Ah, yes, that's one of those simple observations that lures people into
making false generalizations. I think you'll find that your observation
isn't true for any length, but only for lengths of a quarter wavelength
(for a monopole) and shorter. And only for an antenna consisting of a
single straight wire. Under those conditions, the phase of the current
is nearly constant along the wire, so the fields from the various parts
of the antenna add together in phase at a distant point broadside to the
wire. The maximum field strength is, therefore, proportional to the sum
of the fields from the individual segments which, in turn, is
proportional to the integral of the currents on the segments. Since the
maximum field strength (or gain) doesn't change much from a very short
wire to a quarter wavelength one, the integral of the current stays
pretty constant. But don't, for heaven's sake, think you've discovered a
rule that applies for all antennas. Not even all straight, single wire
monopoles.

Roy Lewallen, W7EL

Frank wrote:
Concerning current distribution -- at least on a monopole above a perfectly
conducting ground. I have noticed that in any antenna, of any length,
inductively loaded, or not, the: Integral of I(z)dz (where the units of dz
are in fractions of a wavelength, and I(z) the current distribution) is
virtually a constant. Assuming the same input power in all cases. Suppose
it seems pretty obvious since the total radiated power from any structure is
also essentially constant. I must admit I have not seen gain increasing,
with decreasing size, but then I have not seriously tried.

Regards,

Frank