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Modelling a Reflector on a SurfaceThis is an abbreviated version of a paper presented at ICAP2001.Manchester, UK, 2001 by P R Foster, MAAS and Soe Min Tun, SMT Consultanices Ltd. INTRODUCTIONMany papers (1), (2) have been published on the computation of the final radiation pattern of a low gain antenna when sited on or near a structure. For high-frequency problems, where the dimensions of the structure is many wavelengths, ray tracing and diffraction techniques can be used (3). In the high frequency case, it is sufficient to model a low gain antenna as though it radiated from its phase centre. When the antenna gain is high, this is inaccurate because the wavefronts from the antenna striking the structure would not be well formed and ray tracing techniques would be invalid. Some work has been carried out dealing with high gain antennas when the antenna is a phased array (4). This is a straight-forward but time-consuming procedure. Modelling a reflector is a more complex problem than modelling an array because the radiation pattern from a reflector is the sum of radiation from the aperture, diffracted radiation from the edges of the reflectors, spillover of feed radiation past the reflector and radiation from struts plus other small contributions from interacting parts of the reflector. The objective is to provide a method of modelling the radiation from a reflector antenna in the presence of other conducting structures which is 1) accurate. The definition of accuracy is dependent on the circumstances but will be taken here as +/- 0.5 dB at -25 dB below peak gain and +/- 1.0 dB at -40.0 dB below peak gain 2) suitable for use with a diffraction program. The radiating elements used for the reflector model must be of low enough gain to provide well-formed wavefronts on the structure. The diffraction program used is ALDAS (8) MODELLING AN ISOLATED REFLECTORThere are several methods of determining the radiation from an isolated reflector. The method discussed here (5) uses Physical Optics (PO) (6), to model the currents on the main reflector and model the edge diffraction round the reflector rim using Physical Theory of Diffraction (PTD) (6). This method (implemented in the program REFLECT (5)) has the advantage that the PTD currents are summed into the PO currents on the reflecting surface and the currents can then be treated in a unified way to generate radiation patterns in the near and farfield. An offset reflector with an aperture of 401 mm and a focal length of 254.7 mm has been used as a baseline at a frequency of 10 GHz. The feed, offset at 45.0 degrees, was a Potter horn. The input feed data to the reflector program was in the form of 20 modes in the aperture computed using mode-matching. To provide data with which diffraction results could be compared, a square plate was placed parallel to the reflector boresight as shown in Figure 1. This geometry can be analysed using the PO program directly. MODELLING A REFLECTOR PLUS LOCAL STRUCTURESeveral methods can be used when the reflector is installed near a structure and are as follows (in increasing order of accuracy). but only two were found to be of any importance Method 1Compute the radiation pattern of the reflector in a plane close to the aperture of the reflector including all contributions. Subdivide the aperture into elements with the appropriate amplitude and phase and use these as individual antennas in the diffraction program as though the antenna was an antenna array near the structure. The field from the reflector alone was computed over a squared plane which was 300 mm forward of the vertex. The dimensions of the plane were 810 by 810 mm and the interval at which the field was output was 15 mm. In the diffraction program, each output point with its associated field was modelled as two separate antenna elements (orthogonally polarised Huygens elements). The area modelled in ALDAS was varied from 600 mm square to 810 mm square (Figure 2 ). The same exercise was repeated with the geometry of Figure 2 (Figure 3 and Figure 4). The peak gains agree to within 0.05 dB. The use of more elements provides better agreement at the cost of increased runtime. 40.0 minutes to 68 minutes for two principal plane patterns (266 MHz machine). See Table 1. Method 6Compute the currents on the reflector surface. using Physical Optics and Physical Theory of Diffraction. Use these currents as individual elements in the diffraction program. In this case 5169 current elements were used over the reflector. The circular aperture is 401 mm diameter which is 13.5 wavelengths at 10 GHz. The effect of the feed has been to be included and this is done by taking the free space pattern of the feed and adding it into the final patterns computed by ALDAS. The radiation patterns of the reflector alone are in good agreemtn with those predicted using PO/PTD. The radiation pattern of the reflector plus flat plate are shown in Figure 5 to Figure 7. The agreement is much better than with Method 1. In this method, the radiation patterns patterns beyond 90.0 degrees from boresight can be computed and compare well with the PO/PTD method (Figure 8) See Table 1. CONCLUSIONS Method 6 is far more accurate that the other methods which is as expected. However runtimes are longer than those of Method 1 (Table 1). The runtime using a diffraction program is proportional to the number of antenna elements included in the model. When a high gain reflector is modelled with a structure, it would be cost-effective to use Method 1 for all initial trials in order to discover where the problems lay and then to repeat the computations using Method 6 for accuracy. Figure 9 compares Methods 1 and 6 with PO + PTD for the reflector and plate. Figure 10 is on an expanded angular scale. The runtimes quoted are for two principal plane cuts, each containing 1441 points and run on a 266 MHz machine. For runs with a complicated structure like a helicopter (9), the runtime rose to 500 minutes for two principal plane cuts. When modelling a reflector on a platform, it is likely to be mechanically rotated so that many runs will be required to examine the effect of the structure on performance. Contour plots rather than two principal plane cuts will be required and this will put up the runtime to several hours per configuration. REFERENCES Table 1 Runtimes and Accuracy Table 1: RUNTIME AND ACCURACY Method 1 2 No of Elements 2916 5169 Reflector (mins) 11.0 24.0 + Plate (mins) 34.0 72.0 Error (dB) -30 dB 1.0 <0.5 Error (dB) -40 dB 2.0 <1.5
FIGURE 1 Plan View of Offset Reflector plus Flat Plate
FIGURE 2 Azimuth Copolar Pattern Method 1 with three different planar apertures - Reflector alone
FIGURE 3 Azimuth Copolar pattern Method 1 with three different planar apertures - Reflector plus plate
FIGURE 4 Azimuth Crosspolar pattern Method 1 with three different planar apertures - Reflector plus plate
FIGURE 5 Azimuth Copolar pattern Method 6 Reflector plus plate
FIGURE 6 Azimuth Crosspolar pattern Method 6 Reflector plus plate
FIGURE 7 Elevation Copolar pattern Method 6 Reflector plus plate
Figure 8 Elevation radiation patterns over +/-180.0 degrees Method 6:- Reflector plus plate
Figure 9 Comparison of Methods 1 and 6 with PO/PTD: Azimuth radiation pattern of Reflector plus Plate
Figure 10 Expanded version of Figure 8
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