[Lowfer] Calculating approximate antenna radiation resistance

[Alan Melia]

Hi Andy,
No that is not the way it works.

Take a pure vertical. The radiation from is a function of the current
flowing in each small segment. With a quarterwave physical height the
current distribution looks like a quarter of a sinewave. Averaged over the
full height of the antenna this becomes equivalent to half the peak current
flowing in all the elements. Put another way the base feed current flowing
through all the elements making up half the height of the physical antenna
(approximately) So the effective height (He) of a vertical is around half
its physical height.

Now take a shorter vertical antenna when you extend the top the current also
flows in the topload. This means that there is no longer a zero current
point at the top of the vertical section. Then the average current flowing
in the vertical part becomes greater than half the feed point current and
the effective height increases. The (British) Admiralty Handbook defines a
"form factor" for this effect. It works out that when the length of the
top-load is about equal to the physical height of the antenna the effective
height becomes about 95% of the physical height. Up to this stage you gain
an advantage in increasing effective height (or radiation resistance).
Increasing the top-load beyond this point has little further effect on the
effective height. However it does increase the antenna capacitance, which
can have useful often neglected effects. Doubling the antenna capacitance by
means of the top-load (provided this extra capacitance does not couple to
lossy buildings or foliage will half the ground loss, increasing the antenna
efficiency. The effect is measurable by an rf bridge measurement of the
unloaded wire at the desired frequency. You measure R and C in series and R
is almost entirely the loss (a very small part of a small antenna is the
radiation resistance)

Unfortunately some of the effect of a short top load is that the capacitance
is mainly to the vertical wire and not to the ground. Nevertheless the short
top-load will provide some small advantage but it will be very dependent on
the surroundings. Straight calculations rarely work. Jim Moritz  has found a
5 to 6 dB lower value for antennas in "normal" amateur surroundings. The
equations work if you built it in the middle of a field!!.

NB if the top-hat is "circular" the value for the form-factor equation is
the radius not the diameter, though the wire on the "other side" certainly
increases the capacitance.

I hopes that "math-less" explanation helps a bit.

Alan G3NYK