ECE3300 Lecture 4-1 Transmission Line Introduction

Welcome to ECE 3300, Introduction to
Electromagnetics at the University of Utah. In lecture
number four, we're going to be talking about
transmission lines, a basic introduction so that you can
understand the important parameters we'll be using
the rest of the semester.
One of the most common kinds of
transmission lines is a coaxial line. In a coaxial line, you
have a center conductor usually cylindrical. It could
either be solid or it could be hollow like a pipe and it's
metal. Around the outside of that, you have another
piece of metal that's also cylindrical. Most often that's
braided just kind of a metallic braid like this but it can
also be solid. This piece right here is metal and the
internal piece is metal.
In order to put a voltage between them, we
normally would put a positive voltage here on the
center conductor and the negative voltage or ground on
the outside conductor. In between them is some kind
of insulator. It might be air. It might be ceramic. It
might be some kind of foam.
So if we modeled this transmission line, I'm
going to say that this point here is A and this point
here is A prime and that this voltage is VG for voltage
of the generator, and let that be a time domain voltage
for now. So if I drew a picture of this transmission
line, at least the start of it, it would look something
like this, A and A prime, and then I'd have a
transmission line. Here's the inner conductor of the
coax and here's the outer conductor of the coax, and
then some place on the end, I would have a load. So
that's a basic model of this transmission line.
Here's a picture of that put together. So
right here, you can see the voltage of the generator,
positive and negative. We're going to have a generator
resistance. Typically, that might be, I don't know, high
impedance, low impedance. In most of the cases, for
our electromagnetics, this would be a 50 ohm
generator and then we connect between A and A prime
on to the transmission line. Again, this top piece would
be the inner conductor and the lower piece would be
the outer conductor, and then we connect it onto some
kind of load whatever we were trying to take the power
to that we wanted to drive, and we'll connect the load
through B and B prime, and we're going to call the
resistance to the load, RL. So that's the basic model of
this transmission line.
Now, there are other kinds of transmission
lines too, for instance, the circuit board. Let's take a
little piece of circuit board like this and let's suppose
that we want to connect a digital chip. Perhaps it's a
clock chip. We want to connect a clock onto a memory
chip. So here's pin number one, here's pin number one,
here's the clock, and here's the memory, and as we
send our clock signal like this, we're sinusoidal. We
want to be able to trigger something over here on the
memory. If this board is pretty small then this clock
signal is almost going to instantaneously get to the
memory and trigger it, but if this board happens to be
large this clock signal could be delayed substantially
before it gets to the memory.
In order for us to decide if this is a large or a
small board this depends on two things. It depends on
the actual dimensions so the size in meters and it
depends on the frequency. The reason it depends on
the frequency is because that controls the wavelength.
If we consider a transmission line like this, the only
time we're going to have a substantial delay between
points A and points B is if this length, L, is on the
order of a wavelength or if it's bigger than a
wavelength. A wavelength, if you remember -- so the
wavelength is 360 degrees or two pi radians. So if I
had a sine wave like this and I was off by, let's say, ten
degrees, there's the delay that I might be
experiencing, but if I were off by a 180 degrees, here
would be my delay. So you can see that we need to
consider transmission line effects any time that our
transmission line is a significant portion of a
wavelength long.