ECE3300 Lecture 12b-3 Smith Chart transmission coefficient

Uploaded by cfurse on 24.09.2009

Now let's talk about how to use the Smith Chart to found the transmission coefficient. The transmission
coefficient is 1+ the reflection coefficient. The transmission coefficient tells us how much voltage is
transmitted divided by how much voltage was incident on a load for instance. The transmission
coefficient can be found using a different set of axes. So instead of using the axis that said angle of
reflection coefficient I'm going to use this axis that says angle of transmission coefficient in degrees. See
how it goes around like this. It is the inner most line of the Smith Chart axes out here. So that's where
I'm going to find the angle of the transmission coefficient. Then I'm going to find right here this line
right here that tells me the transmission coefficient for E or I is the same thing for the transmission
coefficient for the voltage. Now let's suppose for instance that I had a reflection coefficient here at 45
degrees, let's find our transmission coefficient 45 degrees. Sorry our reflection coefficient. That's the
angle of the reflection coefficient let's draw our straight line from the center of the Smith Chart out to
the point like this, and let's just chose a point right here, that's my reflection coefficient. I can also find
the transmission coefficient from that same point and what I do is read off the angle of the transmission
coefficient. So you can see here it is 10, 15, 20, 25. It looks like the angle of the transmission coefficient
is about 22.5 degrees in this example. Let's find its magnitude. We do that the same way that we found
the magnitude of the reflection coefficient, except that instead of using the reflection coefficient we use
the transmission coefficient axis. So take your piece of paper, mark this distance right here from the
center to the point that you're interested in. Bring it down to the Smith Chart and line it up again from
the center, we always start at the center, then draw a line right down here. It looks lying the magnitude
of the transmission coefficient is about 1.55. Now again let me emphasize that this center point right
here is always where we are going to start. We are always going to line up this point right here with this
point right here, whatever measurement that we are doing. What if I wanted to find the transmission
coefficient for power? Look there's another axis right here that will give me the transmission coefficient
for power. Its magnitude is 0.7. Its phase is the same as you see up her here at the top 22.5 degrees.
There also is a reflection coefficient for power right there. And we can use that for measurement as well