1 00:00:02,540 --> 00:00:08,340 Welcome back to Linear Circuits. This lesson is going to be a lab demo. 2 00:00:08,340 --> 00:00:12,945 We're going to be looking at the frequency response of an RLC circuit. 3 00:00:12,945 --> 00:00:16,770 And basically trying to reemphasize some material that we learned in our last 4 00:00:16,770 --> 00:00:22,010 lesson, which was more general, the theoretical aspects. 5 00:00:22,010 --> 00:00:24,953 We are still in the topic of frequency response in this module. 6 00:00:24,953 --> 00:00:31,980 In module three we built an RLC circuit and we had a lab demo of it. 7 00:00:31,980 --> 00:00:35,770 And that was to look at a transient response, for we want to plot, look at 8 00:00:35,770 --> 00:00:41,090 the very same system and as you recall in the last. 9 00:00:41,090 --> 00:00:44,970 Module, we had to build a buffer circuit in there to be able to boost the power. 10 00:00:44,970 --> 00:00:48,770 So, if this is our function generator, we built in our little [INAUDIBLE] circuit, 11 00:00:48,770 --> 00:00:53,940 here, in order to be able to produce the correct signal that we needed here, with 12 00:00:53,940 --> 00:00:58,850 enough power to run this circuit. So, this is a circuit schematic of what 13 00:00:58,850 --> 00:01:03,870 we're building. So, the lab demo is the RLC circuit 14 00:01:03,870 --> 00:01:10,410 frequency response. >> So, this is a RLC circuit that we've 15 00:01:10,410 --> 00:01:15,200 already built before. Recall in the lesson, in the last module 16 00:01:15,200 --> 00:01:18,800 when we were looking at transient response of second order systems. 17 00:01:18,800 --> 00:01:24,755 We built a circuit like this. So, this has an inductor in series with a 18 00:01:24,755 --> 00:01:31,100 resistor in series with a capacitor. And we are measuring the voltage source, 19 00:01:31,100 --> 00:01:35,330 which is across these green wires as our input to our circuit. 20 00:01:35,330 --> 00:01:40,160 And out output is the voltage across this capacitor. 21 00:01:40,160 --> 00:01:50,450 Looking at our screen and our actual response, if I gave it a square wave what 22 00:01:50,450 --> 00:01:54,430 I would see is the characteristic response of an over-damped system. 23 00:01:54,430 --> 00:01:57,460 So, with these values, it's an over-damped system. 24 00:01:57,460 --> 00:01:59,530 Now we're interested in the frequency response. 25 00:01:59,530 --> 00:02:07,700 So, we want to see sinusoidal responses. At this frequency of ten hertz the output 26 00:02:07,700 --> 00:02:10,650 looks very much like the input. So, the output is in blue. 27 00:02:10,650 --> 00:02:14,590 That's the capacitor voltage. The input is in green and that's the 28 00:02:14,590 --> 00:02:17,810 source voltage. I'm going to do a sine sweep. 29 00:02:17,810 --> 00:02:21,855 Where I change the frequency slowly in my input and you'll what happens to the 30 00:02:21,855 --> 00:02:28,544 output. So, as I increase it what you're seeing 31 00:02:28,544 --> 00:02:32,280 and I have wait till it reaches steady state so what you're seeing is the 32 00:02:32,280 --> 00:02:36,290 amplitude is decaying. Lets change my scale here. 33 00:02:39,950 --> 00:02:44,220 So, the amplitude is changing as I change the frequency and also there's a lag 34 00:02:44,220 --> 00:02:48,870 that's appearing. So, the amplitude, so the response of the 35 00:02:48,870 --> 00:02:53,359 system is a function of the frequency of the input. 36 00:02:53,359 --> 00:03:01,990 So you see as I'm changing that frequency in input. 37 00:03:01,990 --> 00:03:05,721 My amplitude actually is going lower, and my phase is changing. 38 00:03:05,721 --> 00:03:14,240 I can take these, this data. I can measure the amplitude change, the 39 00:03:14,240 --> 00:03:16,750 ratio of the output amplitude over the input amplitude. 40 00:03:16,750 --> 00:03:21,430 For each point frequency that I've looked at the forcing signal at. 41 00:03:21,430 --> 00:03:25,510 And I can also measure the phase lag for each point. 42 00:03:25,510 --> 00:03:29,578 So, if I measure it at each frequency and then plot it, I will get the frequency 43 00:03:29,578 --> 00:03:34,140 response. Well, fortunately, most instruments do 44 00:03:34,140 --> 00:03:40,980 that automatically for you and I'm going to close these and go ahead and open up 45 00:03:40,980 --> 00:03:47,670 the bode plot. So, this automatically does the 46 00:03:47,670 --> 00:03:55,533 calculations in the measurements to do a bode plot for you, automatically. 47 00:03:55,533 --> 00:04:02,029 So, I'm going to go from 10 hertz to a 1000 hertz. 48 00:04:04,100 --> 00:04:14,610 And I'm going to run this. What you're seeing at each one of these 49 00:04:14,610 --> 00:04:21,211 point where it, it shows a point, it has input a sine wave into my circuit and it 50 00:04:21,211 --> 00:04:24,870 measured the output amplitude and it measured the phase. 51 00:04:24,870 --> 00:04:30,390 In the output amplitude, it divided by the input amplitude, took the log of 52 00:04:30,390 --> 00:04:34,430 that, and multiplied by 20 to get values in decibels. 53 00:04:34,430 --> 00:04:40,550 So, these are the amplitudes given in decibels and then its measured versus 54 00:04:40,550 --> 00:04:44,360 frequency on a log scale. And then these are the phase lags 55 00:04:44,360 --> 00:04:48,225 measured in degrees, and it did it automatically for you. 56 00:04:48,225 --> 00:04:54,400 Now let's go back and look at this same, experiment but within under damp system. 57 00:04:54,400 --> 00:04:58,830 So, an over damp system, you see something that tails off like this. 58 00:04:58,830 --> 00:05:03,190 And I want to mention one other thing is that, we can calculate the bandwidth as 59 00:05:03,190 --> 00:05:11,590 being the value at which this is three decibels below the low value, low 60 00:05:11,590 --> 00:05:15,230 frequency value. So, three decibels is about right here. 61 00:05:15,230 --> 00:05:19,700 So, I would say the bandwidth of this particular circuit is in the range that's 62 00:05:19,700 --> 00:05:24,040 about 20,30. In the range of about 40 hertz, that's 63 00:05:24,040 --> 00:05:27,060 when I'm down three decibels from my low frequency value. 64 00:05:29,089 --> 00:05:35,834 So, let's go back to this circuit. I am replacing this resistor, which was 65 00:05:35,834 --> 00:05:40,910 20K, with a much smaller resistor. And, as we've seen before, if I decreases 66 00:05:40,910 --> 00:05:46,450 resistance, that will lower my damping to the point where this is now an under 67 00:05:46,450 --> 00:06:01,580 damped response. So, this particular case. 68 00:06:01,580 --> 00:06:08,550 Change my values here, want to look at the response due to square wave. 69 00:06:10,790 --> 00:06:17,700 And, I need to enable the, any other thing I need to do is check the trigger 70 00:06:17,700 --> 00:06:21,490 so that my display looks better. You can see that it oscillates there, it 71 00:06:21,490 --> 00:06:24,840 over shoots and then comes back. That characteristic of an under damped. 72 00:06:24,840 --> 00:06:27,280 Response, that means I've got complex roots. 73 00:06:27,280 --> 00:06:32,150 Now lets look at the frequency response of an under damped case. 74 00:06:32,150 --> 00:06:38,230 First of all lets do a sine sweep. Start out with a frequency of 100 hertz 75 00:06:38,230 --> 00:06:41,137 and I'm going to be increasing the frequency. 76 00:06:41,137 --> 00:06:51,959 My two signals, one in green is my. Input voltage, and one in blue is my 77 00:06:51,959 --> 00:06:57,900 output voltage. You see here, in this frequency range 78 00:06:57,900 --> 00:07:01,210 there is a difference. My output is lagging my input. 79 00:07:04,070 --> 00:07:07,400 My output starts lagging my input, but one thing you'll see is that my output 80 00:07:07,400 --> 00:07:09,712 has a higher amplitude. Than my input. 81 00:07:09,712 --> 00:07:16,090 See the output amplitude's getting larger and then it goes smaller. 82 00:07:16,090 --> 00:07:19,300 So, this is a difference between an a under damped system and the over damped 83 00:07:19,300 --> 00:07:21,890 system. The under damp system, the output starts 84 00:07:21,890 --> 00:07:26,470 becoming a little bit larger, and then it gets smaller. 85 00:07:26,470 --> 00:07:29,220 So, this is a case of my damping it's really, really small. 86 00:07:29,220 --> 00:07:34,360 I have that situation. Now let's look at the bode part. 87 00:07:34,360 --> 00:07:40,080 What I should see in the bode part is that my frequency response should pick up 88 00:07:40,080 --> 00:07:44,380 right above this frequency, that's about the frequency at which I get may be the 89 00:07:44,380 --> 00:07:50,630 largest. Value, that's around 4, 4000 hertz, and 90 00:07:50,630 --> 00:07:55,920 we call that a resonant frequency, is when my output frequency my output 91 00:07:55,920 --> 00:08:00,341 amplitude becomes the largest relative to my input amplitude. 92 00:08:00,341 --> 00:08:12,750 And that would be resonance. Let's look at our bode plot now. 93 00:08:12,750 --> 00:08:22,660 Okay, I'm going to go ahead and run this. It is automatically doing a sine sweep. 94 00:08:22,660 --> 00:08:28,780 You see this is the output amplitude over the input amplitude in the log scale. 95 00:08:28,780 --> 00:08:32,250 And you see how it peaks up. This, in this range it means that the out 96 00:08:32,250 --> 00:08:34,980 put amplitude is lager than the input amplitude. 97 00:08:34,980 --> 00:08:40,105 And this happened, the peak happened at about, it's 2000, 3000, around 4000. 98 00:08:40,105 --> 00:08:44,310 Around 4000 hertz. Is when we hit that resonant right there, 99 00:08:44,310 --> 00:08:49,430 and we call that the resonant frequency. When we run this with a few more points 100 00:08:49,430 --> 00:09:03,770 in there, so get better resolution. [SOUND] So, it's just checking more 101 00:09:03,770 --> 00:09:10,020 frequencies. A smoother plot. 102 00:09:10,020 --> 00:09:11,725 Okay, so checking a little bit better, it's still. 103 00:09:11,725 --> 00:09:14,160 It's now between, that's two, three, four. 104 00:09:14,160 --> 00:09:19,190 Really between four and five K hertz is what my resonant frequency looks like. 105 00:09:19,190 --> 00:09:24,130 And the other thing to notice is that my phase goes from zero down and it's 106 00:09:24,130 --> 00:09:27,714 approaching minus 180. So, the characteristics of an under 107 00:09:27,714 --> 00:09:32,610 damped system with low damping is that the frequency response peaks up. 108 00:09:32,610 --> 00:09:36,425 Now, what's the bandwidth in this case? Well it's a frequency at which we're at 109 00:09:36,425 --> 00:09:38,690 three decibels below my low frequency value. 110 00:09:38,690 --> 00:09:46,150 Low frequency is at 0 db and my bandwidth is right around here which looks to be 111 00:09:46,150 --> 00:09:56,470 around, around 8K, I would call that my, my bandwidth around 8K. 112 00:09:56,470 --> 00:09:59,960 So, in summary we've looked at the frequency response. 113 00:09:59,960 --> 00:10:04,960 We generated it automatically using a bode analyzer which is a very common 114 00:10:04,960 --> 00:10:09,010 instrument in, in electronic applications. 115 00:10:09,010 --> 00:10:13,770 Thank you. >> So, in summary what we found is that 116 00:10:13,770 --> 00:10:18,220 in low R in an RLC circuit. Means that you've got low damping. 117 00:10:18,220 --> 00:10:22,048 And a high resonant peak. And that resonant peak means that my 118 00:10:22,048 --> 00:10:27,477 output amplitudes, when I've got frequency, a sine wave at that frequency, 119 00:10:27,477 --> 00:10:33,110 my output amplitudes are going to be very large compared to my input amplitude. 120 00:10:33,110 --> 00:10:35,960 And we've found that we can generate the bode plot by a sine sweep. 121 00:10:37,080 --> 00:10:41,400 Where we input sine waves of different frequencies, and then we calculate the 122 00:10:41,400 --> 00:10:44,490 amplitude ratio. The amplitude of the output signal versus 123 00:10:44,490 --> 00:10:48,060 that of the input signal. And we also look a the phase lag for each 124 00:10:48,060 --> 00:10:52,520 response, and then we plot that. In doing a bode plot you have to first 125 00:10:52,520 --> 00:10:55,480 take 20 times the log of that ratio before you plot it. 126 00:10:55,480 --> 00:10:59,770 Would plot both the magnitude and the phase versus frequency and that gives us 127 00:10:59,770 --> 00:11:02,120 a bode pot. And this can be done automatically and 128 00:11:02,120 --> 00:11:03,560 there're a lot of instruments that do that. 129 00:11:06,350 --> 00:11:09,550 Our next lesson with be an introduction to filtering. Thank you.