I believe that all three people (Richard, Roy, and Fred) who have
commented on this topic have misread the figure in Kraus. The gain at
one-half wave spacing from the reflector is *zero*, not zero dB
(relative to a dipole), nor zero dBi.

As expected from the simple mirror image model there is complete far
field cancellation in the phi = 0, theta = 0 direction. That is the only
direction referenced in the figure.

73,
Gene
W4SZ



Roy Lewallen wrote:
The only way to get 0 dBi maximum gain from a lossless antenna is to
have a perfectly circular pattern in all azimuths and elevations. It's
not possible to have a maximum gain (that is, gain in the best
direction) less than 0 dBi unless loss is present. This is something
everyone with a basic understanding of antennas should know.

So it seemed to me very unlikely that a dipole spaced a half wavelength
from a reflector would have a perfectly circular pattern and, therefore,
it must have gain greater than 0 dBi in some direction. I don't have
Kraus' third edition (yet), but there's a diagram on p. 546 of the
second edition which I suspect is the same as the one Richard is
referring to. The caption under the graph clearly says that the gain at
0.5 wavelength is 0 dB *relative to a half wave dipole in free space*,
or about 2.15 dBi, not 0 dBi.

If the third edition really says that the gain of a half wave antenna
spaced 0.5 wavelength from a reflector is 0 dBi, it's an error and
should be brought to the editor's attention so it can be corrected.

I also believe that while you might draw some possible parallels, you
can't directly apply the characteristics of an antenna in proximity to
an infinite reflecting plane (as in Kraus) to those of an antenna in
proximity to a tower.

Roy Lewallen, W7EL

Richard Harrison wrote:

. . .
The 3rd edition of Kraus` "Antennas" has a graph on page 350 of gain in
field intensity versus spacing from a flat reflector. At 0.5 wavelength
the gain is 0 dBi. That`s less than the resonant 1/2-wave antenna alone
which has about 2.14 dB gain over an isotropic.

The graph shows a gain of about 2.14 dBi with a spacing of only 0.1
wavelength spacing. So, anything greater than 0.1 wavelength from the
tower should be fine. That`s 20 cm in the 2-meter band, or about 8
inches. More distance means less coupling and should be better.

Best regards, Richard Harrison, KB5WZI

I have to apologize. I also misinterpreted the graph. The confusing
graph is, in the Second Edition, Fig. 12-4 on p. 546. I've uploaded it
temporarily to http://eznec.com/misc/Kraus2_Fig_12-4.JPG.

The caption says that the gain is relative to a half wave dipole in free
space with the same power input. The numbers on the left side Y axis are
the numerical gain, 0 to 3, relative to a dipole. 0 represents a
numerical gain mulitplier of zero, or no field intensity at all. 1 is
the gain of a half wave dipole in free space (about 2.15 dBi). A value
of 2 represents a gain in field intensity by a factor of 2, or 6 dB
relative to a dipole. The right hand side Y axis labels are the gain in
dBi. Note that 2.1 dBi corresponds approximately with the value of 1.0
on the left side. The bottom horizontal line corresponds to zero field
strength -- a gain of minus infinity dBi -- *not* zero dBi as Richard
said, or zero dB relative to a dipole, which I initially assumed.

What I missed was that the gain is "in direction [phi] = 0", quoting
from the caption. So this isn't a graph of the maximum gain, but the
*gain in one specific direction* -- normal to the reflecting plane. At
0.5 wavelength spacing, the "gain in field intensity" (left set of Y
axis labels) is a *factor* of zero, meaning that the field strength is
zero, or minus infinity dBi. Sure enough, if you model the antenna, or
two elements spaced one wavelength, you find that the pattern has a null
directly broadside to the antenna ([phi] = 0). It has gain in other
directions, but that's not what the graph is showing.

Of course, any lossless antenna has a gain of 0 dBi in some directions.
In the case of the element and reflecting plane, the gain directly
broadside to the antenna has a gain of 0 dBi at spacings of roughly
0.425 and 0.575 wavelengths. There's no particular significance to this
-- the maximum gain is greater in other directions.

These gains and patterns can easily be seen with any modeling program,
including the EZNEC demo, by modeling a dipole over perfect ground. You
can also model two elements fed 180 degrees out of phase at twice the
spacing and no ground and see that the pattern is identical except for
being bidirectional.

Roy Lewallen, W7EL

Fred W4JLE wrote:
Roy, I looked at the graph and get a different interpretation. Every spacing
except 1/2 wave length spacing shows gain. That being the case the pattern
must be distorted for all cases except .5 wavelength.

I have Kraus 1950 edition

"Richard Harrison" wrote in message
...

Roy Lewallen
, W7EL wrote:
"I don`t have Kraus` 3rd edition (yet), but there`s graph on p 546 of
thye second edition which I suspect is the same as the one Richard is
referring to."

I`m sure that`s it. I have Kraus` 1950 edition of "Antennas" and the
identical groph is on page 327 in it.

If you look at the patterns of a 1/2-wavelength antenna at spacings of
1/4, 1/2, and 1/16 wavelengths spacing from a flat reflector nearby,
they are all nearly circular, indicating little distortion in their
unblocked direction.

Best regards, Richard Harrison, KB5WZI

You're absolutely correct.

Roy Lewallen, W7EL

Gene Fuller wrote:
I believe that all three people (Richard, Roy, and Fred) who have
commented on this topic have misread the figure in Kraus. The gain at
one-half wave spacing from the reflector is *zero*, not zero dB
(relative to a dipole), nor zero dBi.

As expected from the simple mirror image model there is complete far
field cancellation in the phi = 0, theta = 0 direction. That is the only
direction referenced in the figure.

73,
Gene
W4SZ

Gene Fuller, W4SZ wrote:
"As expected from the simple mirror image model there is complete far
field cancellation in the phi = 0. theta = 0 direction."

Right. Real and virtual imaqges are equidistant and 180-degrees out of
phase perpendicular to the reflector.

The more distant the radiator from the reflector, the smaller its image
appears. The phase difference between the radiator and its image varies
with the distance between them.

At 1/2-wavelength from the reflector, a round-trip takes 360-degrees and
leaves the phase unchanged. However, the reflection inverts the phase.
Incident and reflected waves cancel perpendicular to the reflector.

Two antenna elements, or one with its image in a reflectoe, will be
directional. An unobtainable isotropic is the reference, so te antenna
has gain.

There is no way to mount a J-pole next to a tower and preserve its omni
characteristics. The question is which directions would you favor and
which would you diminish?

You know the tower may be impenetrable, and the vector sum of incident
and reflected signals directly opposite the tower depends on the antenna
to tower spacing.

An antenna modeling program should be able io show you your options.

You know thet 1/2-wave spcing cancels in the diretion of the antenna
mounted on the tower face. Add or subtract a 1/4-wave to the spacing,
and the incident and reflected waves reinforce instead of cancel. As I
think Roy said, you pay your money and take your choice.

Best regards, Richard Harrison, KB5WZI