Uploaded by cfurse on 24.09.2009

Transcript:

Now let's talk about how to find the admittance on a Smith Chart.

I'm going to begin with the example

where ZL was 50+j50 on a 50 ohm transmission line, so it was 1+j1,

which we plotted right here on the

Smith Chart. This was ZL. If I want to find YL that is 1 over ZL.

The way we find that is called translating

through the center of the Smith Chart. You take your straight edge

and you draw a line from the

center through your point and you continue it on here.

So it's one straight line, right through there,

right through the center of the Smith Chart. Then you mark your

distance like so and you copy that

distance right here, starting at the center, going to this point right there,

this is YL so you can say it's

translating through the center of the Smith Chart to the point YL.

Let's read the value of YL. YL has a real part of about 0.5 and it has an imaginary part

which is negative. Remember down here we have

the ngative imaginary part. Read it right out here.

It has a negative j0.5. If we wanted to know the

admittance in mhos, we would have to denormalize.

So in order to find YL in mhos we are going to

take YL on the Smith Chart and we're going to multiply it by Y-naught.

Y-naught is 1 over Z -naught so it

is 1 over 50. So YL is going to be equal to 0.5 minus j0.5

then we need to multiply 1 divided by 50 and

that's going to give us the value in mhos. And that's equal to 0.01 minus j0.01 mhos.

That's our YL.

Now let's also talk about some very special cases.

We're going to consider an open circuit and short

circuit because they are very important because.

We use them for building things and also many of

our devices end up acting like high or low impedance close to open circuit or short

circuit. So for an open we know that the impedance of an open circuit is

equal to infinity. So let's find where the real

part becomes very very big. Here's the real part of 1, here's the real

part of 2, 50 and so on. Right here

is where we have the impedance of an open circuit. The impedance of a short

circuit is 0. So where is our real part 0 and our imaginary part 0. Our real part

is 0 every place on the outside of the Smith Chart.

So this circle right there is where the real part of 0.

The imaginary part of 0 right along this axis.

So that point right there is Z of a short circuit. Now how about the

admittance of an open or short?

Remember if we wanted to find the admittance we simply

translate through the center of the Smith Chart.

Let's do the short circuit first. We're just going to translate

that through the center of the Smith Chart right over to here.

So this is the admittance of a short circuit. Let's do the same thing with open

circuit and this is the admittance of an open circuit.

Let's also read the reflection coefficient.

So the reflection coefficient of an open circuit we know that ought to be 1.

Let's check ourselves. Right here is the point where I have the Z of the open

circuit and that's where I'm going to find the reflection coefficient.

Its phase is 0, just as we expect, and it's magnitude if you take these two points,

put them on your piece of paper and mark them down here is magnitude of one.

How about reflection coefficient of the short circuit? We know it should be

minus one. So here's the point where we are going to consider the short circuit.

Let's come over here and measure the phase which is 180 degrees,

and then let's bring this magnitude right there, down here to the center,

and it has a magnitude of 1 and a phase of 180 degrees which is -1.

Let me make a note here that when finding the reflection coefficient use the

impedance points. Do not use the Y points in order to find your reflection coefficient.

I'm going to begin with the example

where ZL was 50+j50 on a 50 ohm transmission line, so it was 1+j1,

which we plotted right here on the

Smith Chart. This was ZL. If I want to find YL that is 1 over ZL.

The way we find that is called translating

through the center of the Smith Chart. You take your straight edge

and you draw a line from the

center through your point and you continue it on here.

So it's one straight line, right through there,

right through the center of the Smith Chart. Then you mark your

distance like so and you copy that

distance right here, starting at the center, going to this point right there,

this is YL so you can say it's

translating through the center of the Smith Chart to the point YL.

Let's read the value of YL. YL has a real part of about 0.5 and it has an imaginary part

which is negative. Remember down here we have

the ngative imaginary part. Read it right out here.

It has a negative j0.5. If we wanted to know the

admittance in mhos, we would have to denormalize.

So in order to find YL in mhos we are going to

take YL on the Smith Chart and we're going to multiply it by Y-naught.

Y-naught is 1 over Z -naught so it

is 1 over 50. So YL is going to be equal to 0.5 minus j0.5

then we need to multiply 1 divided by 50 and

that's going to give us the value in mhos. And that's equal to 0.01 minus j0.01 mhos.

That's our YL.

Now let's also talk about some very special cases.

We're going to consider an open circuit and short

circuit because they are very important because.

We use them for building things and also many of

our devices end up acting like high or low impedance close to open circuit or short

circuit. So for an open we know that the impedance of an open circuit is

equal to infinity. So let's find where the real

part becomes very very big. Here's the real part of 1, here's the real

part of 2, 50 and so on. Right here

is where we have the impedance of an open circuit. The impedance of a short

circuit is 0. So where is our real part 0 and our imaginary part 0. Our real part

is 0 every place on the outside of the Smith Chart.

So this circle right there is where the real part of 0.

The imaginary part of 0 right along this axis.

So that point right there is Z of a short circuit. Now how about the

admittance of an open or short?

Remember if we wanted to find the admittance we simply

translate through the center of the Smith Chart.

Let's do the short circuit first. We're just going to translate

that through the center of the Smith Chart right over to here.

So this is the admittance of a short circuit. Let's do the same thing with open

circuit and this is the admittance of an open circuit.

Let's also read the reflection coefficient.

So the reflection coefficient of an open circuit we know that ought to be 1.

Let's check ourselves. Right here is the point where I have the Z of the open

circuit and that's where I'm going to find the reflection coefficient.

Its phase is 0, just as we expect, and it's magnitude if you take these two points,

put them on your piece of paper and mark them down here is magnitude of one.

How about reflection coefficient of the short circuit? We know it should be

minus one. So here's the point where we are going to consider the short circuit.

Let's come over here and measure the phase which is 180 degrees,

and then let's bring this magnitude right there, down here to the center,

and it has a magnitude of 1 and a phase of 180 degrees which is -1.

Let me make a note here that when finding the reflection coefficient use the

impedance points. Do not use the Y points in order to find your reflection coefficient.