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An approach based on the method of moments is presented for the computation of the sensitivity of infinite and finite receiving phased arrays with active beamforming networks. The sensitivity is characterized in terms of signal-to-noise element patterns. Coupling of noise through the array is included in the analysis, as well as noise resulting from losses in the antennas. Simulation results are shown for arrays consisting of tapered-slot antennas made of metallic plates. For finite arrays, the average signal-to-noise ratio per element is not necessarily smaller than in the infinite-arraycase. For an 8×8 array, the average signal-to-noise element pattern is somewhat more narrow than for the infinite array. At broadside, the sensitivity of relatively small arrays (4×4 to 8×8) is described within order 1 dB by the infinite-array solution.