Symmetry in Single-Polarization Reflector Impulse Radiating Antennas
There are various construction details for reflector impulse-radiating antennas (IRAs) which limit the achievement of the ideal performance characteristics. Symmetry planes are important for polarization purity in the direction of the main beam. This involves details of the feed cables, possible inc...
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irk-123456789-1223322017-07-03T03:03:04Z Symmetry in Single-Polarization Reflector Impulse Radiating Antennas Baum, C.E. There are various construction details for reflector impulse-radiating antennas (IRAs) which limit the achievement of the ideal performance characteristics. Symmetry planes are important for polarization purity in the direction of the main beam. This involves details of the feed cables, possible inclusion of a ground plane perpendicular to the ideal electric field, and location of perturbations in low-field regions. Another symmetry concerns the balancing of the low-frequency electric and magnetic dipoles by including special structures connected to the feed arms. В импульсных рефлекторных антеннах (IRAs) имеются различные детали конструкций, которые ограничивают возможность получения идеальных рабочих характеристик. Наличие плоскостей симметрии важно для чистоты поляризации в направлении основного луча. На это влияют детали кабелей питания, возможность включения плоскости земли перпендикулярно идеальному электрическому полю и положение возмущений в затененной области. Другая симметрия связана с уравновешиванием низкочастотных электрических и магнитных диполей за счет включения специальных структур, связанных с фидерными кронштейнами. У імпульсних рефлекторних антенах (IRAs) присутні різні деталі конструкцій, які обмежують можливість отримання ідеальних робочих характеристик. Наявність площин симетрії є важливою для чистоти поляризації у напрямку основного променя. На це впливають деталі кабелів живлення, можливість включення площини землі перпендикулярної ідеальному електричному полю та розміщення збурень у затіненій зоні. Друга симетрія пов’язана з урівноваженням низькочастотних електричних і магнітних диполів за рахунок включення спеціальних структур, пов’язаних з фідерними кронштейнами. 2002 Article Symmetry in Single-Polarization Reflector Impulse Radiating Antennas / C.E. Baum // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 345-350. — Бібліогр.: 18 назв. — англ. 1027-9636 http://dspace.nbuv.gov.ua/handle/123456789/122332 en Радиофизика и радиоастрономия Радіоастрономічний інститут НАН України |
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There are various construction details for reflector impulse-radiating antennas (IRAs) which limit the achievement of the ideal performance characteristics. Symmetry planes are important for polarization purity in the direction of the main beam. This involves details of the feed cables, possible inclusion of a ground plane perpendicular to the ideal electric field, and location of perturbations in low-field regions. Another symmetry concerns the balancing of the low-frequency electric and magnetic dipoles by including special structures connected to the feed arms. |
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Baum, C.E. |
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Baum, C.E. Symmetry in Single-Polarization Reflector Impulse Radiating Antennas Радиофизика и радиоастрономия |
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Baum, C.E. |
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Baum, C.E. |
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Symmetry in Single-Polarization Reflector Impulse Radiating Antennas |
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Symmetry in Single-Polarization Reflector Impulse Radiating Antennas |
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Symmetry in Single-Polarization Reflector Impulse Radiating Antennas |
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Symmetry in Single-Polarization Reflector Impulse Radiating Antennas |
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Symmetry in Single-Polarization Reflector Impulse Radiating Antennas |
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symmetry in single-polarization reflector impulse radiating antennas |
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Радіоастрономічний інститут НАН України |
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2002 |
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citation_txt |
Symmetry in Single-Polarization Reflector Impulse Radiating Antennas / C.E. Baum // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 345-350. — Бібліогр.: 18 назв. — англ. |
series |
Радиофизика и радиоастрономия |
work_keys_str_mv |
AT baumce symmetryinsinglepolarizationreflectorimpulseradiatingantennas |
first_indexed |
2025-07-08T21:31:49Z |
last_indexed |
2025-07-08T21:31:49Z |
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1837115965696901120 |
fulltext |
Radio Physics and Radio Astronomy, 2002, v. 7, No. 4, pp. 345-350
SYMMETRY IN SINGLE-POLARIZATION REFLECTOR
IMPULSE RADIATING ANTENNAS
Carl E. Baum
Air Force Research Laboratory
Directorate Energy Directorate
Kirtland Air Force Base, New Mexico, United States
E-mail: magdalena.lopez@kirtland.af.mil
There are various construction details for reflector impulse-radiating antennas (IRAs) which limit the
achievement of the ideal performance characteristics. Symmetry planes are important for polarization purity in
the direction of the main beam. This involves details of the feed cables, possible inclusion of a ground plane
perpendicular to the ideal electric field, and location of perturbations in low-field regions. Another symmetry
concerns the balancing of the low-frequency electric and magnetic dipoles by including special structures con-
nected to the feed arms.
1. Introduction
Impulse-radiating antennas (IRA) have many appli-
cations and a large literature has developed [18]. For
some applications (e.g., polarimetry) a controlled
frequency-independent polarization is important [10,
11]. An important technique for polarization control
is symmetry in the antenna geometry. Here our at-
tention is directed to polarization on the beam center
which can be a symmetry axis for the antenna.
The present paper can be considered an exten-
sion of [5] where various features (including symme-
try) of the TEM feed of a reflector IRA are consid-
ered. Besides the general overall geometry of the
IRA, now smaller pieces are considered for their ef-
fects on the symmetry. Inevitably some small
asymmetries will be present, but the effects of these
can be minimized by judicious positioning of the
signal cables, and by the positioning of conductors
which minimize undesirable field components. Note
that here we are not considering high-voltage opera-
tion with, say, a spark gap at the focal point. Rather
we are considering a low-voltage type with two
100 Ω feed cables from a single 50 Ω cable as dis-
cussed in [5 (Fig. 4.1B)].
Another symmetry considered is that of duality
(in the Maxwell equations) as applied to the low-
frequency electric- and magnetic-dipole moments so
as to better achieve the desirable balance between
these two.
2. Symmetry Planes
Fundamental to the design of such reflector
IRAs is symmetry planes and the division of elec-
tromagnetic fields into symmetric and antisymmetric
parts which do not interact with each other [14, 17].
Fig. 1 shows a four-arm reflector IRA (front view)
with beam center on the z+ axis. By placing the
four identical arms on planes defined by
, , , 2o o o oφ φ π φ π φ π φ= − + − (1)
(for arms labeled 1 through 4 respectively) in the
cylindrical ( , ,zφΨ ) coordinate system defined by
cos( ), sin( )x yφ φ= Ψ = Ψ (2)
the antenna can be constructed with two symmetry
planes: the 0y = plane with respect to which the
fields (in transmission) are symmetric, and the
0x = plane with respect to which the same fields
are antisymmetric. The four terminating resistors are
typically each 200 Ω to match a 200 Ω conical
transmission line. This in turn matches the series
combination of two 100 Ω coaxes per the technique
in [5 (fig. 4.1B)]. These cables are not shown in the
figure.
With only one of the two aforementioned planes
as a symmetry plane the fields in transmission on the
z axis have pure vertical polarization. Of course,
real antennas are not constructed perfectly, so two
symmetry planes as in Fig. 1 can improve the polari-
zation purity on the z axis. Note that the symmetry
planes are associated with the groups (dyadic repre-
sentation) as
{ } 2
R 1, , 1x xx R R
↔ ↔↔ ↔
= =
1 1 1 1 1 1 1x x y y z z
↔ → → → → → →
= + + =
Carl E. Baum
346 Radio Physics and Radio Astronomy, 2002, v. 7, No. 4
1 0 0
0 1 0 identity
0 0 1
1 0 0
1 2 1 1 0 1 0
0 0 1
reflection through = 0 plane
x xxR
x
↔ ↔ → →
= ≡
− = − =
≡
{ } 2
R 1, , 1y yy R R
↔ ↔↔ ↔
= =
1 0 0
1 2 1 1 0 1 0
0 0 1
reflection through = 0 plane
y yyR
y
↔ ↔ → →
= − = −
≡
(3)
Adjoining these two groups gives the four-element
group
{ }2aC R R 1, , ,x y x yx y R R R R
↔ ↔ ↔ ↔↔
= ⊗ = i
1 0 0
0 1 0
0 0 1
zx y y xR R R R I
↔ ↔ ↔ ↔ ↔
− = ≡ = −
i i (4)
inversion transverse to axis or
(180 ) rotation about axis
z
zπ
≡
°
y
2 1
z
x
3 4
0
reflector
rim
0
0
0
Fig. 1. Four-arm reflector IRA with two symmetry
planes
This defines the z axis as a 2-fold rotation axis
as indicated by 2C with (in addition) two axial
symmetry planes or 2aC .
While the fields incident on the antenna (in re-
ception) have, in general, both symmetric and anti-
symmetric parts with respect to the various symmetry
planes, reciprocity assures us that the polarization in
transmission is also the polarization in reception.
Furthermore, a symmetry plane in the antenna im-
plies the same symmetry in the pattern, applying to
both transmission and reception. So, polarization
purity is also present on the symmetry planes in the
pattern.
Note that oφ is not specified here. Early de-
signs had /4 (45 )oφ π= due to the simple par-
allel addition of two 400 Ω edge-on feed-arm pairs
which do not interact with each other (one feed-arm
pair being perpendicular to the electric field from the
other feed-arm pair). More recently [9, 12] calcula-
tions which allow oφ to take on other values have
been performed showing some improved perform-
ance for somewhat larger oφ , while keeping the
200 Ω feed impedance.
While, as in Fig. 1, the paraboloidal reflector
has a circular rim, the truncation of the reflector can
have other shapes of rims as projected on the 0z =
plane for various applications [13]. In keeping with
the symmetries discussed here, one can easily have
the 0x = and/or 0y = planes as symmetry planes.
One example is a rectangular aperture [13].
Now let us consider the positioning of the signal
cables. Fig. 2 shows a blowup of the region where
the feed arms approach the paraboloid focal point.
Here we have one 100 Ω coax on the z axis with
center conductor connecting to arms 3 and 4. The
other coax is bonded to arm 2 with center conductor
passing through a hole in the connection between
arms 1 and 2 to reach the shield of the other coax.
As the coax on arm 2 approaches the focus the outer-
conductor diameter may eventually approach or even
exceed the width of the flat-plate cone (apex at the
focus). This is eventually truncated before reaching
the focus and electrically connected to arm 1 by a flat
piece of metal parallel to the 0y = plane. The
presence of this coax (and its connection through to
the shield of the other coax) is a necessary perturba-
tion of the ideal geometry. One can make this coax
as small in diameter (in the region near the focus) as
practical. In order to remove the asymmetry associ-
ated with this coax outer shield, one can add other
dummy coaxes (or just conducting tubes of the same
outer diameter) at appropriate symmetrical locations.
In order to preserve the Rx symmetry, one can
add such a dummy on arm 1. For Ry symmetry one
z
Symmetry in Single-Polarization Reflector Impulse Radiating Antennas
Radio Physics and Radio Astronomy, 2002, v. 7, No. 4 347
can be added on arm 3. For preserving both symme-
try planes ( 2aC symmetry) one can add, in addition, a
third dummy on arm 4.
Another aspect of antenna symmetry concerns
the connection of signal cables and other conductors
(and to a lesser degree dielectrics) to the antenna. In
particular, the typically 50 Ω coax, which divides
(parallel connection) behind the reflector into two
100 Ω coaxes, will in general scatter the fields. So
this cable should be positioned on any symmetry
planes of the antennas. For two symmetry planes this
implies that this cable should lie on the antenna axis
(z axis). Since the junction to the 100 Ω coaxes (for
minimum length) is not on the antenna axis, the 50 Ω
cable should be routed along the reflector back sur-
face until the antenna axis is reached as indicated in
Fig. 3. At this point, the 50 Ω cable is bent to leave
the antenna via the (negative) z axis. Note that all
three cables should be bonded (or very frequently
electrically connected) to the back of the reflector so
that these cable shields are topologically part of the
reflector surface, and only small perturbations on it
[16]. Especially on the z axis there should be a
good electrical connection from the 50 Ω cable shield
to the reflector.
y
100 cablesΩ
2
3
possible addition of
choke for current
suppression
50 cable
carrying signal
to/from antenna
Ω
electrical
connection
to reflector
Fig. 3. Symmetric positioning of 50 Ω cable connec-
tion to antenna
For various instrumentation reasons the 50 Ω
cable and/or conductors connected to it will, in gen-
eral, need to depart from the z axis. Also, other
scatterers will generally be in proximity to the an-
tenna and will scatter fields which interact with the
cable shield. So, some improvement may be ex-
pected by the addition of chokes to suppress such
external shield currents as indicated in Fig. 3.
Recall the choke on one of the 100 Ω cables as
it passes by one of the four terminating resistors. No
choke is perfect, but has some finite inductance. If
this is a problem, especially at low frequencies, in-
ducing a lack of symmetry in the antenna feed, then
symmetry can be restored by introducing one or more
similar impedances in parallel with the other termi-
nating resistors.
3. Additional Suppression of Crosspol
on Axis
With symmetry as a basic design principle, the cross-
pol on axis (beam center) is ideally zero. However,
various details of construction invariably introduce
asymmetries. One then needs to consider various
ways to make such asymmetries less significant.
Suppose, for example, that the currents on the
feed arms are not all exactly the same. Returning to
Fig. 1, suppose that the currents on arms 1 and 2 are
slightly different. As one increases oφ toward
/2 (90 )π the two arms are merged into one and
the symmetry ( 0x = plane) is restored. So increas-
ing oφ from the traditional angle of /4π , in general,
increases the polarization purity on axis.
Another technique for minimizing the effects of
asymmetries is to place such objects in low-field re-
gions of the antenna so that the scattering by such
symmetry-perturbing objects is minimized. As an
example, returning to Fig. 2, consider the signal cable
bonded to feed arm 2. Arms 1 and 2 being fed in
x
Fig. 2. Addition of dummy coaxes to give more ac-
curate symmetry planes
Carl E. Baum
348 Radio Physics and Radio Astronomy, 2002, v. 7, No. 4
parallel the fields between them are small compared
to the fields between this arm pair and the arm pair
comprising arms 3 and 4. So one should place the
100 Ω signal carrying coax on arm 2 on the side fac-
ing arm 1. Note also that as oφ is increased the field
near the coax is further reduced.
Going further, this 100 Ω feed coax is only a
small perturbation on feed arm 2 near termination
resistor 2. As the cable progresses toward the focal
point it becomes a larger and larger perturbation to
the arm geometry, and may eventually be of compa-
rable size. This effect can be minimized by transi-
tioning between different diameters of 100 Ω coax,
using a very small diameter for a short length near
the focus, but a larger diameter with lower loss for
most of the distance back to the 50 Ω coax.
Yet another technique for minimizing the effects
of asymmetries involves suppression of the resulting
asymmetric field components in antenna transmission.
Where some electric-field component is supposed to
be zero one can place thin conductors to force such
field components to (near) zero. A well-known ex-
ample of this [5] consists of a metal sheet about which
the fields are antisymmetric, in this case on the
0y = plane. Such a conducting sheet forces the
electric field to have only a y component there. Of
course, such a sheet cannot extend to infinity but must
be truncated at dimensions comparable to the rest of
the antenna so that this sheet does not become the
dominant factor in the antenna size (the antenna aper-
ture being the most important factor in antenna size).
In this context, then the width of this sheet can appro-
priately have the full width of the reflector on the
0y = plane and electrically bonding to the reflector
continuously across this width. In the z+ direction
the sheet can extend to include the focal region.
The presence of such a conducting sheet gives
some additional flexibility in the design of the cable
connections near the focus. Consider the connection
to arm pair 3 and 4 (negative y in Figs. 1 and 2) as
illustrated in Fig. 4. The presence of the ground
plane allows one to reroute the 100 Ω cable from the
z axis to a more general path on the 0y = plane.
In particular, the cable can be routed around to the
opposite side ( z+ side) of the paraboloidal focus so
as to launch the wave from the coax in the direction
toward the reflector. The coax shield can be opened
in a gradual manner so as to smoothly transition from
a coax to an asymmetrical strip line (also called an
unzipper [15]) while maintaining the same character-
istic impedance (100 Ω in this case) at every cross
section. The coax shield blending into the ground
plane, the wave from the coax is next launched on the
conical transmission line consisting of arms 3 and 4
and the ground plane. The region near the focus is
now clear of scatterers (such as cable shields) in the
direction toward the reflector. Note that the 100 Ω
coax should be bonded (frequently electrically con-
nected) to the ground plane, and perhaps even re-
cessed into the ground plane to better preserve the
Ry symmetry of the overall antenna. (One could
also include a dummy cable at the opposite x coor-
dinate (positive x in Fig. 4) to better maintain Rx
symmetry.)
This still leaves various details of the focal re-
gion to optimize. The two arms 3 and 4 need to con-
nect to the coax center conductor with as little distor-
tion of the spherical TEM wave in the focal region as
possible. Launching from the strip line with its di-
electric insulation onto an air-dielectric conical
transmission line brings into consideration the dielec-
tric/air boundary, a lens-design consideration.
Comparing the focal-region design for negative
y to that for positive y (the other side of the ground
plane) there are significant differences. The 100 Ω
cable has been shifted away from the z axis, clear-
ing up the focal region here as well. (See Fig. 2)
The 100 Ω cable on arm 2 now has its center conduc-
tor connected to the ground plane on the y+ side.
This then leaves the question of the details of how
the coax center conductor leaves the coax and transi-
tions to the ground plane in a way which minimizes
the distortion of the spherical TEM wave to be
launched. Note now that the wave from the coax has
to change direction (bend) back toward the reflector,
a bend of typically greater than /2 (90 )π [8]. On
the inside of the bend (toward the reflector) the wave
should propagate slower than on the outside, another
lensing problem.
to reflector
3 4
Keep the region
in front of the
launch clear.
x
unzipper
ground
plane
z
Fig. 4. Focal region with ground plane for arm pair
3 and 4
Symmetry in Single-Polarization Reflector Impulse Radiating Antennas
Radio Physics and Radio Astronomy, 2002, v. 7, No. 4 349
4. Symmetry Between Electric and
Magnetic Dipoles for Low-Frequency
Performance
Another kind of symmetry is duality, an invariance to
interchange of electric and magnetic parameters in
the Maxwell equations [17]. A special case of this
concerns the electric and magnetic dipoles describing
the low-frequency antenna performance. As shown
in [1] there is a special balance between the dipoles
in which each contributes equally to the fields and
gives special properties to the fields. In the coordi-
nates of Fig. 1 we have the balance conditions
[ ]
1
20 0
1 , , (electric moment),
(speed of light),
1 (magnetic moment),
1 1 , (direction of beam center
in transmission).
y
x
c z
m
p p p
c
c
m m
µ ε
→→
−
→→
→ →
= =
=
= −
=
(5)
This assures a cardiod pattern centered on the
z+ axis [6] and makes electric and magnetic fields
on the z axis have the ratio 0Z (wave impedance of
free space 377 Ω ), even including the near-field
dipole terms.
As discussed in [4] the resistive terminations at
the reflector approximately give the balance condi-
tions, making the low-frequency radiation maximized
in the z+ direction. For long focal lengths com-
pared to reflector diameter (large /F D ) a transmis-
sion-line model of the terminated feed gives exactly
the /p m c= condition [2, 3]. (The symmetry
gives the vector orientations exactly.) However, for
realistic values of /F D [8], the match is not per-
fect. The charge on the feed arms produces an elec-
tric-dipole moment which is partly cancelled
(shielded) by the charge distribution induced on the
reflector. Calculations of this are contained in [7].
Detailed calculations including reflector and feed-
arm detailed shapes are also needed.
One can consider modifications to the design for
improving the low-frequency electric/magnetic bal-
ance, such as illustrated in Fig. 5. Here one modifies
each feed arm in the region beyond a distance F
from the focus [8]. Besides the terminating resistor
tR (typically 200 Ω) one may add a special feedlet
(armlet or whatever, analogous to winglet), the pur-
pose of which is to extend the charge on the feed arm
to distances farther from the z axis and thereby in-
crease the low-frequency electric-dipole moment.
This feedlet might be resistive (sheet resistance sR )
so as to let the low-frequency magnetic field pene-
trate and thereby not change the low-frequency mag-
netic-dipole moment. This can also absorb some of
the electromagnetic energy that would otherwise con-
tribute to a sidelobe in the direction of the feed arm.
This feedlet can have various geometries, even ex-
tending behind the reflector. It may even be com-
prised of anisotropic (e.g., uniconducting) materials.
Note that the introduction of non-circular reflector
truncation to give other antenna apertures (e.g., rec-
tangular) further complicates the low-frequency elec-
tric/magnetic balancing problem. Detailed calcula-
tions of both moments, including the effects of vari-
ous feedlet designs would help considerably. Ex-
periments with tuning for the low-frequency null in
the z− direction may also help.
R s
R t F
z = -F z = 0
(focus)
Only one feed arm (typical) is shown
L
Fig. 5. Feedlets for balancing electric- and mag-
netic-dipole moments
5. Concluding Remarks
This paper has discussed several improvements. De-
tailed calculations and experimental optimization are
appropriate. For the small structures in the focal re-
gion, these can be investigated experimentally by
inverse scale models (structures many times larger
than the actual desired sizes).
References
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Magnetic Antennas for Radiating Transient Pulses.
Sensor and Simulation Note 125, January 1971.
2. J. S. Yu, C.-L. Chen, and C. E. Baum. Multipole Ra-
diations: Formulation and Evaluation for Small EMP
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1978.
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for EMP Measurements, Sensor and Simulation Note
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105-112.
4. C. E. Baum. Radiation of Impulse-Like Transient
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10. C. E. Baum. Symmetry and SAR Antennas. Sensor
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an Arbitrary Crossed-Feed-Arm Impulse Radiating
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High-Voltage Unzipper Balun. Measurement Note 50,
December 1996.
16. C. E. Baum. Electromagnetic Sensors and Measure-
ment Techniques, pp. 73-144, in J. E. Thompson and
L. H. Luessen (eds.), Fast Electrical and Optical
Measurements, Martinus Nijhoff, Dordrecht, 1986.
17. C. E. Baum and H. N. Kritikos. Symmetry in Electro-
magnetics. Ch. 1, pp. 1-90, in C. E. Baum and H. N.
Kritikos (eds.), Electromagnetic Symmetry, Taylor &
Francis, 1995.
18. C. E. Baum, E. G. Farr, and D. V. Giri. Review of
Impulse-Radiating Antennas. Ch. 16, pp. 403-439, in
W. R. Stone (ed.), Review of Radio Science 1996-
1999, Oxford U. Press, 1999.
СИММЕТРИЯ В
ОДНОПОЛЯРИЗАЦИОННЫХ
ИМПУЛЬСНЫХ РЕФЛЕКТОРНЫХ
АНТЕННАХ
К. Э. Баум
В импульсных рефлекторных антеннах (IRAs)
имеются различные детали конструкций, которые огра-
ничивают возможность получения идеальных рабочих
характеристик. Наличие плоскостей симметрии важно
для чистоты поляризации в направлении основного
луча. На это влияют детали кабелей питания, возмож-
ность включения плоскости земли перпендикулярно
идеальному электрическому полю и положение возму-
щений в затененной области. Другая симметрия связана
с уравновешиванием низкочастотных электрических и
магнитных диполей за счет включения специальных
структур, связанных с фидерными кронштейнами.
СИМЕТРІЯ В ОДНОПОЛЯРИЗАЦІЙНИХ
ІМПУЛЬСНИХ РЕФЛЕКТОРНИХ
АНТЕНАХ
К. Е. Баум
У імпульсних рефлекторних антенах (IRAs) при-
сутні різні деталі конструкцій, які обмежують можли-
вість отримання ідеальних робочих характеристик.
Наявність площин симетрії є важливою для чистоти
поляризації у напрямку основного променя. На це
впливають деталі кабелів живлення, можливість вклю-
чення площини землі перпендикулярної ідеальному
електричному полю та розміщення збурень у затіненій
зоні. Друга симетрія пов’язана з урівноваженням низь-
кочастотних електричних і магнітних диполів за раху-
нок включення спеціальних структур, пов’язаних з
фідерними кронштейнами.
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