Uploaded by cfurse on 24.09.2009

Transcript:

Welcome to ECE 3300 at the University of Utah. In Lecture No. 13

we're going to be talking about impedance matching. The idea of

impedance matching is to be able to connect something like an

antenna or another kind of load that might not be 50 ohms. We

want to be able to connect that to a 50-ohm generator or 50-ohm

transmission line and not have any reflections and therefore we

want to do an impedance matching circuit. The first thing that

we're going to learn is how to add parallel or series lumped

elements to a circuit. Sometimes this is done for matching but it

can also be done for other reasons. We also are going to learn to

use single stubs to match our circuits. The stubs could be either

series or parallel, open or short-circuited. Sometimes single

stub matching is called distributed, matching or matching with

distributed elements. We also are going to learn how to match a

complex load with a quarter wave transformer. So here's the idea

of single stub matching networks. If we have a transmission line

which has a characteristic impedance Z naught and a load which is

not equal to Z naught, we want those to be able to be matched. So

sometimes we will put just a stub in series here. Get rid of this

little part right there. And what we'd be looking for is the

distance between the stub and the load and the length of the stub.

This is shown as a short-circuited stub. We also have

open-circuited stubs. And by the time we get right here to this

point, the input impedance of our line should equal the

characteristic impedance. This is matched. Another way to do

this is to use a parallel stub. That's, again, where our load is

not equal to our characteristic impedance and we just put a stub

in parallel. Again, we design D and we design L and this one is

shown as an open circuit. Here's the basic idea behind stub

matching. Let's consider what would happen on our Smith chart if

we were right here and we said we wanted Zin to equal Z naught plus

J0. If we normalize this, this would be 1 plus J0 and that's what

we would want to plot on our Smith chart. So if we were designing

a series stub match like this right here, we would know that at

this point we want to be a real part of 1 and an imaginary part of

0. Well, what happens when we rotate on the Smith chart a

distance D? We can rotate on the Smith chart and change both the

real and imaginary part. So this value changes -- I'm going to

use delta to mean change -- the real and the imaginary part of ZL.

But what about this little stub right here? This stub can either

be an inductor or capacitor but it can't be a resistor. So the

only thing this can change is the imaginary part. So what I'm

going to need to do is to rotate a distance D to fix my real part.

It will also change my imaginary part, and I'm going to call that

ZA. That point I'm going to consistently use as ZA. And then

when we add in this stub, we're going to remove the imaginary part

and not change the real part and that way we'll end up with the

real part we want and also the imaginary part that we want. So

there are several things that we need to learn in order to do

this. One is how to add series elements. Another is what it

means to rotate and design a single stub matching network. We

also need to know how to make a short-circuited or open-circuited

line act like the imaginary part that we want. So that's what

we're going to be working on in the next several set of slides.

we're going to be talking about impedance matching. The idea of

impedance matching is to be able to connect something like an

antenna or another kind of load that might not be 50 ohms. We

want to be able to connect that to a 50-ohm generator or 50-ohm

transmission line and not have any reflections and therefore we

want to do an impedance matching circuit. The first thing that

we're going to learn is how to add parallel or series lumped

elements to a circuit. Sometimes this is done for matching but it

can also be done for other reasons. We also are going to learn to

use single stubs to match our circuits. The stubs could be either

series or parallel, open or short-circuited. Sometimes single

stub matching is called distributed, matching or matching with

distributed elements. We also are going to learn how to match a

complex load with a quarter wave transformer. So here's the idea

of single stub matching networks. If we have a transmission line

which has a characteristic impedance Z naught and a load which is

not equal to Z naught, we want those to be able to be matched. So

sometimes we will put just a stub in series here. Get rid of this

little part right there. And what we'd be looking for is the

distance between the stub and the load and the length of the stub.

This is shown as a short-circuited stub. We also have

open-circuited stubs. And by the time we get right here to this

point, the input impedance of our line should equal the

characteristic impedance. This is matched. Another way to do

this is to use a parallel stub. That's, again, where our load is

not equal to our characteristic impedance and we just put a stub

in parallel. Again, we design D and we design L and this one is

shown as an open circuit. Here's the basic idea behind stub

matching. Let's consider what would happen on our Smith chart if

we were right here and we said we wanted Zin to equal Z naught plus

J0. If we normalize this, this would be 1 plus J0 and that's what

we would want to plot on our Smith chart. So if we were designing

a series stub match like this right here, we would know that at

this point we want to be a real part of 1 and an imaginary part of

0. Well, what happens when we rotate on the Smith chart a

distance D? We can rotate on the Smith chart and change both the

real and imaginary part. So this value changes -- I'm going to

use delta to mean change -- the real and the imaginary part of ZL.

But what about this little stub right here? This stub can either

be an inductor or capacitor but it can't be a resistor. So the

only thing this can change is the imaginary part. So what I'm

going to need to do is to rotate a distance D to fix my real part.

It will also change my imaginary part, and I'm going to call that

ZA. That point I'm going to consistently use as ZA. And then

when we add in this stub, we're going to remove the imaginary part

and not change the real part and that way we'll end up with the

real part we want and also the imaginary part that we want. So

there are several things that we need to learn in order to do

this. One is how to add series elements. Another is what it

means to rotate and design a single stub matching network. We

also need to know how to make a short-circuited or open-circuited

line act like the imaginary part that we want. So that's what

we're going to be working on in the next several set of slides.