A highly efficient power supply, a method for supplying power, and a method for arranging a power supply, for a UHF or microwave radio frequency amplifier intended for operation with a signal that has a power level which varies at a high frequency rate. The power supply has an output for connecting to a power supply input of the radio frequency power amplifier and includes a high rate controllable voltage supply employing electronic linear devices connected to the output, an element for quantifying power dissipated by the electronic linear devices and a low rate controllable current supply connected to the output. Preferably, the current supply is a substantially constant current supply at the frequency of the radio frequency signal. Preferably, the controllable voltage supply has a control input and is arranged to be controlled for outputting a voltage that is a function of the high frequency power variation.