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.
