How come the “r=1 circle” (green) is most important?
Well, assuming that the system impedance is 50 ohm, which is usually the case, r=1 means the actual resistance is 50 [ohm].
So at any point on the green circle, the actual impedance is Z=50+j*X [ohm], right?
Exactly, and since your transmitter is usually designed to work best with the lord impedance of Z0=50 [ohm], once you are on a green circle, all you need to do is to add some reactance to cancel out “j*X” part of Z, which you can realize by adding in series to Z either a capacitor or an inductor with the reactance of “-X”.
You mean if the reactance X is positive, we need a negative reactance to cancel it out, so we put a capacitor in series.
Right, and if the reactance X is negative?
We put an inductance in series!