Mathematical proof of Leeson's oscillator noise spectrum model

IEICE Electronics Express

Takashi Ohira¹ 

[1] ATR Wave Engineering Laboratories

关键词: oscillator;    phase noise;    Q factor;    multiple time scale;   

DOI  :  10.1587/elex.1.109

学科分类：电子、光学、磁材料

来源: Denshi Jouhou Tsuushin Gakkai

【 摘 要 】

References(6)This letter presents a mathematical formulation that clearly explains the result that was heuristically introduced by Leeson for the oscillator noise spectrum. We consider the voltage and current in a simple equivalent circuit consisting of only linear components. To analyze both the oscillation and noise behaviors simultaneously without resort to frequency-domain transfer functions, we introduce dual coordinates in the time domain. Equivalent device temperature and Q factor are appropriately defined to support Leeson's result. It is successfully clarified, without taking any nonlinear effects into account, that the noise from a white source is converted up into a sharp spectrum around the oscillation frequency.

【 授权许可】

Unknown