Uploaded by cfurse on 24.09.2009

Transcript:

Welcome to ECE3300 at of University of Utah. In lecture number 12, we're going to be talking about

Smith charts. Before we start please go to the class website and print out a few Smith Charts to take

notes on. The other reason you'll need some Smith Charts is because the numbers are really tiny to be

able to see them on this video and you will need a Smith chart in front of you. A Smith chart is very

useful for two things. The first is calculation, particularly kind of back-of- the-envelope rough

calculations. The second and perhaps more tant use of the Smith chart today is much of our measuring

equipment in the RF region displays our results on a Smith Chart. So it is important to understand what

you see when you see values plotted on a Smith Chart A Smith Chart can is it used to analyze a

transmission line that is working in steady state. That means that the generator is sinusoidal. So our

signal is sinusoidal, all the transients have died away, and now we are working in a steady state or

continuous wave. Sometimes it is called continuous wave or CW. So it's a sinusoidal exultation with no

transients, it has reached its steady state and that's what we are going to be analyzing with the Smith

Chart. These are the things we are going to be studying. How to plot or find the reflection coefficient in

its real and imaginary or polar form. The transmission coefficient. The various impendence on the line.

How to rotate or move distances toward the generator or toward the load. How to calculate the

admittance on the line, the voltage standing wave ratios and the location of the minima and maxima of

the standing wave envelope. Let's first talk about the reflection coefficient. Remember the reflection

coefficient is related to the load impedance and the characteristic impedance of the line. The largest

reflection coefficient we would have will happen when we have an open circuit. In that case ZL is equal

to infinity and the reflection coefficient will be 1. The small evident coefficient will happen when we

have a short circuit in that case the load is 0 and the reflection coefficient is-1. So the reflection

coefficient ranges between +1 and -1. It has various phases so it is very natural to plot the reflection

coefficient on a polar plot. Let's first consider how the real and imaginary parts of the reflection

coefficient would be plotted. This axis right here would be the real part of the reflection coefficient and

this top part would be the imaginary part of the reflection coefficient. So if I had a real part right here of

a half, and I had an imaginary part of a half, my reflection coefficient would be plotted right here. Now I

could also convert this to a polar form. We start the phase right here from 0. So here is phase equals 0

on the real axis. Phase equals 90 degrees would be here on the imaginary axis. Phase is 180 degrees on

the negative real axis. Phase is 270 degrees on the negative imaginary axis. So the point that I just drew

that had a reflection coefficient of 0.5+j0.5 can also be written as this magnitude. So it's going to have a

magnitude and what's that going to be? 0.5ē+ 0.5ē square-rooted, that's its magnitude and it's going to

have a phase. What's that phase? 45 degrees. So if has a magnitude given here and a phase of 45

degrees. That's how we plot our reflection coefficient. Now let's consider how it would look in polar

form. In polar form remember we said the maximum magnitude is going to be 1. So I'm going to draw a

circle right here that has a radius of 1. And I can plot my reflection coefficient right here if it is 1 at a

phase of 0 and I can plot it up here if it is 1 at the phase of 90 and over here 1 if it is a phase of 180 and so on. If it

happens to be a half right here with a phase of 45 degrees as my previous example, there's the location I

would plot my reflection coefficient.

Smith charts. Before we start please go to the class website and print out a few Smith Charts to take

notes on. The other reason you'll need some Smith Charts is because the numbers are really tiny to be

able to see them on this video and you will need a Smith chart in front of you. A Smith chart is very

useful for two things. The first is calculation, particularly kind of back-of- the-envelope rough

calculations. The second and perhaps more tant use of the Smith chart today is much of our measuring

equipment in the RF region displays our results on a Smith Chart. So it is important to understand what

you see when you see values plotted on a Smith Chart A Smith Chart can is it used to analyze a

transmission line that is working in steady state. That means that the generator is sinusoidal. So our

signal is sinusoidal, all the transients have died away, and now we are working in a steady state or

continuous wave. Sometimes it is called continuous wave or CW. So it's a sinusoidal exultation with no

transients, it has reached its steady state and that's what we are going to be analyzing with the Smith

Chart. These are the things we are going to be studying. How to plot or find the reflection coefficient in

its real and imaginary or polar form. The transmission coefficient. The various impendence on the line.

How to rotate or move distances toward the generator or toward the load. How to calculate the

admittance on the line, the voltage standing wave ratios and the location of the minima and maxima of

the standing wave envelope. Let's first talk about the reflection coefficient. Remember the reflection

coefficient is related to the load impedance and the characteristic impedance of the line. The largest

reflection coefficient we would have will happen when we have an open circuit. In that case ZL is equal

to infinity and the reflection coefficient will be 1. The small evident coefficient will happen when we

have a short circuit in that case the load is 0 and the reflection coefficient is-1. So the reflection

coefficient ranges between +1 and -1. It has various phases so it is very natural to plot the reflection

coefficient on a polar plot. Let's first consider how the real and imaginary parts of the reflection

coefficient would be plotted. This axis right here would be the real part of the reflection coefficient and

this top part would be the imaginary part of the reflection coefficient. So if I had a real part right here of

a half, and I had an imaginary part of a half, my reflection coefficient would be plotted right here. Now I

could also convert this to a polar form. We start the phase right here from 0. So here is phase equals 0

on the real axis. Phase equals 90 degrees would be here on the imaginary axis. Phase is 180 degrees on

the negative real axis. Phase is 270 degrees on the negative imaginary axis. So the point that I just drew

that had a reflection coefficient of 0.5+j0.5 can also be written as this magnitude. So it's going to have a

magnitude and what's that going to be? 0.5ē+ 0.5ē square-rooted, that's its magnitude and it's going to

have a phase. What's that phase? 45 degrees. So if has a magnitude given here and a phase of 45

degrees. That's how we plot our reflection coefficient. Now let's consider how it would look in polar

form. In polar form remember we said the maximum magnitude is going to be 1. So I'm going to draw a

circle right here that has a radius of 1. And I can plot my reflection coefficient right here if it is 1 at a

phase of 0 and I can plot it up here if it is 1 at the phase of 90 and over here 1 if it is a phase of 180 and so on. If it

happens to be a half right here with a phase of 45 degrees as my previous example, there's the location I

would plot my reflection coefficient.