On the exact design of RF oscillators

Important requirements for oscillators used in RF applications typically include well controlled amplitude, low phase noise relative to the carrier and low power consumption. This paper presents a rigorous analysis of phase noise for the Colpitts oscillator and derives an exact formula for the phase noise to carrier ratio. The latter is inversely proportional to the bias current and the quality factor of the LC resonator. Improvement in the active device has only a minor impact on the oscillator performance at 1-2 GHz.