The high-frequency operation of an abrupt-heterojunction transistor with ballistic transport in the base is considered. The coherent regime arises at temperatures low enough compared to the injection energy that the injected minority carriers form a nearly collimated and monoenergetic beam. The coherent transistor can have both current gain and power gain at frequencies far above the conventional cutoff. The extended frequency of an intrinsic transistor is limited by the dispersion in the minority-carrier times of flight across the base, rather than the average time of flight itself. The unilateral gain U calculated for an exemplary heterostructure, including the parasitics, demonstrates an active behavior of the coherent transistor in extended frequency ranges.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>