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 are used, 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, 
the way that the mutual inductions works. 
We're going to make use of that analysis 
today to see a little bit about how these 
LVDT systems work. 
We'll 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. 
And this blue bar is a ferrous core, and 
this ferrous 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 cross 
one of the secondary coils as v1 and 
voltage cross the other as v2. 
Now, given the sinusoidal input, I see 
that we get a, an output that's 
sinusoidal here for v1 and an 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. 
And in 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 core 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 v out again is 
sinusoidal. 
If I move the bar the other direction, 
the opposite happens. 
Now, v2, remember, had an opposite phase. 
It started down, somewhere up, and now it 
starts down. 
Typically, we're going to find that the 
bar is going to be somewhere in between 
the two extremes. 
So here, v1 is at its maximal 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 the maximum 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 that there is a 
primary coil here in the middle and then 
two secondary coils. 
And these represent r, 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, there's 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, a factor 
line is producing devices that have 
correct measurements to spec, their 
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've described the 
behavior of LVDT sensors and described 
how to identify the position based on 
amplitude and the phase. 
Then we describe benefits of using such a 
sensor. 
And this concludes the Modulel five 
material so, we will have a wrap up and 
that will conclude the course. 
That's all then.