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Now, we've just done a series stub match. Let's consider a
parallel stub match. In this case, again, I have ZL and I'm going
to move a distance D to match my line, and then I'm going to add
in a parallel stub. And this time let's do a parallel stub with a
short-circuit on the end. And what I want to know is the length
that I need for this stub. So the first thing that I'm going to
do is normalize and plot my ZL. Let's just use the same one. 2
plus J2. So that's right there. There's my ZL. Now what I'm
going to do is rotate, actually the easiest thing is I can see
that I've got a stub that's in parallel. So it's going to be
easier for me to add admittance at this point. I might just as
well convert to admittance right now. So let's just take ZL and
translate it through the center of the Smith chart. Here is my
distance right there. Mark from here to here on your paper.
Bring it from the center to right there. This is my YL point.
Now, I'm going to rotate YL until I get the real part matched.
That's the same matching circle that I had before. It's right
here. That's the real part. It's equal to 1. So I'm going to
rotate YL, make a note that I converted that to YL. Rotate YL
towards the generator to the matching circle. So here I am
rotating towards the generator. Here we go around towards the
generator. Again, if you had a protractor. Put the center of
your protractor right here. Put the pencil part and draw your
circle. But as usual I didn't bring my protractor. So I'm going
to use just a piece of paper. I'm going to center it here at the
center of the Smith chart, and then I'm going to line up my
distance right there. So this is going to be YA. There's going
to be another choice over here. Again, line up at the center like
this and mark the distance right there on the matching circle. So
here is YA-1 and here is YA 2. I'm going to use YA 1 again
because I'm going to go for the shortest distance (. So this
the generator, is about .455. So that's that one little piece.
And then I'm going to add in this piece, which when this comes
here it's about .175 plus or .175 wavelengths, I guess it's
getting late. So that's my distance D. Now, my real part is
matched, and I need to find out what kind of imaginary value I'm
going to match. What I'm going to do right now is change to a
different color of pen, because I'm going to be doing this stub,
and it acts like it's sort of like a different transmission line.
So let's read off the imaginary part of YA. It's about 1.6. I
know that I want Y stub to equal minus JX. So instead of 1.6, I'm
going to come down here to minus 1.6. And I'm going to call that
Y stub. That is Y at the input of the stub. So let me mark that
by drawing a line straight through it. And then I'm going to
rotate towards the load, the load of the stub, to Y short-circuit.
Y short-circuit is over here. So let's rotate towards the load
this distance right there. And we can read that L is equal to
read on this inside curve right there 0.25, my final destination,
minus the value that's right there, which is about .165
wavelengths. So that's my distance L. If you were asked to
design a parallel...