L5 3 Inductors

An introduction to inductors and series RL circuits. Support materials can be found in Introduction to Circuits by FT Ulaby, MM Maharabiz, CM Furse, 3ed edition. For ECE1250 at the University of Utah

>> 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.