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Design and performance details are given for the Cosmic Background Imager (CBI), an interferometer array that is measuring the power spectrum of fluctuations in the cosmic microwave background radiation (CMBR) for multipoles in the range 400< l< 3500. The CBI is located at an altitude of 5000 m in the Atacama Desert in northern Chile. It is a planar synthesis array with 13 0.9 m diameter antennas on a 6 m diameter tracking platform. Each antenna has a cooled, low‐noise receiver operating in the 26–36 GHz band. Signals are cross‐correlated in an analog filterbank correlator with 10 1 GHz bands. This allows spectral index measurements that can be used to distinguish CMBR signals from diffuse galactic foregrounds. A 1.2 kHz 180 phase‐switching scheme is used to reject cross talk and low‐frequency pick‐up in the signal processing system. The CBI has a three‐axis mount that allows the tracking platform to …