Richard Fry wrote:
"---range from about 690 mV/m for a 0.05 wavelength vertical to about
641 mV/m for a 0.625 wavelength vertical.

On page 871 of the 1955 edition of Terman`s "Electronics and Radio
Engineering" is Table 23-1, "Directive Gain of Simple Antennas Relative
to Isotropic Radiator".

The directive gain of an elementary doublet, assumed to be
infinitesimally short, is given as 1.5. A resonant 1/2-wave wire is
given a gain of 1.64 in the same table.

Terman says on page 870:
"Directive gain depends entirely on the distribution in space of
radiated power."

So, the miniscule doublet puts 1.5 x as much power in its best direction
as does an isotropic. This is 1.76 dBi according to Kraus.

From Terman`s dB table on page 8, a power gain of 1.5 is a little less
than 2 dB gain. Kraus says 1.76 dB. A power ratio of 1.64 is more tha 2
dB, but less than 2.5 dB gain. The gain difference between a tiny dipole
and a 1/2-wave dipole is almost insignificant. Certainly it is less than
1 dB.

Kraus`s 3rd edition of "Antennas" has Figure 6-2 pn page 192 which gives
gains of common antennas:

An isotropic (uncommon) has a directivity of h1.00, and a gain of 0 dBi.

An elementary dipole has a directivity of 1.5, and a gain of 1.76 dBi.

a 1/2-wave dipole has a directivity of 1.64 and a gain of 2.15 dBi

A short monopole gas a directivity of 3 and a gain of 4.8 dBi.

A 1/4-wave monopole has a directivity of 3.28 and a gain of 5.2 dBi.

A 1/2-wave monopole has a directivity of 4.8 and a gain of 6,8 dBi.

With specific gain figures, we don`t need to characterize figures as
large or small. I just hope I copied them correctly. Better yet, get
your own copy of Kraus. It`s in print and well worth the price.

Best regards, Richard Harrison, KB5WZI

"Richard Harrison" wrote:
The directive gain of an elementary doublet, assumed
to be infinitesimally short, is given as 1.5. A resonant
1/2-wave wire is given a gain of 1.64. The gain difference
between a tiny dipole and a 1/2-wave dipole is almost
insignificant. Certainly it is less than 1 dB.
______________

This is all true, of course, but might lead some to the invalid conclusion
that it also applies to monopoles (whips) of 1/2 wavelength or less working
against a ground plane, such as in mobile operations or back yard verticals.

When a vertical radiator works against a perfect ground plane, the
electrical length of that radiator effectively is doubled. So in reality an
electrical "1/4-wave vertical" has twice the gain of a *1/2-wave* dipole
because of the image effect of the ground plane, and the fact that all
radiation is confined to one hemisphere (above ground). Note in your quote
from Kraus, p 192 that the short monopole and the 1/4-wave monopole each
have 3dB more gain, respectively, than the free space elementary (short)
dipole and the 1/2-wave dipole he also lists there.

Using your statements above the line, one might think that it rather
pointless to use anything longer than a 1/4-wave vertical. But going from a
1/4-wave to a 1/2-wave vertical in fact will add ~1.6dB of gain at the peak
of the pattern envelope, and a 5/8-wave vertical will add almost 3dB. These
are worthwhile improvements in system performance. Broadcast engineering
consultants have recognized this, and used it to advantage for decades.

Better yet, get your own copy of Kraus. It`s in print and
well worth the price.

Good advice (I already have it).

RF

Richard Fry wrote:
. . .
Using your statements above the line, one might think that it rather
pointless to use anything longer than a 1/4-wave vertical. But going
from a 1/4-wave to a 1/2-wave vertical in fact will add ~1.6dB of gain
at the peak of the pattern envelope, and a 5/8-wave vertical will add
almost 3dB. These are worthwhile improvements in system performance.
Broadcast engineering consultants have recognized this, and used it to
advantage for decades.
. . .

It's important to realize that the graphs you posted are for surface
wave field strengths. This is equivalent to far field strengths at zero
elevation angle over perfect ground.

Amateurs seldom communicate by surface wave, except for local contacts.
When the vertical is surrounded by real ground, attenuation of the sky
wave at lower angles occurs. One of the results of this is that the
antennas which concentrate energy more at lower angles end up losing a
greater fraction of the total radiated energy. This tends to decrease
the gain difference between a 5/8 and 1/4 wave vertical, for example,
over a typical sky wave path.

In the case of VHF/UHF mobile operations, which are essentially line of
sight, the finite size of most ground planes (e.g. a car top) can affect
the pattern considerably, again altering the gain difference between
various heights of verticals.

While there's an extensive body of well established and proven knowledge
in the broadcast industry, we have to be careful in applying it to
typical amteur communications. Often, the conditions are different (as
in this discussion, of surface vs sky wave propagation; or fixed vs
variable frequency operation), and the important criteria are different
(a few percent difference in coverage area is important to a broadcaster
because of its impact on advertising revenue, but a fraction of a dB is
seldom important to an amateur; a broadcast phased array can take a long
time to design and adjust, but amateurs want to switch or change
directions). So we can't just assume that an antenna or method that's
best for a broadcaster is best for us.

Roy Lewallen, W7EL

"Roy Lewallen" wrote:
Amateurs seldom communicate by surface wave, except for local contacts.
When the vertical is surrounded by real ground, attenuation of the sky
wave at lower angles occurs. One of the results of this is that the
antennas which concentrate energy more at lower angles end up losing a
greater fraction of the total radiated energy. This tends to decrease the
gain difference between a 5/8 and 1/4 wave vertical, for example, over a
typical sky wave path.
__________________

I investigated your concept statements using NEC-2 models of 1/4-wave and
5/8-wave verticals in the 40m band (7.3MHz), working against the same
infinite ground plane of "Average" parameters.

* The 5/8-wave vertical has a peak gain of 0.2dBi,
16 degrees above the horizon.

* The 1/4-wave vertical has a peak gain of -6.4dBi,
26 degrees above the horizon, and its entire radiation
envelope is always within that of the 5/8-wave.

I don't know which range of elevation angles is considered most useful for
skywave paths on 40m, but it would appear that with equal tx power, a
5/8-wave vertical always will have a usefully better skywave than a 1/4-wave
vertical over a typical ground plane -- and probably by more than 3dB.

If you could check my conclusions on this I'd be grateful.

RF

It sounds like you might have made the mistake of connecting a wire
directly to Sommerfeld or reflection coefficient ground. Doing this with
NEC-2 (or EZNEC) produces a resistance of unpredictable and meaningless
value at the connection point, lowering the indicated field strength by
an unpredictable amount. (EZNEC gives you a warning message when you try
to do this.)

EZNEC provides an option not available in NEC-2, a "MININEC-type"
ground. This functions as a perfect ground when calculating impedances
and currents, but uses the user-specified ground constants (conductivity
and dielectric constant) when calculating the pattern. It simulates an
antenna with a lossless ground system, allowing you to separately see
the effect of ground conductivity on the pattern without the magnitude
of the field being affected by changes in the ground system loss. The
best you can do with either EZNEC or NEC-2 if you want to include ground
system loss is to include radial wires just above the ground in the
model and connect the vertical to them. Then, however, any differences
you see will hold only for that particular ground system -- and, the
above-ground approximation isn't a terrifically accurate representation
of a buried system.

Using the MININEC-type ground with EZNEC (and only 10 segments, so this
can easily be done with the demo program) and starting with the Vert1.ez
example file, the gain of a resonant (~0.24 wavelength) high vertical at
7 MHz with "average" ground is -0.0 dBi at an elevation angle of 26
degrees. Changing the height to 0.625 wavelengths (easily done by first
changing Units to Wavelengths) produces a maximum gain of 1.19 dBi at 15
degrees elevation angle. The 1/4 wave trace protrudes outside the 5/8
wave trace only from about 25 to 41 degree elevation.

But more interesting is the gain difference at various low elevation
angles. The comparison is easily done with EZNEC v. 4.0 by saving the
trace from one antenna, then superimposing that pattern on the pattern
of the second antenna. By clicking the name of the superimposed pattern
in the 2D plot window, a new entry appears in the data box showing the
difference between the two at the angle of the cursor.

It turns out that the 5/8 wave really shines at really low angles when
the ground is poor, but isn't so impressive when the ground is very good
-- at least at 7 MHz. Over average ground, the gain difference is at or
just above 3 dB up to about 10 degrees. (My explanation of the reason
for the difference over real ground was overly simplistic. I apologize.)
Above 10 degrees, the difference decreases. Over poor ground, the gain
difference is about 4.5 dB up to 5 degrees, and over 4 at 10. So if you
have poor ground, you can really benefit from a higher radiator. Over
very good ground, though, the difference is about 2 dB up to 5 degrees
elevation, only 1.2 at 10 degrees, and less than a dB at 12 degrees and
above. So it might or might not be worthwhile to extend the height of a
tower for that amount of benefit.

Those figures depend on frequency, too, and the pattern shape varies
considerably with frequency and ground characteristics. So modeling the
particular situation would be a good idea before doing any expensive and
extensive tower lengthening. In all the cases I looked at, however, the
5/8 wave vertical did show some gain over a quarter wave vertical up to
at least 14 degrees. Whether the difference is worth the added height is
up to the individual.

Roy Lewallen, W7EL

Richard Fry wrote:
__________________

I investigated your concept statements using NEC-2 models of 1/4-wave
and 5/8-wave verticals in the 40m band (7.3MHz), working against the
same infinite ground plane of "Average" parameters.

* The 5/8-wave vertical has a peak gain of 0.2dBi,
16 degrees above the horizon.

* The 1/4-wave vertical has a peak gain of -6.4dBi,
26 degrees above the horizon, and its entire radiation
envelope is always within that of the 5/8-wave.

I don't know which range of elevation angles is considered most useful
for skywave paths on 40m, but it would appear that with equal tx power,
a 5/8-wave vertical always will have a usefully better skywave than a
1/4-wave vertical over a typical ground plane -- and probably by more
than 3dB.

If you could check my conclusions on this I'd be grateful.

RF

Roy Lewallen wrote:
[...]
modeling the particular situation would be a good idea before doing
any expensive and extensive tower lengthening. In all the cases I
looked at, however, the 5/8 wave vertical did show some gain over a
quarter wave vertical up to at least 14 degrees. Whether the difference
is worth the added height is up to the individual.

Another height-related factor that may be worth considering is the
effect of surrounding the lower part of the antenna by nearby buildings.
Inside a typical 2-floor home are 3-D grounded meshes of electrical
wiring and (in many countries) central heating pipes. The wiring mesh
typically extends up to 6m/20ft above ground, which may be a significant
fraction of the antenna height.

For example, in the suburban situation here, the lower part of my
vertical for 40m was almost completely surrounded by these "scattering
objects" at distances ranging from 0.5 to 2 wavelengths. I never got
around to modeling the effects of these objects... though someone could
easily try it.


--
73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek

"Roy Lewallen" wrote:
... the gain of a resonant (~0.24 wavelength) high vertical at
7 MHz with "average" ground is -0.0 dBi at an elevation angle of 26
degrees. Changing the height to 0.625 wavelengths produces
a maximum gain of 1.19 dBi at 15 degrees elevation angle...

Thanks for your comprehensive, civil analysis. It appears either that my
incarnation of NEC-2 doesn't deal with this situation properly, or I didn't
use it right (the latter is more likely). I'll have a look into it.

In all the cases I looked at, however, the 5/8 wave vertical
did show some gain over a quarter wave vertical up to at least 14 degrees.
...Over average ground, the gain difference is at or just above 3 dB up to
about 10 degrees.

.... which supports my contention earlier in this thread: The peak gain
increase between a 1/4-wave and a 1/2-wave or 5/8-wave vertical is 3dB above
the gain differences of those antennas as dipoles of _twice_ that length in
free space.

Repeating the reasons for this...

* the electrical length of the vertical is doubled by its image below the
ground plane (a 1/4-wave vertical monopole becomes an electrical
1/2-wave dipole)

* the peak "free space" gain of the monopole and its image is increas-
ed 3dB, because all radiation from it is confined to one hemisphere
(above the ground).

RF

Richard Fry wrote:
* the peak "free space" gain of the monopole and its image is increas-
ed 3dB, because all radiation from it is confined to one hemisphere
(above the ground).

Remember, that's for perfect ground only (and maybe salt
water ground). If one buries half of a dipole in earth
ground, one loses most of that 3 dB to the ground.

For instance, EZNEC reports: The max gain of a 40m 1/4WL
vertical with 8 horizontal radials one foot above average
ground is -0.29 dBi. Raising the radials to one wavelength
above ground increases the max gain to +3.23 dBi. (Of course,
the 3D radiation patterns are not exactly the same but the
correlation to that 3 dB of image power is in there because
of decreased ground losses at increased height.)

Problem: Most everyone with a 1/4WL vertical and four buried
radials is throwing away about half of his/her source power.
Solution: Put up a horizontal dipole. :-)
--
73, Cecil http://www.qsl.net/w5dxp

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Richard Fry wrote:

... which supports my contention earlier in this thread: The peak gain
increase between a 1/4-wave and a 1/2-wave or 5/8-wave vertical is 3dB
above the gain differences of those antennas as dipoles of _twice_ that
length in free space.

Things seem to be getting a little confused here.

When you replace a free space environment with a perfect ground plane,
the *average* field strength of *all antennas* increases by 3 dB for a
given power input because of the reduced volume. This shows up as a 3 dB
gain increase when the gain is referenced to a free-space antenna such
as an isotropic source. No antenna is given any additional advantage
over any other - they all get the same amount of increase. So if I read
the above statement correctly, it's not true. The gain increase between
a 1/4 and 1/2 or 5/8 wave antenna over a perfect ground is the *same* as
the gain increase between a 1/2 and 1 or 5/4 wave dipole in free space.
Not 3 dB greater. If you'll look at the patterns of the antennas, you'll
find that the pattern of a 1/4 wave vertical over perfect ground is
identical in shape to half the pattern of a 1/2 wave free space dipole,
but 3 dB stronger. Likewise for any other vertical and its twice-as-long
free space dipole counterpart.

When the perfect ground is replaced by real ground, an attenuation
factor is introduced which actually changes the pattern shape. This
pattern shape change is different for each height of vertical because it
depends on the angle at which the radiation from each part of the
antenna strikes the ground. The different antenna heights have different
current distributions and so different fractions of the total radiation
hits the ground at different angles. The effect of the attenuation at
each elevation angle depends on the ground constants and the frequency.

You're probably more used to looking at surface wave attenuation, where
this ground reflection effect doesn't exist. Instead, there's a single
frequency and ground dependent attenuation that's essentially the same
for all antenna heights. What I'm talking about here is sky wave
radiation which consists of both a directly radiated "ray" (which
undergoes no attenuation other than that caused by its expanding volume
with distance) and a "ray" reflected from the ground. It's the
attenuation and phase shift of this second "ray", which depends on the
elevation angle, ground constants, and frequency, which causes the
pattern shape modification and attenuation of low angle signals. If you
look into the way NEC-2 operates you'll see that it does just this
calculation. The relationship of the reflected ray before and after
striking the ground is described by a fairly simple reflection
coefficient, which is quite different for horizontally and vertically
polarized waves. If you assume a current distribution, it's not
difficult to calculate the pattern manually. The reflection coefficients
can be found in Kraus.


Repeating the reasons for this...

* the electrical length of the vertical is doubled by its image below the
ground plane (a 1/4-wave vertical monopole becomes an electrical
1/2-wave dipole)

I don't think that's a good use of the term "electrical length". It is
true that the radiation pattern of a 1/4 wave vertical over perfect
ground (but not imperfectly conducting ground) is the same as that of a
half wave dipole in free space. Also, its feedpoint impedance assuming
no loss is exactly 1/2 that of a 1/2 wave dipole in free space.


* the peak "free space" gain of the monopole and its image is increas-
ed 3dB, because all radiation from it is confined to one hemisphere
(above the ground).

Yes, but this is altered if the ground isn't perfect. When the ground
isn't perfect, the shape of the pattern of the monople is no longer the
same as half a free space dipole, so the gain difference is no longer a
constant 3 dB at all angles. Some of the radiated energy is lost in the
ground reflection, and the fraction which is, depends on the angle at
which it strikes the ground.

Roy Lewallen, W7EL