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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spelling 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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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description 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.
format Article
author Baum, C.E.
spellingShingle Baum, C.E.
Symmetry in Single-Polarization Reflector Impulse Radiating Antennas
Радиофизика и радиоастрономия
author_facet Baum, C.E.
author_sort Baum, C.E.
title Symmetry in Single-Polarization Reflector Impulse Radiating Antennas
title_short Symmetry in Single-Polarization Reflector Impulse Radiating Antennas
title_full Symmetry in Single-Polarization Reflector Impulse Radiating Antennas
title_fullStr Symmetry in Single-Polarization Reflector Impulse Radiating Antennas
title_full_unstemmed Symmetry in Single-Polarization Reflector Impulse Radiating Antennas
title_sort symmetry in single-polarization reflector impulse radiating antennas
publisher Радіоастрономічний інститут НАН України
publishDate 2002
url http://dspace.nbuv.gov.ua/handle/123456789/122332
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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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 1. C. E. Baum. Some Characteristics of Electric and 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 Simulators. Sensor and Simulation Note 243, July 1978. Carl E. Baum 350 Radio Physics and Radio Astronomy, 2002, v. 7, No. 4 3. E. G. Farr and J. S. Hofstra. An Incident Field sensor for EMP Measurements, Sensor and Simulation Note 319, November 1989; IEEE Trans. EMC, 1991, pp. 105-112. 4. C. E. Baum. Radiation of Impulse-Like Transient Fields. Sensor and Simulation Note 321, November 1989. 5. C. E. Baum. Configurations of TEM Feed for an IRA. Sensor and Simulation Note 327, April 1991. 6. C. E. Baum. General Properties of Antennas. Sensor and Simulation Note 330, July 1991. 7. D. V. Giri and S. Y. Chu. On the Low-Frequency Electric Dipole Moment of Impulse Radiating Anten- nas (IRAs). Sensor and Simulation Note 346, October 1992. 8. C. E. Baum. Some Topics Concerning Feed Arms of Reflector IRAs. Sensor and Simulation Note 414, Oc- tober 1997. 9. C. E. Baum. Selection of Angles Between Planes of TEM Feed Arms of an IRA. Sensor and Simulation Note 425, August 1998. 10. C. E. Baum. Symmetry and SAR Antennas. Sensor and Simulation Note 431, November 1998. 11. C. E. Baum. Unipolarized Currents for Antenna Po- larization Control. Sensor and Simulation Note 437, June 1999. 12. J. Scott Tyo. Optimization of the Feed Impedance for an Arbitrary Crossed-Feed-Arm Impulse Radiating Antenna. Sensor and Simulation Note 438, Nov. 1999. 13. C. E. Baum. Optimization of Reflector IRA Aperture for Filling a Rectangle. Sensor and Simulation Note 439, September 1999. 14. C. E. Baum. Interaction of Electromagnetic Fields With an Object Which Has an Electromagnetic Sym- metry Plane. Interaction Note 63, March 1971. 15. G. D. Sower, L. M. Atchley, and D. E. Ellibee. Low- Voltage Prototype Development of an Ultra-Wideband 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.