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A first-order azimuth-steerable superdirectional microphone response can be constructed by means of a linear combination of three eigenbeams (monopole and two orthogonal dipoles). Via this method, we can construct any first-order directivity pattern (monopole, cardioid, hypercardioid, etc.) that can be electronically steered to a certain angle on the 2-D plane to capture the desired signal. In this paper, the superdirectional responses are generated via a planar microphone array with a square geometry. We analyze the influence of spatial aliasing on the captured desired signal and the directivity index. Furthermore, we investigate the sensitivity for uncorrelated sensor noise and the sensitivity for phase- and magnitude-errors on the individual sensors. Finally, two rules of thumb are derived to choose the size of the microphone array.