Abstract

A new approach to optical analog-to-digital (A/D) conversion based on oversampling and interpolative coding techniques is described, and both interferometric and noninterferometric architectures based on this method are presented. This new approach combines the high resolution of classical oversampled A/D conversion with the high speed of optical processing technology to extend the resolution and conversion rates beyond that currently possible with other electronic or optical converters. The proposed optical converters are simple, consisting of multiple quantum well self-electro-optic effect devices, photodetectors, and common optical components that are capable of operating at sampling rates of up to 15 Gbits/s and that can provide scalable resolutions of 16 and 8 bits at a conversion rate of 117 and 938 MHz, respectively.

© 1992 Optical Society of America

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  1. H. F. Taylor, “An electrooptic analog-to-digital converter,” Proc. IEEE 63, 1524–1525 (1975).
    [CrossRef]
  2. R. A. Becker, C. E. Woodward, F. J. Leonberger, R. W. Williamson, “Wideband electrooptic guided-wave analog-to-digital converters,” Proc. IEEE 72, 802–819 (1984).
    [CrossRef]
  3. H. Inose, Y. Yasuda, “A unity bit coding method by negative feedback,” Proc. IEEE 51, 1524–1535 (1963).
    [CrossRef]
  4. J. C. Candy, “A use of limit cycle oscillations to obtain robust analog-to-digital converters,” IEEE Trans. Commun. COM-22, 298–305 (1974).
    [CrossRef]
  5. R. Floyd, L. Steinberg, “An adaptive algorithm for spatial gray scale,” Soc. Inf. Disp. Digest 36, 36–37 (1975).
  6. D. Anastassiou, “Error diffusion coding for A/D conversion,” IEEE Trans. Circuits Syst. 36, 1175–1186 (1989).
    [CrossRef]
  7. S. K. Tewksbury, R. W. Hallock, “Oversampled, linear predictive and noise shaping coders of order N > 1,” IEEE Trans. Circuits Syst. CAS-25, 436–447 (1978).
    [CrossRef]
  8. R. M. Gray, “Quantization noise spectra,” IEEE Trans. Inf. Theory 36, 1220–1244 (1990).
    [CrossRef]
  9. K. Uchimura, T. Hayashi, T. Kimura, A. Iwata, “Oversampled A-to-D and D-to-A converters with multistage noise shaping modulators,” IEEE Trans. Acoust. Speech Signal Process. 36, 1899–1905 (1988).
    [CrossRef]
  10. J. C. Candy, “Decimation for sigma-delta modulation,” IEEE Trans. Commun. COM-34, 72–76 (1986).
    [CrossRef]
  11. J. C. Candy, B. A. Wooley, O. J. Benjamin, “A voiceband codec with digital filtering,” IEEE Trans. Commun. COM-29, 815–830 (1981).
    [CrossRef]
  12. B. E. Boser, “Design and implementation of oversampled analog-to-digital converters,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1988).
  13. A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set-reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
    [CrossRef]
  14. J. E. Bowers, P. A. Morton, A. Mar, S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25, 1426–1439 (1989).
    [CrossRef]
  15. G. D. Boyd, A. M. Fox, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, J. M. Kuo, R. F. Kopf, A. L. Lentine, “33 ps optical switching of symmetric self-electro-optic effect devices,” Appl. Phys. Lett. 57, 1843–1845 (1990).
    [CrossRef]
  16. D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, “The quantum well self-electrooptic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1475 (1985).
    [CrossRef]
  17. D. A. B. Miller, AT&T Bell Laboratories, Holmdel, N.J. 07733 (personal communication).
  18. D. A. B. Miller, “Quantum-well self-electro-optic effect devices,” Opt. Quantum Electron. 22, S61–S98 (1990).
  19. J. A. Bell, M. C. Hamilton, D. A. Leep, T. D. Morgan, H. F. Taylor, Y.-H. Lee, “Extention of electronic A/D converters to multi-gigahertz sampling rates using optical sampling and demultiplexing techniques,” in 23rd Asilomar Conference on Signals, Systems, and Computers (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 289–293.
  20. B. A. Wooley, Department of Electrical Engineering, Stanford University, Stanford, Calif. 94305 (personal communication).

1990 (3)

R. M. Gray, “Quantization noise spectra,” IEEE Trans. Inf. Theory 36, 1220–1244 (1990).
[CrossRef]

G. D. Boyd, A. M. Fox, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, J. M. Kuo, R. F. Kopf, A. L. Lentine, “33 ps optical switching of symmetric self-electro-optic effect devices,” Appl. Phys. Lett. 57, 1843–1845 (1990).
[CrossRef]

D. A. B. Miller, “Quantum-well self-electro-optic effect devices,” Opt. Quantum Electron. 22, S61–S98 (1990).

1989 (3)

D. Anastassiou, “Error diffusion coding for A/D conversion,” IEEE Trans. Circuits Syst. 36, 1175–1186 (1989).
[CrossRef]

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set-reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

J. E. Bowers, P. A. Morton, A. Mar, S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25, 1426–1439 (1989).
[CrossRef]

1988 (1)

K. Uchimura, T. Hayashi, T. Kimura, A. Iwata, “Oversampled A-to-D and D-to-A converters with multistage noise shaping modulators,” IEEE Trans. Acoust. Speech Signal Process. 36, 1899–1905 (1988).
[CrossRef]

1986 (1)

J. C. Candy, “Decimation for sigma-delta modulation,” IEEE Trans. Commun. COM-34, 72–76 (1986).
[CrossRef]

1985 (1)

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, “The quantum well self-electrooptic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1475 (1985).
[CrossRef]

1984 (1)

R. A. Becker, C. E. Woodward, F. J. Leonberger, R. W. Williamson, “Wideband electrooptic guided-wave analog-to-digital converters,” Proc. IEEE 72, 802–819 (1984).
[CrossRef]

1981 (1)

J. C. Candy, B. A. Wooley, O. J. Benjamin, “A voiceband codec with digital filtering,” IEEE Trans. Commun. COM-29, 815–830 (1981).
[CrossRef]

1978 (1)

S. K. Tewksbury, R. W. Hallock, “Oversampled, linear predictive and noise shaping coders of order N > 1,” IEEE Trans. Circuits Syst. CAS-25, 436–447 (1978).
[CrossRef]

1975 (2)

R. Floyd, L. Steinberg, “An adaptive algorithm for spatial gray scale,” Soc. Inf. Disp. Digest 36, 36–37 (1975).

H. F. Taylor, “An electrooptic analog-to-digital converter,” Proc. IEEE 63, 1524–1525 (1975).
[CrossRef]

1974 (1)

J. C. Candy, “A use of limit cycle oscillations to obtain robust analog-to-digital converters,” IEEE Trans. Commun. COM-22, 298–305 (1974).
[CrossRef]

1963 (1)

H. Inose, Y. Yasuda, “A unity bit coding method by negative feedback,” Proc. IEEE 51, 1524–1535 (1963).
[CrossRef]

Anastassiou, D.

D. Anastassiou, “Error diffusion coding for A/D conversion,” IEEE Trans. Circuits Syst. 36, 1175–1186 (1989).
[CrossRef]

Becker, R. A.

R. A. Becker, C. E. Woodward, F. J. Leonberger, R. W. Williamson, “Wideband electrooptic guided-wave analog-to-digital converters,” Proc. IEEE 72, 802–819 (1984).
[CrossRef]

Bell, J. A.

J. A. Bell, M. C. Hamilton, D. A. Leep, T. D. Morgan, H. F. Taylor, Y.-H. Lee, “Extention of electronic A/D converters to multi-gigahertz sampling rates using optical sampling and demultiplexing techniques,” in 23rd Asilomar Conference on Signals, Systems, and Computers (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 289–293.

Benjamin, O. J.

J. C. Candy, B. A. Wooley, O. J. Benjamin, “A voiceband codec with digital filtering,” IEEE Trans. Commun. COM-29, 815–830 (1981).
[CrossRef]

Boser, B. E.

B. E. Boser, “Design and implementation of oversampled analog-to-digital converters,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1988).

Bowers, J. E.

J. E. Bowers, P. A. Morton, A. Mar, S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25, 1426–1439 (1989).
[CrossRef]

Boyd, G. D.

G. D. Boyd, A. M. Fox, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, J. M. Kuo, R. F. Kopf, A. L. Lentine, “33 ps optical switching of symmetric self-electro-optic effect devices,” Appl. Phys. Lett. 57, 1843–1845 (1990).
[CrossRef]

Burrus, C. A.

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, “The quantum well self-electrooptic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1475 (1985).
[CrossRef]

Candy, J. C.

J. C. Candy, “Decimation for sigma-delta modulation,” IEEE Trans. Commun. COM-34, 72–76 (1986).
[CrossRef]

J. C. Candy, B. A. Wooley, O. J. Benjamin, “A voiceband codec with digital filtering,” IEEE Trans. Commun. COM-29, 815–830 (1981).
[CrossRef]

J. C. Candy, “A use of limit cycle oscillations to obtain robust analog-to-digital converters,” IEEE Trans. Commun. COM-22, 298–305 (1974).
[CrossRef]

Chemla, D. S.

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, “The quantum well self-electrooptic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1475 (1985).
[CrossRef]

Chirovsky, L. M. F.

G. D. Boyd, A. M. Fox, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, J. M. Kuo, R. F. Kopf, A. L. Lentine, “33 ps optical switching of symmetric self-electro-optic effect devices,” Appl. Phys. Lett. 57, 1843–1845 (1990).
[CrossRef]

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set-reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

Corzine, S. W.

J. E. Bowers, P. A. Morton, A. Mar, S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25, 1426–1439 (1989).
[CrossRef]

Cunningham, J. E.

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set-reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

D’Asaro, L. A.

G. D. Boyd, A. M. Fox, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, J. M. Kuo, R. F. Kopf, A. L. Lentine, “33 ps optical switching of symmetric self-electro-optic effect devices,” Appl. Phys. Lett. 57, 1843–1845 (1990).
[CrossRef]

Damen, T. C.

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, “The quantum well self-electrooptic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1475 (1985).
[CrossRef]

Floyd, R.

R. Floyd, L. Steinberg, “An adaptive algorithm for spatial gray scale,” Soc. Inf. Disp. Digest 36, 36–37 (1975).

Fox, A. M.

G. D. Boyd, A. M. Fox, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, J. M. Kuo, R. F. Kopf, A. L. Lentine, “33 ps optical switching of symmetric self-electro-optic effect devices,” Appl. Phys. Lett. 57, 1843–1845 (1990).
[CrossRef]

Gossard, A. C.

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, “The quantum well self-electrooptic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1475 (1985).
[CrossRef]

Gray, R. M.

R. M. Gray, “Quantization noise spectra,” IEEE Trans. Inf. Theory 36, 1220–1244 (1990).
[CrossRef]

Hallock, R. W.

S. K. Tewksbury, R. W. Hallock, “Oversampled, linear predictive and noise shaping coders of order N > 1,” IEEE Trans. Circuits Syst. CAS-25, 436–447 (1978).
[CrossRef]

Hamilton, M. C.

J. A. Bell, M. C. Hamilton, D. A. Leep, T. D. Morgan, H. F. Taylor, Y.-H. Lee, “Extention of electronic A/D converters to multi-gigahertz sampling rates using optical sampling and demultiplexing techniques,” in 23rd Asilomar Conference on Signals, Systems, and Computers (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 289–293.

Hayashi, T.

K. Uchimura, T. Hayashi, T. Kimura, A. Iwata, “Oversampled A-to-D and D-to-A converters with multistage noise shaping modulators,” IEEE Trans. Acoust. Speech Signal Process. 36, 1899–1905 (1988).
[CrossRef]

Henry, J. E.

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set-reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

Hinton, H. S.

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set-reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

Inose, H.

H. Inose, Y. Yasuda, “A unity bit coding method by negative feedback,” Proc. IEEE 51, 1524–1535 (1963).
[CrossRef]

Iwata, A.

K. Uchimura, T. Hayashi, T. Kimura, A. Iwata, “Oversampled A-to-D and D-to-A converters with multistage noise shaping modulators,” IEEE Trans. Acoust. Speech Signal Process. 36, 1899–1905 (1988).
[CrossRef]

Kimura, T.

K. Uchimura, T. Hayashi, T. Kimura, A. Iwata, “Oversampled A-to-D and D-to-A converters with multistage noise shaping modulators,” IEEE Trans. Acoust. Speech Signal Process. 36, 1899–1905 (1988).
[CrossRef]

Kopf, R. F.

G. D. Boyd, A. M. Fox, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, J. M. Kuo, R. F. Kopf, A. L. Lentine, “33 ps optical switching of symmetric self-electro-optic effect devices,” Appl. Phys. Lett. 57, 1843–1845 (1990).
[CrossRef]

Kuo, J. M.

G. D. Boyd, A. M. Fox, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, J. M. Kuo, R. F. Kopf, A. L. Lentine, “33 ps optical switching of symmetric self-electro-optic effect devices,” Appl. Phys. Lett. 57, 1843–1845 (1990).
[CrossRef]

Lee, Y.-H.

J. A. Bell, M. C. Hamilton, D. A. Leep, T. D. Morgan, H. F. Taylor, Y.-H. Lee, “Extention of electronic A/D converters to multi-gigahertz sampling rates using optical sampling and demultiplexing techniques,” in 23rd Asilomar Conference on Signals, Systems, and Computers (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 289–293.

Leep, D. A.

J. A. Bell, M. C. Hamilton, D. A. Leep, T. D. Morgan, H. F. Taylor, Y.-H. Lee, “Extention of electronic A/D converters to multi-gigahertz sampling rates using optical sampling and demultiplexing techniques,” in 23rd Asilomar Conference on Signals, Systems, and Computers (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 289–293.

Lentine, A. L.

G. D. Boyd, A. M. Fox, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, J. M. Kuo, R. F. Kopf, A. L. Lentine, “33 ps optical switching of symmetric self-electro-optic effect devices,” Appl. Phys. Lett. 57, 1843–1845 (1990).
[CrossRef]

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set-reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

Leonberger, F. J.

R. A. Becker, C. E. Woodward, F. J. Leonberger, R. W. Williamson, “Wideband electrooptic guided-wave analog-to-digital converters,” Proc. IEEE 72, 802–819 (1984).
[CrossRef]

Mar, A.

J. E. Bowers, P. A. Morton, A. Mar, S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25, 1426–1439 (1989).
[CrossRef]

Miller, D. A. B.

G. D. Boyd, A. M. Fox, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, J. M. Kuo, R. F. Kopf, A. L. Lentine, “33 ps optical switching of symmetric self-electro-optic effect devices,” Appl. Phys. Lett. 57, 1843–1845 (1990).
[CrossRef]

D. A. B. Miller, “Quantum-well self-electro-optic effect devices,” Opt. Quantum Electron. 22, S61–S98 (1990).

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set-reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, “The quantum well self-electrooptic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1475 (1985).
[CrossRef]

D. A. B. Miller, AT&T Bell Laboratories, Holmdel, N.J. 07733 (personal communication).

Morgan, T. D.

J. A. Bell, M. C. Hamilton, D. A. Leep, T. D. Morgan, H. F. Taylor, Y.-H. Lee, “Extention of electronic A/D converters to multi-gigahertz sampling rates using optical sampling and demultiplexing techniques,” in 23rd Asilomar Conference on Signals, Systems, and Computers (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 289–293.

Morton, P. A.

J. E. Bowers, P. A. Morton, A. Mar, S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25, 1426–1439 (1989).
[CrossRef]

Steinberg, L.

R. Floyd, L. Steinberg, “An adaptive algorithm for spatial gray scale,” Soc. Inf. Disp. Digest 36, 36–37 (1975).

Taylor, H. F.

H. F. Taylor, “An electrooptic analog-to-digital converter,” Proc. IEEE 63, 1524–1525 (1975).
[CrossRef]

J. A. Bell, M. C. Hamilton, D. A. Leep, T. D. Morgan, H. F. Taylor, Y.-H. Lee, “Extention of electronic A/D converters to multi-gigahertz sampling rates using optical sampling and demultiplexing techniques,” in 23rd Asilomar Conference on Signals, Systems, and Computers (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 289–293.

Tewksbury, S. K.

S. K. Tewksbury, R. W. Hallock, “Oversampled, linear predictive and noise shaping coders of order N > 1,” IEEE Trans. Circuits Syst. CAS-25, 436–447 (1978).
[CrossRef]

Uchimura, K.

K. Uchimura, T. Hayashi, T. Kimura, A. Iwata, “Oversampled A-to-D and D-to-A converters with multistage noise shaping modulators,” IEEE Trans. Acoust. Speech Signal Process. 36, 1899–1905 (1988).
[CrossRef]

Wiegmann, W.

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, “The quantum well self-electrooptic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1475 (1985).
[CrossRef]

Williamson, R. W.

R. A. Becker, C. E. Woodward, F. J. Leonberger, R. W. Williamson, “Wideband electrooptic guided-wave analog-to-digital converters,” Proc. IEEE 72, 802–819 (1984).
[CrossRef]

Wood, T. H.

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, “The quantum well self-electrooptic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1475 (1985).
[CrossRef]

Woodward, C. E.

R. A. Becker, C. E. Woodward, F. J. Leonberger, R. W. Williamson, “Wideband electrooptic guided-wave analog-to-digital converters,” Proc. IEEE 72, 802–819 (1984).
[CrossRef]

Wooley, B. A.

J. C. Candy, B. A. Wooley, O. J. Benjamin, “A voiceband codec with digital filtering,” IEEE Trans. Commun. COM-29, 815–830 (1981).
[CrossRef]

B. A. Wooley, Department of Electrical Engineering, Stanford University, Stanford, Calif. 94305 (personal communication).

Yasuda, Y.

H. Inose, Y. Yasuda, “A unity bit coding method by negative feedback,” Proc. IEEE 51, 1524–1535 (1963).
[CrossRef]

Appl. Phys. Lett. (1)

G. D. Boyd, A. M. Fox, D. A. B. Miller, L. M. F. Chirovsky, L. A. D’Asaro, J. M. Kuo, R. F. Kopf, A. L. Lentine, “33 ps optical switching of symmetric self-electro-optic effect devices,” Appl. Phys. Lett. 57, 1843–1845 (1990).
[CrossRef]

IEEE J. Quantum Electron. (3)

D. A. B. Miller, D. S. Chemla, T. C. Damen, T. H. Wood, C. A. Burrus, A. C. Gossard, W. Wiegmann, “The quantum well self-electrooptic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1475 (1985).
[CrossRef]

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set-reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

J. E. Bowers, P. A. Morton, A. Mar, S. W. Corzine, “Actively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 25, 1426–1439 (1989).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (1)

K. Uchimura, T. Hayashi, T. Kimura, A. Iwata, “Oversampled A-to-D and D-to-A converters with multistage noise shaping modulators,” IEEE Trans. Acoust. Speech Signal Process. 36, 1899–1905 (1988).
[CrossRef]

IEEE Trans. Circuits Syst. (2)

D. Anastassiou, “Error diffusion coding for A/D conversion,” IEEE Trans. Circuits Syst. 36, 1175–1186 (1989).
[CrossRef]

S. K. Tewksbury, R. W. Hallock, “Oversampled, linear predictive and noise shaping coders of order N > 1,” IEEE Trans. Circuits Syst. CAS-25, 436–447 (1978).
[CrossRef]

IEEE Trans. Commun. (3)

J. C. Candy, “Decimation for sigma-delta modulation,” IEEE Trans. Commun. COM-34, 72–76 (1986).
[CrossRef]

J. C. Candy, B. A. Wooley, O. J. Benjamin, “A voiceband codec with digital filtering,” IEEE Trans. Commun. COM-29, 815–830 (1981).
[CrossRef]

J. C. Candy, “A use of limit cycle oscillations to obtain robust analog-to-digital converters,” IEEE Trans. Commun. COM-22, 298–305 (1974).
[CrossRef]

IEEE Trans. Inf. Theory (1)

R. M. Gray, “Quantization noise spectra,” IEEE Trans. Inf. Theory 36, 1220–1244 (1990).
[CrossRef]

Opt. Quantum Electron. (1)

D. A. B. Miller, “Quantum-well self-electro-optic effect devices,” Opt. Quantum Electron. 22, S61–S98 (1990).

Proc. IEEE (3)

H. F. Taylor, “An electrooptic analog-to-digital converter,” Proc. IEEE 63, 1524–1525 (1975).
[CrossRef]

R. A. Becker, C. E. Woodward, F. J. Leonberger, R. W. Williamson, “Wideband electrooptic guided-wave analog-to-digital converters,” Proc. IEEE 72, 802–819 (1984).
[CrossRef]

H. Inose, Y. Yasuda, “A unity bit coding method by negative feedback,” Proc. IEEE 51, 1524–1535 (1963).
[CrossRef]

Soc. Inf. Disp. Digest (1)

R. Floyd, L. Steinberg, “An adaptive algorithm for spatial gray scale,” Soc. Inf. Disp. Digest 36, 36–37 (1975).

Other (4)

B. E. Boser, “Design and implementation of oversampled analog-to-digital converters,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1988).

J. A. Bell, M. C. Hamilton, D. A. Leep, T. D. Morgan, H. F. Taylor, Y.-H. Lee, “Extention of electronic A/D converters to multi-gigahertz sampling rates using optical sampling and demultiplexing techniques,” in 23rd Asilomar Conference on Signals, Systems, and Computers (Institute of Electrical and Electronics Engineers, New York, 1989), pp. 289–293.

B. A. Wooley, Department of Electrical Engineering, Stanford University, Stanford, Calif. 94305 (personal communication).

D. A. B. Miller, AT&T Bell Laboratories, Holmdel, N.J. 07733 (personal communication).

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Figures (6)

Fig. 1
Fig. 1

Oversampled A/D converter block diagram.

Fig. 2
Fig. 2

Block diagram of recursive error diffusion modulator.

Fig. 3
Fig. 3

Two-stage error diffusion architecture.

Fig. 4
Fig. 4

SQNRmax of Nth-order modulators.

Fig. 5
Fig. 5

First-order interferometric error diffusion modulator.

Fig. 6
Fig. 6

First-order noninterferometric error diffusion modulator.

Equations (12)

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u n = x n - ɛ n - 1 = x n + u n - 1 - q ( u n - 1 ) ,             n = 1 , 2 , .
q ( u n ) = { + Δ 2 if u n 0 - Δ 2 otherwise ,
q ( u n ) = x n signal + ɛ n - ɛ n - 1 quantization error .
E ( z ) = Q ( z ) - U ( z ) = Q ( z ) - X ( z ) + z - 1 E ( z ) H ( z ) .
G ( z ) = E ^ ( z ) E ( z ) = 1 - z - H ( z ) ,
w i = - ( - 1 ) i ( N i )             for i = 1 , 2 , , N .
D 1 ( z ) = sinc k ( z ) ( 1 M 1 1 - z - M 1 1 - z - 1 ) k ,
H 1 ( f ) = sinc k ( f ) ( sin M 1 π f T M 1 sin π f T ) k magnitude exp ( - j π f T M 1 ) exp ( - j π f T ) phase ,
SQNR max ( M , N ) = 3 2 ( 2 N + 1 π 2 N ) M 2 N + 1 ,
M f s f N .
SQNR max ( b ) = 3 × 2 2 b - 1 .
P a = h ν η e I c ,

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