feed cable in small antenna measurements
OK, if that is the case lets forget about the picture
since is not relevant.
The line of thought would be if you have a balance
structure then you need a differential feeding system.
In other words, if your feeding is a already differential
you do not need BALUN, and if your feeding is single
ended then you need a BALUN or any single ended
to differential transformer.
You were talking about a "monopole" that you connect
and does not have good results. A monopole is not a
balanced structure so it does NOT need a balun.
For dipole, which is a real balanced structure, you will need
a balun. If you connect a coax cable directly to a DIPOLE
the cable becomes an antenna itself. That is what most
of the reference talked about.
For other side you talked about a SMA connector, if the
connector is too big will have an effect over the antenna,
but is not clear in the paragraph below what is the antenna,
a monopole or a dipole........
BUT...if I take my small PCB antenna and I connect
the VNA trought a coax cable placing an SMA connector on
the feed point of the antenna I won't found absolutely correct
results...the problem is always and always the effect of the
cable on the antenna; the dual effect: the cable that acts as
a reflector of the incident field radiated by the antenna and
the active radiation due to the current flowing on the external
face of the coax due to the unbalanced connection of cable to
the antenna.