ECE3300 Lecture 12b-6 Smith Chart input impedance Zin

Uploaded by cfurse on 24.09.2009

Now we're going to talk about how to find the input impedance of a
transmission line when you know its length L and you know its
load, ZL. And you also need to know its characteristic impedance
Z naught. Let's say that ZL is 100 plus J 100 ohms and that the
characteristic impedance is 50 ohms. So in order to plot this on
the Smith chart I'm going to take my load and divide it by my
characteristic impedance which gives me 2 plus J2. Let's plot it.
Here's the circle with the real part of 2. And here is the
imaginary circle with the real part plus 2. So right there is my
load impedance. And I want to be able to find my input impedance
ZN when my length is 0.2 wavelengths, the way I do that is I plot
my load as I have here and then I'm going to use my distance
access. To use the distance access, draw a straight line from the
center of the Smith chart out here to the outside of the Smith
chart. Go through this point. I kind of missed it. But pretty
close. A little hard on a tablet PC. The line that I'm going to
be using to measure distance is going to be on the very outside of
the Smith chart. If I want to go from my load in this direction
to the input impedance, that is towards the generator. The
generator is over here. So I'm going to come to this outside axis
where it says wavelengths towards the generator and it tells me it
goes in this direction. So this axis right here is the one that
I'm going to be reading. Right along there. Now, it does not
matter exactly where I begin on this outside axis. What matters
is the relative distance between two points. Here's the point
that I'm starting with right here. I'm going to kind of put a
little "you are here" point. So right there. There's my "you are
here" point. And that's at the load, and I'm going to move towards
the generator .2 wavelengths. So first I'm going read this value,
which is .21, and then I'm going to add .2 wavelengths. So I want
to come over here, go in this direction, remember that's towards
the generator, until I get to .41. Here's .38, .39, .4. Right
there is .41 wavelengths. That is .21 plus .2 wavelengths. So
now I'm going to draw another straight line from the center of my
Smith chart out to this distance point. And I'm also going to
measure the distance, the magnitude right there, the same way I
have from the beginning. Except I'm going to put it on this axis.
It's going to go from the center, always start at the center,
right to here. So I rotated 0.2 wavelengths. That's L. Towards
the generator. And that brought me to my input impedance. Let's
read its real and imaginary parts. So the input impedance has a
real part right here of about 0.35. The imaginary part is
negative, because I'm below this axis. Negative J. And let's
read the imaginary part, which is right here. Looks like that,
0.6. This is not in ohms. This is a normalized value. So to get
it in ohms I denormalize by multiplying by Z naught. So that
gives me 17.5 minus J, 30 ohms. Now, what if instead of finding
the input impedance I wanted to start at the input and find the
load impedance. That's the topic of our next video.