Microwave Antennas by A. Z. Fradin (Auth.)
By A. Z. Fradin (Auth.)
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Example text
1 ) . The arbitrary character of the auxiliary field permits our taking it so as to eliminate from ( 2 . 9 ) the maximum number of terms and thus to simplify it. Further, the right- and left-hand sides of ( 2 . 9 ) are integrated over the volume containing all sources of electromagnetic field and points at which the field is defined. Let us employ the method of auxiliary sources for the derivation of a number of important relationships, widely used in the theory of microwave antennas. At the same time these calculations will serve to illustrate the method.
1 3 ) the aperture. For a parabola of revolution the aperture has, generally speaking, the form of 32 MICROWAVE ANTENNAS a circle of diameter D, and, for the parabolic cylinder, the form of a rectangle with sides and D^. In a number of practical cases various fonns of truncated paraboloids of revolution are employed. In these cases the aperture may take the form of a rectangle or a circle with excised segments. We shall call the axis of the reflector the line AA» , perpendicular to the plane of the aperture and passing through the centre of the latter.
9 ) over the volume - Y^. Since the volume Y^ is excluded from the volume of integration, in the remaining portion obtain: = 0. 9a) where η is the internal normal with respect to the volume Y - Y . 5). -*^-». ^ ^ since (^Qe¿) = (e¿ e^) while Gq^q) = 0 and (e¿ r^) = 0 , as the scalar products of perpendicular vectors. The surface integral over found in the following manner. Let us integrate the right- and left-hand sides of equation ( 2 . 9 ) over the volume V^. On the left-hand side of ( 2 . 11) the positive sign is taken since η denotes the normal external to the volume V^.