Antennas/Antennas_CD-ROM_Walnut_Creek_September_1996.iso/articles/supergan/supergai.txt

Text File | 1996-06-30 | 54KB | 1,229 lines

SUPERGAIN ANTENNAS
Possibilities and Problems
R. P. Haviland, W4MB


In principle, any desired amount of gain can be developed from an
antenna of arbitrary size. The phenomena of high gain from very
small antennas is called "Supergain".

THE OPTICS APPROACH TO PROOF OFSUPERGAIN

To see why this statement might be so, let us recall the
construction used in optics, known as Huygens principle. This
states that every point on a wave front can be regarded as a
source of radiation, as sketched in Fig. 1. At the end of a short
period of time, the envelope of all of these individual wavelets
forms the new wave front. For example, this construct explains
why a shadow is not perfectly sharp, and why interference fringes
form.

The construct is applicable to all wave propagation, including
the signals from antennas. But for this discussion, let us
reverse the direction of application of the construct. Now, in
Fig. 1, the right most wavefront is regarded as existing at some
instant. Each point on it has been created by the sum of the
individual point waves of an earlier wavefront. Thus the leftmost
wave represents the position of the front at an earlier time.
This process can be repeated again and again, until the source of
the wave is reached.

In tracing the front back toward the source, there is no
restriction in the number of steps. Therefore, a given pattern
can be generated by many different sizes of antenna. But this is
just a different way of repeating the opening sentence.

THE END-FIRE ANTENNA APPROACH TO PROOF OF SUPERGAIN

We can develop the same conclusion by a completely different
approach. Consider the case of two parallel ideal half-wave
dipoles fed 180 degrees out of phase, and at various spacings.
These form the basic end-fire array, also known as the flat-top
beam or the 8JK antenna.

Following Kraus(1) in his book on antennas, the radiation pattern
of this antenna can be regarded as the product of two terms, one
for the coupling between the antennas, and one for the phase
relations of the two sources. The complete expression for the
gain in the plane at right angles to the antennas is:

     G=SQR(2*R11/(R11-R12))*SIN(D/2*Sin(Ang))           (1)

Where G is the gain
      R11 is the radiation resistance of an element
      R12 is the mutual resistance between elements
      D is the element spacing
      ANG is the angle from the line perpendicular to the
elements.

At very large distances the mutual resistance is zero. It
increases cyclically as the separation becomes less, then
monotonically, and is equal to the radiation resistance of a
single element when the spacing is zero . As a result, as the
spacing of the dipoles is reduced, the magnitude of the coupling
term becomes large, while the angle term becomes small. The
overall effect is shown in Fig. 2, which shows the magnitude of
the two terms as a function of distance, and the magnitude of
their product, the gain. The surprising result is that an array
of two dipoles at near zero separation has a gain of 4 db, nearly
3 db more than that of a single dipole occupying essentially the
same space.

Now let us follow an approach used by Schelkunoff and Friis(2).
Suppose we have a two element array, with some spacing, say a
quarter wavelength, and that these are fed out of phase with a
current of one ampere. The currents can be represented by the
number pair, 1,-1. In the plane at right angles to the antennas,
the radiation pattern is the figure 8 of the end-fire array.

Now suppose that each element is replaced by a pair of elements,
one fed by a current 1,-1, the other by -1,1. Let the spacing be
half the original spacing, or 1/8 wavelength. Suppose also that
the total width of the array is kept the same as the original, or
1/4 wavelength. Now two elements are at the same place at the
center of the array, so they can be replaced by a single element
carrying twice the current. The array is now of three elements,
with currents of 1,-2,1. The pattern is the figure 8 of the
original antenna pair pattern multiplied by another figure 8 due
to spacing between the two pairs of antennas. The directivity of
the antenna has been increased, even though there has been no
change in overall dimensions.

In principle this process can be extended without limit by adding
elements and changing the excitation currents. The successive
currents are:
      2 elements,    1,-1
      3 elements,    1,-2,1
      4 elements,    1,-3,3,-1
      5 elements,    1,-4,6,-4,1
      6 2l2ments     1,-5,10,-10,5,-1
     etc.
Each time there is a further increase in gain.

The minus currents mean that the particular element is delivering
power to the exciting system. This is not a common design
problem, but with inductors and capacitors of low resistance this
can be handled with standard design equations.

While these approaches are not rigorous in the mathemetical
sense, they can be made so. Thus the statement that any desired
amount of gain can be developed from an antenna of arbitrary size
is soundly based.

Antennas which develop gain or directivity beyond that normal for
their size are commonly called Supergain Antennas, and are said
to be in the supergain regime.

DIMENSIONS OF SUPERGAIN ANTENNAS.

Some work by Harrington(3) and Chu(4) provides a method of
determining when an antenna is normal and when it is supergain (a
summary of this is found in Hansen(5) ). Let the antenna be
enclosed in a the smallest sphere which just encloses all
elements of the antenna. Then the maximum gain which can be
developed by an antenna operating by the normal regime is:

     Gnmax=(2*PI*A/LAM)squared+4*PI*A/LAM                (2)

           Where A is the radius of the enclosing sphere, and LAM
is the wavelength. Any antenna having greater gain is in the
supergain regime. This equation is plotted in Fig. 3.

As an example, consider a half wave dipole. The radius of the
enclosing sphere A/LAM is 1/4, so:

     Gnmax=(6.28/4)squared+12.56/4                       (3)

or a gain of 5.6 relative to isotropic, or 7.4 db. Since the
known gain of a practical dipole is 2.14 db it is definitely in
the normal gain range.

However, assume that the dipole is shortened to a length of 1/16
wavelength by loading. For this case, from the figure, Gnmax is
0.93 relative to isotropic, or to -.27 db. Now the gain of a
shortened dipole approaches the constant value of 1.5 or +1.76 db
as the dipole length is shortened. Thus markedly shortened
dipoles are in the supergain region.

Now consider the two element flat-top beam. When the elements are
very close together, the sphere of containment is essentially the
same as for a dipole, 1/4 wavelength in radius. The supergain
point is essentially 7.4 db. Since the gain of a two element
flat-top beam approaches 4.0 db, it also operates in the normal
regime, but by a smaller margin than for a full size dipole.
Decreasing the length of the elements in the array will place it
in the supergain regime, as will using the method of element
doubling described above.

For a one wavelength loop, the basic element of quads, the sphere
radius is half the diagonal of the loop, or .35 wavelengths. From
Fig. 3 Gnmax is 9.3, relative to isotropic, or to 9.65 db. Since
the gain of a single quad loop is 3.4 db, it is operating in the
normal regime. As for the dipole, the gain becomes constant as
the size is decreased, so very small loops are also supergain
regime devices.

It seems clear from these examples that the common basic antennas
operate in the normal regime. But it also seems clear that it is
not difficult to throw antenna designs into the supergain regime.

SUPERGAIN PROBLEMS- DRIVE RESISTANCE.

In a pair of coupled circuits driven by a voltage in one circuit,
the drive impedance is:

     Zin=Z11-Z12*Z12/Z22                           (4)
     where Zin is the input impedance
           Z11 is the self impedance of the first circuit
           Z22 is the self impedance of the second circuit
           Z12 is the mutual impedance.

When the coupled circuits are two identical antennas, as for the
flat top beam example above, Z11 and Z22 are equal. Also, as the
antennas are moved closer together, Z12 approaches Z11 in value.
Acordingly, the drive resistance decreases markedly for elements
very close together.

Actually, this is not altogether bad. The distant field of an
antenna is proportional to the current flowing in it. For a given
power, the current increases as the drive resistance falls. Thus
the gain also increases.

The phenommena of drive resistance decrease and current increase
is even more marked when adjacent antennas are driven in the
opposite polarity sense, a characteristic of the element doubling
technique. Hansen(5) reports a calculation of Yaru, for a 9
element symmetrical array, compressed to 1/16 of its original
size. The calculated currents in amperes are:

     I0, I8     8,893,659,368.7
     I1, I7   -14,253,059,703.2
     I2, I6     7,161,483,126.6
     I3, I5    -2,062,922,999.4
     I4           260.840,226.8

The net current is only 19.5 amperes. Maintaining the required
currents requires that component values be maintained to one part
in 10000 million.

Note the alternation of phase from one element to the next. This
is characteristic of this method of supergaining. Variations of
the technique will be found in the literature, with phase
difference of less or more than 180 degrees. The characteristics
of marked phase change between adjacent elements, and power being
fed from some elements to the source network exists in these
variations.

The current values per element are much less with fewer elements,
as tabulated above, and the accuracy requirements are less
severe. The limit of reasonable design is considered below.

SUPERGAIN PROBLEMS- ELEMENT RESISTANCE

Real world antenna elements have some resistance, which must be
accounted for. In Equation 1, this enters in the coupling term,
as:

G=SQR(2*(R11+R1L)/(R11+R1L-R12))*SIN(D/2xSin(Ang))     (5)
     Where R1L is the loos resisatance.

The result of this resistance is shown by the curves of Fig. 3.
For a given value of resistance there is a spacing giving maximum
gain. At lesser spacings the gain falls rapidly. The rapidly
increasing currents in the elements causes an equally rapid
increase in power lost in the element resistances.

One result of the element resistance is that the antenna
efficiency is less than 100 percent. The radiating efficiency is:

     EFF=R11/(T11+R1L)X100   percent    (6)

This calculation is valid if the current on the elements is a
half sine curve. This is never exactly true, but the departure
form the sine curve is small in practical antennas.

Computer programs for calculation of antenna performance close to
and in the supergain regime should include element resistance as
a factor. In the case of Mininec, this can be done by introducing
a loading resistance in the pulse at the center of the radiator.
In standard Mininec this must be done manually. It is easy to
write a small routine to add this automatically, based on the
length and diameter of the element.

A suitable relation for copper tubular elements, from Terman(6),
is:

     R=83.2*SQR(FREQ)/DIA                        (7)
Where R is the resistance in milli-microhms per centimeter of
length
      FREQ is the frequency in Hertz
      DIA is the conductor diameter in centimeters.

For example, the resistance of 1 inch tubing at 14 MHz is 3.6
milliohms per foot. For Aluminum, this value is multiplied by the
conductivity ratio, or by 1.6, but check the value for the alloy
used.

Slightly better modelling of resistance divides the load
resistance among the segments used in the model. This can also be
done by a short routine added to Mininec. Some versions, and
other antenna modelling programs have this included.

In the regime of normal operation, element resistance is not of
great importance unless the elements are very thin. Fig. 5 shows
a Mininec calculation of efficiency for a dipole as a function of
element diameter. Normal sizes of tubing and even wire do not
have great loss. The situation becomes different, of course, with
the high currents of the supergain regime.

Texts normally neglect other effects of element resistance. One
is the fact that current distribution changes. This is shown in
Table 1, giving the theoretical sine wave currents at several
points, plus Mininec calculated currents with and without element
resistance included. For the normal range of operation the
current change itself is negligible. However, there can be
changes in drive resistance and reactance, as shown in Figs. 6
and 7. In particular, the change in reactance also means a change
in resonant frequency. This is shown in Fig. 8 for one particular
wire size. The effects are appreciable in the wire sizes found in
"invisible antennas".

SUPERGAIN PROBLEMS- Q AND BANDWIDTH

The fact that individual element currents are high while the
effective radiating current remains low means that there is a
large amount of energy stored in the space surrounding a
supergain antenna. This is a way of saying that the Q of the
antenna is high. In turn, this means that the usable bandwidth of
a supergain antenna will be low.

The above mentioned work of Chu and Harrington gives data on
this. They consider that the radiation leaving the enclosing
sphere can be described by a set of spherical harmonics. (The
colored multi-segmented bouncing balls found on computer displays
are an example of these.) A large number of terms in the harmonic
series is necessary to describe the pattern of narrow beam, high
directivity antennas.

If point-source antennas were really available, the number of
sources in any size sphere would be unlimited. But in the real
world, antennas must have physical size, preferably around a half
wavelength in length. Thus, practically, the number of terms in
the series is determined by the number of elements in the array.

The derived relation between antenna Q and the size of the
enclosing sphere is shown in Fig. 9. The number N on each curve
is the number of terms in the harmonic series. For our purposes,
the number of terms is also the number of radiating elements in
the antenna, each being a half-wave long, or at least a large
fraction of this length.

The intersection of each curve with the Q=1 axis is the size of
the enclosing sphere for an antenna which is just at the boundary
betweeen normal and supergain regimes. This point can also be
taken as the normal design point for an antenna of N elements.

If supergain operation is attempted by reducing the length of the
elements or moving them closer together, operation moves along
the numbered curve to the intersection with the new enclosing
sphere size. Accordingly, the antenna Q increases. This is the
consequence of the increase in energy stored in the space
surrounding the antenna. The nature of the curves is such that
the Q change for antennas with a large number of elements becomes
very high if appreciable size change is attempted. This shows
clearly in Fig. 10, which shows the Q for a 2:1 improvement in
gain directivity, as a function of the original enclosing sphere
size.

At the present state of knowledge and technology, size reduction
and supergaining will have to be limited to antennas which are
initially small in the sense of having relatively few elements.
The situation may change if room temperature super-conductors
become available, but there will still be the matter of
bandwidth.

To see the importance of this, recall that a Q of 1000 would mean
that an antenna on 80 meters would have a bandwidth of 3.5 kHz.
Even a Q of 100 is troublesome if variable frequency operation is
needed. Perhaps a new term would be in order: instead of being
rock-bound, the supergain antenna station would be wire-bound to
a single frequency.

It should be noted that this antenna bandwidth limitation is not
the same as that usually encountered in feeding the antenna.
Antennas themselves are wideband when operating in the normal
radiation regime. The proof of this is that retuning of the
"match-box" restores full operation. Since the antenna has not
changed, the usual limit is due the the matching system, not the
antenna.

SUPERGAIN AND THE DIPOLE

It was noted earlier that physically small antennas are easy to
supergain. This is the case for short dipoles. As the length of a
dipole reduces, (in fractions of a wavelength), its gain
decreases slowly, from the initial 2.15 db to a constant value of
1.76 db. Even an elemental dipole has this gain. From Fig. 3, any
dipole which fits in a .08 wavelength sphere, i. e., which is
less than 0.16 wavelengths long, is operating in the supergain
regime. The same is true for a ground-mounted vertical less than
0.08 wavelengths high.

The practical aspects of using short dipoles are well worked out.
Just to review, the large reactance at the feed point can be
canceled by a local reactance of opposite sign, by adding a
loading coil, or by adding capacity at the dipole end: often a
combination is used. This leaves a resistance, the sum of the low
radiation resistance of the dipole plus the loss resistance of
the dipole and the added elements. Separate impedance
transformation may be used, or it may be combined with the
reactance cancelling elements. Note that these steps do not
change the operating mode of the antenna. For practical details,
see, for example, the work of Hall(7) on dipoles and Sevik(8) on
verticals.

A typical 2 meter "Rubber Duckie" has a length of 6 inches, about
0.16 wavelength. Assuming that the body of the transceiver is the
effective ground, this is operating in the normal regime. The
Short Duckie, 3-4 inches long is just at the edge of normal
operation.

160 meter antennas, in particular, are often in the supergain
regime. For example, a 40 foot vertical has a length of of about
.075 meters, just in the supergain regime. The feed resistance is
about 2.3 ohms, not too difficult to feed. But an 8 foot whip has
a length of 0.015 wavelengths. Reflecting the penetration into
the supergain regime, the feed resistance is about 0.2 ohms. This
antenna system will be low efficiency because of loss in matching
and in element resistance. But it will have the same gain as the
larger vertical, 1.5 db. The hoped-for room temperature
superconductor whould have a big impact on the whip system.

Top hat loading is used to increase the feed resistance. For
example, consider a common situation, a 20 meter dipole at 40
feet, with the feed line ends tied together and fed against
ground for operation on a lower band. On 160 meters the enclosing
sphere radius has increased to 0.08 wavelengths, just out of the
supergain regime. Mininec gives a gain of 1.8 db for this
condition, with a drive resistance of 4.8 ohms.

Top loading of an 8 foot whip also helps, even though operation
may still remain in the supergain regime. This is the principle
of the DDRR antenna, (described in the ARRL Antenna Handbook (9)
).

The fact that a simple element can be operating in the supergain
regime means that there are four array regime types:

     Normal array, normal elements
     Normal array, supergain elements
     Supergain array, normal elements
     Supergain array, supergain elements.

A close spaced array of short loaded dipoles would be an example
of the last.

SUPERGAIN AND END-FIRE ARRAYS.

The earlier discussion of endfire arrays promised an
investigation of practical operation of these. Let us start with
the two element array fed out of phase, the 8JK array. The
general form of results with this beam alone are shown in Fig.
11, based on data in Lawson (10). This shows the expected gain
increase and resistance decrease as spacing is reduced. Element
resistance is not included.

To investigate the effects of conductor resistance on supergain
operation, it is convenient to use the ELNEC version of Mininec,
since it is set up for current feed, whereas the voltage feed of
standard Mininec requires successive approximations to set
currents precisely.

The example is based on two meter long elements, with a copper
element radius of .00625 meter, about one quarter inch, operating
at 73 mHz. Calculations were made with and without element
resistance included. Results are essentially the same for a 20
meter element one inch in diameter.

For a single 8JK, with a spacing of one meter and no element
resistance, the drive impedances of each of the two elements are
33.4 +j47.8 ohms. Gain is  5.7 db,with a beamwidth of 90 degrees.
With resistance included, the impedances are 33.6 +j47.8 ohms.
This antenna is operating in the normal regime, with no special
problems, and good efficiency.

Now suppose two of these are reduced to half spacing and combined
into a 3 element array of the same boom length, as described
above. Feed currents are 1,-2,1 amperes. With no resistance, the
drive resistances are -16.8 -j6.5, 10.4 +j17.6 and -16.8 -j6.4
ohms. The minus resistances mean that the two end elements are
capturing power and feeding it to the center element. The gain
has increased to 7.3 db, and beamwidth decreased to 56 degrees.

With the effect of resistance included, the drive resistances are
-16.7 -j6.4, 10.5 +j17.6 and -16.7 -j6.4 ohms. Gain has
decreased, but only to 7.0 db. Except for he matter of designing
three feeds, this amount of supergain appears practical.

With 4 elements at .333333 meters spacing, and currents of 1, -3,
3, -1 amperes, the no element resistance drive impedances are
-2.7 -j24.3, .33 -j.93, .33 -j.93 and -2.7 -j24.3 ohms. Gain has
increased further, to 8.4 db. Beamwidth is 48 degrees.

With element resistance considered, the impedances are -2.6
-j24.3, .45 -j.93, .45 -j.93, and -2.6 -j24.3 ohms. Gain falls
dramatically from the ideal condition, to 0.7 db, with a
beamwidth of 90 degrees. This amount of supergain has become
impractical.

An additional amount of supergain could be attained if the
initial pair spacing was increased, or if the element resistance
were decreased by a larger diameter or by silver plating. But the
complexity of multiple feeds and of extremely low driving
resistance does not make the attempt to increase the amount of
supergain appear to be practical.

However, there is another feed technique which avoids part of the
problems. The starting point for this is the unidirectional
end-fire array, where the phasing between elements is equal to
their spacing in degrees. For the 4 elements at .33333 meter
spacing, the element currents are one ampere at 0, 29, 58 and 87
degrees.

With no element resistance, the drive impedances are 229 -j116,
255 +j40, 211 -j61 and 107 -j130 ohms. The main lobe gain is 3.9
db, with a beamwidth of 76 degrees, and the back lobe is -2.9 db.
With element resistance included, the element resistances are
again 229 +j116, 255 +j40, 211 -j61 and 107 -j130 ohms. Gain and
beamwidth remain the same. Except for the multiple feeds, this
antenna is quite practical.

Hansen and Woodward (11) showed that the directivity of this type
of antenna could be increased if the phasing between elements
were increased. They concluded that the best design was obtained
if the total phase shift across the antenna was equal to the boom
length in degrees plus 171.9 degrees (3 radians), with the shift
between each element in proportion. For the 4 element .3333 meter
spacing, the phases are 0, 87, 174, and 261 degrees.

With these conditions and no element resistance, the computed
element impedances are -24.2 +j77.0, 31.1+j36.9, 21.6 +j21.0 and
49.5 +j1.0 ohms. The main lobe gain is 7.8 db, with a beamwidth
of 60 degrees.The backlobe gain is 1.6 db. The backlobe level is
higher than theoretically obtainable. The reason for the high
level was not investigated, but may be related to use of spacing
below the best value, or to rounding of the phase relations.

Including element resistance changes drive impedances negligibly
to -24.0 +j77.0, 31.2 +j36.9, 21.7 +j21.0 and 49.6 +j.1.0 ohms.
Main lobe gain remains at 7.8 db, (actually a reduction of 0.018
db) with a beamwidth of 60 degrees.The back lobe increases by
0.02 db.

This method of increased directivity is practical in this size
antenna if single-frequency operation is needed. The technique
may be extended to more elements, but feed network complexity
seems too great to expect extensive use.

SUPERGAIN AND THE YAGI

We can start study of Yagis in the supergain regime by reviewing
the extensive data in Lawsons book(10). His Figs. 2.4 and 2.5
show that the gain of a particular two element length combination
in low at small and large spacings, with a maximum at some
intermediate spacing.

If element lengths are adjusted at each spacing, the gain
increases as the spacing reduces, as shown in his Table 2.1, and
summarized in Fig. 11. At least down to 0.025 wavelength spacing,
the gain increases, with a limit of about 7.5 db. As the spacing
decreases, the drive resistance decreases, from about 30 ohms at
a typical 0.15 wavelangth spacing to 1.1 ohm at 0.025 wavelength.

At close spacing, the enclosing sphere radius is .25 wavelength,
so the maximum normal gain is 8.5 db. The close-spaced 2 element
Yagi is just outside the supergain regime. If the elements are
shortened to less than about .2 wavelengths by loading, the beam
will enter the supergain regime.

Fig. 12 shows the Q of the two element Yagi as calculated by
Lawson. The plot is based on the assumption that the initial
spacing is 0.5 wavelength, and that the smaller sizes result from
attempts to move into the supergain region by reducing the
element spacing. The Q is the ratio of element reactance to
resistance, and is not precisely the same as that of Fig. 9.
However, this Q is a true measure of array bandwidth.

Consider now a multielement beam, using Fig. 2.9 in Lawson. He
shows a 4 element beam with a 0.7 wavelength boom to have a gain
of 11 db if designed for maximum gain. The enclosing sphere
radius is 0.43 wavelengths, with the maximum normal gain being
just over 11 db. This antenna is at the boundary between the
normal and the supergain regimes.

Suppose this antenna is shrunk until the boom length is 0.4
wavelength. For this condition, the enclosing radius is 0.27
wavelengths, with a maximum normal gain of 8 db. For the tuning
conditions used by Lawson, he calculates a gain of 9.5 db. The
shrunk beam is in the supergain regime.

Lawson does not report the drive resistance for these beams. It
is not possible to determine if the loss of gain in shrinking the
beam is due to element loss, or if different element lengths
would restore the original gain. In general Lawson slanted his
study to a balance of good performance features: gain, F/B ratio
and easy drive. It appears that he purposely avoided the
supergain conditions, since this demands  "single-minded"
attention to gain.

We can investigate Yagi supergain by using the computer program
YAGIMAX, which includes routines for optimizing for gain. For
example, one design in the files included with the program is
SUPER610, a 6 element beam on a 1 wavelength boom. The program
gives a calculated gain of 11.84 db at 28.5 mHz, with a reduction
of .62 db or less at 28 and 29 MHz. F/B ratio is nearly 30 db.

The enclosing sphere radius is .56 wavelengths, for a maximum
normal gain of 13 db. The antenna is in the normal regime. The
calculated pattern of the array is shown in Fig. 13A.

Suppose the boom is shortened to 60 percent of original length.
With no other change, the effect is relatively small. The gain
reduces to 10.35 db, a loss of 1.5 db. F/B ratio drops to 15 db.
The drive resistance also reduces, from the original 20.7 ohms to
12.5 ohms. Since the enclosing sphere radius is .39 wavelengths,
the normal maximum gain is 10.5 db. As also shown by the
relatively high driving resistance, the antenna remains in the
normal regime, but by a small amount.

Changing to the supergain condition requires retuning of
elements. Using the optimization routine included in the program
on the reflector has a small effect, changing from 10.36 db gain
to 10.41 for a length reduction of 4.5 inches. F/B increases
slightly, to 16.2 db. Drive resistance decreases, to 10.22 ohms.

Leaving this condition set and changing the first director has a
small additional effect. A 5.8 inch increase in length increases
the gain to 10.44 db, and reduces the drive resistance to 2.5
ohms.

Moving now to the second director quickly shows the problems of
supergain. For example, a 20 inch reduction in this director
length increases the gain to 11.22 db.  F/B ratio drops to 7.3
db. But the drive resistance drops to about 0.8 ohm. The step
also produces pattern changes, the most marked being an increase
in back lobe size, see Fig. 13B.

The detail performance is made evident by comparing Table 2, for
theoriginal beam, and Table 3 for the size reduced retuned beam.
The steps have converted an easily fed Yagi of good performance
to a narrow band, hard to feed design. These are the penalties
for maintaining the same gain in a beam of 60 percent theoriginal
boom length.

Probably additional gain could be developed by tuning the other
directors. But another effect must be watched. All analysis
programs which have been used by the author become inaccurate
when the degree of supergain becomes large. The most noticeable
effects are very high values of gain, sometimes reaching 100
times (+20db) as compared to usual values, and negative values of
drive resistance.

A large part of the problem is the very high element currents
calculated, and the mutual effects of these. The problems can be
alleviated by using double precision arithmetic, and a large
number of segments in moment analysis programs. However, the
steps are not really worth while, because the drive resistance
goes out of reasonable range. In fact, as noted by Kraus,
supergain drive resistances can go below values which can be
reached by the best transmission line short known.

The overall conclusions for Yagis are:

-Conventional Yagi maximum or near maximum gain designs are at or
close to the lower limit of the normal operating regime. Quite
small changes will throw the design into the supergain regime,
with its attendant problems;
-If the problems can be accepted, boom lengths can be shortened
appreciably;
-Although not shown here, it appears that a better supergain
design compromise can be reached if the gain goal can be secured
with director tuning only; this leaves reflector tuning for F/B
ratio adjustment.

Another point to remember is that the single feed point of the
Yagi is much simpler than the multiple feeds necessary with
end-fire arrays.

There is, however, another important possibility which we have
ignored so far. The antennas considered above have been one or
two dimensional. But the enclosing sphere is three dimensional.
It would seem possible to get better gain while avoiding the
problems of supergain by going to three dimensional antennas. In
the case of Yagis, this means stacking.

Lawson includes some data on this. He shows a 3 element 0.3
wavelength boom Yagi at one wavelength elevation above ideal
ground as having a gain of 14.10 db with a drive resistance of
16.6 ohms. Two such antennas spaced 3/4 wavelength and with the
center at one wavelength give a gain of 16.27 db. Since the gain
due to ground reflection is very nearly 5.0 db, the free space
gain of these antennas would be 9.10 and 11.27 db.

The enclosing sphere for the single Yagi is about .29 wavelength,
and for the stacked pair about .47 wavelength. The maximum normal
gains are about 9.0 and 11.5 db respectively. The stacked pair
remains in the normal operating regime, with none of the
supergain problems. As compared to a long boom design of the same
gain, the problems of boom length and rigidity have changed to a
problem of vertical stacking and adjustment of double the number
of feeds. The stacked array will usually have fewer elements for
the same gain.

The overall conclusion seems to be that stacking should be
considered for Yagis before supergain is attempted.

SUPERGAIN AND THE QUAD

In one sense, the quad in supergain conditions will behave the
same as the Yagi. For the supergain regime, both depend on the
fact that the mutual impedance approaches isolated element
impedance at close spacings.

However, there is one difference. The quad is already a 3
dimensional antenna. Further, the gain of an individual quad loop
is greater than that of a dipole. In the usual configuration, the
boom length is the same as in Yagis, but the element span is half
that of the Yagi, and the height is much greater.

A typical compromise design three element quad in free space will
have a gain of 8.7 db with a boom length of .45 wavelength. The
enclosing sphere radius is .42 wavelengths, for a maximum normal
gain of 11 db. Such a compromise design is well in the normal
regime.

Suppose the boom length is shrunk to .288 wavelength (a 20.5 foot
boom on 20 meters). If elements remain the same, gain will drop
slightly to 8.37 db. Drive resistance will also drop, to 84 ohms.
Gain can be increased by retuning the elements or by adding
reactance. Reducing the reflector perimeter and increasing that
of the director (i.e., bringing the element resonances closer)
will give gains as high as 9.8 db. For this condition, the
enclosing sphere radius is .23 wavelengths, with a maximum normal
gain of 7 db. The antenna is in the supergain regime. The drive
resistance does drop appreciably for this tuning, but is still
12.2 ohms, not particularly troublesome to feed.

A second way of reducing the size of the enclosing sphere is to
reduce the size of the elements by loading. The ways of doing
this include inductive loading at or near high current points,
capacitor loading between high voltage points, and "linear
loading" by folding the sides to resemble a three wire
transmission line. For example, it is not difficult to make a 20
meter size loop which is resonant on 40 meters. There is some
loss in gain, but even very small loops have a gain of 1.5. As
for the dipole, these loops go into the supergain regime. One
result is that the four classes of antenna arrays tabulated above
also exist in the quad family.

As an alternate to loading, suppose that the loop is opened at
the side opposite the feed point. The loop is now parallel
resonant at its original operating frequency. Series resonance
occurs at half this frequency. In one sense, the series resonant
quad loop has been converted to a bent dipole of square
configuration, with sides of .125 wavelength. Such a loop fits in
a sphere of 0.088 wavelength radius, for a maximum normal gain of
1.5 db. Since the calculated gain of the bent dipole around the
resonant point is about 0.2 db, the loop is in the normal regime.
Drive resistance is about 10 ohms.

Arrays of these open loop quads can have good performance.
Consider 2 identical open loops of .00625 meter radius copper
tubing, each 2 meters on a side, spaced 2 meters to give a cubic
antenna. The 8 meter conductor length means that the resonance
point will be around 18.75 mHz.

The Mininec calculated performance of this antenna, including
element resistance, shows a maximum director gain of 5.2 db at
19.7 mHz, with a drive resistance of 2.5 ohms. F/B ratio is poor,
only 1.8 db. The maximum reflector gain is just over 6 db, with a
F/B of 6.3 db, and a drive resistance of 3.4 ohms. Maximum F/B
occurs for reflector action, and is 23.3 db at 19.6 mHz. Gain,
however, has dropped to 5.0 db, with a drive resistance of 7.2
ohms. Fig. 14 shows the variation in gain toward and away from
the parasitic, and the drive resistance vs frequency. The antenna
is narrow band, the gain dropping to 3.8 db at 19.4 and 19.7 mHz.

The antenna enclosing sphere is just 1.73 meters in radius, or
.11 wavelengths at the best gain point. The maximum normal gain
is 3.5 db. The antenna is in the supergain regime. Despite this,
the feed resistance is not impossibly low. The calculated antenna
efficiency is good, 92 percent. This does not include the loss in
the matching section.

A trial at a spacing of 1 meter showed essentially the same
performance, with a gain of 6 db at 19.7 mHz. Drive impedance was
markedly reduced, however, to 0.9 ohm, and efficiency was 87
percent.

This design seems to be good for mimimum space beams. These
antennas could be scaled to 20 and 15 meters, by the multipling
ratios 1.39 and .925. It would probably be worthwhile to increase
tubing size. It would be possible to compensate for the
relatively narrow bandwidth by designing for the top end of the
band and adding capacity plates at open element ends for tuning.
Experimental work on the matching system seems indicated; gamma
and delta matches seem possible. Use of voltage feed to the open
end of the driven element might be good.

Some data on multi-element designs and other variations at or
near the supergain regime is given in Haviland(12).

NEUTRALIZATION AND THE ANTENNA

The British Amateur, Les Moxon, G6XN (13), has concluded that the
reason for the low driving resistance of the family of antennas
which are size reduced is that the elements are over-coupled.
This led him to the concept of antenna neutralization. The
concept is the same as the neutralization employed in RF
amplifier design, in which an out-of-phase voltage is coupled
from the drive to the driven circuit.

The physical concept proposed by Moxon for a two element
end-folded shortened beam is shown in Fig. 15. An additional pair
of elements are introduced. These are not resonant, but are
regarded as transmission line sections feeding the small voltages
capacity coupled from the antenna element to the transmission
line ends. The diagional placement makes the voltages out of
phase, as required for neutralization.  Another physical layout
is shown in the references.

This is not an easy design to analyze. The number of bends means
that a large number of wires are involved. For really good
accuracy there should be a minimum of 4 segments per wire in the
neutralizing area, and preferably more. In addition, the problems
of analysis of very closely spaced wires mentioned above appear.

So far, the results of Mininec analysis of capacity coupled
neutralization has been inconclusive. Increases in drive
resistance by a factor as large as 3:1 as compared to no
neutralization have been found. However, in all cases tried, this
increase was found at frequencies well away from those giving
maximum or near maximum gain. At and around the maximum gain
frequency, the drive resistance varied by no more than a few
percent among the various conditions tried. This included various
spacings, plus direct connection with resistive, capacitive and
inductive isolation elements.

It is not apparent whether this finding is a real reflection of
antenna performance, or whether it is due to the known analysis
limitations of Mininec, or whether a larger computer would give a
confirmable answer. In an effort to get an understanding of the
concept, several different approaches were tried.

In one, a small additional amount of excitation was introduced at
the center of the second element of a two dipole array. The
magnitude of this was varied up to 50 percent of the main
excitation, both in and out of phase to the main excitation.
Reults as to drive resistance increase were again inconclusive,
possibly because only 0 and 180 degree phase differences were
used.

Fig. 16 shows the genesis of a different approach. At A two
parallel dipoles are shown, the basic Yagi or 8JK beam, depending
on excitation. If a connecting boom is introduced, as at B, and
this is symmetrical, it has only a small effect, primarily
equivalent to shortening the elements. See the discussion in
Lawson(10) about this.

However, if the boom is not symmetric, it will introduce an
additional current path. This path can in the direction of
increasing  element coupling, as at C, or of reducing it, as at
D. The amount of coupling can be changed by changing the
intersection points, as in E and F. A further change can be made
in the length of the coupling diagonal, which requires canting
the elements, as at G.

Analysis of this family of designs seems to show convincingly
that the concept of antenna neutralization is real. The first
indication found is summarized in Table 4. This tabulates the
gain and drive resistance for four spacings, with no boom and
with symmetrical cross connection at five distances along the
element, the last being at the ends. It was found that there is
no particular effect when the connecting points are close to the
center. But as shown, with widely separated diagonal connections,
there can be marked increase in drive resistance, in some cases
with gain loss, in others gain improvement.

Figs. 17 to 19 show typical overall effects. Fig. 17, drive
resistance, shows a minimum near the single element resonant
frequency, the minimum resistance increasing and the frequency of
occurance decreasing as the element spacing increases. Figs. 18
and 19 show the effect on gain away from and towards the undriven
element, respectively, for two of the spacings. The most
noticeable gain effects are on the low frequency side of the peak
gain point, where the parasitic is acting as a director. Overall,
conditions can be found to give a marked increase in drive
resistance, plus a small improvement in gain with little change
in F/B ratio. This is generally the claim of Moxon.

Much more analytical and experimental work on this concept is
needed before design rules can be set forth. This brief account
is included here in the hope of stimulating such work by others.

THE ZIG-ZAG BEAM

The antenna of Fig. 16G was described by Cumming (14) a number of
years ago. He has regarded it as a special case of the Helix
antenna, wound on an ellipse of zero minor axis. As seen above,
it can also be regarded as the end point of a series of
cross-diagonal feed. In the form described by Cumming, the
antenna is used with a reflecting screen. The data given here is
for the zig-zag (Z-Z) element alone, with no reflector, and for
feed at the center of one end element.

The Z-Z is an end-fire array, with the direction of maximum
radiation being a function of element length and spacing.
The gain in the direction away from the feed (taken from the
center of the antenna) is shown in Fig. 20. At each spacing,
there is a change from reflector to director action. At close
spacing the change is quite rapid as frequency is varied. (Note
that there is a change in element length as the spacing is
varied.)

The gain in the direction toward the feed is shown in Fig. 21.
This also shows the change from director to reflector action, but
this is much less marked than for the other lobe. Maximum gain is
a function of spacing, reaching 8.6 db for the 0.1 wavelength
between adjacent element ends case.

Fig. 22 shows the calculated drive resistances. The curves show a
resistance minimum, which varies with spacing. Most if not all of
the change in the frequency of the minimum is due to the
lengthening of the element as spacing increases, since the span
of the antenna was kept constant, rather than element length. The
magnitude of the resistance at minimum increases as spacing
increases, reflecting the reduction in coupling. It should be
noted that the antenna approaches a long wire at large spacings.

This data was developed using Mininec 3.12. It is likely that
calculated values would be different with earlier versions, which
lack the small angle correction feature. The regular variation of
the curves in Figs. 20-22 is an indication that the calculated
results are trustworthy. Marked discontinuities over a range of
conditions indicates that results are suspect, and should be
checked, for example by increasing the number of segments used in
analysis.

The enclosing sphere for these antennas is around 0.25
wavelengths radius. The maximum normal gain is thus around 7.5
db. At the wider spacings, the antenna is in the normal regime,
but the close spacings it shows supergain. This is further
indicated by the calculated decrease in bandwidth. For example,
for  the 0.4 meter spacing, the gain varies by 1.4 db over the
range from 61 to 78 mHz, while for a spacing of 0.1 meter, the
frequency range is from 72.5 to 76.5 for the same variation.
Drive resistance also changes with spacing and frequency.

Cumming shows a design using two mirror image zig-zag elements
closely stacked, using a reflector screen. A measured gain of 6.2
db at 64 mHz, increasing to 10.2 db at 86 mHz was obtained. SWR
was an average of 1.8 and a peak if 2.2 over this band using 300
ohm feed. Cumming notes that the antenna family can be regarded
as a traveling wave antenna, of the slow-wave class, with a
propagation velocity of 0.91. This suggests that very wide band
operation could be obtained if the length of each rod was
progressively decreased, as in the log periodic.

This is another antenna where more analysis and experiment is
needed to develop practical design rules.

SUMMARY

The work reported here was started as a result of encountering
supergain phenomena in a comprehensive study of Quads, reported
elsewhere, Haviland (12).

In the process of study, several unexpected features have shown.

One is the degree to which quite common antennas are either in
the supergain regime, or are close to it. The matter of regarding
short dipoles as supergain antennas had not been encountered
before.

Another was the importance of the enclosing sphere in determining
whether attempts to achieve supergain were worthwhile. This was
particulary noticeable when high gain Yagis were considered.

One feature which can only be called "disappointing" was the
speed with which conditions became unattractive or even
impossible in the practical sense as the supergain regime was
entered. The small high gain and highly directive beam remains
"pie in the sky".

On the other hand, some lines of approach with promise have
appeared. One is the importance of stacking, both as a way of
increasing performance while skirting the supergain regime, and
in securing increased performance with short boom antennas.
Others are the interesting miniaturization possibilities of the
open loop quad, and the zig-zag antenna family. All of these, and
in particular the possibility of antenna neutralization, need
more work, both analytical and experimental.

LEGENDS, Supergain Antennas

Fig. 1     Illustrating Huygens Principle, where a new wave-front
is created by the envelope of wavelets originating from each
point on the original front.


Fig. 2     Theoretical gain of a two element end-fire array, or
8JK antenna, showing the pattern factor, the coupling factor and
the overall gain. Element resistance is neglected.


Fig. 3     Maximum normal gain of an antenna from Harrington and
Chu, as a function of the radius of the sphere just enclosing the
antenna. If the gain is less than the curve value, the antenna is
in the normal (gain) regime, if greater, in the supergain regime.


Fig. 4     Effect of element resistance on the overall gain of a
8JK array. Compare to Fig. 2. Calculation is based on resistance
being distributed along the antenna length. Ususal caculation
assumes that the resistance is concentrated at the center of the
element.


Fig. 5     Calculated efficiency of a dipole as a function of
element size. Based on a 2 meter long element at 75 MHz. Curve is
approximately correct for any dipole of the same length/diameter
ratio, but the exact value varies due to skin effect on element
resistance.


Fig. 6     As for Fig. 5, but showing the effect of element size
on drive point resistance. See text.


Fig. 7     As for Fig. 5, but showing the effect of element size
on drive point reactance.


Fig. 8     Change in reactance with frequency for a fine wire
element with element resistance neglected and considered. The
resonant frequency is affected, with a small change in reactance
slope. The effects in Figs. 5-8 are commonly neglected in antenna
textbooks.


Fig. 9     Quality factors for antennas, specifically for the
TMmn and TEmn propagation modes, as a function of the enclosing
sphere radius in wavelengths. The quality factor is the ratio of
stored to dissipated energy, essentially the common Q. See text
for useage. After Harrington and Chu.


Fig. 10     Quality factors for antennas reduced 2:1 in size, as
a function of the original enclosing sphere radius. Note that
reducing the size of large antennas means that they rapidly
become narrow-band devices.


Fig. 11     Effect of element spacing of a two element Yagi, both
elements 0.5 wavelangths long. Gain decreases slowly as spacing
is reduced, but drive resistance reduces rapidly, becoming zero
at very close spacing.


Fig. 12     Quality factor for a two element Yagi, assuming that
original size is 0.5 wavelength spacing, and that spacing is
gradually decreased. This the drive point Q, the ratio of drive
reactance to drive resistance, and is not the same as that shown
in Fig. 9.


Fig. 13     Effect of shrinking the boom length of a 6 element
Yagi to 60% of its original size, and retuning some elements. A
is for the original size, B for the reduced size. Further element
adjustment can increase the smaller antenna gain. See text.


Fig. 14     Swept frequncy performance of a close-space two
element open-loop quad. Elements are of copper tubing, identical
in length. The marked change in drive resistance is
characteristic of close-spaced arrays, and is not normally found
at wide spacing. This antenna gives quite good performance in a
small space.


Fig. 15     Principle of "Antenna Neutralization" as developed by
Moxon, G6XN. Two dipoles are shortened by folding the element
ends, resulting in over-coupling and low drive resistance. The
coupling is opposed or "neutralized" by introducing a pair of
short elements which couple small out-of-phase components into
the wire ends. See text.


Fig. 16     Schematic of a family of direct coupled antennas. A,
no coupling, B neutral coupling, C positive coupling, D, E, F,
negative coupling of varying magnitude, G a variation of F. See
text for concept.


Fig. 17      Drive resistance of negative direct coupled antennas
of varying spacing. Both elements identical in size.


Fig. 18     As Fig. 17, but for Gain away from the parasitic
element (reflector action). Over much of the frequency range,
this mode gives the best forward gain.

Fig. 19     As Fig. 17, but for gain towards the parasitic
element (director action).


Fig. 20     Gain away from the feed point for a Zig-Zag antenna
of several element end spacings. Note that the span is kept
constant, which means that the element length increases as end
spacing increases.


Fig. 21     As Fig. 20 but for the gain away from the feed point.
In this direction, the antenna gives good wide-band performance.


Fig. 22     As Fig. 20, but showing the variation in drive
resistance.


Table 1     Distribution of current in a dipole for three
calulation conditions. Ideal assumes sine-curve distribution, as
ususally found in textbooks. No Res. is calculated by Mininec
with no element resistance. With Res. is calculate by Mininec
with element resistance divided among the 40 segments used in
calculation. See text.


Table 2     Gain and drive impedance vs frequency for a 6 element
1 wavelength boom Yagi (Yagimax file SUPER610).


Table 3     Gain and drive impedance for the antenna of Table 2
reduced to 60% of its original length, with reflector and
directors 1 and 2 retuned. See text for steps followed.


Table 4     Gain and drive resistance for a family of two direct
coupled dipoles, with isolated element conditions for comparison.
Note that the effects are small until the end separation of the
neutralizing element becomes large, as in E and F of Fig. 16.
Mininec calculations with element resistance included. These
results were the first indication that the concept of antenna
neutralization can increase the drive resistance.m



2
hR.P.Haviland,1035 Green Acres Cir N,Daytona Beach FL 32119
fc#




References, Supergain Antennas


(1) John D. Kraus, Antennas, any ed., McGraw-Hill, New York


(2) Sergei A. Schelkunoff and Harald T. Friis, Antennas, Theory
and Practice, Wiley, 1952


(3) R. F. Harrington, Time Harmonic Electromagnetic Fields,
McGraw-Hill, New York, 1961


(4) L. J. Chu, Physical Limitations of Omni-Directional Antennas,
J. Appl. Phys., V 19, Dec. 1848


(5) R. C. Hansen, Microwave Scanning Antennas, Academic Pr., New
York, 1966


(6) F. E. Terman, Radio Engineers Handbook, McGraw-Hill, New
York, 1943


(7) J. Hall, Off-Center Loaded Dipole Antennas, QST, Sep. 1974.
See summary in (9)


(8) J. Sevik, a High Performance 20-, 40- and 80 Meter Vertical
System, QST, Mar. 1974. See summary of this and related work in
(9).


(9) G. Hall ed., The ARRL Antemma Book, 15th ed, ARRL, Newington
Ct., 1988


(10) W. W. Hansen and J. R. Woodyard, A New Principle in
Directional Antenna Design, Proc. IRE, 26, 333-345


(11) J. L. Lawson, Yagi Antenna Design, ARRL, Newington Ct., 1986


(12) R. P. Haviland, Quads, publication scheduled May 1992, CQ,
Hicksville NY


(13) L. A. Moxon, hf antennas for all locations, RSGB, London,
1982. See also Ham Radio, March 1979


(14) W. A. Cumming, A Nonresonant Endfire Antenna Array for VHF
and UHF, IEEE Trans. Ant. & Prop., Apr. 1955


ws2
hR.P.Haviland,1035 Green Acres Cir N,Daytona Beach FL 32119
fc#




Corrections, Supergain Antennas


Page 1, center to read, OF GAIN

Page 6, last para:
     Change .35 to .185
     Change 9.3 to "about 4"
     Change 9.65 to 6.0

Page 21,  first full para, change 0.27 to 0.32

Page 26, 2nd full para
     Change .42 to .29
     Change 11 to 9
     last line, delete "well"

Page 31, 2nd para, 2nd line, add "be" after "can"

References #4, date is 1948

Legends, Fig.4, "ususal"

Legends, Fig. 11, 2nd line, "Gain increases"

Fig. 16, Drive Resistance, renumber as 17.

Figs 17 to 21, renumber +1.