I've used Smith charts many times on my NanoVNA analysing antennas, but despite being mathematically inclined I never thought of the complex plane mapping invol

I've used Smith charts many times on my NanoVNA analysing antennas, but despite being mathematically inclined I never thought of the complex plane mapping involved f(z) = (z − 1)/(z + 1) The Smith chart is useful to electronic engineers because a given VSWR (the thing you try to minimise to get a good antenna) becomes a circle about the center of the Smith chart VSWR= (1 + | Γ |)/(1 - | Γ |) So to make your antenna better, get the plot closer to the center. Whether it is above the line or below tells you whether the antenna is inductive or capacitive and hence which kind of loading to add.