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The basic design equations for symmetrical sub-reflectarrays are derived. These provide the required phase-distribution on the sub-reflectarray surface. Both ellipsoidal-type and hyperboloidal-type sub-reflectarrays are designed and fabricated using single-layer rectangular patch elements. Measured amplitude and phase patterns are shown for both types of sub-reflectarray, and compared to predictions. The behaviour of the ellipsoidal-type sub-reflectarray is furthermore compared to measured patterns of its solid subreflector counterpart. These experimental results show that the sub-reflectarrays indeed emulate the behaviour of their solid subreflector counterparts, and the validity of the basic design equations is thus established.