A RF transmitter has at least one amplifier having an input terminal for receiving a phase modulated signal to be transmitted on an RF carrier and an input node for receiving a modulation signal for amplitude modulating the RF carrier. The RF transmitter further includes an amplitude modulator having an output coupled to the input node of the power amplifier through a low-pass filter. The low-pass filter includes at least one variable filter component for varying a bandwidth of the low-pass filter. In a preferred embodiment an envelope elimination and restoration (EER) RF transmitter includes at least one power RF amplifier having the input terminal for receiving the phase modulated signal to be transmitted on the RF carrier, and further including an input power node for receiving a modulated voltage for amplitude modulating the RF carrier. The EER RF transmitter further includes a class-S modulator having a variable bandwidth low-pass filter having an output coupled to the input power node and including at least one first variable capacitance.