1/f Phase Noise in Oscillators Modeled with Q and Its Entropy Origin

Abstract

Noise in operating systems has been strongly linked to degradation. One such type of noise of interest in this paper is phase noise, which we model and describe its significance in thermodynamic degradation science. Phase noise of an oscillator is perhaps one of the most important oscillator parameters and the source of the noise is not well understood. Phase noise is important as it degrades the purity of the carrier frequency when used in transmission which is only one of the many applications in oscillator usage. It is known that the unloaded Q in phase noise goes as the inverse of Q to the forth power observed in the low frequency area (i.e. near the carrier frequency) as noted in oscillator power noise spectral density. In this paper we provide a model that leads to this observed unloaded Q dependence noted in the power spectral density. We then provide specific comparison to an LRC oscillator circuit to establish a parametric useful analogy. A second model links Q to entropy which we show produces this type of noise. Although this noise’s origin is not well understood in terms of reliability, we have previously found that noise is typically attributed to entropy (disorder). This is because temporal coherence of a signal from an operating device can be correlated to disorder in the spatial coherence in the device. Once understood, the phase noise has an entropy explanation that yields the inverse frequency dependence observed. Therefore, this type of noise measurement is of importance in thermodynamic degradation process as it has applications to understanding noise in other areas besides oscillators. Results show consistency with damage entropy principles in terms of purity of materials and measurement methods observed in the literature. Because entropy is an expression of the disorder, or randomness of a system, we anticipate that such results can be applied in assessing stability issues in many fabricated electronic devices.