Understanding Smith Charts and TL Equations

[Marcin H]

Homework Statement

Homework Equations

Smith Charts
TL equations

The Attempt at a Solution

So I am having a hard time understanding how smith charts work. for this problem in part a, I know we have to find the Normalized impedance first which is:

.5 + j0

And then we have to go to our smith chart to find Gamma. I can plot .5 +j0, but then I am not sure what to do from there. I drew a circle from the center to .5 on the smith chart, but I don't know how to find Gamma using the information given. I think I found the magnitude of gamma correctly (.348) but I don't know how to find the angle. How can we use l=0.4lambda to help us here? Using a formula in the book:

theta = (2d/lamda)*360˚ --> gives me theta=288 but I don't think that is right and I am unsure what to do with that value...

 

[scottdave]

Can you take a picture of what you did on the Smith Chart, so we can see what you were doing?

 

[Marcin H]

might be a bit hard to se, but I put a dot at the normalized impedance and then drew a circle at that radius. I believe I found the magnitude correctly by taking the distance from the center of the circle to the normalized impedance and then checking the length on the bottom ruler. I'm confused by what the distance tells me on the smith chart. l=.4lambda. How can I use that to help me find the angle? I believe the magnitude and angle will give me the generalized reflection coeff like part a ii asksEdit* I also noticed on some youtube videos that you're supposed to draw a line through the normalized impedance point and that will give you the angle. The line that intersects the very inner circle with the angles in degress on the smith chart. But I am not sure if that is correct. Would the angle simply be 0˚?