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Now let's take a look at the Smith Chart and how we use that plot the reflection coefficient. On the
Smith Chart we are going to plot the reflection coefficient in its polar form, which means it has a
magnitude and a phase. Let's take a look at the various places we are going to be examining for the
reflection coefficient. I want you to notice right here there's a little wording that says angle of the
reflection coefficient and the degrees. When we read this axis right here, that's the axis that tells us
the polar degrees, the polar angle of the reflection coefficient. So let's look and see if that is
consistent with what we had seen in our previous example before we actually included the Smith
Chart. So let's take a look. Let's suppose that we wanted to plot a magnitude of 1. I'm going to come
right out here to the edge. There's my magnitude of 1. That should be magnitude of 1 with a phase of
0 degrees. Let's see if we can read that. Well, it's hard to see right here, but if I use that center point.
See how it is +20 over here and -20 over here. Well, inbetween that would be 0. So here's 1 at an
angle of 0. Let's look at our angle of 45 degrees here. Here's the angle of reflection coefficient at 20,
30, 40, 50. Right there is an angle of 45 degrees. So if I wanted to plot my reflection coefficient with an
angle of 45 degrees, I would take a straight edge or piece of folded paper and I would simply draw a
line like this between the center of the Smith Chart and the outside of the Smith Chart at 45 degrees.
So that's how we find the angle. That's by reading the yellow circle on the outside. Now let's talk
about how to find its magnitude, and let me show you where that is. Right down here is a little axis
that says the reflection coefficient of E or I that is also the reflection coefficient of the voltage. And
that's what I'm going to be able to read to tell me the magnitude of the reflection coefficient. Let's
check right out here, Let's check our value where we know the magnitude should be 1 with a phase of
0 degrees. I'm going to take my piece of paper and I'm going to mark these two points because that's
showing me the magnitude of the reflection coefficient. So I'm going to mark that on my piece of
paper or my straight edge, then I'm going to bring it down here. I'm going to start it here at the center,
see right there, and I'm going to come over to where my mark is right there at 1. So the magnitude of
this reflection coefficient when I read it right there is 1. What would have happened if I had my
reflection coefficient right here? Let's mark that one, see mark right here at the center, mark right
there on your piece of paper, then bring it down to your reflection coefficient axis. Start at the center,
always start here at the center and come out to this point. In this case the magnitude of the reflection
coefficient is 0.3. I can read that number right there. Now let's go back to our other case, where I was
centered here on the line, centered here up on the imaginary part. My reflection coefficient is right
here. Let's see what that is. Take my straight edge, my paper, same thing, mark from the center out
to the point that I'm interested in, bring it down to the reflection coefficient axis, mark first at the
center and then at the next point. That would have a reflection coefficient magnitude of 0.6. So this is
how I find the reflection coefficient.