David wrote:
Can someone provide a full description of how a quarterwave vertical antenna
with radials works? Length of radials is also a quarterwave.

When you connect a source or feedline to this antenna, the same amount
of current which flows into the vertical flows into the radials. First
consider one which is well above the ground. The current in each pair of
radials flows in physically opposite directions. So the radiation from
the radials cancels completely at right angles to the radials, and
nearly completely in other directions. The vertical acts like a dipole
except with half the length and twice the current, resulting in the same
pattern and field strength as a dipole.

If the radials are buried, the current into the radials spreads into the
ground. Current through the ground results in loss due to the ground's
resistance. Therefore many radials are required to force the majority of
current to flow in the wires rather than the ground. This is
particularly important close to the vertical where the current density
is high.

I find that many books give a good description of antennas like the Yagi,
and then suddenly become very vague when describing the quarterwave
vertical. Books
refer to image theory where an image of the radiating element is produced by
the radials, and show a spear shape going into the ground. Some say the
radials are the other half of a dipole.

That's probably because the authors don't understand some fundamental
principles, or else they oversimplify to the point where the explanation
isn't correct. Radials are nothing more nor less than conductors
carrying current, and radiate accordingly. But they're placed and fed so
the radiation nearly cancels.

What difference does it make if the radials are in free space or in the
ground? Some articles claim that the radials tend not radiate because they
cancel out, while other other articles claim that the radials simulate a
ground plane and reflect the radio wave. Can you explain this contradiction?

It's a lousy explanation of what's going on, written by someone who
doesn't really understand. When the radiation from the vertical strikes
the ground, it's reflected. If the ground were perfectly conductive,
flat, and infinite in extent, it would be like a mirror. But real ground
isn't any of these things, so a mirror is a very poor representation.
The reflection from the ground causes the formation of a vertical
radiation pattern which looks very different from what you'd get from a
perfect, mirror-like ground, with the exception that salt water does
approximate a mirror reasonably well. Except at high radiation angles,
this reflection takes place well beyond any radials, so the radials
don't contribute at all except at high angles.

The vertical element is usually called the radiating element. How well do
the radials radiate? The same magnitude of current flows into the vertical
element as the radials, although the current into the radials is split.

Correct. See above.

A normal ground plane is a large sheet of metal that reflects the radio wave
emitted by the radiating element.

"Normal"? Where have you seen an antenna mounted over a metal ground
plane many wavelengths in diameter? Perhaps a UHF antenna in the middle
of the top of a car, but that's about it.

If there are four radials, each a
quarterwave long, do the radials form a ground plane?

Radials do not form a flat metal conductor many wavelengths in diameter,
if that's what you're asking. And they don't reflect the radiation from
the vertical, either.

Or is there too much
of a gap for them to form a ground plane?

They're much too short to reflect the radiation. Or are there other
properties you require for something to qualify as a "ground plane"?

If the radials are disconnected and taken away, with the vertical
quarterwave element still connected to centre conductor, do I still have a
radiating element?

Yes. Whatever current you put into the element, an equal current flows
elsewhere. If the element is connected to a coax transmission line, it
flows down the outside of the coax, so the coax radiates just like the
element. If you just plug it into a coax connector on a transmitter, the
current flows out of the connector onto the outside of the transmitter,
so it and the path to the Earth radiate just like the element. Current
on a conductor creates radiation. It doesn't matter one bit whether you
declare the conductor to be "ground", a "ground plane", or a "transmitter".

What happens to the SWR?

You now have an asymmetrical antenna. One "half" is the vertical and the
other is whatever conductor the return current flows on. The SWR will
almost certainly be different than it was for a typical ground plane
antenna.

Roy Lewallen, W7EL