Provisional page, work in progress
Supplementary Material
Open literature
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
- 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.
- 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.
- 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
- 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.
- 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
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Oscilloquartz 8600 5 MHz OCXO
Fig. 6.4
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Oscilloquartz 8600 5 MHz OCXO
Fig. 6.4 (unannotated)
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Oscilloquartz 8607 5 MHz OCXO
Fig. 6.5
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Oscilloquartz 8607 5 MHz OCXO
Fig. 6.5 (unannotated)
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Rakon Pharao 5 MHz OCXO
Fig. 6.6
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Rakon Pharao 5 MHz OCXO
Fig. 6.6 (unannotated)
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FEMTO-ST prototype 10 MHz OCXO
Fig. 6.7
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FEMTO-ST prototype 5 MHz OCXO
Fig. 6.7 (unannotated)
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Agilent 10811 10 MHz OCXO
Fig. 6.8
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Agilent 10811 10 MHz OCXO
Fig. 6.8 (unannotated)
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Agilent prototype 10 MHz OCXO
Fig. 6.9
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Agilent prototype 10 MHz OCXO
Fig. 6.9 (unannotated)
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Wenzel 501-04623 100 MHz OCXO
Fig. 6.10
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Wenzel 501-04623 100 MHz OCXO
Fig. 6.10 (unannotated)
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Miteq D210B 10 GHz DRO
Fig. 6.11
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Miteq D210B 10 GHz DRO
Fig. 6.11 (unannotated)
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Poseidon DRO-10.4 10.4 GHz DRO
Fig. 6.12
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Poseidon DRO-10.4 10.4 GHz DRO
Fig. 6.12 (unannotated)
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Poseidon Shoebox 10 GHz sapphire whispering-gallery oscillator
Fig. 6.14
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Poseidon Shoebox 10 GHz sapphire whispering-gallery oscillator
Fig. 6.14 (unannotated)
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UWA prototype Cryogenic 10 GHz sapphire whispering-gallery oscillator
Fig. 6.15
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UWA prototype Cryogenic 10 GHz sapphire whispering-gallery oscillator
Fig. 6.15 (unannotated)
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NIST prototype Optical-fiber 10.6 GHz delay-line oscillator
Fig. 6.16
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NIST prototype Optical-fiber 10.6 GHz delay-line oscillator
Fig. 6.16 (unannotated)
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OEwaves Tidalwave Optical-fiber 10 GHz delay-line oscillator
Fig. 6.18
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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."
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