Oscillator frequency spectrum as viewed from resonant energy storage and complex Q factor

Abstract

The complex power theory is applied to characterize a passive linear circuit as the resonating load of an oscillator. Thanks to Tellegen's theorem relating the port impedance and internal status, the Q factor for use in Leeson's spectrum model is derived in regard to the behavior of the stored energy. The concept of complex Q factor is introduced in terms of the power dissipation slope and the energy difference between inductive and capacitive groups of components. As their relationship results in mathematical complication, it is visualized in Pythagorean charts for ease of phenomenological comprehension.