From (8), CONCLUSIONSNumber of SPDT switches = 20 610.Comparing this with the matrix of Fig. 6, from (21, Number of SPDT switches = 24 950.For this example, the matrix of Fig. 10 requires 4340 fewer switches than the matrix of Fig. 6 which represents a savings of about 20 percent. Therefore, the matrix of Fig. 10 requires fewer switches than the other selection methods considered. This minimization is obtained at the expense of restricting each selected cluster to a particular portion of the m first level output lines and at the same time restricting the cluster movement to dF receive beamwidth steps.An important conclusion which can be made for this method of beam selection is that the total number of switches required is less than 5 percent greater than the total number of receive beam positions u-hen the number of beams per group n is 100 or larger.Several conclusions can be made concerning the selection of simultaneous receive beams from multiple beam forming antennas. The independence of the several selected beams is a critical factor in the design of the matrix, and in general, the greater the independence of the beam choices, the greater the number of switches required and the greater the cost of the matrix. The most versatile design is one with groupings of several beam positions using a block technique. The excluded beam positions are scattered throughout the scanning volume using this technique. Finally, the grouping of individual beams in clusters allows further reduction in the required number of switching junctions. The most efficient design from the standpoint of minimum number of slvitches required is one which uses less than five percent more switches than the total number of available beam positions.Abstract-Phase error in the aperture field of a microwave paraboloidal antenna degrades antenna gain in two ways: the asynchronism of partial field contributions arriving at an axial field point reduces the magnitude of the total field there, and the phase error may generate a cross-polarized component of the aperture field that further reduces the axial gain. Because of phase ripples in the field reflected from the subdish, a Cassegrainian-fed antenna may be considerably more susceptible to phaseerror effects than conventional focal-point-fed antennas. Consequently, a two-part analysis was conducted to evaluate the importance of these phase-error effects in Cassegrainian systems. The feed-system fields were computed and a best-fit phase center was found. Then the axial gain was computed in terms of the feed-system fields. An expression for the phaseerror loss was defined to evaluate the effects of dfiactive phase ripple, feed-system misalignment, etc. Numerical analyses were carried out