We consider the high-frequency operation of an abrupt-heterojunction t
ransistor with ballistic transport in the base. The coherent regime ar
ises at temperatures low enough compared to the injection energy, that
the injected minority carriers form a nearly collimated and monoenerg
etic beam. The coherent transistor can have both the current gain and
the power gain at frequencies far above the conventional cutoff. The e
xtended frequency of an intrinsic transistor is limited by the dispers
ion in the minority-carrier times of flight across the base, rather th
an the average time of flight itself. The unilateral gain U calculated
for an exemplary heterostructure, including the parasitics, demonstra
tes an active behavior of the coherent transistor in extended frequenc
y ranges.