CHAPTER 3 SIDELOBE PERFORMANCE OF REFLECTOR / ANTENNAS

Transcription

1 16 CHAPTER 3 SIDELOBE PERFORMANCE OF REFLECTOR / ANTENNAS 3.1 INTRODUCTION In the past many authors have investigated the effects of amplitude and phase distributions over the apertures of both array antennas and reflector antennas with a view to achieving low sidelobe levels in the radiation patterns of the antennas. Sciambi [44] has obtained a closed form expression for the far-field of a circular aperture with an illuminating function involving two parameters controlling the sidelobe levels. Hansen [5] has replaced the above illumination function with a simple one involving only a single parameter. With these functions, illumination tapers giving rise to very low sidelobe levels have been analysed. Eventhough these investigations can be directly applied to array antennas, there are certain unique problems existing in reflector antennas such as spillover loss of the feed system, aperture blocking and feed phase error. These factors have to be taken into account while analysing the sidelobe levels of reflector antennas. This Chapter summarises the sidelobe level performances of the parabolic reflector antenna, taking into account the effect of amplitude taper, feed phase error, f/d ratio, and aperture blocking. Mention has also been made on the effects of surface tolerance, scattering from the supporting struts, and spillover sources for the case of axisymmetric cassegrainian systems. Besides, a procedure for selecting a corrugated conical horn as feed for illuminating a given reflector is also presented*

2 17 D T d i FIG GEOMETRY OF THE CROSS SECTION OF A PARABOLOID OF REVOLUTION

3 EFFECT OF AMPLITUDE TAPER Fig. 3.1 gives the geometry of the cross**«ction of a paraboloid of revolution illuminated by a feed located at the origin. The physical optics (PO) aperture field method [ 36J is employed to determine the far-field of the paraboloidal reflector. The radiation patterns with the following characteristics have been evaluated analytically and plotted in Figs. 3.2, 3.3 and 3.4: a) D = 20 * f/d = 0.33 Edge taper =10, 15, 17.5, 20 db b) D = 40 X f/d = 0.33 Edge taper = 10, 15, 20 db c) D = 20 X f/d =0.5 Edge taper = 10, 15, 20 db The feed illumination has been assumed to be o-f the form cos11 (0^) where n is given by c sn (efm) = t (3.1) where n indicates the nature of variation of illumination, and T indicates the amount of taper required corresponding to the' maximum angle 0^ subtended by the reflector at the feed. The above illumination function has been chosen since it has been known to represent the radiation patterns of circularly symmetric corrugated conical horns from the radiation

4 K v«j=-s- 19. FIG', 3*2: EFFECT OF AMPLITUDE TAPER ON SIDELOBE LEVELS K

5 o f/d Edge taper Edge taper Edge taper 40 A 0.33 IO db 15 db 20 db ,deg FIG.3.3: EFFECT OF AMPLITUDE TAPER ON SI0ELQBE LEVELS

6 . i ' v :f. Ms*--: 21 0,,deg TIG. 3.4: EFFECT OF AMPLITUDE TAPER ON SIDELOBE LEVELS t * 4,, ^

7 22 patterns of the reflector the following conclusions can be made: a. The sidelobe levels are independent of the diameter of the reflector; b. There is a reduction of sidelobe level with increase of edge taper level; c. In general, for any particular edge taper, the sidelobe levels are monotonically decreasing. But for large edge tapers, the second sidelobe is higher than the first sidelobe level; d. Due to the increase of space attenuation taper and the resulting increase in the overall illumination taper, the sidelobe levels of the reflectors of small f/d ratio are lesser than the sidelobe levels of reflectors of larger f/d ratio; and e. An illumination taper of about 20 db is required to achieve a sidelobe level of -35 db or more, 3.3 EFFECTS OF PHASE ERROR The phase error over the aperture of the paraboloid is contributed by the following factors: a. The misalignment of the focus of the paraboloid with the phase center of the feed; b. The inherent phase error in the illumination of the feed; and c. Errors due to the deviation of the paraboloidal reflector surface from its true configuration. V -

8 23 The phase error caused by the feed radiation pattern can be minimized by deliberately dafocussing the phase center of the feed with reference to the reflector focus. This method minimizes the effects o* the feed phase error. The shift Dg of the phase center of the feed from the focus of the paraboloid results in a symmetric quadratic phase error. The effects on the radiation pattern due to the phase center shift of D = 0.05 X, D = 0,1 and D = 0.15 have been analysed and s s s plotted in Figs. 3.5, 3.6 and 3.7. From the graphs it is seen that' a. For a given taper, increase of defocussing broadens the main beam by introducing a shoulder and also reduces the first minimum level? and b. With increase of taper broadening of main beam and reduction in sidelobe levels are noted. In a later section, it is shown that the deterioration of sidelobe level due to phase error o-f the feed can be very much minimized by determining the optimum phase center. The phase patterns of corrugated conical horns are generally characterised by a uniform region followed by a rapidly varying region as in Fig. 3.22(a). For analysis, the phase distribution has been approximated (from the experimental results of an ideal corrugated conical horn with f/d = 0.33) as 0(9f) =0 for 0 < Qf < o 0(ef) = Vl X l) - 1] for e0 < of < ef[n (3.2)

9 24

10 25

11 'A - < 26 FIG.3.7: EFFECT OF AXIAL DEFOCUSSING ON THE SIDELOBE LEVELS

12 27 where = maximum phase error, 0^ = feed angle, 0 m = maximum feed angle 0Q = angle below which phase error is zero. The effects of such phase variations of the feed over the radiation patterns of the reflector have been analysed and plotted in Figs. 3.8 and 3.9. It is seen that while there is a 5 db increase in the first sidelobe level due to the phase error of 45 there is only a marginal increase in the sidelobe level when the phase error is 22,5. Hence the phase error of the feed should be kept within 22.5 to improve the sidelobe level performance. 3.4 EFFECTS OF APERTURE BLOCKING The effects of aperture blocking of the reflector by the feed have been analysed by many authors. The blocking of the central portion of the aperture has been found to result in alternate increase and decrease of sidelobe levels. In the conventional prime focus systems, using horn feeds, the effect of aperture blocking is negligible because the aperture blocking ratio (d/d)(the ratio of the feed diameter to the reflector diameter) is usually less than 0,1. In the case of a dual reflector system, which employes a subreflector of finite size, the effects of aperture blocking cannot be neglected unless the d/d ratio is very small. The effect of aperture blocking has been analysed for different blocking ratios under different conditions of aperture illumination taper.

13 w- 28 FI6.3.8: EFFECT OF FEED PHASE ERROR ON SIDE LOBE LEVELS

14 29 ^ FIG.3.9: EFFECT OF FEED PHASE ERROR ON SIDELOBE LEVELS

15 30 Fig, 3,10 shows the radiation pattern of the reflector having an illumination taper of 10 db for different values of aperture blocking ratios. It is clear from the plots that the blocking ratio less than 0,06 results in negligible deteriorations in the radiation patterns. Figs, 3,11 and 3,12 lead to a similar conclusion for the edge tapers of 15 db and 20 db. The effects of aperture blocking in the case of reflectors of different diameters and different illumination tapers are compared in Fig, 3,13, It is also evident from the plots that the effects of aperture blocking are more prominent in the case of reflectors of low edge tapers. The increase in the first sidelobe level for the blocking ratio of 0.1 has been found to be 4 db* 8.5 db and 21,5 db respectively for the edge tapers of 10 db, 15 db and 2D db, (In the case of 20 db taper, since the second sidelobe is the prominent one, -the effective increase in sidelobe level due to the aperture blocking is only 10,5 db). Similar observations can be made with respect to the blocking ratio of 0,06. Even a blocking ratio of 0.06 results in considerable increase in the levels of near-in sidelobes. Thus it can be concluded that to have the maximum advantage of -a low edge taper for achieving low sidelobe level, the aperture" blocking ratio should be kept within 0,06. This is very difficult to achieve except in the case of very large prime focus systems. This necessitates the implementation of offset geometries which completely eliminate aperture blocking, 3.5 CHARACTERISTICS OF FEEDS To summarise, the characteristics of the feed for low

16 i;..is*'

17 32

18 33 FIG-3.12: EFFECT OF APERTURE BLOCKING ON SIDELOBE LEVELS

19 34 Relative power, db Blocking ratio FIG. 3.13:EFFECT OF APERTURE BLOCKING ON SIDE LOBE LEVELS

20 35 sidelobe level antennas are as follows: a. The backlobe levels of the feed should be as low as possible to avoid a direct contribution to the farfield; b. The radiation pattern should be circularly symmetric$ c. The phase error over the required edge taper should be kept to a minimum; d. The aperture size of the feed should be as small as possible so as to keep the blocking ratio as minimum as possible? and e. The feed should possess a well defined phase center. The corrugated conical horn satisfies most of the above mentioned characteristics and hence it is in use as an ideal feed. The geometry of the corrugated conical horn is shown in Fig. 3,14. The effects of flare length (r ) and flare angle (a ) of the horn on its radiation characteristics have been studied by many authors [72,73], Using Kirchoff aperture integration method the radiation patterns of the corrugated conical horn have been analysed by varying its flare angle (aq) and flare length (rq) to ensure its suitability for low sidelobe antenna applications. The analysis has been carried out to find out the angle of 20 db beamwidth as required in low sidelobe antennas. The computed radiation pattern of typical corrugated conical horns are plotted in Figs. 3.15, 3.16 and 3.17 which give the value of corresponding to 20 db for different values of rq and a. Since f/d ratio of the

21 *. '% '%v" ; - 36 FIG GEOMETRY OF CORRUGATED CONICAL HORN

22 37 ' V? $>.<'%#.< J?.' '*#.,fb ^y. 0p U( jadej. aprunduiy o CO oon oco o in o o r> O CM o o cn N XS CD FIG. 3-15: EFFECT OF FLARE ANGLE ON THE RADIATION PATTERN OF CORRUGATED CONICAL HORN

23 _L X _i l FIG.3J6 : EFFECT OF FLARE LENGTH ON THE RADIATION PATTERN OF CORRUGATED CONICAL HORN

24 39 FIG EFFECT OF FLARE ANGLE ON THE 20dB POINT OF A CORRUGATED CONICAL HORN' *

25 40 reflector decides the maximum angle subtended at the feed C^m)» a suitable feed can be chosen for a given reflector. The phase patterns of corrugated conical horns are plotted in Figs. 3.18, 3.19, 3.20 and While it has been observed that the phase center of the wide flare horns lies St the throat, low flare horns (aq < 30 ) have their phase centers between.the throat and aperture. Further it is observed that it is possible to restrict the phase error within about + 5 for low flare horns, by a suitable choice of the phase reference. But the wide flare horns show a larger phase error over the region of interest upto db amplitude taper. The influence of the phase reference on the phase error in the feed illumination has been studied and plotted in Figs. 3.18, 3.19, 3.2D and 3.21 for different illumination tapers. From the figures it can be inferred that it is possible to determine a well defined phase center associated with a small phase error for low flare horns. Further, to study the effects of the variation in phase error of the feed on the secondary radiation patterns of the reflector system, two types of phase variations as shown in Fig are considered. It is found from the secondary radiation patterns of the reflector that the deterioration on the sidelobe levels due to case (a) is more severe than that due to the case (b). I Thus it can be concluded that low flare corrugated conical horns and hence reflectors of large f/d ratio are preferred for low sidelobe applications. To eliminate apertute blocking

26 41 phase (D, deg ,deg FIG EFFECT OF PHASE REFERENCE ON THE PHASE ERROR IN THE REED ILLUMINATION.

27 + - '*S ^ 42 phase (D/ deg «9,deg FIG EFFECT OF PHASE REFERENCE ON THE PHASE ERROR IN THE FEED ILLUMINATION. :3% r ;. w'

28 JfcijSSln OJ - # M M Q. to to at U) to JC a , deg FIG EFFECT OF PHASE REFERENCE ON THE PHASE ERROR IN THE FEED ILLUMINATION

29 40 20 ct> oi xi U) ta JZCl BO 0,deg FIG.3.21, EFFECT OF PHASE REFERENCE ON THE PHASE ERROR IN THE FEED ILLUMINATION x- 4N

30 45 phase error (j),deg phase error (ft* deg phase error (a)normalised radius of the aperture of the reflector of the reflector FIG TYPES OF PHASE ERROR TN THE FEED ILLUMINATION

31 46 effects one has to go in for offset configuration as discussed in the previous section* But this configuration suffers mainly from the cross-polarization effects, inherently due to its asymmetrical structure. To minimize the cross-polarization effects, offset reflectors of large f/d ratios are preferred. Thus it is seen that offset reflectors, with large f/d ratio, fed by low flare angle corrugated conical horns, meet the requirements of low sidelobe reflector antennas. A detailed analysis of a offset reflector and its performance characteristics are considered in Chapter EFFECTS OF SPILLOVER, SCATTERING AND SURFACE ERRORS. For the widely used axisymmetric cassegrainian antennas three distinct significant sources of sidelobe radiations may be identified as follows [82], a. Spillover past, and diffraction from, the reflectors; b. Scattering from the subreflector support struts; and c. Deviation of the reflector surface from the ideal profiles. In dual reflector systems, there will be contribution to wide angle sidelobe levels from the edge-diffraction fields from the two reflectors combined with the primary and secondary feed radiation spilling over beyond the reflector edges. The primary spillover energy will emanate directly from the feed horn and will peak close to the angle subtended by the subreflector edge at the feed, generally between 5 and 50 from the boresight. The secondary spillover will emanate from the. subreflector as a secondary or indirect feed for the mainreflector, and will peak in a narrow region typically at 100

32 47 from the boresight. The primary and secondary spillover sources are shown in Fig for an axisymmetrical antenna* In addition to these relatively narrow peaks, the sidelobes of the feed pattern will radiate directly into the space where not blocked geometrically by the reflector. The feed horn spillover sidelobes dominate the antenna sidelobe pattern in the region of 2D to 80. The primary spillover peak has been found to be a major contribution to sidelobe envelope, particularly for electrically small antennas (Diameter < 200 X) and the antennas using older smooth walled feed horns. The levels and shape of the spillover peaks will be determined both by the feed itself and the size and geometry of the subreflector. It has been found that to minimize the levels of the spillover peak the desirable conditions are: a. low edge illumination at subreflector} b. low feed horn aperture phase error (narrow flare angles)} c. low angle subtended by the subreflector at the feed} and d. small subreflector electrical diameter. High efficiency corrugated conical horns or dual mode feed hoiyas have been used either as direct primary source or as part of a beam waveguide feed system. These feed sources will have low sidelobes in all planes so that direct spillover of the primary feed sidelobes will not cause the antenna sidelobe levels to increase. Optimization of the antenna efficiency by reflector shaping will automatically produce a steep taper at the edge of the main reflector, thus ensuring low edge diffraction and

33 48 Secondary FIG-3-23:SOURCES FOR PRIMARY SPILLOVER / SCATTERING

34 *:y!' -i'j;^,,':'^;'jsi 49 low secondary spillover levels. For the dual reflector system antennas, the aperture will be blocked by the structure supporting the subreflector from the mainreflector or feed horn. The support strut will intercept and scatter incident radiation in two modes: a. From the radiation between the subreflector and the mainreflector (spherical wave blocking); and b. From the plane wave radiation between the mainreflector and free space (planewave blocking). These two blocking effects contribute to the increase of sidelobe levels near the beam axis. This problem is overcome by introducing slow wave structure such as rectangular corrugations along the length of the supporting struts [45]. The prediction of sidelobe levels due to the reflector profile errors may be treated on a statistical basis* For a large main r#f4wt r 9ii«*the surface will be constructed from a number of individual panels mounted on to a backing framework. By optical or microwave holographic techniques, it is possible to set the positions of the panels relative to each other according to the required profile. Once the panels have been correctly set, any profile deviations will be either due to distortion of the reflector framework (caused by gravitational, or wind loading or by differential solar heating) or due to error within the panels themselves. The former errors will be systematic and correlated over the entire reflector surface so that the pattern degradation will be restricted*to the

35 50 mainlobe and the first few sidelobes, The latter errors will show a much smaller correlation,intervals equal to the panel diameter or less so that significant sidelobe energy may be scattered beyond 1 into the region covered by wideangle sidelobe regulations. The control of reflector profile errors becomes more difficult as higher frequency bands are introduced, placing more stringent demands on the structural quality of earth station antennas, 3.7 MEASUREMENT OF LOW SIDELOBE ANTENNA PATTERNS When making far-field antenna pattern measurements, the range distance required to get accurate far-field patterns is dependent on the sidelobe levels and the accuracy desired. The well known 2D /A rule of thumb is applicable for moderate sidelobe levels (down to about -25 db), but is inadequate for low sidelobes (-30 db to 40 db) and ultralow (below -40 db) sidelobes. Recently a sttady has been made [83,84] on the effects of quadratic phase error due to finite range distances on a number of classical antenna patterns. A -40 db sidelobe level Chebyshev pattern requires a range of 6 D/A if the first sidelobe is to be accurate within 1 db. At distances less than about 3.5 D A> the first sidelobe is lost, i.e,, merges into the mainlobe. Hence,if measurements are made at ranges less than the required value, first one or two sidelobes will be lost, while the rest of the sidelobes will be quite accurate in spite of the quadratic error.

36 CONCLUSION The sidelobc performance characteristics of reflector antennas thus depend both on the characteristics of the, primary feed and the secondary feed as well as characteristics of the mainreflector. Consequently, only a judicious choice of these characteristics will give rise to a reflector system with low sidelobe characteristics. a