Abstract

A 10Gb/s NRZ burst-mode optical receiver suitable for receiving asynchronous bursts with power variations of up to 7 dB is presented. The digital burst mode receiver is based on a standard AC-coupled photodiode followed by asynchronous analogue to digital conversion at 20 GS/s. Symbol timing, amplitude and baseline wander corrections are implemented in digital signal processing without the need for additional linecoding, such as 8B10B, and special AC-coupling schemes. It is assumed that G.709 framing together with enhanced FEC is used therefore the receiver is characterized using a pre eFEC BER of 10-3 at an input OSNR of 10 dB. We show that the addition of an electronically controlled SOA for optical power equalization before the receiver extends the burst-to-burst dynamic range from the 7 dB provided by the digital receiver alone to 16.5 dB. The large dynamic range, low overhead, and burst length versatility make this type of receiver ideal for applications in both synchronous and asynchronous dynamic network architectures with burst timescales ranging from nanoseconds through to continuous data.

© 2007 Optical Society of America

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References

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  1. P. Bayvel and M. Düser, “Optical burst switching: research and applications,” Optical Fiber Communications Conference,  FO1, 22–27, (2004).
  2. Y. Ota and R. G. Swartz, “Burst-mode compatible optical receiver with a large dynamic range,” IEEE J. Lightwave Technol.,  8, 1897–1903, (1990).
    [Crossref]
  3. NRZ Bandwidth — LF Cutoff and Baseline Wander, Maxim inc. application note HFAN-09.0.4, http://pdfserv.maxim-ic.com/en/an/4hfan904.pdf
  4. C. Su, L-K. Chen, and K-W. Cheung, “Theory of burst-mode receiver and its applications in optical multiaccess networks,” IEEE J. Lightwave Technol.,  15, 590–606, (1997).
    [Crossref]
  5. C. Su, L. K. Chen, and K. W. Cheung, “BER performance of digital optical burst-mode receiver in TDMA all optical multiaccess network,” IEEE Photon. Technol. Lett.,  7, 132–134, (1995).
    [Crossref]
  6. P. Ossieur, “A 1.25-Gb/s burst mode receiver for GPON applications,” IEEE, Journal of Solid-State Circuits,  40, 1180–1189, (2005).
    [Crossref]
  7. A. Dupas, B. Lavigne, W. Lautenschlaeger, and S. Schabel, “10 Gbit/s RZ asynchronous packet mode receiver with high input power dynamic for future optical packet switching systems,” Photonics in switching, Monterey USA, (2001).
  8. M. Duelk et al., “Fast packet routing in a 2.5Tb/s optical switch fabric with 40Gb/s duobinary signals at 0.8b/s/Hz spectral efficiency,” Optical Fiber Communications Conference, PD8, (2003).
  9. F. M. Gardner, “Interpolation in digital modems — Part I: Fundamentals,” IEEE Trans. Commun.,  41, 501–507, (1993).
    [Crossref]
  10. B. C. Thomsen, B. J. Puttnam, and P. Bayvel, “10 Gb/s AC-Coupled Digital Burst-Mode Optical Receiver,” Optical Fiber Communication Conference, OThK5, (2007).
  11. H. Wessing, B. Sorensen, B. Lavigne, E. Balmefrezol, and O. Leclerc,” Combining control electronics with SOA to equalize packet-to-packet power variations for optical 3R regeneration in optical networks at 10 Gbit/s,” Optical Fiber Communication Conference, OFC04, WD2, (2004).
  12. S. J. Lee, “A new non-data-aided feedforward symbol timing estimator using two samples per symbol,” Comms. Lett.,  6, 205–207, (2002).
    [Crossref]
  13. J. H. Baek, J. H. Hong, M. H. Sunwoo, and K. U. Kim, “Efficient digital baseline wander algorithm and its architecture for fast ethernet,” IEEE SIPS, (2004).
  14. M. Kawai, H. Watanabe, T. Ohtsuka, and K. Yamaguchi, “Smart optical receiver with automatic decision threshold setting and retiming phase alignment,” IEEE J. Lightwave Technol.,  7, 1634–1640, (1989).
    [Crossref]
  15. V. J. Mazurczyk, R. M. Kimball, and S. M. Abbott, “Using optical noise loading to estimate margin in optical amplifier systems,” Optical Fiber Communication Conference, OFC97, TuP5, 85, (1997).
  16. N. S. Bergano, F. W. Kerfoot, and C. R. Davidson, “Margin measurements in optical amplifier system,” IEEE Photon. Technol. Lett.,  5, 304–306, (1993).
    [Crossref]
  17. P. J. Winzer, et al., “10-Gb/s upgrade of bidirectional CWDM systems using electronic equalization and FEC,” IEEE J. Lightwave Technol.,  23, 203–210, (2005).
    [Crossref]
  18. C. Eldering, “Theoretical determination of sensitivity penalty for burst mode fiber optic receivers,” IEEE J. Lightwave Technol.,  11, 2145–2149, (1993).
    [Crossref]
  19. E. T. Aw, T. Lin, A. Wonfor, M. Glick, K. A. Williams, R. V. Penty, and I. H. White, “Layered Control to Enable Large Scale SOA Switch Fabric,” European Conference on Optical Communications, Th1.2.5, (2006).

2006 (1)

E. T. Aw, T. Lin, A. Wonfor, M. Glick, K. A. Williams, R. V. Penty, and I. H. White, “Layered Control to Enable Large Scale SOA Switch Fabric,” European Conference on Optical Communications, Th1.2.5, (2006).

2005 (2)

P. J. Winzer, et al., “10-Gb/s upgrade of bidirectional CWDM systems using electronic equalization and FEC,” IEEE J. Lightwave Technol.,  23, 203–210, (2005).
[Crossref]

P. Ossieur, “A 1.25-Gb/s burst mode receiver for GPON applications,” IEEE, Journal of Solid-State Circuits,  40, 1180–1189, (2005).
[Crossref]

2004 (1)

P. Bayvel and M. Düser, “Optical burst switching: research and applications,” Optical Fiber Communications Conference,  FO1, 22–27, (2004).

2002 (1)

S. J. Lee, “A new non-data-aided feedforward symbol timing estimator using two samples per symbol,” Comms. Lett.,  6, 205–207, (2002).
[Crossref]

2001 (1)

A. Dupas, B. Lavigne, W. Lautenschlaeger, and S. Schabel, “10 Gbit/s RZ asynchronous packet mode receiver with high input power dynamic for future optical packet switching systems,” Photonics in switching, Monterey USA, (2001).

1997 (1)

C. Su, L-K. Chen, and K-W. Cheung, “Theory of burst-mode receiver and its applications in optical multiaccess networks,” IEEE J. Lightwave Technol.,  15, 590–606, (1997).
[Crossref]

1995 (1)

C. Su, L. K. Chen, and K. W. Cheung, “BER performance of digital optical burst-mode receiver in TDMA all optical multiaccess network,” IEEE Photon. Technol. Lett.,  7, 132–134, (1995).
[Crossref]

1993 (3)

F. M. Gardner, “Interpolation in digital modems — Part I: Fundamentals,” IEEE Trans. Commun.,  41, 501–507, (1993).
[Crossref]

C. Eldering, “Theoretical determination of sensitivity penalty for burst mode fiber optic receivers,” IEEE J. Lightwave Technol.,  11, 2145–2149, (1993).
[Crossref]

N. S. Bergano, F. W. Kerfoot, and C. R. Davidson, “Margin measurements in optical amplifier system,” IEEE Photon. Technol. Lett.,  5, 304–306, (1993).
[Crossref]

1990 (1)

Y. Ota and R. G. Swartz, “Burst-mode compatible optical receiver with a large dynamic range,” IEEE J. Lightwave Technol.,  8, 1897–1903, (1990).
[Crossref]

1989 (1)

M. Kawai, H. Watanabe, T. Ohtsuka, and K. Yamaguchi, “Smart optical receiver with automatic decision threshold setting and retiming phase alignment,” IEEE J. Lightwave Technol.,  7, 1634–1640, (1989).
[Crossref]

Abbott, S. M.

V. J. Mazurczyk, R. M. Kimball, and S. M. Abbott, “Using optical noise loading to estimate margin in optical amplifier systems,” Optical Fiber Communication Conference, OFC97, TuP5, 85, (1997).

Aw, E. T.

E. T. Aw, T. Lin, A. Wonfor, M. Glick, K. A. Williams, R. V. Penty, and I. H. White, “Layered Control to Enable Large Scale SOA Switch Fabric,” European Conference on Optical Communications, Th1.2.5, (2006).

Baek, J. H.

J. H. Baek, J. H. Hong, M. H. Sunwoo, and K. U. Kim, “Efficient digital baseline wander algorithm and its architecture for fast ethernet,” IEEE SIPS, (2004).

Balmefrezol, E.

H. Wessing, B. Sorensen, B. Lavigne, E. Balmefrezol, and O. Leclerc,” Combining control electronics with SOA to equalize packet-to-packet power variations for optical 3R regeneration in optical networks at 10 Gbit/s,” Optical Fiber Communication Conference, OFC04, WD2, (2004).

Bayvel, P.

P. Bayvel and M. Düser, “Optical burst switching: research and applications,” Optical Fiber Communications Conference,  FO1, 22–27, (2004).

B. C. Thomsen, B. J. Puttnam, and P. Bayvel, “10 Gb/s AC-Coupled Digital Burst-Mode Optical Receiver,” Optical Fiber Communication Conference, OThK5, (2007).

Bergano, N. S.

N. S. Bergano, F. W. Kerfoot, and C. R. Davidson, “Margin measurements in optical amplifier system,” IEEE Photon. Technol. Lett.,  5, 304–306, (1993).
[Crossref]

Chen, L. K.

C. Su, L. K. Chen, and K. W. Cheung, “BER performance of digital optical burst-mode receiver in TDMA all optical multiaccess network,” IEEE Photon. Technol. Lett.,  7, 132–134, (1995).
[Crossref]

Chen, L-K.

C. Su, L-K. Chen, and K-W. Cheung, “Theory of burst-mode receiver and its applications in optical multiaccess networks,” IEEE J. Lightwave Technol.,  15, 590–606, (1997).
[Crossref]

Cheung, K. W.

C. Su, L. K. Chen, and K. W. Cheung, “BER performance of digital optical burst-mode receiver in TDMA all optical multiaccess network,” IEEE Photon. Technol. Lett.,  7, 132–134, (1995).
[Crossref]

Cheung, K-W.

C. Su, L-K. Chen, and K-W. Cheung, “Theory of burst-mode receiver and its applications in optical multiaccess networks,” IEEE J. Lightwave Technol.,  15, 590–606, (1997).
[Crossref]

Davidson, C. R.

N. S. Bergano, F. W. Kerfoot, and C. R. Davidson, “Margin measurements in optical amplifier system,” IEEE Photon. Technol. Lett.,  5, 304–306, (1993).
[Crossref]

Duelk, M.

M. Duelk et al., “Fast packet routing in a 2.5Tb/s optical switch fabric with 40Gb/s duobinary signals at 0.8b/s/Hz spectral efficiency,” Optical Fiber Communications Conference, PD8, (2003).

Dupas, A.

A. Dupas, B. Lavigne, W. Lautenschlaeger, and S. Schabel, “10 Gbit/s RZ asynchronous packet mode receiver with high input power dynamic for future optical packet switching systems,” Photonics in switching, Monterey USA, (2001).

Düser, M.

P. Bayvel and M. Düser, “Optical burst switching: research and applications,” Optical Fiber Communications Conference,  FO1, 22–27, (2004).

Eldering, C.

C. Eldering, “Theoretical determination of sensitivity penalty for burst mode fiber optic receivers,” IEEE J. Lightwave Technol.,  11, 2145–2149, (1993).
[Crossref]

Gardner, F. M.

F. M. Gardner, “Interpolation in digital modems — Part I: Fundamentals,” IEEE Trans. Commun.,  41, 501–507, (1993).
[Crossref]

Glick, M.

E. T. Aw, T. Lin, A. Wonfor, M. Glick, K. A. Williams, R. V. Penty, and I. H. White, “Layered Control to Enable Large Scale SOA Switch Fabric,” European Conference on Optical Communications, Th1.2.5, (2006).

Hong, J. H.

J. H. Baek, J. H. Hong, M. H. Sunwoo, and K. U. Kim, “Efficient digital baseline wander algorithm and its architecture for fast ethernet,” IEEE SIPS, (2004).

Kawai, M.

M. Kawai, H. Watanabe, T. Ohtsuka, and K. Yamaguchi, “Smart optical receiver with automatic decision threshold setting and retiming phase alignment,” IEEE J. Lightwave Technol.,  7, 1634–1640, (1989).
[Crossref]

Kerfoot, F. W.

N. S. Bergano, F. W. Kerfoot, and C. R. Davidson, “Margin measurements in optical amplifier system,” IEEE Photon. Technol. Lett.,  5, 304–306, (1993).
[Crossref]

Kim, K. U.

J. H. Baek, J. H. Hong, M. H. Sunwoo, and K. U. Kim, “Efficient digital baseline wander algorithm and its architecture for fast ethernet,” IEEE SIPS, (2004).

Kimball, R. M.

V. J. Mazurczyk, R. M. Kimball, and S. M. Abbott, “Using optical noise loading to estimate margin in optical amplifier systems,” Optical Fiber Communication Conference, OFC97, TuP5, 85, (1997).

Lautenschlaeger, W.

A. Dupas, B. Lavigne, W. Lautenschlaeger, and S. Schabel, “10 Gbit/s RZ asynchronous packet mode receiver with high input power dynamic for future optical packet switching systems,” Photonics in switching, Monterey USA, (2001).

Lavigne, B.

A. Dupas, B. Lavigne, W. Lautenschlaeger, and S. Schabel, “10 Gbit/s RZ asynchronous packet mode receiver with high input power dynamic for future optical packet switching systems,” Photonics in switching, Monterey USA, (2001).

H. Wessing, B. Sorensen, B. Lavigne, E. Balmefrezol, and O. Leclerc,” Combining control electronics with SOA to equalize packet-to-packet power variations for optical 3R regeneration in optical networks at 10 Gbit/s,” Optical Fiber Communication Conference, OFC04, WD2, (2004).

Leclerc, O.

H. Wessing, B. Sorensen, B. Lavigne, E. Balmefrezol, and O. Leclerc,” Combining control electronics with SOA to equalize packet-to-packet power variations for optical 3R regeneration in optical networks at 10 Gbit/s,” Optical Fiber Communication Conference, OFC04, WD2, (2004).

Lee, S. J.

S. J. Lee, “A new non-data-aided feedforward symbol timing estimator using two samples per symbol,” Comms. Lett.,  6, 205–207, (2002).
[Crossref]

Lin, T.

E. T. Aw, T. Lin, A. Wonfor, M. Glick, K. A. Williams, R. V. Penty, and I. H. White, “Layered Control to Enable Large Scale SOA Switch Fabric,” European Conference on Optical Communications, Th1.2.5, (2006).

Mazurczyk, V. J.

V. J. Mazurczyk, R. M. Kimball, and S. M. Abbott, “Using optical noise loading to estimate margin in optical amplifier systems,” Optical Fiber Communication Conference, OFC97, TuP5, 85, (1997).

Ohtsuka, T.

M. Kawai, H. Watanabe, T. Ohtsuka, and K. Yamaguchi, “Smart optical receiver with automatic decision threshold setting and retiming phase alignment,” IEEE J. Lightwave Technol.,  7, 1634–1640, (1989).
[Crossref]

Ossieur, P.

P. Ossieur, “A 1.25-Gb/s burst mode receiver for GPON applications,” IEEE, Journal of Solid-State Circuits,  40, 1180–1189, (2005).
[Crossref]

Ota, Y.

Y. Ota and R. G. Swartz, “Burst-mode compatible optical receiver with a large dynamic range,” IEEE J. Lightwave Technol.,  8, 1897–1903, (1990).
[Crossref]

Penty, R. V.

E. T. Aw, T. Lin, A. Wonfor, M. Glick, K. A. Williams, R. V. Penty, and I. H. White, “Layered Control to Enable Large Scale SOA Switch Fabric,” European Conference on Optical Communications, Th1.2.5, (2006).

Puttnam, B. J.

B. C. Thomsen, B. J. Puttnam, and P. Bayvel, “10 Gb/s AC-Coupled Digital Burst-Mode Optical Receiver,” Optical Fiber Communication Conference, OThK5, (2007).

Schabel, S.

A. Dupas, B. Lavigne, W. Lautenschlaeger, and S. Schabel, “10 Gbit/s RZ asynchronous packet mode receiver with high input power dynamic for future optical packet switching systems,” Photonics in switching, Monterey USA, (2001).

Sorensen, B.

H. Wessing, B. Sorensen, B. Lavigne, E. Balmefrezol, and O. Leclerc,” Combining control electronics with SOA to equalize packet-to-packet power variations for optical 3R regeneration in optical networks at 10 Gbit/s,” Optical Fiber Communication Conference, OFC04, WD2, (2004).

Su, C.

C. Su, L-K. Chen, and K-W. Cheung, “Theory of burst-mode receiver and its applications in optical multiaccess networks,” IEEE J. Lightwave Technol.,  15, 590–606, (1997).
[Crossref]

C. Su, L. K. Chen, and K. W. Cheung, “BER performance of digital optical burst-mode receiver in TDMA all optical multiaccess network,” IEEE Photon. Technol. Lett.,  7, 132–134, (1995).
[Crossref]

Sunwoo, M. H.

J. H. Baek, J. H. Hong, M. H. Sunwoo, and K. U. Kim, “Efficient digital baseline wander algorithm and its architecture for fast ethernet,” IEEE SIPS, (2004).

Swartz, R. G.

Y. Ota and R. G. Swartz, “Burst-mode compatible optical receiver with a large dynamic range,” IEEE J. Lightwave Technol.,  8, 1897–1903, (1990).
[Crossref]

Thomsen, B. C.

B. C. Thomsen, B. J. Puttnam, and P. Bayvel, “10 Gb/s AC-Coupled Digital Burst-Mode Optical Receiver,” Optical Fiber Communication Conference, OThK5, (2007).

Watanabe, H.

M. Kawai, H. Watanabe, T. Ohtsuka, and K. Yamaguchi, “Smart optical receiver with automatic decision threshold setting and retiming phase alignment,” IEEE J. Lightwave Technol.,  7, 1634–1640, (1989).
[Crossref]

Wessing, H.

H. Wessing, B. Sorensen, B. Lavigne, E. Balmefrezol, and O. Leclerc,” Combining control electronics with SOA to equalize packet-to-packet power variations for optical 3R regeneration in optical networks at 10 Gbit/s,” Optical Fiber Communication Conference, OFC04, WD2, (2004).

White, I. H.

E. T. Aw, T. Lin, A. Wonfor, M. Glick, K. A. Williams, R. V. Penty, and I. H. White, “Layered Control to Enable Large Scale SOA Switch Fabric,” European Conference on Optical Communications, Th1.2.5, (2006).

Williams, K. A.

E. T. Aw, T. Lin, A. Wonfor, M. Glick, K. A. Williams, R. V. Penty, and I. H. White, “Layered Control to Enable Large Scale SOA Switch Fabric,” European Conference on Optical Communications, Th1.2.5, (2006).

Winzer, P. J.

P. J. Winzer, et al., “10-Gb/s upgrade of bidirectional CWDM systems using electronic equalization and FEC,” IEEE J. Lightwave Technol.,  23, 203–210, (2005).
[Crossref]

Wonfor, A.

E. T. Aw, T. Lin, A. Wonfor, M. Glick, K. A. Williams, R. V. Penty, and I. H. White, “Layered Control to Enable Large Scale SOA Switch Fabric,” European Conference on Optical Communications, Th1.2.5, (2006).

Yamaguchi, K.

M. Kawai, H. Watanabe, T. Ohtsuka, and K. Yamaguchi, “Smart optical receiver with automatic decision threshold setting and retiming phase alignment,” IEEE J. Lightwave Technol.,  7, 1634–1640, (1989).
[Crossref]

Comms. Lett. (1)

S. J. Lee, “A new non-data-aided feedforward symbol timing estimator using two samples per symbol,” Comms. Lett.,  6, 205–207, (2002).
[Crossref]

IEEE J. Lightwave Technol. (5)

M. Kawai, H. Watanabe, T. Ohtsuka, and K. Yamaguchi, “Smart optical receiver with automatic decision threshold setting and retiming phase alignment,” IEEE J. Lightwave Technol.,  7, 1634–1640, (1989).
[Crossref]

P. J. Winzer, et al., “10-Gb/s upgrade of bidirectional CWDM systems using electronic equalization and FEC,” IEEE J. Lightwave Technol.,  23, 203–210, (2005).
[Crossref]

C. Eldering, “Theoretical determination of sensitivity penalty for burst mode fiber optic receivers,” IEEE J. Lightwave Technol.,  11, 2145–2149, (1993).
[Crossref]

C. Su, L-K. Chen, and K-W. Cheung, “Theory of burst-mode receiver and its applications in optical multiaccess networks,” IEEE J. Lightwave Technol.,  15, 590–606, (1997).
[Crossref]

Y. Ota and R. G. Swartz, “Burst-mode compatible optical receiver with a large dynamic range,” IEEE J. Lightwave Technol.,  8, 1897–1903, (1990).
[Crossref]

IEEE Photon. Technol. Lett. (2)

C. Su, L. K. Chen, and K. W. Cheung, “BER performance of digital optical burst-mode receiver in TDMA all optical multiaccess network,” IEEE Photon. Technol. Lett.,  7, 132–134, (1995).
[Crossref]

N. S. Bergano, F. W. Kerfoot, and C. R. Davidson, “Margin measurements in optical amplifier system,” IEEE Photon. Technol. Lett.,  5, 304–306, (1993).
[Crossref]

IEEE Trans. Commun. (1)

F. M. Gardner, “Interpolation in digital modems — Part I: Fundamentals,” IEEE Trans. Commun.,  41, 501–507, (1993).
[Crossref]

IEEE, Journal of Solid-State Circuits (1)

P. Ossieur, “A 1.25-Gb/s burst mode receiver for GPON applications,” IEEE, Journal of Solid-State Circuits,  40, 1180–1189, (2005).
[Crossref]

Optical Fiber Communications Conference (1)

P. Bayvel and M. Düser, “Optical burst switching: research and applications,” Optical Fiber Communications Conference,  FO1, 22–27, (2004).

Photonics in switching, Monterey USA (1)

A. Dupas, B. Lavigne, W. Lautenschlaeger, and S. Schabel, “10 Gbit/s RZ asynchronous packet mode receiver with high input power dynamic for future optical packet switching systems,” Photonics in switching, Monterey USA, (2001).

Other (7)

M. Duelk et al., “Fast packet routing in a 2.5Tb/s optical switch fabric with 40Gb/s duobinary signals at 0.8b/s/Hz spectral efficiency,” Optical Fiber Communications Conference, PD8, (2003).

B. C. Thomsen, B. J. Puttnam, and P. Bayvel, “10 Gb/s AC-Coupled Digital Burst-Mode Optical Receiver,” Optical Fiber Communication Conference, OThK5, (2007).

H. Wessing, B. Sorensen, B. Lavigne, E. Balmefrezol, and O. Leclerc,” Combining control electronics with SOA to equalize packet-to-packet power variations for optical 3R regeneration in optical networks at 10 Gbit/s,” Optical Fiber Communication Conference, OFC04, WD2, (2004).

NRZ Bandwidth — LF Cutoff and Baseline Wander, Maxim inc. application note HFAN-09.0.4, http://pdfserv.maxim-ic.com/en/an/4hfan904.pdf

E. T. Aw, T. Lin, A. Wonfor, M. Glick, K. A. Williams, R. V. Penty, and I. H. White, “Layered Control to Enable Large Scale SOA Switch Fabric,” European Conference on Optical Communications, Th1.2.5, (2006).

V. J. Mazurczyk, R. M. Kimball, and S. M. Abbott, “Using optical noise loading to estimate margin in optical amplifier systems,” Optical Fiber Communication Conference, OFC97, TuP5, 85, (1997).

J. H. Baek, J. H. Hong, M. H. Sunwoo, and K. U. Kim, “Efficient digital baseline wander algorithm and its architecture for fast ethernet,” IEEE SIPS, (2004).

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Figures (4)

Fig. 1.
Fig. 1.

Experimental burst transmitter, optical equaliser and digital burst-mode receiver. The burst structure is also shown.

Fig. 2.
Fig. 2.

Burst-mode receiver digital signal processing schematic.

Fig. 3.
Fig. 3.

The required OSNR for an error rate of 10-3 as a function of the received power.

Fig. 4.
Fig. 4.

An illustration showing the clipping that occurs, in the ADC, at the start of the burst signals when (a) an AC-coupled photo receiver followed by (b) an AC-coupled variable gain amplifier are used before the ADC. Also shown for comparison are the outputs of (c) a DC coupled photo receiver followed by (d) variable gain amplifier where clipping is avoided.

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