>> This is Dr. Cynthia Furse of the University of Utah.
Today, I'd like to talk about inductors.
We're going to talk about what is inductance and how
does it relate to the magnetic field and current?
We'll explain the effect of different inductor parameters,
and finally what it does to a voltage and current in the circuit.
An inductor is a passive element that stores energy in the magnetic field.
Passive means that whether or not it's connected to a voltage source,
it's still an inductor.
An inductor is basically a coil of wire.
You can just take a wire
and wrap it around your pencil and you have an inductor.
When you drive current through it as shown here,
you have the effect of the inductance.
The inductance is given in Henries and its N squared.
That's the number of turns,
the number of coil squared times the magnetic permeability times the area,
that's the surface area of this core,
divided by the total length.
Again, it is given in Henries.
The magnetic permeability is a property of the material of the core.
It's given by the magnetic permeability
constant times the relative permeability.
For air mu.R is one.
The core is generally made out of ferrite or magnetic material,
and that's because it increases the total inductance.
So ferrite is typically the material that's used in this core.
This is how you can tell which direction the magnetic field goes.
Take your fingers and wrap them in the direction of current,
the fingers of your right hand and your thumb
will show you which direction the magnetic field goes.
In this case, wrap your fingers in the direction of
the core and you'll see that the magnetic field comes out of the top,
and because magnetic field lines are always closed lines,
it comes back in the bottom.
The magnetic field for this solenoid inductor, is basically doughnut-shaped.
Here's an example of a wire wound inductor.
The core is a non magnetic ceramic.
So it's more or less like air,
except the ceramic holds it together and also dissipates heat.
A very thin wire, thin like is about as thick as your hair,
is wrapped around the ceramic and then attached on
either side to electrodes with a resin coating over the top.
Here's a multi-layer inductor.
The electrodes or connections are on either side,
and you can see that you can just print
a series of loops and you connect them by vias.
Here's an example of a via, here's another via.
A via is where you drill a hole and fill it with solder,
and that basically connects two different layers of your multilayer inductor.
Here's a thin-film inductor made a very similar way where you have
several layers of coils to make the total inductance.
Now, let's talk about the electrical properties of the inductor.
Remember, it's a passive element that stores energy in the magnetic field.
Again, here's a solenoid.
The voltage is given by the inductance times the derivative of the current.
That means, that at DC when there is
no change in the inductance that the voltage will be zero.
That effectively means that the inductor looks like a short circuit at DC.
Here's the equation for the current.
It's the integral of the voltage divided by the inductance.
Here's the equation for the energy.
This is what happens to the inductor.
The current basically starts out at zero and
gradually rises to its full total value for current.
The total value for current,
remember that the inductor would be a short circuit in that case,
would simply be V over R in its final state.
The voltage on the other hand, does change quickly.
It goes from zero to all of a sudden going up
to a maximum value and then dropping on down.
The maximum value of this voltage is the source voltage.
So we can see the time t equals zero,
the current is zero, and the voltage across the resistor is zero.
But the voltage across the inductor is the source voltage.
At time equal infinity or late time steady state,
the current is Vb over R as if the inductor were
a short circuit and the voltage across the resistor goes to Vb,
where as the voltage across the inductor would be zero.
This is all controlled by a time constant.
The time constant for this circuit,
is L over R. Time constant tells us how
quickly the voltage drops or the current rises.
So the way this works,
is current begins to flow in the inductor
and it starts to create a magnetic field.
At time t equals zero,
this acts like an open circuit.
The voltage is high and the current is low.
But very quickly as soon as the magnetic field is established,
the current flows freely.
So at time t equal infinity,
it acts like a short circuit where the voltage is low and the current is high.
So what does the inductor do in a circuit?
Here basically is the equation for the voltage considering the time constant.
This is a picture of the current for this particular example,
where we have a 1K resistor and a one millihenry inductor.
The current rises reaching 66 percent of its value at time tau.
This is what happens to the voltage,
it starts at zero,
it jumps up to the source voltage,
and at tau it's 36 percent of its original value.
So this is what the inductor does to the voltage and current in the circuit.
This is what it would look like if you hit an inductor with a square wave.
The voltage would rise and fall,
and then when the square wave drop,
it would fall and rise.
This is basically acting like a device that gives you
the derivative of the voltage that was initially put on the inductor.
Inductors in series and parallel.
Inductors that are in series add just like they did if they were resistors,
and inductors in parallel add as if they were resistors.
So here's how we can use inductors.
There are many applications for inductors.
Inductive coupling is a very cool thing where you
use the current to produce a magnetic field,
the magnetic field moves to another coil right here where it is picked up,
and a current comes out of this coil.
Here's an example of inductive coupling on the University of Utah campus.
Wave has created an electric powered bus.
Underneath, there's a coil of wire in the bottom of
the Wave bus and then in the concrete underneath is another coil.
The current is induced in the coil on the concrete,
which is picked up in the coil of the bus in
order to charge its batteries at a stop.
Blackrock Microsystems has created
an inductively coupled brain stimulator
where you have a 100 electrodes shown right here,
very small needle electrodes,
and this coil right here with a lot of different turns,
is used to couple to power outside through the skin.
Here's a picture of a passive ID chip.
This is often used in theft detection devices in commercial sales.
Here's a little circuit right there,
and here's the inductor that is picking up the current,
that's picking up the magnetic field from an externally generated source.
Here's a picture of the passive ID that's normally used to tag animals,
and there's the coil inside.
Here's an application of a transformer.
On one side on the primary winding,
you'll have a number of windings N1,
and they will generate a magnetic field which is
going to go through this transformer core shown here.
This doughnut-shaped thing. Then on the other side,
you can have a different number of windings and two,
to pick up the magnetic flux that's going through there.
What will happen, is you will change
the current on this side and you'll get
out actually less current on this side,
less voltage so that you're able to change the voltage across the transformer.
Here are several places that you might have seen transformers;
upon a power pole,
as a charger for your devices,
as a taser or on top of an electric power system.
Inductors can be used as both high and low pass filters.
Here's a picture of a low pass filter,
where the inductor is here and we're reading the voltage
across the resistor. So what happens?
If a DC signal goes through,
the inductor acts like a short-circuit,
and so a large voltage is read across the resistor.
But if a high frequency goes through,
the inductor acts like
an open circuit and so no voltage makes it through to the resistor.
Here is the high pass configuration,
and that's just the opposite.
So I'm sure you're very curious about where the picture
was from the introductory slide.
This is in White Canyon, in American Fork.