Front cover

E. Rubiola

Phase noise and frequency stability in oscillators

Cambridge University Press, 2008

ISBN 978-0-521-15328-7 (paperback)

ISBN 978-1-139-23940-0 (Adobe eBook)

Presenting a comprehensive account of oscillator phase-noise and frequency stability, this practical text is both mathematically rigorous and accessible. An in-depth treatment of the noise mechanism is given, describing the oscillator as a physical system, and showing that simple general laws govern the stability of a large variety of oscillators differing in technology and frequency range, and in lasers. Special attention is given to amplifiers, resonators, delay lines, feedback, and flicker (1/f) noise. The reverse engineering of oscillators based on phase-noise spectra is also covered, and end-of-chapter exercises are given. Uniquely, numerous practical examples are presented, including case studies taken from laboratory prototypes and commercial oscillators. Based on tutorials given by the author at the Jet Propulsion Laboratory, international IEEE meetings, and in industry, this is a useful reference for academic researchers, industry practitioners, and graduate students in RF and communications engineering.

Foreword;  Preface;  List of symbols;  1. Phase noise and frequency stability;  2. Phase noise in semiconductors and amplifiers;  3. Heuristic approach to the Leeson effect;  4. Phase noise and linear feedback theory;  5. Noise in delay-line oscillators and lasers;  6. Oscillator hacking;  A Laplace transform;  References.  Bibliography;  Index.

Important notice: this book supersedes and makes obsolete the draft version E. Rubiola, The Leeson effect - Phase noise in quasilinear oscillators, arXivphysics/0502143, February 2005.

Provisional page, work in progress

Supplementary Material

Open literature

  1. E. Rubiola, R. Brendel, A generalization of the Leeson effect, April 2010 (48 pages, PDF 2.3 MB). arXiv:1004.5539 [physics.ins-det]. This report extends the Leeson effect to the analysis of amplitude noise and to the amplitude-phase coupling, introducing a theoretical framework for the analysis of other oscillators, like masers, lasers, and opto-electronic oscillators. Though recommended as a complement to the book, the text is self-consistent.

Seminars

  1. E. Rubiola, The Leeson effect (88 slides, PDF, 17.3 MB).

    The oscillator, inherently, turns a phase shift of the loop into a change of the oscillation frequency, hence phase noise into frequency noise. Hence the phase, which is the integral of the frequency, diverges in the long run. The same behavior shows up in all feedback oscillators, independently of technology and frequency, thus also in lasers. This mechanism is known as the "Leeson model" after a short article published in 1964. On my part, I prefer the term "Leeson effect" in order to emphasize that this phenomenon is far more general than a simple model.

    After a limited-time tenure given at the NASA-Caltech Jet Propulsion Laboratory in 2004, this is the initial seed of the book.

  2. E. Rubiola, V. Giordano, On the 1/f noise of ultra-stable quartz oscillators (23 slides, PDF, 3 MB). Listen the conference (MPEG-4 audio+slides, 100 MB).

    In quartz oscillators, the fluctuation of the resonator's natural frequency is larger than the phase noise of the electronics turned into frequency noise via the Leeson effect. This conclusion comes only after undisclosing all the secrets of the phase-to-frequency conversion in oscillators.

    This conference, presented at the 2006 IEEE IFCS and at the 2006 EFTF, is the basis of a peer-reviewed article (IEEE Tr. UFFC 54(1) p.15-22, Jan 2007) and of Chapter 6 of my book.

  3. E. Rubiola, Basics of phase noise (71 slides, PDF 7 MB).

    Before getting through the Leeson effect, you may need a general introduction to phase noise and frequency stability. These slides were prepared for a 2-hour tutorial, presented at several editions of the IEEE IFCS.

Seminars on related subjects

  1. E. Rubiola, The magic of cross-spectrum measurements from DC to optics (54 slides, 10.1 MB).

    When it is possible to measure a device with two equal instruments, the cross-spectrum measurement enables to reduce the instrument background noise proportionally to 1/√m, where m is the number of averaged spectra. Besides the measurement of the oscillator phase noise and frequency stability, this technique finds applicatgions in a variety of fields, from fundamental DC voltage measurements to radio astronomy.

    These slides were prepared for a 2-hour seminar and for an invited talk at the 2008 EFTF.

  2. E. Rubiola, High-resolution frequency counters (53 slides, PDF 6.2 MB).

    Whoever works with precision oscillator will need a deep understanding of the frequency counter. Some of the techniqiues described are of general usefulness, and suitable to implementation in a small FPGA.

    These slides were prepared for a 1-2hour seminar given at the FEMTO-ST Institute, at the Université Henri Poincaré, and at the NASA-Caltech Jet Propulsion Laboratory.

Download the spectra of Chapter 6

Fig. 6.4 Oscilloquartz 8600
5 MHz OCXO

Fig. 6.4
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Fig. 6.4 Oscilloquartz 8600
5 MHz OCXO

Fig. 6.4 (unannotated)
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Fig. 6.5 Oscilloquartz 8607
5 MHz OCXO

Fig. 6.5
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Fig. 6.5 Oscilloquartz 8607
5 MHz OCXO

Fig. 6.5 (unannotated)
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Fig. 6.6 Rakon Pharao
5 MHz OCXO

Fig. 6.6
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Fig. 6.6 Rakon Pharao
5 MHz OCXO

Fig. 6.6 (unannotated)
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Fig. 6.7 FEMTO-ST prototype
10 MHz OCXO

Fig. 6.7
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Fig. 6.7 FEMTO-ST prototype
5 MHz OCXO

Fig. 6.7 (unannotated)
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Fig. 6.8 Agilent 10811
10 MHz OCXO

Fig. 6.8
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Fig. 6.8 Agilent 10811
10 MHz OCXO

Fig. 6.8 (unannotated)
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Fig. 6.9 Agilent prototype
10 MHz OCXO

Fig. 6.9
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Fig. 6.9 Agilent prototype
10 MHz OCXO

Fig. 6.9 (unannotated)
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Fig. 6.10 Wenzel 501-04623
100 MHz OCXO

Fig. 6.10
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Fig. 6.10 Wenzel 501-04623
100 MHz OCXO

Fig. 6.10 (unannotated)
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Fig. 6.11 Miteq D210B
10 GHz DRO

Fig. 6.11
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Fig. 6.11 Miteq D210B
10 GHz DRO

Fig. 6.11 (unannotated)
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Fig. 6.12 Poseidon DRO-10.4
10.4 GHz DRO

Fig. 6.12
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Fig. 6.12 Poseidon DRO-10.4
10.4 GHz DRO

Fig. 6.12 (unannotated)
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Fig. 6.14 Poseidon Shoebox
10 GHz sapphire
whispering-gallery oscillator

Fig. 6.14
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Fig. 6.14 Poseidon Shoebox
10 GHz sapphire
whispering-gallery oscillator

Fig. 6.14 (unannotated)
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Fig. 6.15 UWA prototype
Cryogenic 10 GHz sapphire
whispering-gallery oscillator

Fig. 6.15
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Fig. 6.15 UWA prototype
Cryogenic 10 GHz sapphire
whispering-gallery oscillator

Fig. 6.15 (unannotated)
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Fig. 6.16 NIST prototype
Optical-fiber 10.6 GHz
delay-line oscillator

Fig. 6.16
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Fig. 6.16 NIST prototype
Optical-fiber 10.6 GHz
delay-line oscillator

Fig. 6.16 (unannotated)
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Fig. 6.18 OEwaves Tidalwave
Optical-fiber 10 GHz
delay-line oscillator

Fig. 6.18
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Fig. 6.18 OEwaves Tidalwave
Optical-fiber 10 GHz
delay-line oscillator

Fig. 6.18 (unannotated)
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Errata Corrige

Acknowledgements

The gratitude I owe to my colleagues and friends who contributed to the rise of the ideas contained in this book is disproportionate to the small size: R. Brendel, G. Brida, G. J. Dick, M. Elia, P. Féron, S. Galliou, V. Giordano, C. A. Greenhall, J. Groslambert, J. L. Hall, V. S. Ilchenko, L. Larger, L. Maleki, A. B. Matsko, M. Oxborrow, S. Römisch, A. B. Savchenkov, F. Vernotte, N. Yu.

Special thanks to L. Maleki for the opportunity of spending four long periods at the JPL and for numerous discussions and suggestions. To G. J. Dick, for giving invaluable ideas and suggestions during numerous and stimulating discussions. To R. Brendel, M. Oxborrow, and S. Römisch for personal effort in reviewing the manuscript, and for a wealth of suggestions and criticism. To V. Giordano for supporting me for more than 10 years, and for his contribution with frequent and stimulating discussions.

I wish to thank the manufacturers and their people and prompt help: J.-P. Aubry from Oscilloquartz; V. Candelier from RAKON (formerly CMAC); C. Hennes from Agilent Technologies; A. Faverio and C. Nasrallah from Miteq; J. H. Searles from Poseidon Scientific Instruments; M. Henderson and L. Maleki from OEwaves.

Thanks to Roberto Bergonzo for the superb picture on the front cover, entitled "The amethyst stairway."