1 00:00:01,490 --> 00:00:04,298 Welcome back to linear circuits. Today we're going to be talking about the 2 00:00:04,298 --> 00:00:08,148 linear variable differential transformer. We'll introduce LVDT sensors, which are 3 00:00:08,148 --> 00:00:11,498 devices that are used, that make use of mutual inductance for their measurement 4 00:00:11,498 --> 00:00:15,075 and show the applications where they can be used. 5 00:00:15,075 --> 00:00:18,660 In the previous lesson, we talked about the ideal transformer model. 6 00:00:18,660 --> 00:00:22,365 And how we can find the various voltages based upon the number of turns and the, 7 00:00:22,365 --> 00:00:27,303 the way that the mutual inductions works. We're going to make use of that analysis 8 00:00:27,303 --> 00:00:30,919 today to see a little bit about how these LVDT systems work. 9 00:00:30,919 --> 00:00:34,455 We'll start by explaining the behavior of these systems and how they operate, and 10 00:00:34,455 --> 00:00:37,575 then identify how you can find the relative position measured by an LVDT 11 00:00:37,575 --> 00:00:43,400 based upon the magnitude and the phase of the measured voltages. 12 00:00:43,400 --> 00:00:47,112 So, first of all, an LVDT, we can put up a little bit of a technical drawing here 13 00:00:47,112 --> 00:00:51,110 to show how they're constructed and how they work. 14 00:00:51,110 --> 00:00:56,752 We have first of all, a source right here, some kind of input that is putting 15 00:00:56,752 --> 00:01:04,454 a sinusoid on a primary coil, right here. And this blue bar is a ferrous core, and 16 00:01:04,454 --> 00:01:09,210 this ferrous core can move. Then we have two secondary coils: one is 17 00:01:09,210 --> 00:01:13,045 wrapped in one direction, the other is wrapped in the other direction and they 18 00:01:13,045 --> 00:01:19,029 are connected together. I will be designating the voltage cross 19 00:01:19,029 --> 00:01:23,745 one of the secondary coils as v1 and voltage cross the other as v2. 20 00:01:23,745 --> 00:01:29,274 Now, given the sinusoidal input, I see that we get a, an output that's 21 00:01:29,274 --> 00:01:35,425 sinusoidal here for v1 and an output here for v2. 22 00:01:35,425 --> 00:01:40,270 Now, v2 is in the opposite direction or opposite phase of v1. 23 00:01:40,270 --> 00:01:44,119 Here it goes up, here it goes down first. And that's because this coil is wrapped 24 00:01:44,119 --> 00:01:47,847 in the opposite direction. But both of these secondary coils are 25 00:01:47,847 --> 00:01:51,035 responding to a current put through the primary. 26 00:01:51,035 --> 00:01:55,437 If I take the voltage across the whole thing, we can take the sum of v1 plus v2 27 00:01:55,437 --> 00:02:01,660 to find that v out is approximately zero. It's almost flat. 28 00:02:01,660 --> 00:02:05,410 This indicates that our bar is in a neutral position. 29 00:02:05,410 --> 00:02:07,920 And in LVDT the bar is the thing that moves. 30 00:02:07,920 --> 00:02:10,970 So, as I move this bar, we change the mutual inductance. 31 00:02:12,470 --> 00:02:20,390 This v2 coil, this secondary, is now not as inductive mutually to the primary. 32 00:02:20,390 --> 00:02:22,840 Because there's no ferrous core moving through it. 33 00:02:22,840 --> 00:02:27,260 However, v1 continues to be just as linked as before. 34 00:02:27,260 --> 00:02:32,410 So, v1 has the same voltage measurement here, v2 is now flat. 35 00:02:32,410 --> 00:02:35,000 And so, we see that v out again is sinusoidal. 36 00:02:35,000 --> 00:02:39,410 If I move the bar the other direction, the opposite happens. 37 00:02:39,410 --> 00:02:43,860 Now, v2, remember, had an opposite phase. It started down, somewhere up, and now it 38 00:02:43,860 --> 00:02:46,671 starts down. Typically, we're going to find that the 39 00:02:46,671 --> 00:02:49,555 bar is going to be somewhere in between the two extremes. 40 00:02:49,555 --> 00:02:54,990 So here, v1 is at its maximal value, v2 has a smaller amplitude. 41 00:02:54,990 --> 00:02:58,884 And when I put them together, Vout has the same phase as v1, but a smaller 42 00:02:58,884 --> 00:03:03,007 amplitude. This means that it is somewhere between 43 00:03:03,007 --> 00:03:05,483 the neutral state and the maximum v1 state. 44 00:03:05,483 --> 00:03:10,441 So, consequently, amplitude shows the amount of displacement, and phase shows 45 00:03:10,441 --> 00:03:14,799 the direction. If it's in the same phase as the input, 46 00:03:14,799 --> 00:03:18,560 then that means that it is in this positive direction. 47 00:03:18,560 --> 00:03:21,620 If it's in the opposite phase of the input, it's in the negative direction. 48 00:03:23,150 --> 00:03:27,470 An LVDT could be diagrammed sort of like this, where we see that there is a 49 00:03:27,470 --> 00:03:33,060 primary coil here in the middle and then two secondary coils. 50 00:03:33,060 --> 00:03:35,805 And these represent r, wires that are wrapped around and around again and 51 00:03:35,805 --> 00:03:38,845 again. And it's here cutaway. 52 00:03:38,845 --> 00:03:42,365 And then here we have the ferrous core, which is connected to a piston that can 53 00:03:42,365 --> 00:03:46,377 move back and forward. This allows the mutual inductance to 54 00:03:46,377 --> 00:03:49,684 occur. And by taking measurements, we can see 55 00:03:49,684 --> 00:03:54,390 how far this is displaced. It's capable of very high precision since 56 00:03:54,390 --> 00:03:58,610 we have devices that are able to very accurately measure voltages. 57 00:03:58,610 --> 00:04:02,948 It's completely electrically shielded. So, the moving parts here are protected 58 00:04:02,948 --> 00:04:06,352 from the wires. There's no actual connection, there's it 59 00:04:06,352 --> 00:04:09,770 doesn't have to touch it just needs to be close. 60 00:04:09,770 --> 00:04:13,522 And so, consequently, LVDTs can operate in very extreme conditions without any 61 00:04:13,522 --> 00:04:16,590 problem. We also see that there's all sorts of 62 00:04:16,590 --> 00:04:20,074 ability of removing this core, replacing it if there's some mechanical problem 63 00:04:20,074 --> 00:04:23,605 with it. So, LVDTs often find application in 64 00:04:23,605 --> 00:04:27,540 situations where you need precise measurements. 65 00:04:27,540 --> 00:04:31,140 Perhaps to make sure that a, a factor line is producing devices that have 66 00:04:31,140 --> 00:04:35,220 correct measurements to spec, their specifications, and they can operate in 67 00:04:35,220 --> 00:04:40,930 very extreme conditions without harm to the devices. 68 00:04:40,930 --> 00:04:42,990 All you need to be able to do is get to the wires to measure. 69 00:04:44,030 --> 00:04:46,865 So, in summary, we've described the behavior of LVDT sensors and described 70 00:04:46,865 --> 00:04:50,830 how to identify the position based on amplitude and the phase. 71 00:04:50,830 --> 00:04:52,935 Then we describe benefits of using such a sensor. 72 00:04:52,935 --> 00:04:55,924 And this concludes the Modulel five material so, we will have a wrap up and 73 00:04:55,924 --> 00:04:58,670 that will conclude the course. That's all then.