Multi beam antenna and its configuration process

Claim 2

A multi-beam antenna comprising a main reflector, a sub-reflector, and a plurality of horns for exciting the main reflector, characterized in that the beam phase errors generated at the main reflector are corrected by the sub-reflector and the shape Z s of said sub-reflector is determined by the equation: z.sub.s =.sup.t b·g(x.sub.s, y.sub.s) where b stands for an expansion coefficient, g(x s , y s ) is an expansion function, and t b a transpose of a matrix of expansion coefficient b, the shape Z s of the sub-reflector satisfying a minimum value of the least square means I of the difference between Z s and Z si referred to below, and being formed in such a way as to have the least aperture surface phase error in each beam direction, where I=z.sup.2 -.sup.t z[G]b and where [G] is a matrix MN×Mb consisting of MN expansion function vector g, z is a vector (of MN dimensions) whose elements are given by (z s - z si ), b is a vector given by b=[.sup.t [G][G]].sup.-1t [G]z N is the number of beams, and M is the number of points on the main reflector considered for each of the N beams, so that a total of MN points are taken into consideration to obtain Z si (where i=1, . . . MN) for each point on the sub-reflector.

Claim 3

A multi-beam antenna comprising a main reflector, a sub-reflector, and a plurality of horns for exciting the main reflector, characterized in that the beam phase errors generated at the main reflector are corrected by the sub-reflector and the shape Z s of said sub-reflector is determined by the equation: z.sub.s =.sup.t b·g(x.sub.s,y.sub.s) where b stands for an expansion coefficient, g(x s ,y s ) is an expansion function, and t b a transpose of a matrix of expansion coefficient b, the shape Z m of the main reflector being determined by following formula: z.sub.m =z.sub.m (x.sub.m,y.sub.m,a) and a normal to the main reflector surface being determined by the equation: ##EQU4## where a stands for an unknown parameter vector (Ma dimensions), and Z m stands for an arbitrary given function that satisfies the following relation: ∂.sup..sub. z.sbsb.m ·/∂.sub.x.sbsb.m ∂.sub.y.sbsb.m =∂.sup.2.sub.z.sbsb.m /∂.sub.y.sbsb.m ∂.sub.x.sbsb.m

Claim 4

A multi-beam antenna comprising a main reflector, a sub-reflector, and a plurality of horns for exciting the main reflector, characterized in that the beam phase errors generated at the main reflector are corrected by the sub-reflector and the shape Z s of said sub-reflector is determined by the equation: z.sub.s =.sup.t b·g(x.sub.s,y.sub.s) where b stands for an expansion coefficient, g(x s ,y s ) is an expansion function, and t b a transpose of a matrix of expansion coefficient b, the shape Z m of the main reflector being determined by following formula: z.sub.m =z.sub.m (x.sub.m,y.sub.m,a) and a normal to the main reflector surface being determined by the equation: ##EQU4## where a stands for an unknown parameter vector (Ma dimensions), and Z m stands for an arbitrary given function that satisfies the following relation: ∂.sup..sub. z.sbsb.m ·/∂.sub.x.sbsb.m ∂.sub.y.sbsb.m =∂.sup.2.sub.z.sbsb.m /∂.sub.y.sbsb.m ∂.sub.x.sbsb.m

Claim 5

A configuration process of the multibeam antenna of claim 1 or 2 consisting of a main reflector, an integrated sub-reflector placed in front of said main reflector and feed horns placed at the foci or near the foci for said integrated sub-reflector, comprising the following procedure: (a) determine the main reflector surface Z m by z.sub.m =z.sub.m (X.sub.m,y.sub.m,a) (2) notice M points on the main reflector for each of the N beams and obtain MN points z si (i=1, . . . MN on sub-reflectors corresponding to MN points on the main reflector, (b) determine the surface of the integrated sub-reflector by z.sub.s =.sup.t b·g(x.sub.s,y.sub.s) and obtain the least square means I of the difference between z s and z si from the equation I=z.sup.2 -.sup.t z[G]b (c) obtain the mininum value of I by looking upon the I as an objective function of an optimization problem concerning a, K i , X fi , and (d) determine the surfaces of the main antenna and the integrated sub-reflector, the position of the feed horns, and the relative position of the said three in such a way as to minimize I, where a=an unknown parameter vector, b=an expansion coefficient series, g(x s ,y s )=an expansion function series, z=a vector comprising its elements z s - z si , and ∂G]=a matrix consisting of expansion function vector g.