During the Sept. 7 ALPB meeting the subject of radial radiation came up and it was reviewed that if radials are 180 degrees apart and are equal length then the fields produced by their radiation cancel as seen from a distance because the currents in each set of paired radials (180 degrees apart) is equal and opposite and there is no net radiation. The question was then posed if an odd number of radials can be arranged so the net radiation is zero, for example three equal length radials 120 degrees apart.
The way to approach this is to use what is called a projection of the radials on an axis line as viewed from within the plane of the radials. This is equivalent to the apparent length of each radial as seen from the edge of the plane of the radials. (A projection example is if you view a yardstick from the side and it is 1 yard long. Now rotate the yardstick around its center so one end is closer and the other farther and it appears shorter. This is the idea behind the math of projection.)
Align a 3 spoke radial system so the rightmost radial appears full length (call it L), in otherwords, as viewed from the top the rightmost radial is along the X axis and the other two appear to the left with angles of 120 and -120 degrees with the axis. The projections seen from the side are L for the right radial, Lcos(120) for the top left one, and Lcos(-120) for the lower left one. To account for the currents all flowing toward the junction of the radials the projections include the sign of the cosines, in other words, lengths to the right of zero are positive and to the left, negative. Doing this gives the vector length of the sum of the projections which represents the sum (S) of the three fields as viewed from a distance.
This is S = L + Lcos(120) + Lcos(-120) the sum of the projections.
Substituting for the cosines:
S = L - 1/2L - 1/2L
which equals zero, showing that there is no net radiation in this case.
But does this happen for different viewing angles where the rightmost radial is not along the axis? Similar trig for the rotation through any angle of the three radials about the axis going through their junction shows the projections and hence the fields sum to zero as long as the angle between them is 120 degrees.
Here's the math:
S = LcosA + Lcos(A+120) + Lcos(A-120) where A is any arbitrary angle of rotation.
Applying a trig. identity for the sum of angles,
S = LcosA + Lcos(A)cos(120) - Lsin(A)sin(120) + Lcos(A)cos(-120) - Lsin(A)sin(-120)
Substituting for the sines and cosines of 120 and -120
S = LcosA -1/2LcosA - .866LsinA - 1/2LcosA + .866LsinA = 0.
The key appears to be that as viewed from the side the sum of the radials' projections need to be symmetrical (and sum equally) to the left and right of the junction. Another example with 5 radials was sketched (no math) and it does not have this symmetry and the projections (fields) would not cancel so though it was shown that for three radials cancellation happens this is apparently not true in general for any odd number of radials.
It can be speculated that multiples of three radial sets would show cancellation since these could be broken down to individual sets of three 120 degrees apart with no radiation. From this the next odd set which would not radiate would be 3 X 3 = 9 radials, and so on.
Neil
Thank you for this Neil.
I never in my life thought I would be so
interested in the subject of grounds and
ground systems. You come up with this
wonderful information - that is very hard
to find. For the reader who is trying to
understand and doesn't know quite what
to look for, this is a real good thing.
I have been pretty happy with my 16
radial ground system - which still sits
in the back yard - even though my 1690 Part 15 rig
is off the air. My backyard is full of big rocks
and hills and tree roots, Putting the radials
in was hard.
I can see now - with your information -
the next ground system will be a better one.
(Wherever we end up living.)
Bruce. DOGRADIO
Bruce, I am glad you found this interesting but it is only an academic exercise and it does not predict the effectiveness of the radial system, only the conditions to produce no net radiation. More radials are better than few and longer are better than shorter, but if for some reason the installation is constrained to a few radials this might be helpful.
The radials do not necessarily have to be buried to work. They can be placed on top of the soil.
Neil
My "minimal radial" setup, in which a perfectly straight horizontal ground wire is tapped in the exact center by transmitter ground, forming two equal-opposite wires 180-degrees out of phase, has one particular drawback, and that is that it causes a non-circular signal pattern. I estimate that the signal would have stronger lobes on either side of the radials than at the tips.
I am guessting that Neil's presentation of a three-pronged set of radials at 120-degrees of each other would be the minimal means of creating a perfectly circular signal pattern.
There have been a few articles in the Ham publication QST about ground mounted "quicky" antennas using just 2 radials. I have seen at least one antenna advertised stating it works well with just 2 radials.
The writers of the "quicky" articles felt the radiation pattern was mostly omni directional although conventional thought would lead one to believe the pattern would be skewed in the direction of the radials.
The concept of RF radiation from ground radial wires is pretty much absent from all theory, calculations and detailed reports written mostly by hams. To be clear, I think we are talking only about radials laying on the earth or buried slightly. Elevated ground planes operate under a totally different set of rules.
Ground level radials don't exhibit any resonant properties. They may be any length. There are only recommendations for the number and lengths of radials with the general guideline of "the more the better and the longer the better".
Their purpose is to "collect" RF ground currents to be returned to the transmitter in the circuit consisting of the transmitter, antenna and earth ground. Insulated or non-insulated wires may be used. They conduct the ground currents because the wires are in close enough proximity to earth to be capacitively coupled to the earth. The overall parallel capacitance of all the wires is enough to allow the RF ground current to pass relatively unimpeded from the earth through the capacitance to the radials. This effectively places the radials at the same potential as the earth.
Radials conduct RF ground current, but they are simply conducting the same RF ground current that is flowing in the earth under the radials.
Ground currents do not radiate. Ground at earth level does not radiate.
You may detect some radiation in the vertical direction with a FS meter in close proximity to one radial wire, particularly if you have less than a desirable number of radials. This is an aberration related to typical short radials used in Part 15 AM being in the near field. Your meter is being inductively and/or capacitively coupled to the close radial wire. At a distance, outside the near field, this type of reading can't be made. At a distance, the FS is higher with radials than without radials not because the radials radiate, but rather because they decrease the ground loss resistance of the antenna causing more of the transmitter power to go the antenna.
Radial wires are just a practical substitute for a continuously conductive metal plate or metal mesh screen. It's easy to visualize that a huge metal plate forms one side of a physically huge capacitor, with the earth underneath forming the other plate. Ground currents are collected by the capacitor over a large area. This compensates for the imperfect conductivity of the earth. A "perfect" ground is a theoretical concept. If there were such a thing as a perfect ground, no plate, mesh or radials would be needed. Salt water is a very conductive medium (still not perfect). Over salt water, you don't need an elaborate radial system. It's only necessary to provide a relatively small area to contact the water.
They conduct the ground currents because the wires are in close enough proximity to earth to be capacitively coupled to the earth.
Good point here. Another example is bonding vehicle parts together like the trunk lid, hood, doors, etc. for an amateur radio HF mobile installation. The car's body is capacitivly coupled to earth enhancing the performance of a short vertical antenna, not unlike a Part 15 operation.
Interesting subject, capacitive coupling.
I was made aware that my Wintenna design, consisting of an indoor 2.5' wire vertically up a wall to a metal window frame for another 6' and then, on the outdoor side, a wire from the top of the frame to a total of 3-meters, would have capacitive coupling with the surrounding wall and its contents, be it wiring, plumbing, or stucco netting.
What we find is a difference between vertical capacitive coupling vs. horizontal capacitive coupling.
One is bad, the other good.
http://www.mwpersons.com/nott-elevated-ground.html
The website at the above address offers a simple design for an elevated ground radial system for AM stations using only 6 radials. They claim it fully complies with FCC requirements.
Of course, it's not practical for most of us as the radials at 1700 kHz would be 150 feet and they recommend putting them 18 feet above earth.
But, if you live on a farm and have the room...
This gets into the near field / far field part of the radio wave theory. Most descriptions I have seen tend to be confusing and somewhat squishy as far as defining where the boundary exists between near and far. The "reactive near field" is a sub-classification that should be of major concern when locating a Part 15 AM antenna.
Good old Wikipedia has a good section that shows the field regions for electromagnetically short antennas (our short Part 15 AM verticals)
http://en.wikipedia.org/wiki/Near_and_far_field#Electromagnetically_short_antennas and it has another section that further discusses the "reactive near field", http://en.wikipedia.org/wiki/Near_and_far_field#Reactive_near-field.2C_or_the_nearest_part_of_the_near-field
The Reactive Near Field spans the distance from the antenna to .159 * wavelength. At 1600 kHz, one wavelength is 615 ft. and the reactive near field extends out to 98 ft. "Reactive fields" are the same as the magnetic coupling in transformers and electric coupling in capacitors. The magnitude of the reactive field is maximum right up close to the antenna and diminishes rapidly as you move away.
We have all experienced the effect on the tuning peak when you move your hand closer and closer to the antenna starting at about 2 ft. or so. This is a good demonstration of capacitive coupling in the reactive near field. Your body capacitance is coupling to the antenna resulting in an increase of the total antenna capacitance seen by the transmitter and thus lowering the resonant frequency of the antenna tuning circuit.
Any conductive material can be substituted for your hand in this experiment, even relatively poor conductors. Most often the coupling is capacitive, but if you move an inductive conductor like a long wire or coil near the antenna, you can also get inductive coupling. The effect of nearby conductors is usually called "stray capacitance" or "stray inductance". If your signal is being coupled to a lossy load, the overall level of your signal will be diminished.
We often hear recommendations to locate your antenna away from "obstacles" such as trees, shrubs, foliage, buildings, etc. The effect of obstacles is most pronounced within a few feet from the antenna, but there is still interaction with obstacles, although diminishing rapidly, out to .159 * wavelength, or 98 ft. at 1600 kHz.
I haven't seen any detailed analysis, but it stands to reason that the poor range of indoor antennas is due to the almost infinite number of obstacles surrounding the antenna, all in the "reactive near field" and all absorbing part of the signal.
All of this reminds me of the
guy in Connecticut with the truck
Part 15 station. Every Saturday
he parked his truck near a lake (?)
and went on the air. In order to do
this, he put a portable ground system
down at the edge of the parking lot,
and put the Part 15 antenna stick up
with the transmitter attached to the
bottom. I have seen pictures of this
operation, but they are not clear enough
to show the fine points in how everything
was bolted together.
Anyway, this guy ran his operation on
1620 kHz from early morning until local
sunset every Saturday. Since he was outside and his
truck was so visible to people walking and
driving by - he did have listeners.
He did this for a very long time - many years.
I don't know if he is still running the set-up
now. What a cool idea.
Bruce, DOGRADIO
An ancient secret to having a perfect indoor antenna is to get everything to couple so that the whole house (no reference to Wholehouse brand transmitters) becomes resonant. To do this the house and furniture should be made of copper.
To be compliant with Part 15 the house should stand no more than 10-feet high.
Fully comples for a commercial FCC licensed AM station. NOT Part 15.
WDCX has a point, unless the 10-foot-high copper house is a 10-foot-diameter circle... what you might call "a walk-in antenna."
But let's try another approach...
Are there building materials that are invisible at RF frquencies and do not have a capacitive presence when located near an antenna?
It has been stated by knowledgable members of this forum that a proper radial system does not radiate.
It has been stated by knowledgable members of this forum that an elevated radial system is a different animal.
My point was that here is a simple elevated radial system for the AM band using only six radials which apparently works as it satisfies FCC performance standards.
It would be interesting to see how it works with a 3 meter loaded antenna.
Now, unless they have a problem with the radial system being visible why couldn't it be used for a Part 15 installation?