Analytic Integration of a Common Set of Microwave Beam Intensity Functions Seth D. Potter * Summary: When designing a -wireless power transmission system, a virtually limitless number of aperture illumination functions are available. However, a commonly-used set of beam tapers results in received intensities that involve Bessel functions. This family of intensities is convenient to study and compare systematically. A constraint on the calculation of reception efficiency is the need to write numerical routines to integrate such functions. It is shown that these functions can be integrated analytically, resulting in a concise formula for reception efficiency as a function of rectifying antenna (rectenna) diameter. Introduction Microwave beams from phased array antennas are often transmitted with an amplitude that is tapered across the face of a circular phased array, in order to yield a desired field intensity pattern. As the amplitude of the transmitted beam becomes more sharply tapered, the sidelobe power density decreases, the percent of power in the main lobe increases, and the main lobe broadens. Tapering the beam may therefore be desirable for radar systems, since reducing the sidelobes may reduce clutter; however, the antenna gain will be decreased. In addition, microwave beams have been proposed as a means of transmitting power from space to Earth (as in solar power satellites) [1], Earth to space [2], space to space [3], and other uses. The microwave energy can be received and converted to DC by a rectifying antenna (rectenna). Choosing an amplitude taper is a key issue in the design of a wireless power transmission system [3,4] particularly for solar power satellite applications [5,6], in which large amounts of power may be transmitted to a rectenna located near a populated area. The beam sidelobes may contain power that is too spread out to rectify economically, but may be undesired by surrounding populations [7,8] and may be a source of electromagnetic interference to communications and navigation. A commonly considered family of beam tapers found in Skolnik [9] and other references will be investigated. Radiation Intensity If p is the dimensionless radial distance from the center of a circular transmitting antenna, then the aperture illuminations to be considered are of the form [1 - p2](n-1), where n = 1, 2, 3,... . Note that n = 1 refers to an untapered beam. If u is the dimensionless radial distance from the center of the beam at the rectenna site, then the resulting radiation intensity pattern is of the form * New York University Applied Science Program 34 Stuyvesant Street, 5th floor New York, NY 10003-7599 Telephone: (212) 998-3744 FAX: (212) 995-3820 E-mail: potter@acf2.nyu.edu
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