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


"Roy Lewallen" wrote in message
...
It might be helpful to elaborate a bit more about radiation resistance.

Consider an antenna that has no loss. If we apply 100 watts, say, to this
antenna, the radiation resistance "consumes" that 100 watts. That is to
say, all 100 watts is radiated.

In the case of a resonant lossless quarter wave vertical, for example, the
current at the base will be about 1.67 amps if 100 watts is being
radiated. We can solve for Rr at the base from P = I^2 * Rr, where I is
the base current, to get Rr = P / I^2, with the result that Rr is about 36
ohms. This is the radiation resistance referred to the base -- it
"consumes" the 100 watts. (We could have calculated Rr at some other point
along the antenna, where I is different, and gotten a different value. But
P still has to equal I^2 * Rr, where I is the current at the point to
which Rr is being referred.)

Now, what determines the current we get at the base, for a given applied
power and radiator length? The answer is the current distribution --
that is, the way the current varies along the length of the conductor.
(I'm only considering a simple single wire antenna here. When other
conductors are involved, mutual coupling between conductors also plays a
role.) Putting a loading coil at the bottom of the antenna doesn't change
the current distribution, it only changes the feedpoint reactance. So it
doesn't change the feedpoint current for a given power input, so the
radiation resistance doesn't change. But if you put a loading coil part
way up the antenna, the current distribution does change. This alters the
base current for the same power input and therefore the radiation
resistance changes. Remember that Rr = P / I^2, where Rr and I are
measured at the same point (in this case the base feedpoint), so if I
changes, Rr changes. Likewise, top loading alters the current distribution
and consequently the radiation resistance. For people who would like to
see this graphically, the demo version of EZNEC is adequate. Just look at
the View Antenna display after running a pattern, source data, or current
calculation, and you'll see how the current varies along the antenna. If
you set a fixed power level in the Options menu (Power Level selection),
you can also see, by clicking Src Dat, exactly how the current at the
source changes as the current distribution does.

If you have a fixed amount of loss, say at the base of the antenna due to
ground system loss, the amount of power dissipated in that loss as heat is
Ploss = I^2 * Rloss, where I is the current flowing through that loss, in
this case the current at the antenna base. So for a given amount of
applied power, you minimize the power lost when you minimize the base
current. This is exactly equivalent to saying you're raising the radiation
resistance referred to the base. That's why mobile antenna users consider
higher radiation resistance a virtue -- it means lower feedpoint current
for a given power input, and therefore less power lost in the necessarily
imperfect ground system.

While the principles are all the same, wire loss has to be treated a bit
differently because altering the current distribution changes the amount
of wire loss (which is usually combined into a single loss resistance
referred to the feedpoint, or the same point where the radiation
resistance is referred). Also, changing the wire length alters the wire
loss, as does the total current in the wire which increases as the wire is
shortened for a given power input. All these can be dealt with
analytically or with a modeling program, but it's easy to lose track of
exactly what's happening when all these factors are present at the same
time. Fortunately, wire loss is insignificant for the vast majority of
typical amateur applications. With modeling, it's easy to determine when
it is and isn't significant, simply by turning wire loss on and off and
observing how much the results change.

Roy Lewallen, W7EL