Abstract

A photonic-delay line is used as a frequency discriminator for measurement of the phase noise—hence the short-term frequency stability—of microwave oscillators. The scheme is suitable for electronic and photonic oscillators, including the optoelectronic oscillator, mode lock lasers, and other types of rf and microwave pulsed optical sources. The approach is inherently suitable for a wide range of frequency without reconfiguration, which is important for the measurement of tunable oscillators. It is also insensitive to a moderate frequency drift without the need for phase locking.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, "Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations," IEEE J. Quantum Electron. 39, 838-849 (2003).
    [CrossRef]
  4. D. J. Jones, K. W. Holman, M. Notcutt, J. Ye, J. Chandalia, L. A. Jiang, E. P. Ippen, and H. Yokoyama, "Ultralow-jitter, 1550-nm mode-locked semiconductor laser synchronized to a visible optical frequency standard," Opt. Lett. 28, 813-815 (2003).
    [CrossRef] [PubMed]
  5. S. T. Cundiff and J. Ye, "Colloquium: femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342 (2003).
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  13. G. J. Dick and R. T. Wang, "Stability and phase noise tests of two cryo-cooled sapphire oscillators," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1098-1101 (2000).
    [CrossRef]
  14. R. A. Woode, M. E. Tobar, E. N. Ivanov, and D. Blair, "An ultra low noise microwave oscillator based on high Q liquid nitrogen cooled sapphyre resonator," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43, 936-941 (1996).
    [CrossRef]
  15. P.-Y. Bourgeois, Y. Kersalé, N. Bazin, M. Chaubet, and V. Giordano, "Cryogenic open-cavity sapphir resonator for ultra-stable oscillator," Electron. Lett. 39, 780-781 (2003).
    [CrossRef]
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  17. R. A. Campbell, "Stability measurement techniques in the frequency domain," in Proceedings of the IEEE-NASA Symposium on Short Term Frequency Stability, (National Aeronautics and Space Administration, Greenbelt, Md., 1964), pp. 231-235.
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    [CrossRef]
  19. R. V. Pound, "Electronic frequency stabilization of microwave oscillators," Rev. Sci. Instrum. 17, 490-505 (1946).
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  22. D. Halford, A. E. Wainwright, and J. A. Barnes, "Flicker noise of phase in RF amplifiers: characterization, cause, and cure," in Proceedings of the Frequency Control Symposium (Institute of Electrical and Electronics Engineers, New York, 1968), pp. 340-341, abstract only.
  23. F. L. Walls, E. S. Ferre-Pikal, and S. R. Jefferts, "Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 326-334 (1997).
    [CrossRef]
  24. A. Hati, D. Howe, D. Walker, and F. Walls, "Noise figure vs. PM noise measurements: a study at microwave frequencies," in Proceedings of the European Frequency and Time Forum & Frequency Control Symposium Joint Meeting (Institute of Electrical and Electronics Engineers, New York, 2003).
  25. E. Rubiola, E. Salik, N. Yu, and L. Maleki, "Phase noise measurement of low power signals," Electron. Lett. 39, 1389-1390 (2003).
    [CrossRef]
  26. E. Rubiola and V. Giordano, "Advanced interferometric phase and amplitude noise measurements," Rev. Sci. Instrum. 73, 2445-2457 (2002).
    [CrossRef]
  27. X. S. Yao and L. Maleki, "Multiloop optoelectronic oscillator," IEEE J. Quantum Electron. 36, 79-84 (2000).
    [CrossRef]
  28. R. Brendel, G. Marianneau, and J. Ubersfeld, "Phase andamplitude modulation effects in a phase detector using an incorrectly balanced mixer," IEEE Trans. Instrum. Meas. 26, 98-102 (1977).
    [CrossRef]
  29. G. Cibiel, M. Régis, E. Tournier, and O. Llopis, "AM noise impact on low level phase noise measurements," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 784-788 (2002).
    [CrossRef] [PubMed]
  30. W. Shieh, X. S. Yao, L. Maleki, and G. Lutes, "Phase-noise characterization of optoelectronic components by carrier suppression techniques," in Digest of the Optical Fiber Communications Conference (Optical Society of America, Washington, D.C., 1998), pp. 263-264.
  31. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, New York, 1997).
  32. D. B. Leeson, "A simple model of feed back oscillator noise spectrum," Proc. IEEE 54, 329-330 (1966).
    [CrossRef]

2003 (5)

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, "Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations," IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

D. J. Jones, K. W. Holman, M. Notcutt, J. Ye, J. Chandalia, L. A. Jiang, E. P. Ippen, and H. Yokoyama, "Ultralow-jitter, 1550-nm mode-locked semiconductor laser synchronized to a visible optical frequency standard," Opt. Lett. 28, 813-815 (2003).
[CrossRef] [PubMed]

S. T. Cundiff and J. Ye, "Colloquium: femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

P.-Y. Bourgeois, Y. Kersalé, N. Bazin, M. Chaubet, and V. Giordano, "Cryogenic open-cavity sapphir resonator for ultra-stable oscillator," Electron. Lett. 39, 780-781 (2003).
[CrossRef]

E. Rubiola, E. Salik, N. Yu, and L. Maleki, "Phase noise measurement of low power signals," Electron. Lett. 39, 1389-1390 (2003).
[CrossRef]

2002 (2)

E. Rubiola and V. Giordano, "Advanced interferometric phase and amplitude noise measurements," Rev. Sci. Instrum. 73, 2445-2457 (2002).
[CrossRef]

G. Cibiel, M. Régis, E. Tournier, and O. Llopis, "AM noise impact on low level phase noise measurements," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 784-788 (2002).
[CrossRef] [PubMed]

2000 (3)

X. S. Yao and L. Maleki, "Multiloop optoelectronic oscillator," IEEE J. Quantum Electron. 36, 79-84 (2000).
[CrossRef]

X. S. Yao, L. Davis, and L. Maleki, "Coupled optoelectronic oscillators for generating both RF signal and optical pulses," J. Lightwave Technol. 18, 73-78 (2000).
[CrossRef]

G. J. Dick and R. T. Wang, "Stability and phase noise tests of two cryo-cooled sapphire oscillators," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1098-1101 (2000).
[CrossRef]

1997 (1)

F. L. Walls, E. S. Ferre-Pikal, and S. R. Jefferts, "Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 326-334 (1997).
[CrossRef]

1996 (2)

R. A. Woode, M. E. Tobar, E. N. Ivanov, and D. Blair, "An ultra low noise microwave oscillator based on high Q liquid nitrogen cooled sapphyre resonator," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43, 936-941 (1996).
[CrossRef]

X. S. Yao and L. Maleki, "Optoelectronic microwave oscillator," J. Opt. Soc. Am. B 13, 1725-1735 (1996).
[CrossRef]

1982 (1)

F. Labaar, "New discriminator boosts phase noise testing," Microwaves RF 21, 65-69 (1982).

1978 (1)

J. Rutman, "Characterization of phase and frequency instabilities in precision frequency sources: fifteen years of progress," Proc. IEEE 66, 1048-1075 (1978).
[CrossRef]

1977 (1)

R. Brendel, G. Marianneau, and J. Ubersfeld, "Phase andamplitude modulation effects in a phase detector using an incorrectly balanced mixer," IEEE Trans. Instrum. Meas. 26, 98-102 (1977).
[CrossRef]

1968 (3)

J. G. Ondria, "A microwave system for the measurement of AM and PM noise spectra," IEEE Trans. Microwave Theory Tech. 16, 767-781 (1968).
[CrossRef]

M. H. Hines, J. C. R. Collinet, and J. G. Ondria, "FM noise suppression of an injection phase-locked oscillator," IEEE Trans. Microwave Theory Tech. 16, 738-742 (1968).
[CrossRef]

K. Kurokawa, "Noise in synchronized oscillators,"IEEE Trans. Microwave Theory Tech. 16, 234-240 (1968).
[CrossRef]

1966 (1)

D. B. Leeson, "A simple model of feed back oscillator noise spectrum," Proc. IEEE 54, 329-330 (1966).
[CrossRef]

1959 (1)

A. L. Withwell and N. Williams, "A new microwave technique for determining noise spectra at frequencies close to the carrier," Microwave J. 2, 27-32 (1959).

1946 (1)

R. V. Pound, "Electronic frequency stabilization of microwave oscillators," Rev. Sci. Instrum. 17, 490-505 (1946).
[CrossRef] [PubMed]

Abeles, J.

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, "Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations," IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

Audoin, C.

J. Vanier and C. Audoin, The Quantum Physics of Atomic Frequency Standards, (Adam Hilger, Bristol, UK, 1989), vol. 2.
[CrossRef]

Barnes, J. A.

D. Halford, A. E. Wainwright, and J. A. Barnes, "Flicker noise of phase in RF amplifiers: characterization, cause, and cure," in Proceedings of the Frequency Control Symposium (Institute of Electrical and Electronics Engineers, New York, 1968), pp. 340-341, abstract only.

Bazin, N.

P.-Y. Bourgeois, Y. Kersalé, N. Bazin, M. Chaubet, and V. Giordano, "Cryogenic open-cavity sapphir resonator for ultra-stable oscillator," Electron. Lett. 39, 780-781 (2003).
[CrossRef]

Blair, D.

R. A. Woode, M. E. Tobar, E. N. Ivanov, and D. Blair, "An ultra low noise microwave oscillator based on high Q liquid nitrogen cooled sapphyre resonator," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43, 936-941 (1996).
[CrossRef]

Bourgeois, P.-Y.

P.-Y. Bourgeois, Y. Kersalé, N. Bazin, M. Chaubet, and V. Giordano, "Cryogenic open-cavity sapphir resonator for ultra-stable oscillator," Electron. Lett. 39, 780-781 (2003).
[CrossRef]

Braun, A.

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, "Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations," IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

Brendel, R.

R. Brendel, G. Marianneau, and J. Ubersfeld, "Phase andamplitude modulation effects in a phase detector using an incorrectly balanced mixer," IEEE Trans. Instrum. Meas. 26, 98-102 (1977).
[CrossRef]

Campbell, R. A.

R. A. Campbell, "Stability measurement techniques in the frequency domain," in Proceedings of the IEEE-NASA Symposium on Short Term Frequency Stability, (National Aeronautics and Space Administration, Greenbelt, Md., 1964), pp. 231-235.

Chandalia, J.

Chaubet, M.

P.-Y. Bourgeois, Y. Kersalé, N. Bazin, M. Chaubet, and V. Giordano, "Cryogenic open-cavity sapphir resonator for ultra-stable oscillator," Electron. Lett. 39, 780-781 (2003).
[CrossRef]

Cibiel, G.

G. Cibiel, M. Régis, E. Tournier, and O. Llopis, "AM noise impact on low level phase noise measurements," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 784-788 (2002).
[CrossRef] [PubMed]

Collinet, J. C. R.

M. H. Hines, J. C. R. Collinet, and J. G. Ondria, "FM noise suppression of an injection phase-locked oscillator," IEEE Trans. Microwave Theory Tech. 16, 738-742 (1968).
[CrossRef]

Cundiff, S. T.

S. T. Cundiff and J. Ye, "Colloquium: femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

Davis, L.

Delfyett, P. J.

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, "Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations," IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

Depriest, C. M.

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, "Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations," IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

Dick, G. J.

G. J. Dick and R. T. Wang, "Stability and phase noise tests of two cryo-cooled sapphire oscillators," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1098-1101 (2000).
[CrossRef]

Ferre-Pikal, E. S.

F. L. Walls, E. S. Ferre-Pikal, and S. R. Jefferts, "Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 326-334 (1997).
[CrossRef]

Giordano, V.

P.-Y. Bourgeois, Y. Kersalé, N. Bazin, M. Chaubet, and V. Giordano, "Cryogenic open-cavity sapphir resonator for ultra-stable oscillator," Electron. Lett. 39, 780-781 (2003).
[CrossRef]

E. Rubiola and V. Giordano, "Advanced interferometric phase and amplitude noise measurements," Rev. Sci. Instrum. 73, 2445-2457 (2002).
[CrossRef]

Halford, D.

D. Halford, A. E. Wainwright, and J. A. Barnes, "Flicker noise of phase in RF amplifiers: characterization, cause, and cure," in Proceedings of the Frequency Control Symposium (Institute of Electrical and Electronics Engineers, New York, 1968), pp. 340-341, abstract only.

Hati, A.

A. Hati, D. Howe, D. Walker, and F. Walls, "Noise figure vs. PM noise measurements: a study at microwave frequencies," in Proceedings of the European Frequency and Time Forum & Frequency Control Symposium Joint Meeting (Institute of Electrical and Electronics Engineers, New York, 2003).

Hines, M. H.

M. H. Hines, J. C. R. Collinet, and J. G. Ondria, "FM noise suppression of an injection phase-locked oscillator," IEEE Trans. Microwave Theory Tech. 16, 738-742 (1968).
[CrossRef]

Holman, K. W.

Howe, D.

A. Hati, D. Howe, D. Walker, and F. Walls, "Noise figure vs. PM noise measurements: a study at microwave frequencies," in Proceedings of the European Frequency and Time Forum & Frequency Control Symposium Joint Meeting (Institute of Electrical and Electronics Engineers, New York, 2003).

Ippen, E. P.

Ivanov, E. N.

R. A. Woode, M. E. Tobar, E. N. Ivanov, and D. Blair, "An ultra low noise microwave oscillator based on high Q liquid nitrogen cooled sapphyre resonator," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43, 936-941 (1996).
[CrossRef]

Jefferts, S. R.

F. L. Walls, E. S. Ferre-Pikal, and S. R. Jefferts, "Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 326-334 (1997).
[CrossRef]

Jiang, L. A.

Jones, D. J.

Kersalé, Y.

P.-Y. Bourgeois, Y. Kersalé, N. Bazin, M. Chaubet, and V. Giordano, "Cryogenic open-cavity sapphir resonator for ultra-stable oscillator," Electron. Lett. 39, 780-781 (2003).
[CrossRef]

Kurokawa, K.

K. Kurokawa, "Noise in synchronized oscillators,"IEEE Trans. Microwave Theory Tech. 16, 234-240 (1968).
[CrossRef]

Labaar, F.

F. Labaar, "New discriminator boosts phase noise testing," Microwaves RF 21, 65-69 (1982).

A. L. Lance, W. D. Seal, and F. Labaar, "Phase noise and AM noise measurements in the frequency domain," in Infrared and Millimeter Waves, K.J.Button, ed., (Academic, New York, 1984), vol. 11, pp. 239-284.

Lance, A. L.

A. L. Lance, W. D. Seal, and F. Labaar, "Phase noise and AM noise measurements in the frequency domain," in Infrared and Millimeter Waves, K.J.Button, ed., (Academic, New York, 1984), vol. 11, pp. 239-284.

Leeson, D. B.

D. B. Leeson, "A simple model of feed back oscillator noise spectrum," Proc. IEEE 54, 329-330 (1966).
[CrossRef]

Llopis, O.

G. Cibiel, M. Régis, E. Tournier, and O. Llopis, "AM noise impact on low level phase noise measurements," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 784-788 (2002).
[CrossRef] [PubMed]

Lutes, G.

W. Shieh, X. S. Yao, L. Maleki, and G. Lutes, "Phase-noise characterization of optoelectronic components by carrier suppression techniques," in Digest of the Optical Fiber Communications Conference (Optical Society of America, Washington, D.C., 1998), pp. 263-264.

Maleki, L.

E. Rubiola, E. Salik, N. Yu, and L. Maleki, "Phase noise measurement of low power signals," Electron. Lett. 39, 1389-1390 (2003).
[CrossRef]

X. S. Yao and L. Maleki, "Multiloop optoelectronic oscillator," IEEE J. Quantum Electron. 36, 79-84 (2000).
[CrossRef]

X. S. Yao, L. Davis, and L. Maleki, "Coupled optoelectronic oscillators for generating both RF signal and optical pulses," J. Lightwave Technol. 18, 73-78 (2000).
[CrossRef]

X. S. Yao and L. Maleki, "Optoelectronic microwave oscillator," J. Opt. Soc. Am. B 13, 1725-1735 (1996).
[CrossRef]

W. Shieh, X. S. Yao, L. Maleki, and G. Lutes, "Phase-noise characterization of optoelectronic components by carrier suppression techniques," in Digest of the Optical Fiber Communications Conference (Optical Society of America, Washington, D.C., 1998), pp. 263-264.

Marianneau, G.

R. Brendel, G. Marianneau, and J. Ubersfeld, "Phase andamplitude modulation effects in a phase detector using an incorrectly balanced mixer," IEEE Trans. Instrum. Meas. 26, 98-102 (1977).
[CrossRef]

Notcutt, M.

Ondria, J. G.

J. G. Ondria, "A microwave system for the measurement of AM and PM noise spectra," IEEE Trans. Microwave Theory Tech. 16, 767-781 (1968).
[CrossRef]

M. H. Hines, J. C. R. Collinet, and J. G. Ondria, "FM noise suppression of an injection phase-locked oscillator," IEEE Trans. Microwave Theory Tech. 16, 738-742 (1968).
[CrossRef]

Pound, R. V.

R. V. Pound, "Electronic frequency stabilization of microwave oscillators," Rev. Sci. Instrum. 17, 490-505 (1946).
[CrossRef] [PubMed]

Régis, M.

G. Cibiel, M. Régis, E. Tournier, and O. Llopis, "AM noise impact on low level phase noise measurements," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 784-788 (2002).
[CrossRef] [PubMed]

Rubiola, E.

E. Rubiola, E. Salik, N. Yu, and L. Maleki, "Phase noise measurement of low power signals," Electron. Lett. 39, 1389-1390 (2003).
[CrossRef]

E. Rubiola and V. Giordano, "Advanced interferometric phase and amplitude noise measurements," Rev. Sci. Instrum. 73, 2445-2457 (2002).
[CrossRef]

Rutman, J.

J. Rutman, "Characterization of phase and frequency instabilities in precision frequency sources: fifteen years of progress," Proc. IEEE 66, 1048-1075 (1978).
[CrossRef]

Salik, E.

E. Rubiola, E. Salik, N. Yu, and L. Maleki, "Phase noise measurement of low power signals," Electron. Lett. 39, 1389-1390 (2003).
[CrossRef]

Seal, W. D.

A. L. Lance, W. D. Seal, and F. Labaar, "Phase noise and AM noise measurements in the frequency domain," in Infrared and Millimeter Waves, K.J.Button, ed., (Academic, New York, 1984), vol. 11, pp. 239-284.

Shieh, W.

W. Shieh, X. S. Yao, L. Maleki, and G. Lutes, "Phase-noise characterization of optoelectronic components by carrier suppression techniques," in Digest of the Optical Fiber Communications Conference (Optical Society of America, Washington, D.C., 1998), pp. 263-264.

Tobar, M. E.

R. A. Woode, M. E. Tobar, E. N. Ivanov, and D. Blair, "An ultra low noise microwave oscillator based on high Q liquid nitrogen cooled sapphyre resonator," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43, 936-941 (1996).
[CrossRef]

Tournier, E.

G. Cibiel, M. Régis, E. Tournier, and O. Llopis, "AM noise impact on low level phase noise measurements," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 784-788 (2002).
[CrossRef] [PubMed]

Ubersfeld, J.

R. Brendel, G. Marianneau, and J. Ubersfeld, "Phase andamplitude modulation effects in a phase detector using an incorrectly balanced mixer," IEEE Trans. Instrum. Meas. 26, 98-102 (1977).
[CrossRef]

Vanier, J.

J. Vanier and C. Audoin, The Quantum Physics of Atomic Frequency Standards, (Adam Hilger, Bristol, UK, 1989), vol. 2.
[CrossRef]

Vig, J. R.

J. R. Vig, IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology-Random Instabilities (IEEE Standard 1139-1999) (IEEE, New York, 1999).

Wainwright, A. E.

D. Halford, A. E. Wainwright, and J. A. Barnes, "Flicker noise of phase in RF amplifiers: characterization, cause, and cure," in Proceedings of the Frequency Control Symposium (Institute of Electrical and Electronics Engineers, New York, 1968), pp. 340-341, abstract only.

Walker, D.

A. Hati, D. Howe, D. Walker, and F. Walls, "Noise figure vs. PM noise measurements: a study at microwave frequencies," in Proceedings of the European Frequency and Time Forum & Frequency Control Symposium Joint Meeting (Institute of Electrical and Electronics Engineers, New York, 2003).

Walls, F.

A. Hati, D. Howe, D. Walker, and F. Walls, "Noise figure vs. PM noise measurements: a study at microwave frequencies," in Proceedings of the European Frequency and Time Forum & Frequency Control Symposium Joint Meeting (Institute of Electrical and Electronics Engineers, New York, 2003).

Walls, F. L.

F. L. Walls, E. S. Ferre-Pikal, and S. R. Jefferts, "Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 326-334 (1997).
[CrossRef]

Wang, R. T.

G. J. Dick and R. T. Wang, "Stability and phase noise tests of two cryo-cooled sapphire oscillators," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1098-1101 (2000).
[CrossRef]

Williams, N.

A. L. Withwell and N. Williams, "A new microwave technique for determining noise spectra at frequencies close to the carrier," Microwave J. 2, 27-32 (1959).

Withwell, A. L.

A. L. Withwell and N. Williams, "A new microwave technique for determining noise spectra at frequencies close to the carrier," Microwave J. 2, 27-32 (1959).

Woode, R. A.

R. A. Woode, M. E. Tobar, E. N. Ivanov, and D. Blair, "An ultra low noise microwave oscillator based on high Q liquid nitrogen cooled sapphyre resonator," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 43, 936-941 (1996).
[CrossRef]

Yao, X. S.

X. S. Yao and L. Maleki, "Multiloop optoelectronic oscillator," IEEE J. Quantum Electron. 36, 79-84 (2000).
[CrossRef]

X. S. Yao, L. Davis, and L. Maleki, "Coupled optoelectronic oscillators for generating both RF signal and optical pulses," J. Lightwave Technol. 18, 73-78 (2000).
[CrossRef]

X. S. Yao and L. Maleki, "Optoelectronic microwave oscillator," J. Opt. Soc. Am. B 13, 1725-1735 (1996).
[CrossRef]

W. Shieh, X. S. Yao, L. Maleki, and G. Lutes, "Phase-noise characterization of optoelectronic components by carrier suppression techniques," in Digest of the Optical Fiber Communications Conference (Optical Society of America, Washington, D.C., 1998), pp. 263-264.

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, New York, 1997).

Ye, J.

Yilmaz, T. A.

T. A. Yilmaz, C. M. Depriest, A. Braun, J. Abeles, and P. J. Delfyett, "Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations," IEEE J. Quantum Electron. 39, 838-849 (2003).
[CrossRef]

Yokoyama, H.

Yu, N.

E. Rubiola, E. Salik, N. Yu, and L. Maleki, "Phase noise measurement of low power signals," Electron. Lett. 39, 1389-1390 (2003).
[CrossRef]

Electron. Lett. (2)

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Figures (10)

Fig. 1
Fig. 1

Oscillator phase noise.

Fig. 2
Fig. 2

Usual schemes for the measurement of S ϕ ( f ) . (A) simple phase-noise measurement, (B) beat-frequency phase-noise measurement.

Fig. 3
Fig. 3

Delay-line homodyne method. (A) time domain, (B) Laplace transform domain.

Fig. 4
Fig. 4

Transfer functions H ϕ ( j f ) 2 and H y ( j f ) 2 plotted for ν 0 = 10 GHz and τ d = 10 μ s .

Fig. 5
Fig. 5

Noise floor as a function of the optical power. The threshold power depends on the noise figure F.

Fig. 6
Fig. 6

Comparison between phase-noise measurement methods. The white noise of the amplifier pair also includes shot noise, calculated from the optical power that gives P μ with m = 1 and η = 0.6 .

Fig. 7
Fig. 7

Scheme of the instrument.

Fig. 8
Fig. 8

Measurement of a multiplied quartz oscillator.

Fig. 9
Fig. 9

Measurement of the multiplied quartz oscillator of Fig. 8, reproduced with a different experimental configuration.

Fig. 10
Fig. 10

Measurement of a photonic oscillator.

Equations (28)

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v ( t ) = V 0 [ 1 + α ( t ) ] cos [ 2 π ν 0 t + ϕ ( t ) ] .
σ y 2 ( τ ) = 1 2 ( y ¯ k + 1 y ¯ k ) 2 ¯ ,
S ϕ ( f ) = i 0 b i f i ,
Φ o ( s ) = H ϕ ( s ) Φ i ( s ) ,
S ϕ o ( f ) = H ϕ ( j f ) 2 S ϕ i ( f ) ,
H ϕ ( j f ) 2 = 4 sin 2 ( π f τ ) .
S y ( f ) = f 2 ν 0 2 S ϕ i ( f ) .
S y ( f ) = H y ( j f ) 2 S ϕ i ( f ) ,
H y ( j f ) 2 = 4 ν 0 2 f 2 sin 2 ( π f τ ) .
P λ ( t ) = P ¯ λ ( 1 + m cos ω μ t ) .
i ( t ) = q η h ν λ P ¯ λ ( 1 + m cos ω μ t ) ,
P ¯ μ = 1 2 m 2 R 0 ( q η h ν λ ) 2 P ¯ λ 2 .
N s = 2 q 2 η h ν λ P ¯ λ R 0 .
N t = F k B T 0 ,
S ϕ 0 = 2 m 2 [ 2 h ν λ η 1 P ¯ λ + F k B T 0 R 0 ( h ν λ q η ) 2 ( 1 P ¯ λ ) 2 ] .
S ϕ 0 = 16 m 2 [ h ν λ η 1 P ¯ λ + F k B T 0 R 0 ( h ν λ q η ) 2 ( 1 P ¯ λ ) 2 ] .
P λ , t = F k B T 0 R 0 h ν λ q 2 η .
T = 1 2 + 1 2 sin π υ V π ,
T ( t ) = 1 2 [ 1 + 2 J 1 ( π V p V π ) cos ω μ t + ] ,
sin ( z cos θ ) = 2 k = 0 ( 1 ) k J 2 k + 1 cos [ ( 2 k + 1 ) θ ] .
m = 2 J 1 ( π V p V π ) .
S ϕ i ( f ) = ( 1 2 π τ d ) 2 1 f 2 S ϕ o ( f ) ,
S ϕ l ( f ) = [ 1 + ν 0 2 4 Q 2 1 f 2 ] S ϕ a ( f ) ,
S ϕ l ( f ) = ( 1 2 π τ d ) 2 1 f 2 S ϕ a ( f ) .
S ϕ ( f ) = 1.66 × 10 1 f 3 + 3 × 10 4 f 2 + 7.7 × 10 12 ,
σ y ( τ ) = 4.9 × 10 11 + 1.24 × 10 12 τ
S ϕ ( f ) = 8 × 10 1 f 3 + 1.2 × 10 3 f 2 ,
σ y ( τ ) = 1 × 10 10 + 2.4 × 10 12 τ .

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