qex-mar-apr-2012.pdf

Rudy Severns, N6LF

PO Box 589, Cottage Grove, OR 97424; n6lf@arrl.net

A Closer Look at Vertical Antennas

With Elevated Ground Systems

N6LF shares his results from more vertical antenna experiments.

[This article is being published in two

parts. — Ed.]

Among amateurs, there has been a long

running discussion regarding the effective-

ness of a vertical antenna with an elevated

ground system compared to one using a

large number of radials either buried or

lying on the ground surface. NEC model-

ing has indicated that an antenna with four

elevated λ/4 radials would be as eficient

as one with 60 or more λ/4 ground based

radials. Over the years there have been a

number of attempts to confirm or refute

the NEC prediction experimentally, with

mixed results. These conflicting results

prompted me to conduct a series of experi-

ments directly comparing verticals with the

two types of ground systems. The results of

my experiments were reported in a series of

QEX 1-7 and QST 8 articles (Adobe Acrobat

.pdf iles of these articles are posted at www.

antennasbyn6lf.com ). From these experi-

ments I concluded that at least under ideal

conditions four elevated λ/4 radials could

be equivalent to a large number of radials on

the ground.

Confirmation of the NEC predictions

was very satisfying but that work must not be

taken uncritically ! My articles on that work

failed to emphasize how prone to asymmet-

ric radial currents and degraded performance

the 4-radial elevated system is. You cannot

just throw up any four radials and get the

expected results! I’m by no means the irst

to point out that the performance of a ver-

tical with only a few radials is sensitive to

even modest asymmetries in the radial fan. 9,

10, 11 It is also sensitive to the presence of

nearby conductors or even variations in the

soil under the fan. 12 These can cause signii-

cant changes in the resonant frequency, the

feed point impedance, the radiation pattern

and the radiation efficiency. While these

problems have been pointed out before, as

far as I can tell no detailed follow-up has

been published. Besides the practical prob-

lem of construction asymmetries, at many

locations it’s simply not possible to build

an ideal elevated system even if you wanted

to. There may not be enough space or there

may be obstacles preventing the placement

of radials in some areas or other limitations. I

think it’s very possible that some of the con-

licting results from earlier experiments may

well have been due to pattern distortion and

increased ground loss that the simple 4-wire

elevated system is susceptible to.

As the sensitivity of the 4-radial system

and its consequences sank into my con-

sciousness I began to strongly recommend

that people use at least 10 to 12 or more

radials in elevated systems. Although I have

heard anecdotal accounts of significant

improvements in antenna performance when

the radial numbers were increased to 12 or

more, I have not seen any detailed justiica-

tion for that. What follows is my justiication

for my current advice.

Severns_QEX_3_12_Fig_2

Figure 1 — A typical counterpoise ground system. Figure adapted

from from Laport. 14

1 Notes appear on page 41

32 QEX – March/April 2012

Reprinted with permission © ARRL

My original intention for this article was

to illustrate the problems introduced by radial

fan asymmetries and to discuss some possible

remedies. In the process, however, I came to

realize that before going into the effects and

cures for asymmetries it was necessary to

irst understand the behavior of ideal systems.

Ideal systems can show us when and why

they are sensitive and point the way towards

possible cures or at least ways minimize

problems. The discussion of ideal antennas

(over real ground however!) also illustrates

a number of subtleties in the design and pos-

sibly useful variations that differ somewhat

from current conventions.

For these reasons, after some histori-

cal examples of elevated wire ground sys-

tems, I’ll spend a lot of time analyzing ideal

systems and then move on to the original

purpose of this article: asymmetric radial

currents and how to avoid them. At the end

of this article I summarize my advice for

verticals using elevated ground systems.

While much of what follows is derived from

NEC modeling, I have incorporated as much

experimental data as I could ind and com-

pared it to the NEC predictions to see if NEC

corresponds to reality.

Figure 2 — A very large LF

elevated ground system.

Adapted from Admiralty

Handbook of Wireless

Telegraphy , 1932. 34

Figure 3 — EZNEC

model of the 1BCG

antenna.

Prior Work on Elevated Ground

Systems

There is a lot of prior information on ele-

vated ground systems: Moxon, 10, 11 Shanney, 13

Laport, 14 Doty, Frey and Mills, 12 Weber, 9

Burke and Miller, 15, 16 Christman, 18 to 33

Belrose 39, 42 and many others. There is also

my own work, some published but most not.

Some History

In the early days of radio, operating wave-

lengths were in the hundreds or thousands

of meters. Ground systems with λ 0 /4 radials

were rarely practical but very early it was

recognized that an elevated system called a

“counterpoise” or “capacitive ground,” with

dimensions signiicantly smaller than λ 0 /4,

could be quite eficient. Note, λ 0 is the free

space wavelength at the frequency of inter-

est. Figure 1 shows a typical example of a

counterpoise.

Here is an interesting quotation from

Radio Antenna Engineering by Edmund

Laport 14 regarding counterpoises:

“ From the earliest days of radio the merits

of the counterpoise as a low-loss ground sys-

tem have been recognized because of the way

in that the current densities in the ground are

more or less uniformly distributed over the

area of the counterpoise. It is inconvenient

structurally to use very extensive counter-

poise systems, and this is the principle reason

that has limited their application. The size of

the counterpoise depends upon the frequency.

It should have suficient capacitance to have

Figure 4 — A λ /4 ground-

plane vertical with four

radials.

Reprinted with permission © ARRL

QEX – March/April 2012 33

that results obtained from them must be used

with some caution. 41 For HF verticals close to

ground this is an important limitation.

antenna is that you take a quarter-wave verti-

cal and add four quarter-wave radials at the

base. It is well known that the elements of a

dipole will be a few percent shorter than λ 0 so

it is usually assumed that in a ground-plane

antenna the vertical and the radial lengths will

also be a few percent less than λ 0 . Typically

a relatively low reactance at the working

frequency so as to minimize the counterpoise

potentials with respect to ground. The poten-

tial existing on the counterpoise may be a

physical hazard that may also be objection-

able. ”

Laport was referring to counterpoises that

were smaller than λ 0 /4 in radius. In situations

where λ 0 /4 elevated radials are not possible

amateurs may be able to use counterpoises

instead. Unfortunately, beyond the brief

remarks made here, I have to defer further

discussion of counterpoises to a subsequent

article.

Rectangular counterpoises, some with a

coarse rectangular mesh, were also common.

A rather grand radial-wire counterpoise is

illustrated in Figure 2.

Amateurs also used counterpoises. Figure

3 is a sketch of the antenna used for the ini-

tial transatlantic tests by amateurs (1BCG)

in 1921-22. 35, 36 The operating frequency

for the tests was about 1.3 MHz (230 m).

At 1.3 MHz, λ 0 /4 = 189 feet, so the 60 foot

radius of the counterpoise corresponds to ≈

0.08 λ 0 .

Note that in all these examples, a large

number of radials are used. The use of only

a few radials, initially with VHF antennas

elevated well above ground, seems to have

started with the work of Ponte 37 and Brown. 38

The Effect of Element Dimensions

on Performance

The simplest idea of a ground-plane

Behavior With Ideal Radial Fans

In this section we’ll look at verticals with

a length (H) ≈ λ 0 /4 (λ 0 is the free space wave-

length) and symmetric elevated radial sys-

tems where the height above ground (J) and

the number (N) and length (L) of the radials

is varied. We’ll also look at the effect of soils

with different characteristics from poor to

very good. Even though we will be looking

at verticals with H ≈ λ 0 /4, keep in mind that

elevated ground systems can also be used

with verticals of other lengths, with or with-

out loading, inverted Ls, and other antenna

types. Elevated radials can also be used with

multi-band antennas.

NEC Modeling

Figure 4 shows a typical model of a verti-

cal with a radial system. Except as noted, the

following discussion will focus on operation

on 3.5 to 3.8 or 7.0 to 7.3 MHz as the operat-

ing band and 3.65 or 7.2 MHz as a spot fre-

quency near mid-band. The conductors (both

the vertical and the radials) are lossless no.

12 wire. Most of the modeling was done over

real grounds. The modeling used EZNEC

Pro4 v.5.0.45, using the NEC4D engine.

The use of NEC4D over real soils gives the

correct interaction between ground and the

antenna. Excellent free programs based on

NEC2 are available, but these do not properly

model the ground-antenna interaction, so

Figure 5 — Dipole half-length for resonance for different values of J and different soils.

Figure 6 — Measured current on a 33 foot radial at 7.2 MHz. This antenna uses four radials

lying on the ground surface.

34 QEX – March/April 2012

Reprinted with permission © ARRL

To better understand what’s happening

we can expand Figure 7 around the 1 A feed

point (indicated by the arrow) as shown in

Figure 8.

For H = 64 feet and L = 80.85 feet, the

current on the vertical has not peaked so the

vertical is too short for resonance. The radial

current peak is well out on the radials, how-

ever, so clearly the radials are too long for

resonance. The reactance of the vertical and

the radials cancels at the feed point so the

antenna is “resonant” but not the vertical and

radials individually. Similarly, for H = 69 feet

and L =58.8 feet, the current in the vertical

peaks and begins to fall (moving from the top

to the bottom of the vertical) before the feed

point is reached. Again, we have a resonant

antenna but the vertical and the radials are not

it is assumed that the vertical and the radials

will be individually resonant at the operating

frequency. Unfortunately it’s not that simple,

because the vertical is coupled to the radi-

als and both interact strongly with ground

because, at least at lower HF (<20 m), the

base of the vertical and radial fan will usually

be only a fraction of λ 0 above ground. What

you have in reality is a coupled multi-tuned

system with complicated interactions. It

turns out that there are a wide range of pairs

of values for H and L that result in resonance,

or X in = 0 at the feed point (where Z in = R in

+ j X in and Z in is the feed point impedance).

Some of these combinations where neither

the vertical nor the radials are individually

resonant may be useful.

Antenna Resonance and Element

Dimensions

The free space wavelength (λ 0 ) at a given

frequency in MHz ( f MHz ) is given as:

299.792

983.570

[ ]

[

]

λ =

feet

MHz

[Eq 1]

At 3.65 MHz, λ 0 /4 = 67.368 feet. If we

model a resonant λ/4 vertical over perfect

ground using no. 12 wire, we ind that at

3.65 MHz, λ/4 = H = 65.663 feet, which is

about 3.5% shorter than λ 0 /4.

To take into account the effect of ground

on radial resonance for a given value of J and

soil characteristic, it has been suggested that

we can erect a low dipole at the desired radial

height (J) and trim its length to resonance.

An example of this is given in Figure 5.

For J = 8 feet, depending on the soil, L

varies from 64.5 feet to 66.4 feet. As we

reduce J we ind that L gets smaller. The shift

in resonance for radials close to ground has

also been demonstrated experimentally. (See

Note 2.) Figure 6 shows the measured radial

current at 7.2 MHz on 33 foot radials (sum of

four radials). Clearly this radial is λ/4 reso-

nant at a lower frequency than 7.2 MHz! As

Figures 5 and 6 show, the effect gets much

larger for small values of J.

What do we mean by “resonant” values

for H and L “independently”? It's not just

that the reactances cancel at the feed point.

When I say “the resonant length for H or L”

I’m talking about the case where the current

distribution on the vertical and the radials

independently corresponds to resonance: in

other words, the current just reaches a maxi-

mum at either the base of the vertical or at

the inner ends of the radials. If either H or L

is made longer than resonance, the current

maximum will move out onto the radials

or up the vertical. Figure 7 shows the cur-

rent distribution on a vertical and the radials

for three combinations of H and L, each of

which yield X in = 0 at the feed point.

Figure 7 — Current distribution on the vertical and the radials. The current starts at the top of

the vertical, runs to the base and then out along the radials. The radial current is the sum of

the currents in the four radials. The currents are for 1 A rms at the feed point.

Figure 8 — Current distribution on the vertical and the radials expanded around the feed

point. The arrows point to the junctions between the vertical and the radials.

QEX – March/April 2012 35

Another way to explore the interaction

between L and N is to set L equal to L r for

some value of N (say 16 radials) and while

watching the resonant frequency (f r ), vary

the number of radials as shown in Figure 10.

Note that the most stable f r is where H = L =

66.71 feet. That is relatively close to the val-

ues we got earlier for independently resonant

vertical and radials. (Be careful, this is par-

ticular to this example; things will vary with

different J, ground type, and other variables).

Note also that for H a bit tall, f r decreases

as radials are added, but if H is a bit short f r

increases as radials are added. This kind of

behavior can be confusing if you are trim-

ming the radials to resonate at a particular

frequency, especially if you add some radi-

als. It is possible you could add some radials

and then have to make all the original radials

longer!

individually resonant. If we set H = 67 feet

and L = 67.66 feet, however, both the vertical

and the radials are λ/4 resonant individually.

The “resonant length” (by the deinition

given above!) of the vertical is 67 feet and the

“resonant” length for the radials is 67.7 feet,

both of these lengths are substantially dif-

ferent than the value we got earlier for λ/4

resonance for a vertical over an ininite per-

fect ground-plane (65.7 feet). The “resonant”

radial length of 67.7 feet is quite different

from the dipole 8 feet above average ground

(64.7 feet). H and L are actually closest to λ 0

(67.4 feet). What we have just seen is only one

particular example. If we change J and/or the

soil characteristics and/or the number of radi-

als, these lengths will change!

Setting up the antenna so that both the ver-

tical and the radials are individually resonant

turns out to not be so simple and we might ask,

“Is it really necessary to have both the verti-

cal and the radials resonant individually?” It

turns out that there are other considerations

besides the current distribution with regard to

the choice of L for a given H. It is possible to

use values of L where X in ≠ 0 and compensate

for that with a tuning impedance at the feed

point for example, or perhaps use some top-

loading. In addition, in some situations it may

not be possible to have radials long enough

to make X in = 0 while keeping the radial fan

symmetric. Further, Weber has suggested that

radials with L <λ/4 or >λ/4 are a possible cure

for radial current division inequality. (See

Note 9.) So we have reasons to investigate

the effect of variations in vertical height and

radial length on antenna behavior.

For each value of H, number of radials

(N), height above ground (J), ground charac-

teristic (σ = conductivity and ε r = permittiv-

ity) and choice of operating frequency, there

will be some radial length (L r ) that makes the

antenna resonant. That’s a lot of variables! So

we will look at only a few examples to get a

general idea of what happens.

Figure 9 gives an example of the variation

in the value for L (L r ) that results in resonance

at the feed point (X in = 0) as a function of N

and several values of H, with ixed values of

f, J and soil.

Notice how widely L r varies with N for

most values of H although there is one value

for H (66.71 feet) that seems to have only a

small variation in L r as N is changed. Note

also how much shorter L r becomes when H is

increased by a few feet. This could be very use-

ful in situations where space for the radial fan

is limited. On the other hand note how quickly

L r grows when H is shortened. For N = 16 we

see that when H = 64 feet, L r = 106 feet but for

H = 69 feet, L r is only 39 feet! That’s a differ-

ence in L r of almost 3:1. If you cannot make H

long enough, all is not lost! A bit of top loading

has an effect much like increasing H.

Figure 9 — Examples of the effect of radial number on the radial length for resonance at

3.650 MHz (L r ) for several different values of H.

Figure 10 — Resonant frequency of the antenna as a function of radial number for several

combinations of H and L that are resonant at 3.650 MHz with N = 16.

36 QEX – March/April 2012

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