The optimum power conversion efficiency and associated gain of an LC CMOS oscillator

According to the well known Barkhausen criteria, an oscillator requires a loop gain of greater than 1 to start up. In order to ensure start-up, the literature invariably advises a gain value of around 3. However, no valid argument exists to support this figure. This work demonstrates that this figure, in the case of the voltage-biased differential LC CMOS oscillator, may have some physical significance. Using a simplified model of the oscillator, a direct relationship between gain and power conversion efficiency is established. It is shown that the oscillator has a unique power conversion efficiency maximum and that this maximum corresponds to a gain of approximately 2.75. Extensive SpectreRF simulations support the claims