Welcome back to Linear Circuits. Today we're going to be talking about the Linear Variable Differential Transformer. We'll introduce LVDT sensors which are devices that make use of mutual inductance for their measurement. And show the applications where they can be used. In the previous lesson we talked about the ideal transformer model and how we can find the various voltages based upon the number of turns and the way that the mutual induction works. We are going to make use of that analysis today to see a little bit about how these LVDT systems work. Let's start by explaining the behavior of these systems and how they operate and then identify how you can find the relative position measured by an LVDT. Based upon the magnitude and the phase of the measured voltages. So first of all an LVDT, we can put up a little bit of a technical drawing here to show how they’re constructed and how they work. We have, first of all, a source right here, some kind of input that is putting a sinusoid on a primary coil right here. Now this blue bar, Is a ferris core, and this ferris core can move. Then we have two secondary coils. One is wrapped in one direction. The other is wrapped in the other direction, and they are connected together. I will be designating the voltage across one of the secondary coils as V1 and the voltage across the other one as V2. Now, given the sinusoidal input I see that we get an output that's sinusoidal here for V1 and a output here for V2. Now V2 is in the opposite direction or opposite phase of V1. Here it goes up, here it goes down first. And that's because this coil is wrapped in the opposite direction. But both of these secondary coils are responding to a current put through the primary. If I take the voltage across the whole thing, we can take the sum of V1 plus v2 to find that v out is approximately zero, it's almost flat. This indicates that our bar is in a neutral position. In a LVDT, the bar is the thing that moves. So as I move this bar, we change the mutual inductance. This V2 coil, this secondary, is now not as inductive mutually to the primary. Because there's no ferrous cord moving through it. However, V1 continues to be just as linked as before. So V1 has the same voltage measurement here, V2 is now flat. And so we see that Vout again is sinusoidal. If I move the bar the other direction, the opposite happens. Now V2 remember had an opposite phase it started down. So my output now starts down. Typically we're going to find that the bar is going to be somewhere in between two extremes. So here V1 is its maximum value, V2 has a smaller amplitude and when I put them together Vout has the same phase as V1, but a smaller amplitude. This means that it is somewhere between the neutral state, and maximal V1 state. So consequently amplitude shows the amount of displacement, and phase shows the direction. If it's in the same phase as the input, then that means that it is in this positive direction. If it's in the opposite phase of the input, it's in the negative direction. An LVDT could be diagrammed sort of like this where we see there is a primary coil here in the middle. And then two secondary coils. And these represent wires that are wrapped around and around, again and again, and it's here cutaway. And then here we have the ferrous core, which is connected to a piston that can move back and forward. This allows the mutual inductance to occur. And by taking measurements, we can see how far this is displaced. It's capable of very high precision, since we have devices that are able to very accurately measure voltages. It's completely electrically shielded, so the moving parts here are protected from the wires. There's no actual connection, it doesn't have to touch, it just needs to be close. And so consequently, LVDTs can operate in very extreme conditions without any problem. We also see that there's all sorts of ability of removing this core, replacing it if there's some mechanical problem with it. So LVDTs often find application in situations where you need precise measurements. Perhaps to make sure that a factory line is producing devices that have correct measurements to specifications. And they can operate in very extreme conditions without harm to the devices. All you need to be able to do is get to the wires to measure. So in summary, we described the behavior of LVDT sensors and described how to identify the position based upon the amplitude and the phase. Then we described the benefits of using such a sensor. And this concludes the module five material, so we will have a wrap up. And that will conclude the course. Until then.