This paper highlights the achievement of constant efficiency (power added efficiency, PAE) across wide output power levels for fixed amplitude constant envelope modulation. Power amplifier drain supply is adjusted while having a fixed load impedance network. Input RF drive to the power amplifier has to change according to the output power in order to maintain the PAE across a wide range of power levels. A novel idea of input RF drive adjustment to the power amplifier is presented. Due to the nonlinear behavior of the transconductance at lower drain voltages, class AB bias scheme is implemented. Constant PAE of 44 % (flatness of +/- 1 %) across 0.5 to 6.5 W is experimentally demonstrated for a LDMOS power amplifier for the frequency range 420 to 440 MHz. Theory and measurement results showed a good agreement.