Jim Reid wrote, about the CTSVR:
> Since it is a "folded dipole"
(well, a "folded monopole"...)
>the radiation
>resistance is higher that would be the case with just a plain
>vanilla short vertical radiator. Claim is 50 ohm radiating resistance
>on 160 meters. I wonder if it isn't just the feedpoint impedance
>which is 50 ohms R on 160, but do not know.
That's right, it is only the feedpoint resistance that is raised. The
radiation resistance stays exactly the same as a non-folded monopole with
the same height, effective diameter and loading.
This was discussed on rec.radio.amateur.antenna some time ago, and W7EL
gave an explanation that was so good and clear, I just had to save it.
Here's Roy Lewallen:
Suppose you have a quarter-wave vertical antenna having a radiation
resistance of 36 ohms, and a ground system with 14 ohms of loss. You're
feeding it with coax. The current flowing into the vertical from the
center of the coax is the same as the current flowing from the ground into
the coax shield. Therefore, the antenna and ground have the same amount of
current flowing through them. Call the current I (how original!). The
ground loss is 14*I^2 watts, and the power radiated is 36*I^2 watts. The
total power supplied is the sum, or 50*I^2. The efficiency is the fraction
of the total power which is radiated, or (36*I^2)/(50*I^2), or 36/50, or
0.72. Ok so far.
Now let's "fold" the antenna to make a folded monopole:
_
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feed ->____O_|____
(ground)
If we look at the feedpoint, we find that for the same power input as
before, the voltage is twice its previous value and the current half its
previous value. From Ohm's law, the feedpoint impedance has quadrupled.
This is due to the transformer action of the folding process, caused by
mutual coupling between the two wires. So now our "radiation resistance"
is 4*36 = 144 ohms. Since the loss resistance is still 14 ohms, isn't our
efficiency now 144/(14+144) or 91%? The answer is NO! But this is the
assumption made to justify the claim of high efficiency in the "Uni-Hat"
antenna.
Here's why not. Since the antenna resistance is now four times its
previous value, and the feedpoint current is 1/2 its previous value, the
power radiated by the antenna is 144*(I/2)^2 = 36*I^2 watts, where I is
the current we had in the monopole. So the radiated power is the same as
for the monopole. How about the ground loss? Well, I/2 is entering (or
exiting, depending on your point of view) the ground where the feedline
shield is connected. But another I/2 is entering the ground system where
the second wire is connected to ground. This current is in phase with the
current from the feedline shield. The result? A total of I amps flowing
through the same 14 ohms of ground resistance as before. The ground loss
is 14*I^2 watts, the same as for the monopole. The efficiency hasn't
changed. Let me say that again: The efficiency hasn't changed.
One could argue about calling the feedpoint resistance of a folded antenna
the "radiation resistance", but technically it's correct. However, if you
do use the term that way, the efficiency is no longer simply the ratio of
radiation resistance to radiation + loss resistances, as I showed above.
The efficiency *is* *always* the fraction of total applied power which is
radiated.
That being said, let me point out that the "folding" process *does* help
wire loss. Wire loss is probably insignificant for this antenna (except
maybe on 160m), but can be important for a small loop. Doubling the number
of turns on a loop effects a 4:1 impedance transformation by the same
mechanism as "folding" a monopole or dipole. You end up with half the
current in twice the length of wire. Since the power loss is directly
proportional to the wire length but to the square of the current, you can
calculate that each doubling of the number of turns in a loop or wires in
a "folded" antenna will halve the wire loss. Of course, just putting two
wires in parallel will do the same thing, although the impedance step-up
is beneficial in making matching easier.
>From the picture and description, it looks like the "Uni-Hat" has several
things going for it. First, a top hat *does* raise the radiation
resistance without affecting the ground current, so it does improve
efficiency. (Its mechanism for raising the radiation resistance is to
change the current distribution in the radiating element.) Also, the
"folded" antenna is fatter than an unfolded one. This has two beneficial
effects. First, it reduces the amount of reactance for a given antenna
height. This lowers the values of lossy loading components necessary to
bring the antenna to resonance. It also widens the bandwidth, as Lew
pointed out. Incidentally, wide bandwidth in a small (in terms of
wavelength) antenna generally is due to loss, although the fattening does
help without incurring additional loss.
Guess a fitting end is a quote from the late Robert Heinlein: "TANSTAAFL"
(There Ain't No Such Thing As A Free Lunch).
73,
Roy Lewallen, W7EL
[end quote]
73 from Ian G3SEK Editor, 'The VHF/UHF DX Book'
'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.demon.co.uk/g3sek
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