Uploaded by cfurse on 24.09.2009

Transcript:

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.

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.