# Apertures by R. C. Hansen

By R. C. Hansen

Microwave Scanning Antennas. quantity 1: Apertures [Hardcover] [Jan 01, 1964] HANSEN, R; Equations; Charts and R. C. Hansen. the 1st in a 3 half sequence Coving All features of gaining knowledge of, construction and Maintainance of Microwave Antennas and their Peripheral apparatus

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Often the conservative value of 2D2/>.. is used. At this distance, the phase error at the aperture edge is >"/16, which produces a negligible effect on directivity and sidelobes. 0 _ . , . . . . . /I. /I. /I. 1 ... J o 10 20 30 8 40 50 60 70 Fig. 15. Fresnel region elevation pattern for a 25 db circular Taylor distribution, D = lOX. with a distance D2/2X, half the optical hyperfocal distance, with its Aj4 phase error, which produces a 20% directivity degradation. , called the radiating near-field region, the pattern varies with the distance and, due to the quadratic phase, perfect interference does not occur.

05[C ~ 2(_1) + S2(_1)] 2~ 2~ (79) If the normalization had occurred at an infinite distance, the coefficients in Eqs. (78) and (79) would be exactly 16 and 4. Because the line source involved a single integral, the original liz factor was changed to 1/0 instead of to 1. Thus Eq. (79) displays a liz dependence whereas Eq. (78) does not. Figure 19 depicts the square-source power density. 5. 5. The dashed line is the envelope of maximum power density that is obtained. Figure 20 shows the power density on-axis for the line source; an R-l dependence may be observed in the oscillatory region.

21. The two Fresnel limits and the far- 1. 31 Aperture Theory field boundary are plotted in Fig. 16. 7 db degradation is probably less than can be tolerated. Of special importance is the fact that the Fresnel approximation is not valid for distances of 1D. In the study of focused apertures it will be shown that these apertures go through a transition around R = D. -< 0 40 20 10 7 FAR-FI ELO APPROXI M ATiON 4 2 I I 2 4 7 10 20 40 70 100 200 400 700 1000 RID Fig. 16. Field integral approximations for unfocused apertures.