let's go to the function generator and oscilloscope panels and I've got my 85 00:07:05,440 --> 00:07:11,190 function generator set to a square wave at 700Hz We start that running, and let 86 00:07:11,190 --> 00:07:19,520 me run the eselescope. And I see that my response looks this way 87 00:07:19,520 --> 00:07:21,600 that the. Let me go ahead and change that. 88 00:07:21,600 --> 00:07:27,061 There it is. I'm displaying channel 1 and channel 0. 89 00:07:27,061 --> 00:07:32,250 So channel 0 is in green and channel 1 is in blue. 90 00:07:32,250 --> 00:07:39,000 Channel green is my voltage source, and channel blue is my capacitor voltage. 91 00:07:39,000 --> 00:07:44,790 So, you see I, I predicted that it would look exponential, and it does. 92 00:07:44,790 --> 00:07:49,020 Because my roots are, it's an overdamped system with my 2 roots that are very 93 00:07:49,020 --> 00:07:52,110 different in magnitude with respect to another. 94 00:07:52,110 --> 00:07:56,670 And so the result looks like a first order system, and I can actually come up 95 00:07:56,670 --> 00:08:03,820 with a time constant here. So this is an overdamped response. 96 00:08:03,820 --> 00:08:13,950 Going back to this slide is schematic. If I changed my, my 20K resistor to 100 97 00:08:13,950 --> 00:08:18,050 ohm resistor, and recalculate what the roots are, I now find that the roots are, 98 00:08:18,050 --> 00:08:22,490 are imaginary or complex, where j is the square root of minus 1. 99 00:08:22,490 --> 00:08:25,580 So, this is the imaginary part versus the real part. 100 00:08:25,580 --> 00:08:31,855 The smaller the value of R, then this becomes, this gets to be low damping. 101 00:08:31,855 --> 00:08:36,800 So, as R is decreased, decreased to some value at which. 102 00:08:36,800 --> 00:08:42,520 I have complex roots, and then if I continue decreasing R, then my system 103 00:08:42,520 --> 00:08:47,480 becomes, has lower and lower damping. So right here, looking at the root, 104 00:08:47,480 --> 00:08:52,520 complex roots meets its under-damped. Low values of r means that the imaginary 105 00:08:52,520 --> 00:08:56,130 part becomes large with respect to the real part. 106 00:08:56,130 --> 00:09:00,110 Where does that happen with regard to the response that I see? 107 00:09:00,110 --> 00:09:08,430 So, what I want to do is take out the 20 k resistor. 108 00:09:08,430 --> 00:09:10,190 So, you're seeing what the 20 k resistor is. 109 00:09:10,190 --> 00:09:17,693 That's an overdamped case. We take that out, and put in 100 ohm 110 00:09:17,693 --> 00:09:21,450 resistor. Can you see that response. 111 00:09:21,450 --> 00:09:24,150 That's an underdamped response. You see that oscillation? 112 00:09:24,150 --> 00:09:28,690 Let me expand the time scan here, so you can see it a little bit better. 113 00:09:28,690 --> 00:09:33,050 You see the oscillatory behavior. The smaller the value of R, in the 114 00:09:33,050 --> 00:09:36,180 circuit, the smaller the resistance, the higher peaks I have. 115 00:09:36,180 --> 00:09:41,100 The more oscillatory that behavior is. The lower ends also known as lower 116 00:09:41,100 --> 00:09:47,533 damping in my system. So, over damp system comes from real 117 00:09:47,533 --> 00:09:50,852 roots, under damp system comes from complex roots. 118 00:09:50,852 --> 00:09:58,042 Thank you. So in summary, we've seen that an 119 00:09:58,042 --> 00:10:01,417 underdamped RLC circuit has the small r value, and results in large peaks. 120 00:10:01,417 --> 00:10:08,130 An over-damped RLC circuit has a large R value and doesn't have any peaks to it, 121 00:10:08,130 --> 00:10:12,460 no oscillatory behavior. In the next lesson, we will look at 122 00:10:12,460 --> 00:10:16,932 applications in inductors and capacitors that exploit mechanical components. 123 00:10:16,932 --> 00:10:19,576 Thank you.