RF signal generators (1) are disclosed, having an amplitude-modulated amplifier (80) whose supply voltage (70) is a signal non-linearly filtered (33) dependent on a signal (30) being representative to an envelope signal of a desired output RF signal (81). The non-linear filtering (33) is performed preferably using an envelope-dependent boundary. An input RF signal (65) to the amplifier (80) is amplified using the supply voltage (70) to produce the desired output RF signal (81). The present invention also presents methods for driving such generators (1).