[Antennas] Elementary Antenna Question

[Andy]

Taking another swing at all this ...

Antenna efficiency, feedpoint resistance, and SWR are not closely related.
Well, yes they are 'related', but not as easy as you may be thinking.

It is easy for the SWR dip to NOT correspond to the point where resistance R
is 50 ohms.  It depends on what the reactance X is doing.  Only when X = 0,
will the SWR dip correspond to R = 50; and you often don't have that.  In
your case X is probably sizable, and happens to become more favorable as far
as SWR is concerned (and probably becomes lower) when R is 38 ohms.

If you want to find where the antenna is resonant, look for X = 0.

If you want to find where the most power is transferred to the load in a 50
ohm system, look for the SWR dip, even if R isn't 50.

But if you are talking about antenna efficiency ... that's harder to define
because the meter doesn't say anything about efficiency.  It only measures
the total resistance / reactance / impedance at the point you are measuring
it, without regard to what component of it is radiation resistance and what
is loss resistance.

If the loss resistance is constant (a big IF), then perhaps looking for a
higher R value would optimize efficiency ... but not necessarily transmitted
signal.

Andy