Cấu trúc sóng chức năng trong điện lý thuyết P8

Rainfall AttenuationInvestigations on the attenuation caused by rain and other hydrometers and their effects on terrestrial communications started as early as in the 1940s. Subsequently, many theoretical and experimental results were obtained and used to predict the effects of interaction between hydrometers and microwave signals. The theories for the prediction of rain attenuation on microwave signals are well established and widely used by many researchers.
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Cấu trúc sóng chức năng trong điện lý thuyết P8 Spheroidal Wave Functions in Electromagnetic Theory Le-Wei Li, Xiao-Kang Kang, Mook-Seng Leong Copyright  2002 John Wiley & Sons, Inc. ISBNs: 0-471-03170-4 (Hardback); 0-471-22157-0 (Electronic) 8 Analysis of RainfallAttenuation Using Oblate Raindrops8.1 INTRODUCTION8.1.1 Rainfall AttenuationInvestigations on the attenuation caused by rain and other hydrometers andtheir effects on terrestrial communications started as early as in the 1940s.Subsequently, many theoretical and experimental results were obtained andused to predict the effects of interaction between hydrometers and microwavesignals. The theories for the prediction of rain attenuation on microwavesignals are well established and widely used by many researchers. Concep-tually, the specific attenuation due to raindrops depends on both the total (extinction) cross section and the raindrop size distribution. In 1908, Mie [161] formulated and put forth the exact formulation for thecalculation of the total cross section (TCS) of an isotropic, homogeneous di-electric sphere of arbitrary size. This is known as A&e theory. Later, Stratton [86] expanded the scattered fields into a series of spherical vector wave func-tions to calculate the TCS from which the attenuation can readily be obtainedupon knowing the raindrop size distribution (DSD). In the work by Oslen et al. [162], an empirical relationship between thespecific attenuation A and a rain rate R was proposed as A = aRb, wherea = a(f) and b = b(f) are frequency-dependent parameters. Based on thisformulation, a and b can readily be obtained via regression analysis for dif-ferent frequencies, a known drop size distribution and a given atmospherictemperature. The International Radio Consultative Committee (CCIR) (now known as CCITT) [163] recommended this relationship based on the Laws 227228 ANALYSIS OF RAlNFALL ATTENUATlON USING OBLATE RAINDROPSand Parsons DSD [164] in the frequency range 1 to 1000 GHz. Using interpolation, the unknowns a and b can be determined using the formula presentedin the report. However, the Laws and Parsons DSD is only a representa-tive one. There are many other DSD models available in the literature, suchas the “Thunderstorm” distribution (J-T) by Joss et al., and the “Drizzle”distribution (J-D) [1651. However, these were generated from measurementstaken in Europe, Canada,the United States and Japan that underestimated the rainfall attenuation andare unsuitable for a tropical climate such as that of Singapore. In fact, stud-ies conducted [166] show that attenuation of microwave signals varies withgeographical locations, even at the same rain rate and frequency. Measure-ments over the years have shown that the specific attenuation in Singaporeis much higher than that predicted by CCIR at various frequencies. Prom atwo-year measurement of rainfall attenuation for a 21.225-GHz signal, Yeo etal. [167] generated a local DSD. Generation of a new DSD based on multiplefrequencies has been proposed, but has not yet been generated.8.1.2 Raindrop Models in Different SizesThe formulation for spherical raindrops is, however, valid for small sizes. Theearliest and best recognized contributions to theories in the prediction of rainattenuation of distorted raindrops were probably made by Oguchi in 1960[168] and 1964 [169], using the boundary-perturbation and point-matchingtechniques. He calculated the TCS values of raindrops with small eccentric-ity using vector wave functions and the first-order perturbation technique toaccount for drop-shape deformations at large sizes. Using these calculations,he predicted the attenuation for horizontally and vertically polarized wavesat 34.88 GHz. However, this method is accurate only for small raindropswith small deformations. As raindrops increase in size, deformations increase(eccentricity increases), leading to inaccuracies in the calculations. He refinedthe method in 1963 using a second-order approximation to account for theshape deformations of large raindrops. Experimentally, photographic measurementsof raindrops reviewed by Ogu-chi in 1981 [170] sh owed increased deformations in raindrops as they increasein size. A similar review of raindrop deformations was published in 1983 [171].Raindrops vary in size from very small to fairly large. The smallest raindropsmay be equivalent to those found in clouds. The largest drops will not exceed4 mm in radius, as otherwise they are hydrodynamically uns ...