Download PDF by R. C. Hansen: Apertures

By R. C. Hansen

ISBN-10: 012323901X

ISBN-13: 9780123239013

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 facets of learning, development and Maintainance of Microwave Antennas and their Peripheral gear

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Y Fig. 18. Uniform square aperture. Fig. 18. ::-'--------"--'---- 2z (73) For the field on-axis, x = 0 = y, and , k2 LI2JL /2 ( . x/2 + E = exp -Jk z J-L/2 -L/2 2z y/2) dx / dy / (74) Various constants and factors such as exp( -jkz) have been deleted since only the magnitude of E is of interest, which will later be normalized. For the line source case, Eq. (74) is simply changed by putting y/ = 0 and deleting one integral. A change of variable is next made for each integral to obtain the standard Fresnel form, and it is important to note that each change produces a factor of (7rZ/k)l/2.

Tapered (1 - p2) circular aperture: R = 1rD2/8A 1. Uniform line source or square aperture: G. FOCUSED APERTURES In that portion of the radiating near-field region from a few D to 2D2lA, the effects of the quadratic phase can be corrected by focusing, just as it Table I DEPTH OF FIELD Focused at 00 2D'/"h D'/"h D'/2"h D'/4"h Depth of field D'/"h to 00 2D'/3"h to 00 D'/2"h to 00 D'/3"h to D'/"h D'/5"h to D'/3"h can be in optics. From the section on Fresnel analysis of a circular aperture, the phase approximation, Eq.

The symbols used for the uniform line source will again be used. Before deriving the Taylor ideal aperture distribution, it is useful to obtain some general theorems (Taylor, 1955) relating the form of the aperture distribution to the pattern or space factor and its zeros. These will be obtained by using complex variables, where z = U + jv and ~ = p + jq. In the ~ plane, the line source is along the real axis between ±'II'". The space factor is F (u) ; Eq. (88) becomes F(z) = -1 J" 2'11'" _ .. , ~ = ±'II'", strongly affects the properties of F (z).

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Apertures by R. C. Hansen


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