A phased-array RF pulse generator is disclosed which includes a video-pulse generator arranged to generate video pulses each having a leading edge. An array of nonlinear and dispersive transmission lines, are arranged to generate RF pulses from the video pulses. At least one sensor is arranged to detect the leading edge of the video pulses after they have passed along the transmission lines. A phase controller is arranged to set the velocity of the video pulses in each transmission line to put the detected leading edges, and hence the generated RF pulses, into a desired phase relationship.