ECE3300 Lecture 3-1 waves

Uploaded by cfurse on 26.08.2009

Welcome to ECE 3300, Introduction to
Electromagnetics. This lecture is lecture number
three. We're going to be talking about traveling waves.
There are three important factors to
remember about waves. The first is that moving waves
actually carry energy. They carry power and voltage
and current from one location to another. For example,
when a ship passes through water and creates a wave,
that's really an energy source. You can certainly feel it
if you are in a boat near that ship.
The second thing to remember is that waves
have velocity. They move with different speeds in
different media. The very fastest velocity in all of our
applications is going to be in air or in vacuum, and the
third is to remember that they are in linear. They add
up so if I have one wave coming from one direction and
another wave coming from another direction, I can find
the total field at any location just by adding up or
summing these two waves.
Now, there are several ways that we
categorize waves in electromagnetics. One of them is a
function of time. So if we put time on this axis, a
sinusoidal wave would come in and run something like
this so it would be a sine wave. A sine wave is also
called a CW wave. CW stands for continuous wave and
what that means is that we assume that a sine wave has
been going forever. We don't assume that it started at
zero and then we saw it coming, you know, from the
left side. We assume that that has been going forever.
So a sine wave or a continuous wave is sometimes also
called a frequency domain wave because the only thing
that we need to know is the frequency and the
amplitude and then the entire wave is defined.
Now a second type of wave would be something
that changes with time so changes substantially with
time; something like a step function from turning a
source on or off, something like a pulse, perhaps like
this maybe another kind of pulse, spike. Another thing
that you might see is a sine wave something stops. All
of these would be called time domain waves because
there's going to be a substantial variation with time.
Some examples of this would be the electromagnetic
pulses that happen because of a large explosion or
turning things on or off, cell phone signals that turn
themselves on or off, those would be typical examples
of time domain for pulsed or electromagnetic pulsed
simulations. Another way that we can describe waves is
in terms of space.
There are three kinds of waves that we
typically talk about in our electromagnetic classes.
One, for instance, is a one dimensional wave. A wave
that has only one dimension is something that is going
to be continuous in a plane and traveling this way. So
this plane right here is going to be copied and copied
and copied, and the only variance in this wave is in this
one dimension, perhaps in the X direction. This would
be typical of waves that are on transmission lines, and
it's equally applicable to something that we call plane
waves, which we will learn about near the end of our
class, near the end of our course. A plane wave is
something that is constant in two directions, say the Y
and the Z direction, but varies in the X direction. So
those would be 1D waves.
2D waves are waves that vary in two
dimensions. That would be typical, for instance,
suppose that I had a current or some source that was
linear that went from minus infinity to plus infinity.
It's an infinitely long type of system, and then I would
see variation in this plane right here. So in this case,
for instance, the wave would propagate out away from
this current. That would be very much the same as
dropping a stone in the water and having the waves
propagate out from the stone. So that's a two
dimensional wave. These are also called cylindrical
waves and typically, those are caused by very long wire
antennas. An example where you might use antennas
like that would be in geophysical prospecting where you
want to be able to find things that are under the
ground and you use a very, very long wire for that.
A third type of wave is a three dimensional
wave. Most of our realistic situations....