Power amplifying system and associated power amplifying method for bluetooth device

A power amplifying system for a Bluetooth device, the power amplifying system being configured to generate an output having a predetermined frequency, the power amplifying system comprising:

• a voltage control oscillator (VCO), configured to provide an input signal having a frequency that is a non-integer multiple of the predetermined frequency;
• a frequency divider, coupled to the VCO, configured to receive the input signal and perform frequency division upon the input signal to respectively generate an in-phase signal and a quadrature signal corresponding to the input signal;
• a mixer, respectively coupled to the VCO and the frequency divider, configured to mix the input signal transmitted from the VCO and the in-phase signal transmitted from the frequency divider to output a mixed signal;
• and
• an adding amplifier, respectively coupled to the mixer and the frequency divider, configured to integrate the mixed signal and the quadrature signal to generate a first output signal having a frequency that is an integer multiple of the predetermined frequency.