Date: Wed, 12 May 2004 18:31:47 -0700
To: "Jerry Keller" <k3bz@arrl.net>
From: Jim Lux <jimlux@earthlink.net>
Subject: Re: [TowerTalk] Wire for Radials
At 07:31 PM 5/12/2004 -0400, you wrote:
Well, ON the ground, actually. I picked up a 33-foot aluminum mast and was
thinking to put it up for 40M. Also, I'm putting a 160M inverted ell. Both
will need a radial system. I was thinking of taking a turn around a common
nail every 30 feet or so, and pressing the nail into the turf to keep the
wires down and tight.... then letting the lawn grow over them in time. But I
was concerned about the wire size (it seemed small) and that it's bare
copper. I occasionally fire up the kilowatt and wasn't sure bare copper was
a good idea, as I've heard that there might be high voltages at the ends of
the radials.
The next question I have is: should I tie the two radial systems together
wherever they cross? And should I tie the radials to the tower ground
system wherever they cross it?
A follow up..
You're basically trying to increase the conductivity of the earth with
this sort of thing. It's not a resonant system, so things like high
voltages, ground loops, etc., aren't really relevant. There's so much
coupling between radials or ground grid and the earth that the earth will
dominate. One could probably do a criss/cross pattern and it would work
almost as well, although, in theory, if you had enough wires, and they are
arranged in the direction of the current flow, it would help.
However, consider this... Let's say we've got a cube of dirt in a big test
cell and we want to put wires into it to reduce the (RF) resistance.
Say you have soil thats 0.005 Siemens/meter conductivity. That means that
if you took a 1x1x1 meter cube of the soil and hooked up a big metal plate
on each end, and measured the DC resistance, it would be 200 ohms. If the
epsilon were 13 (as widely used for modeling), the capacitance in your two
plate apparatus with the dirt in the middle would be about 115 pF. You're
working at 7MHz, so the impedance of that cubic meter of dirt is about 197
ohms (it just came out that way...) (If you're looking in a table of
dielectric properties, this would mean that the dissipation factor (tan d)
is about 1, which it is: http://home.earthlink.net/~w6rmk/soildiel.htm )
Now stick some wires in the dirt to "help" the process along AWG 24 is
about 0.1 ohm/ft and you've got 3 feet or so of it, so it's a LOT more
conductive (at least as far as DC goes). To a first order, you've got a
0.3 ohm resistor in parallel with a 200 ohm resistor and a 200 ohm
capacitor. However, that wire also has some inductance. A good working
number for thin wires is 1 uH/meter, so you've got a 1 uH inductor. That
1uH has an impedance of about 44 ohms at 7MHz, so it's not quite so good
as you originally thought, but still, if you have 1 wire per square meter
of cross sectional area, you've dropped the ground impedance from about
280 ohms to about 15-20% of that.
I've ignored a lot of aspects in this quick analysis (like the fact that
the current flows sideways as well as along, and it flows into and out of
the wire from the soil (because the soil is a lossy capacitor and the wire
is a lossy inductor, and they are in parallel). I've also egregiously
simplified the inductance calculation.
Finally, what you're really worried about is overall total RF losses, and
the current density is higher near the base, so all things being equal,
you'd prefer to have lower resistance there than farther out.
Some other interesting observations...
If the epsilon is much higher, that makes the capacitance larger, which
reduces the loss. if the water content increases, that helps two ways: it
increases the conductivity AND it increases epsilon..
By the way, 13 for epsilon is probably optimistic at 10 MHz kinds of
frequencies... The charts I have(taken from Von Hippel, which is sort of
the dielectric bible) show that dielectric constant varies with frequency
and it tends to be lower at higher frequencies. Those charts you see
everywhere were generally created for the AM broadcast industry, and are
at 1 MHz.
Jim, W6RMK
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