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>> This is Dr. Cynthia Furse
of the University of Utah.

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Today, I'd like to talk about inductors.

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We're going to talk about
what is inductance and how

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does it relate to
the magnetic field and current?

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We'll explain the effect of
different inductor parameters,

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and finally what it does to a voltage
and current in the circuit.

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An inductor is a passive element that
stores energy in the magnetic field.

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Passive means that whether or not
it's connected to a voltage source,

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it's still an inductor.

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An inductor is basically a coil of wire.

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You can just take a wire

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and wrap it around your pencil
and you have an inductor.

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When you drive current
through it as shown here,

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you have the effect of the inductance.

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The inductance is given in
Henries and its N squared.

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That's the number of turns,

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the number of coil squared times
the magnetic permeability times the area,

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that's the surface area of this core,

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divided by the total length.

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Again, it is given in Henries.

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The magnetic permeability is a property
of the material of the core.

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It's given by the magnetic permeability

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constant times the relative permeability.

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For air mu.R is one.

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The core is generally made out
of ferrite or magnetic material,

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and that's because it increases
the total inductance.

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So ferrite is typically the material
that's used in this core.

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This is how you can tell which direction
the magnetic field goes.

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Take your fingers and wrap them
in the direction of current,

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the fingers of your right
hand and your thumb

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will show you which direction
the magnetic field goes.

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In this case, wrap your fingers
in the direction of

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the core and you'll see that
the magnetic field comes out of the top,

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and because magnetic field lines
are always closed lines,

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it comes back in the bottom.

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The magnetic field for this solenoid
inductor, is basically doughnut-shaped.

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Here's an example of a wire wound inductor.

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The core is a non magnetic ceramic.

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So it's more or less like air,

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except the ceramic holds it
together and also dissipates heat.

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A very thin wire, thin like is
about as thick as your hair,

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is wrapped around the ceramic
and then attached on

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either side to electrodes with
a resin coating over the top.

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Here's a multi-layer inductor.

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The electrodes or connections
are on either side,

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and you can see that you can just print

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a series of loops and you
connect them by vias.

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Here's an example of
a via, here's another via.

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A via is where you drill a hole
and fill it with solder,

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and that basically connects two different
layers of your multilayer inductor.

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Here's a thin-film inductor made
a very similar way where you have

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several layers of coils to
make the total inductance.

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Now, let's talk about
the electrical properties of the inductor.

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Remember, it's a passive element that
stores energy in the magnetic field.

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Again, here's a solenoid.

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The voltage is given by the inductance
times the derivative of the current.

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That means, that at DC when there is

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no change in the inductance
that the voltage will be zero.

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That effectively means that the inductor
looks like a short circuit at DC.

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Here's the equation for the current.

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It's the integral of the voltage
divided by the inductance.

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Here's the equation for the energy.

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This is what happens to the inductor.

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The current basically
starts out at zero and

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gradually rises to
its full total value for current.

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The total value for current,

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remember that the inductor would
be a short circuit in that case,

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would simply be V over
R in its final state.

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The voltage on the other hand,
does change quickly.

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It goes from zero to all
of a sudden going up

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to a maximum value and
then dropping on down.

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The maximum value of this voltage
is the source voltage.

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So we can see the time t equals zero,

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the current is zero, and the voltage
across the resistor is zero.

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But the voltage across the inductor
is the source voltage.

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At time equal infinity or
late time steady state,

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the current is Vb over R
as if the inductor were

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a short circuit and the voltage
across the resistor goes to Vb,

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where as the voltage across
the inductor would be zero.

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This is all controlled by a time constant.

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The time constant for this circuit,

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is L over R. Time constant tells us how

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quickly the voltage drops
or the current rises.

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So the way this works,

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is current begins to flow in the inductor

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and it starts to create a magnetic field.

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At time t equals zero,

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this acts like an open circuit.

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The voltage is high and the current is low.

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But very quickly as soon as
the magnetic field is established,

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the current flows freely.

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So at time t equal infinity,

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it acts like a short circuit where the
voltage is low and the current is high.

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So what does the inductor do in a circuit?

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Here basically is the equation for
the voltage considering the time constant.

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This is a picture of the current
for this particular example,

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where we have a 1K resistor
and a one millihenry inductor.

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The current rises reaching
66 percent of its value at time tau.

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This is what happens to the voltage,

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it starts at zero,

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it jumps up to the source voltage,

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and at tau it's 36 percent
of its original value.

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So this is what the inductor does to
the voltage and current in the circuit.

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This is what it would look like if you
hit an inductor with a square wave.

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The voltage would rise and fall,

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and then when the square wave drop,

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it would fall and rise.

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This is basically acting
like a device that gives you

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the derivative of the voltage that
was initially put on the inductor.

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Inductors in series and parallel.

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Inductors that are in series add just
like they did if they were resistors,

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and inductors in parallel add
as if they were resistors.

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So here's how we can use inductors.

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There are many applications for inductors.

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Inductive coupling is
a very cool thing where you

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use the current to
produce a magnetic field,

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the magnetic field moves to another coil
right here where it is picked up,

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and a current comes out of this coil.

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Here's an example of inductive coupling
on the University of Utah campus.

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Wave has created an electric powered bus.

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Underneath, there's a coil
of wire in the bottom of

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the Wave bus and then in the concrete
underneath is another coil.

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The current is induced in
the coil on the concrete,

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which is picked up in
the coil of the bus in

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order to charge its batteries at a stop.

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Blackrock Microsystems has created

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an inductively coupled brain stimulator

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where you have a 100 electrodes
shown right here,

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very small needle electrodes,

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and this coil right here with
a lot of different turns,

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is used to couple to power
outside through the skin.

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Here's a picture of a passive ID chip.

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This is often used in theft detection
devices in commercial sales.

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Here's a little circuit right there,

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and here's the inductor that
is picking up the current,

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that's picking up the magnetic field
from an externally generated source.

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Here's a picture of the passive ID
that's normally used to tag animals,

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and there's the coil inside.

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Here's an application of a transformer.

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On one side on the primary winding,

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you'll have a number of windings N1,

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and they will generate
a magnetic field which is

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going to go through
this transformer core shown here.

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This doughnut-shaped thing.
Then on the other side,

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you can have a different number
of windings and two,

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to pick up the magnetic flux
that's going through there.

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What will happen, is you will change

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the current on this side and you'll get

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out actually less current on this side,

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less voltage so that you're able to change
the voltage across the transformer.

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Here are several places that you
might have seen transformers;

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upon a power pole,

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as a charger for your devices,

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as a taser or on top of
an electric power system.

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Inductors can be used as
both high and low pass filters.

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Here's a picture of a low pass filter,

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where the inductor is here
and we're reading the voltage

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across the resistor. So what happens?

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If a DC signal goes through,

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the inductor acts like a short-circuit,

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and so a large voltage is
read across the resistor.

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But if a high frequency goes through,

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the inductor acts like

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an open circuit and so no voltage
makes it through to the resistor.

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Here is the high pass configuration,

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and that's just the opposite.

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So I'm sure you're very curious
about where the picture

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was from the introductory slide.

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This is in White Canyon, in American Fork.