ECE3300 Lecture 12b-9 Smith Chart slotted line example

Uploaded by cfurse on 24.09.2009

Now let's do an example. Let's do the slotted line example 2-5 on
page 60 of your textbook. This was done in the classical way in
the textbook, and let's look at how to do this with a Smith chart.
This is a problem where you are given the location of the voltage
minimum is 12 centimeters. The voltage standing wave ratio is 3
and you want to find the load impedance. So the first thing that
we're going to do is plot the voltage standing wave ratio of 3.
Right here is the value of 3. So we can see that the voltage
standing wave ratio right here at 3. Now, let's just use a
protractor or my piece of paper and let's draw the voltage
standing wave ratio of 3 kind of going around like so. It's
basically a circle. Like this. That's the voltage standing wave
ratio VSWR equals 3 circle. Now let's find the location of the
voltage minimum. This axis right here is the L-min axis. So this
point right here is L-min. Let's see how far away that is from
the load in terms of wavelengths because that's what we need for
the Smith chart. So L-min in wavelengths is going to be 12
centimeters divided by the wavelength, which is 0.6 centimeters or
0.2 wavelengths. So if I'm at L-min and I go towards the load,
0.2 wavelengths, I'm going to come to the load. So let's read our
value out here. We can see that we are at 0 and we're moving in
wavelengths towards the load. So I'm going to go 0.2. So here's
about 0.1, .15. Make sure I'm getting these values right. I want
to go 0.2 wavelengths. It's right there. Let's draw our straight
line from the center out to 0.2 wavelengths like this, and then
I'm going to mark my distance right there on that point. It's
right here. That is my load value. ZL. I went 0.2 wavelengths
towards the load from the location of the voltage minimum to the
location of ZL. Let's read its value. It looks like its real
part is about 1.8 and its imaginary part is about 1.2. In order
to get this to ohms, I'm going to multiply that by Z naught which
is 50 ohms. Now, one question that comes up and certainly it came
up here in this picture is how accurate do you need to be. A
Smith chart is not an awfully accurate device. It's not as
accurate as calculating this from scratch on your computer, of
course. But it gives us a fantastic feel for what is going on in
our circuits. So frankly if you are as accurate as a broad felt
tip pen I'll be completely content. On the exams what I'm looking
for are that you do the steps correctly; that you follow the right
axes; that you follow these lines, for instance, these lines, and
these and that you go the right directions. The absolute
accuracy, pretty flexible on that.