Further to MFJ-1786 loop antenna – measurements and NEC-4.2 model at 10.1MHz, the question arises as to what commonly used tools readily permit the transformations and analysis.
Some relveant theory: for a load where R is approximately constant and X varies, the half power points occur where R=|X|, and following on from that s11=0.2±j0.4, s11=0.4472∠63.43°, |s11|=-6.99dB, ReturnLoss=6.99dB (yes, the +ve sign is correct), VSWR=2.618 etc.
Finding the points where ReturnLoss is approximately 6.99dB with the cursor on the above diagram is quite easy.
With the VNWA client, Port Extensions is used to rotate the locus, and displaying a “Smith renormalised” plot allow specification of an alternate reference impedance (lower right in green).
Finding the half power points can be done by moving the markers searching for s11=0.2±j0.4.
There are lots of PC clients for analysing antenna impedance measurements, the two presented here are ones I use and are licenced by virtue of ownership of the associated Rigexpert and VNWA products. Not all tools can do these things.
Some of the new clients for the nanoVNA may be suitable… they have all sorts of bells and whisltes but I could not coax them to do these pretty fundamental transformations!
Of course can also write your own code in things like Octave, Matlab, Python etc.