Beam position monitors using stripline pickups for 30 ns long electron and positron beam bunches have been built and responses were measured in the vertical and horizontal directions. Log amplifiers used for signal processing have a dynamic range of 40 dB and are scaled for 50 mV/dB sensitivity. In this paper we describe the design of the detectors, the signal processing electronics, and the results of the position‐to‐signal mapping using a wire. Beam position measurements using a prototype detector and electronics on the APS linac test stand are discussed.