Hi Rik,
Now I have had time to study your web page on 136 antennas, I have the
following comments, which I hope you will find useful.
1. The reason that the antenna current decreases linearly to zero at the end
of the antenna, is because sin(x) = x approx for small values of x, and for
most amateur antennas the lengths involved are only a fraction of a
wavelength.
Similarly the reason the voltage is practically constant over any continuous
segment of wire making up the antenna is because cos(x) =1 approx.
2. There are several useful programs from G4FGQ for determining probable
environmental loss for a given site.
3. The values of Q for loading coils, that you have used in examples are
very conservative, it is not particularly difficult to obtain higher values
of Q especially for small elevated coils.
4. From your explanation of how to calculate ERP, it follows that in order
not to exceed 1 watt ERP, we must not exceed approx. 0.55 watt radiated
power.
5. I thought at first that you had lost a factor of 4 (two squared) in
formula 5a, but later realised that the ratio is calculated with respect to
the average current in a monopole, which is 50%. It might be useful to make
this clear, assuming that it isn't just me who trips over this one.
6. The results of calculations agree well with those obtained from G4FGQ's
program TANT136.
7. The paragraph just above the graph in section 2.2, states that the gain
that can be achieved &is 6dB. The reason for this is that one can at most
double the average current in the vertical, which occurs when the current is
constant over the vertical segment.
8. Concerning Umbrella antennas, i.e. capacitive top loading with down
sloping top loading wires, you suggest a maximum vertical descent of 50%
should not be exceeded. In a comment regarding the Galveston NDB, someone
(sorry I have forgotten who) said that the textbooks on VLF recommend not
more than 30%. I decided to try to determine the optimum value and came up
with the following formula:
The Optimum length of a down sloper from the top is h(sqrt(1+sec(alpha))
1), where h is the height of the main mast and alpha is the angle of the
sloper from the vertical. Which this length the Radiation Resistance
compared with a monopole of the same height is increased by a factor of
4 * (1 + cos(alpa))^2 * (1  sqrt(cos(alpha)/(1+cos(alpha)))^2. This
increases monotonically with alpha. At 89 degrees, L is approx. 6.6 * h and
the Radiation Resistance is approx. 3 * that of Monopole.
For an angle of 45 degrees, the sloper should descend 39% of the height and
the multiplication factor for Rr is only 1.48.
9. You give some useful results and graphs for inductive loading. I would
only like to comment that the elevated coil need not be the full value to
resonate the top part of the antenna. A combination of top capacitive and
inductive loading can be beneficial, e.g a 60 metre horizontal top and a 3
mHenry coil will practically achieve the full 6 dB increase.
10. Section 2.7 Antennas with multiple vertical elements. This looks like a
good idea, which needs to be investigated further.
11. Section 2.10 Helical antenna. You point out that if capacitive top
loading is added the advantage of a helical antenna will be less. This is of
course relatively speaking. This is really a case of "less is more".
Congratulations on a fine piece of work. I for one feel that at last I am
beginning to understand LF antennas.
73 John, G4CNN
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