feed. The fundamental principle of the matched feed depends on the field matching

Transcription

1 CHAPTER-2 MATCHED FEED FOR OFFSET REFLECTOR ANTENNA The primary objective of this chapter is to discuss the basic concept of matched feed. The fundamental principle of the matched feed depends on the field matching theory. According to this theory, the cross-polarization caused by the asymmetry of the offset parabolic reflector antenna can be compensated, if the tangential electric fields at the aperture of the primary feed are complex conjugate to the focal-region fields of the offset parabolic reflector antenna. In order to understand this matching process, it is necessary to first estimate the focal region fields of an offset reflector antenna. Once the focal-region fields are estimated, a multi-mode matched feed which is simpler in configuration may be designed to counter-balance the effect of the cross-polarization of the reflector antenna. In this chapter, the analysis of focal-region fields of an offset parabolic reflector antenna is presented. Following this, the simulated results for cross-polarization variation as a function of F/D ratio and offset angle are presented. Finally, the higher order modes needed in the three matched feed structures (rectangular, cylindrical and corrugated) to provide the conjugate match with the reflector focalfields are summarized. 2.1 FOCAL REGION FIELDS OF AN OFFSET PARABOLIC REFLECTOR ANTENNA In 1969, Bem [33] presented the detailed analysis to evaluate the focal-region fields of an offset parabolic reflector antenna. In [33], Bem used the physical optics (PO) approach to derive the closed form expressions of the transverse focal plane 12

2 fields (i.e. ) for a normally incident plane wave. Later on, Valentino and Toulios [34] extended Bem s work by including the incident plane wave making an angle with the reflector boresight. A similar kind of problem was also solved by Buris and Kauffman [35] with a novel method of discretizing the reflector aperture into a number of small triangles and then applying numerical method to evaluate the integral expressions of the scattered field. In [36], the authors have carried out the parametric analysis of focal-region fields of an offset parabolic reflector for its application to the space-borne microwave radiometers operating at two extreme frequencies i.e., 6.6 and 37 GHz. The focal field distribution of an offset parabolic reflector antenna is obtained by illuminating the reflector surface by a linearly polarized plane wave as shown in Fig Fig. 2.1 Offset parabolic reflector antenna geometry 13

3 The incident plane wave generates current on the reflector surface. Each surface element acts as an elementary dipole and produces an elementary field at a point near the focus [33]. Then the total electric field at a prescribed point can be found out by integration over the entire reflector surface. The knowledge of electric field distribution in the focal plane of an offset reflector becomes helpful in estimating the cross-polarization introduced by the offset reflector geometry. Later on, the computed cross-polarization data can be used to design a matched feed, which improves the cross-polar performance of the offset parabolic reflector antenna. Using the mathematical formulation as suggested by Bem [33], a MATLAB program was developed to estimate the focal-region fields of an offset reflector antenna. In order to solve the double integration involved in the mathematical analysis, a ten-point Gaussian integration [37] method was used. The offset reflector geometry (see Fig. 2.1) under consideration has a projected aperture diameter (D) of 1.2 m, F/D=0.82 and the offset angle Extensive computer simulations were carried out to compute the focal region fields for two different cases i.e., (i) source at boresight and, (ii) source 5 off boresight. The validity of the results has been justified by comparing the results with that of the commercially available antenna design software GRASP- 8W [38]. As evident from Fig. 2.2, the results obtained using MATLAB program are in close agreement with that of the GRASP-8W. It is important to note that, in case of Fig. 2.2(b) the location of the main lobe is shifted approximately equal to, where, = equivalent focal distance ( and = angle of plane wave incidence. 14

4 Relative Power Level (db) Relative Power Level (db) 0-10 Using MATLAB Codes Using GRASP-8W Wavelength (a) 0-10 Using MATLAB Codes Using GRASP-8W Wavelength (b) Fig. 2.2 Focal-field distribution of an offset parabolic reflector antenna (a) Source at boresight (b) Source 5 off boresight 15

5 For the same antenna geometry, the co - polarized and the cross - polarized fields at the focal region, are superimposed and are shown in the form of a contour plot (see Fig. 2.3). The contour plot demonstrates a pair of cross-polar lobes with peak near the - 6 db co-polar contour of the antenna main beam. These cross-polar contours confirm high depolarization of the radiated fields. Further, from Fig. 2.3 it reveals that the cross-polarization is maximum in one of the principal planes (plane of asymmetry), while zero in the other plane. Fig. 2.3 Contour plot of focal-field distribution of an offset reflector antenna In order to study the effect of cross-polarization variation as a function of F/D ratio and the offset angle, a parametric study was carried out. The simulated results are shown in Fig. 2.4 and Fig. 2.5, respectively. From the results, it can be concluded that the cross-polarization reduces as the F/D ratio increases. However, for a high offset angle, the cross-polarization is also high. These observations are in close agreement to those of Chu and Turrin [8]. 16

6 Cross-Polarization (db) Cross Polarization (db) F/D Ratio Fig. 2.4 Cross-polarization variation as a function of F/D ratio (with =34.8 ) Offset Angle (Degree) Fig. 2.5 Cross-polarization variation as a function of offset angle (with F/D=0.82) 17

7 2.2 CONJUGATE FIELD MATCHING CONCEPT The design of matched feed for an offset parabolic reflector antenna using the concept of conjugate field matching was first proposed by Rudge and Adatia [31] in As reported in [31-32], the undesirable high cross-polarization and the beam squinting caused by the asymmetry of the offset reflector antenna can be compensated by suitably matching the radiation field of the primary feed with those of the reflector. To satisfy this matching condition, the primary feed should support appropriate higher order mode(s), in addition to the fundamental mode. The modal amplitudes and phases in the feed are to be adjusted such that, the aperture fields of the feed exhibit similar polarization characteristics as that of the focal plane fields of the offset reflector antenna. However, the cross-polar components of the feed should be in opposite phase with respect to the cross-polar components of the offset reflector. In other words, the primary feed should provide a conjugate match to the incoming fields. As a result of this anti-phase relationship between the cross-polar fields of primary feed and the offset reflector, the undesired cross-polarization, generated by the asymmetry of the reflector structure, are cancelled out. 2.3 ESSENTIAL WAVEGUIDE MODES FOR CONJUGATE FIELD MATCHING As discussed in the previous section, the feed that illuminates the reflector should support a fundamental mode and a few higher order modes such that the aperture fields of a feed effectively match with the focal-region fields of the reflector. The list of essential waveguide modes for three different structures is given in Table

8 Table 2.1 Waveguide modes for conjugate field matching Feed Type Fundamental Essential Higher Phase Relationship Mode Order Mode Rectangular Horn TE 01 TE 11 TE 11 should be -90 w.r.t. TE 01 Cylindrical Horn TE 11 TE 21 and TM 11 TE 21 should be -90 w.r.t. TE 11 TM 11 should be inphase w.r.t. TE 11 Corrugated Horn (cylindrical) HE 11 HE 21 HE 21 should be -90 w.r.t. HE 11 In case of a smooth-walled rectangular horn, addition of higher order TE 11 mode with the fundamental TE 01 mode compensates the asymmetric cross-polarization introduced by the offset geometry. For a cylindrical structure, in addition to a fundamental TE 11 mode, two higher order modes (TE 21 and TM 11 ) are required to configure a conjugate matched feed. In such a tri-mode feed, the TE 21 mode compensates the depolarization introduced by the reflector geometry, whereas the TM 11 mode facilitates cancellation of the cross-polarization of the TE 11 mode and suppression of sidelobes. In case of a cylindrical corrugated horn, a higher order HE 21 mode is required to be added with a fundamental HE 11 mode to match the aperture plane fields with the focal plane fields of the offset reflector antenna. It is to be noted that for all the three feed structures, the higher order modes are immediately adjacent to the fundamental mode in the mode spectrum, and thus maintain the uniform velocities. Generally, the amplitudes of the higher order modes depend on the reflector geometry, i.e., F/D ratio and offset angle. The phase relationships between the higher order mode(s) and the fundamental mode for all the three feed structure are summarized in Table

9 In order to compute the aperture fields for all the three feed structures as mentioned in Table 2.1, a separate MATLAB program was developed. The results are shown in the form of a contour plot in Fig Comparison of Fig. 2.3 and Fig. 2.6 shows that the aperture fields of a matched feed effectively match with the focal region fields of an offset parabolic reflector. However, for exact matching proper amplitude and phase of the higher order mode(s) with respect to the fundamental mode must be maintained. It is then expected that such a feed will cancel the additional cross-polarization of the offset reflector antenna. Fig. 2.6 Contour plot of aperture-field distribution of a matched feed 2.4 CONCLUSION In the present chapter, the concept of matched feed for the offset parabolic reflector has been discussed. Through the focal-region field analysis of the offset parabolic reflector antenna, it has been observed that, the offset reflector generates 20

10 high cross-polarization because of the structural asymmetry. It has been also observed that the cross-polarization increases with the increase in offset angle. This undesired high cross-polarization can be controlled by using a multi-mode matched feed. The essential waveguide modes for the different matched feed structures are summarized in the chapter. 21

11 PUBLICATION RELATED TO THE CHAPTER [1] S. B. Sharma, Dhaval Pujara, and S. B. Chakrabarty, Analysis of Focal Region Field of the Offset-parabolic Reflector for Space-borne Radiometers, IEEE Applied Electromagnetics Conference, Kolkata, India, December