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A low noise transimpedance amplifier (TIA) is used in radiation detectors to transform the current pulse produced by a photo-sensitive device into an output voltage pulse with a specified amplitude and shape. We consider here the specifications of a PET (positron emission tomography) system. We review the traditional approach, feedback TIA, using an operational amplifier with feedback, and we investigate two alternative circuits: the common-gate TIA, and the regulated cascode TIA. We derive the transimpedance function (the poles of which determine the pulse shaping); we identify the transistor in each circuit that has the dominant noise source, and we obtain closed-form equations for the rms output noise voltage. We find that the common-gate TIA has high noise, but the regulated cascode TIA has the same dominant noise contribution as the feedback TIA, if the same maximum transconductance value is considered. A circuit prototype of a regulated cascode TIA is designed in a 0.35 μm CMOS technology, to validate the theoretical results by simulation and by measurement.