Razavi's oscillator theory interpreted in RF circuit port impedance domain to harmonize with Leeson's sideband noise spectrum model

Frequency spectrum purity or phase noise is ever of concern to oscillator engineers. The spectrum model proposed by Leeson predicts noise power density to be observed at frequency offset around the oscillation, provided that the device noise figure and the factor labelled “Q” are given. To develop low-noise oscillators, circuit designers need to know how to estimate the Q from their circuits. This paper traces Q factor formulas derived for oscillators in block-diagram and circuit-scheme models. We find how the Q factor depends upon the oscillator's topology. Typical examples of positive-feedback, negative-resistance, and transistor oscillators are shown. The theory contributes to helping us create new schemes exhibiting high spectrum purity.

[1]  W. A. Edson.  Noise in Oscillators , 1960, Proceedings of the IRE.

[2]  D. Leeson.  A simple model of feedback oscillator noise spectrum , 1966 .

[3]  Behzad Razavi,et al.  A study of phase noise in CMOS oscillators , 1996, IEEE J. Solid State Circuits.

[4]  Ali Hajimiri,et al.  A general theory of phase noise in electrical oscillators , 1998 .

[5]  M. Prigent,et al.  Phase noise in oscillators - Leeson formula revisited , 2003 .

[6]  Kiyomichi Araki,et al.  Active $Q$-Factor and Equilibrium Stability Formulation for Sinusoidal Oscillators , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[7]  Xianhe Huang,et al.  A Revisit To Phase Noise Model Of Leeson , 2007, 2007 IEEE International Frequency Control Symposium Joint with the 21st European Frequency and Time Forum.

[8]  Takashi Ohira,et al.  Pseudolinear Circuit Theory for Sinusoidal Oscillator Performance Maximization , 2008, IEICE Trans. Electron..

[9]  P. Wambacq,et al.  A Compact Wideband Front-End Using a Single-Inductor Dual-Band VCO in 90 nm Digital CMOS , 2008, IEEE Journal of Solid-State Circuits.

[10]  Futoshi Kuroki,et al.  Analytical consideration on reflection type of self-injection locked NRD guide gunn oscillator at 60 GHz , 2009, 2009 European Microwave Conference (EuMC).