1 00:00:02,900 --> 00:00:04,920 Welcome back to Linear Circuits. This Dr. 2 00:00:04,920 --> 00:00:06,310 Ferri. 3 00:00:06,310 --> 00:00:10,180 This lesson is a lab demo. It's on guitar string filtering. 4 00:00:12,490 --> 00:00:14,900 So, filtering again is our last topic 5 00:00:14,900 --> 00:00:18,640 here and very important application of reactive circuits. 6 00:00:20,320 --> 00:00:26,660 So, we're going to be looking at guitar string, and we want to do filtering on it. 7 00:00:26,660 --> 00:00:29,930 So, we're going to use a tone control filter. 8 00:00:29,930 --> 00:00:31,890 I got this from this website right here. 9 00:00:31,890 --> 00:00:34,860 But you, if you play electric guitars, you may be 10 00:00:34,860 --> 00:00:37,810 familiar with tone control, where you would take the output 11 00:00:37,810 --> 00:00:40,960 of your guitar pick up, and then you put it through a circuit. 12 00:00:40,960 --> 00:00:44,420 And, then you look at what goes to your amplifier. 13 00:00:44,420 --> 00:00:49,280 And in tone control, you can adjust certain frequency ranges 14 00:00:49,280 --> 00:00:52,670 and make maybe mid range frequencies higher or, or lower. 15 00:00:52,670 --> 00:00:55,436 So, in this particular circuit, we're 16 00:00:55,436 --> 00:00:58,660 looking at these parameters that we choose. 17 00:00:58,660 --> 00:01:00,430 In this configuration, it's going to be a 18 00:01:00,430 --> 00:01:03,480 low pass filter where we have two potentiometers. 19 00:01:03,480 --> 00:01:06,290 One adjusts the, the tone of it or 20 00:01:06,290 --> 00:01:09,360 adjust the frequency shaping and the other for volume. 21 00:01:13,820 --> 00:01:17,080 So, in a general sense, going back to 22 00:01:17,080 --> 00:01:19,810 what we were looking at with frequency response and 23 00:01:19,810 --> 00:01:22,110 filtering, if this is my circuit, the one 24 00:01:22,110 --> 00:01:24,360 that I just showed you for the tone control. 25 00:01:24,360 --> 00:01:26,430 And this is the input from the guitar pick up. 26 00:01:26,430 --> 00:01:28,540 And this is the output that would be sent to an amplifier. 27 00:01:28,540 --> 00:01:32,320 If I had an input signal that looks like this. 28 00:01:32,320 --> 00:01:34,840 And this was the shape of a low 29 00:01:34,840 --> 00:01:39,566 pass filter, the output would look something like this. 30 00:01:39,566 --> 00:01:42,935 Now, the formulas for it, well, if my input 31 00:01:42,935 --> 00:01:45,880 is a sine wave as I'm showing here, then 32 00:01:45,880 --> 00:01:50,002 the output amplitude, the output corresponding output sine wave 33 00:01:50,002 --> 00:01:54,550 is related to the input amplitude by this magnitude. 34 00:01:54,550 --> 00:01:58,350 So, in other words I can talk about is the magnitude of the input 35 00:01:58,350 --> 00:02:00,280 times the magnitude of the transfer function 36 00:02:00,280 --> 00:02:02,070 gives me the magnitude of the output. 37 00:02:03,310 --> 00:02:05,570 In ability plot I 38 00:02:05,570 --> 00:02:11,160 find the Bode plot by taking 20 times the log of this to give me this right here. 39 00:02:11,160 --> 00:02:17,140 So, in a logarithm scale when I multiply things and then take a log, 40 00:02:17,140 --> 00:02:22,450 it's the same as adding once I've taken the log to get this signal right here. 41 00:02:22,450 --> 00:02:26,450 So, the log scale, I'm adding terms 42 00:02:26,450 --> 00:02:29,270 whereas, in the linear scale I'm multiplying terms. 43 00:02:33,260 --> 00:02:37,410 So, let's do, let's look at the lab demo for the guitar string filtering. 44 00:02:38,410 --> 00:02:40,010 Now, let's take a look at this circuit. 45 00:02:40,010 --> 00:02:43,305 We've built the tone control circuit on this bread board. 46 00:02:43,305 --> 00:02:46,200 These are the two potentiometers. 47 00:02:46,200 --> 00:02:49,900 This is the capacitor right there and the two resistors are right there. 48 00:02:50,910 --> 00:02:54,700 The output of the guitar pickup goes into the circuit 49 00:02:54,700 --> 00:02:56,544 and then the output of the circuit is over here. 50 00:02:56,544 --> 00:02:57,024 So, 51 00:02:57,024 --> 00:03:02,721 remember the way that a guitar pick up works is that it generates electricity. 52 00:03:02,721 --> 00:03:09,350 When I move this and it vibrates, its vibrating metal, vibrating inside of a 53 00:03:09,350 --> 00:03:11,990 magnetic field, it generates it's own electricity 54 00:03:11,990 --> 00:03:14,300 so it generates a signal that way. 55 00:03:14,300 --> 00:03:16,440 And then the output of the circuit is over here and 56 00:03:16,440 --> 00:03:19,430 we're going to measure the output of this circuit with this mideck. 57 00:03:19,430 --> 00:03:22,350 So, let's go ahead and look at the frequency response. 58 00:03:22,350 --> 00:03:26,920 I start out, we start this looking at this display. 59 00:03:26,920 --> 00:03:32,550 What we see before I've done any signals is that there's some noise in here. 60 00:03:32,550 --> 00:03:36,236 Noise at about 3000 hertz and close to 2000 hertz. 61 00:03:36,236 --> 00:03:40,270 That's just and it noise electrical magnetic interference. 62 00:03:40,270 --> 00:03:43,390 Lets ignore that and just concentrate on. 63 00:03:43,390 --> 00:03:46,965 The noise, the signal that we induce when we pluck the string. 64 00:03:46,965 --> 00:03:46,970 [MUSIC] 65 00:03:46,970 --> 00:03:50,837 Okay, we plucked the string, we see all the harmonics in 66 00:03:50,837 --> 00:03:56,832 there, first harmonic, second harmonic, and so on, and so on. 67 00:03:56,832 --> 00:04:01,390 And this is the row signal that is not filtered. 68 00:04:04,900 --> 00:04:07,640 Now, let me change this to look at the other channel. 69 00:04:07,640 --> 00:04:09,132 This is the output of our circuit. 70 00:04:09,132 --> 00:04:12,790 Let me, me start this. 71 00:04:12,790 --> 00:04:12,792 [SOUND] 72 00:04:12,792 --> 00:04:21,150 And what we see is the filter, this is a low pass filter. 73 00:04:21,150 --> 00:04:25,690 It got rid of a lot of these. It really attenuated this high frequency. 74 00:04:25,690 --> 00:04:28,070 Oh, quite a bit in this signal. 75 00:04:28,070 --> 00:04:30,980 So, that's the effectiveness as a low pass filter. 76 00:04:30,980 --> 00:04:32,990 It might help for us to actually see this 77 00:04:32,990 --> 00:04:35,745 filter and see the Bode plot of the filter. 78 00:04:35,745 --> 00:04:44,740 I'm going to go ahead and generate this. 79 00:04:44,740 --> 00:04:49,760 This is just doing a sign sweep. Oh, I need to 80 00:04:51,840 --> 00:04:53,970 take out the guitar string and plug in the 81 00:04:57,320 --> 00:05:00,000 function generator. because that generate it's a sine wave. 82 00:05:00,000 --> 00:05:00,920 Now, let me run this. 83 00:05:05,690 --> 00:05:08,740 So it's automatically generating the Bode plot. 84 00:05:08,740 --> 00:05:11,080 You can see the magnitude part, it's going down like a low 85 00:05:11,080 --> 00:05:17,654 pass filter with a bandwidth that's in the range of about 1,000 hertz. 86 00:05:17,654 --> 00:05:20,800 Now, let's take a look at these signals a little bit more carefully. 87 00:05:23,290 --> 00:05:27,809 This is the free, the frequency response of the low pass filter. 88 00:05:29,030 --> 00:05:32,330 And I've just highlighted the magnitude part of it and if 89 00:05:32,330 --> 00:05:38,170 we look at this at the low frequency it's about minus ten. 90 00:05:38,170 --> 00:05:41,270 So, going over here minus three db from 91 00:05:41,270 --> 00:05:44,139 that is somewhere in this region so the bandwidth 92 00:05:46,860 --> 00:05:48,470 is close to a 1,000 hertz 93 00:05:50,720 --> 00:05:51,530 for this circuit. 94 00:05:58,210 --> 00:06:00,270 Now, the input and output spectra is shown here. 95 00:06:00,270 --> 00:06:03,180 First of all, this is the input spectra. 96 00:06:03,180 --> 00:06:06,970 And again, we've got the different peaks of the harmonics there. 97 00:06:08,900 --> 00:06:10,010 And then this is the output. 98 00:06:10,010 --> 00:06:13,480 So, this is the input to my tone control circuit and then 99 00:06:13,480 --> 00:06:17,720 this is the corresponding output for that same time that I plucked it. 100 00:06:17,720 --> 00:06:23,390 And what you'll find here is that there's a ratio between the initial peak at 101 00:06:23,390 --> 00:06:26,220 the low frequency and than the higher frequencies. 102 00:06:26,220 --> 00:06:29,450 The bandwidth is right around here. 103 00:06:31,090 --> 00:06:35,850 So, prior to this bandwidth, its passing it through without much attenuation. 104 00:06:35,850 --> 00:06:37,710 And then it starts attenuating and the further 105 00:06:37,710 --> 00:06:40,190 out to the right the more it attenuates. 106 00:06:40,190 --> 00:06:43,409 And so if I look at the, the ratio between these 107 00:06:43,409 --> 00:06:48,980 first peeks its a little bit lower here, this being the output. 108 00:06:48,980 --> 00:06:50,130 Again, this is the bandwidth here. 109 00:06:50,130 --> 00:06:54,860 So, the ratio is down a little bit because it does lower it as 110 00:06:54,860 --> 00:06:59,770 we go higher in frequency, but the ratio down here this is attenuated much more. 111 00:06:59,770 --> 00:07:04,020 This peak right here is attenuated much more than this one and we can 112 00:07:04,020 --> 00:07:07,980 see it by looking at the ratio of this peak to the initial peak. 113 00:07:07,980 --> 00:07:14,084 So, this peak if I, if I look at these, these like here, 114 00:07:14,084 --> 00:07:18,740 it goes down much more this does over here. 115 00:07:18,740 --> 00:07:26,539 And that's that additional amount is due to that filtering at the high frequencies. 116 00:07:33,300 --> 00:07:37,740 So, in summary, what we seen is we've 117 00:07:37,740 --> 00:07:41,060 examine the input output relationships on a linear scale. 118 00:07:41,060 --> 00:07:42,980 I multiply the two things. 119 00:07:42,980 --> 00:07:44,970 I multiply the amplitude of the input times the 120 00:07:44,970 --> 00:07:48,840 transfer function and in the bode plot I add them. 121 00:07:48,840 --> 00:07:53,594 So the, so the bode plot of the 122 00:07:53,594 --> 00:07:58,350 filter decreases the value at high frequencies for a 123 00:07:58,350 --> 00:07:59,050 low pass filter. 124 00:07:59,050 --> 00:08:02,270 And we found that the first order filter has 125 00:08:02,270 --> 00:08:05,560 a roll off of minus 20 decibels per decade. 126 00:08:05,560 --> 00:08:08,540 Passive filters are made of R, L and C components. 127 00:08:08,540 --> 00:08:12,960 That's what we built here, was a, one with a RC components. 128 00:08:12,960 --> 00:08:18,540 And it required no power supply. Now, it's very common to build something 129 00:08:18,540 --> 00:08:23,700 called active filters, where we use resisters and capacitors and outbacks . 130 00:08:23,700 --> 00:08:24,200 And 131 00:08:26,010 --> 00:08:28,240 those will require a separate power supply, but 132 00:08:28,240 --> 00:08:31,110 they are much versatile than a passive filter. 133 00:08:31,110 --> 00:08:35,130 And you can get a lot more characteristics and higher order filters. 134 00:08:35,130 --> 00:08:38,900 So, commonly when people have to build filters for 135 00:08:38,900 --> 00:08:43,000 specific measurements, they often times do it out active filters. 136 00:08:43,000 --> 00:08:45,590 Now, beyond the scope of this class but 137 00:08:45,590 --> 00:08:47,728 it's something that you might want to investigate. 138 00:08:47,728 --> 00:08:51,980 Active filters, outback filters, if ever you have to actually build one. 139 00:08:51,980 --> 00:08:54,630 But the fundamental concepts are the same. 140 00:08:57,220 --> 00:09:01,530 So, this is the last lesson in this module prior to the wrap up, so make sure that 141 00:09:01,530 --> 00:09:05,050 you review the wrap up lesson and also go 142 00:09:05,050 --> 00:09:07,280 to the forum to ask questions and answer questions. 143 00:09:07,280 --> 00:09:09,750 And make sure you do the homework and the quiz for this question. 144 00:09:09,750 --> 00:09:10,110 Thank you.