I was thinking about this, and thoughts turned to a rather simpler antenna; the folded dipole and how it would behave when electrically short.
A simple non-folded electrically short dipole (negelecting all losses) has Rin proportional to 1/L^2 and a highly capacitive reactive term
A folded half-wave dipole fed conventionally has Rin about 4* that of a normal dipole due to current sharing in the legs -.
Now the conumdrum - what does an electrically short folded dipole look like? It has got to be inductive, since we're feeding into a squashed shorted turn, and presumably the current distribution looks short dipole-ish.
So is it a loop, is it a dipole, is it both, how can it be both, if it is what's its radiation pattern ?
Similar to the ground loop/dipole question ?
And is there a length where the inductance of the loop bit resonates with the capacitance that 'ought' to be there due to its also being a short dipole.
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(not really an antenna sort of person)