## Analysis and compensation of dispersion-induced bit loss in a photonic A/D converter using time-wavelength interweaved sampling clock

Optics Express, Vol. 17, Issue 20, pp. 17764-17771 (2009)

http://dx.doi.org/10.1364/OE.17.017764

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### Abstract

In this paper, the timing jitter induced by the fiber dispersion in photonic A/D converters using time-wavelength interweaved sampling clocks generated by optical time-division-multiplexing (OTDM) with fiber delay lines is analyzed and effective bit loss is calculated. A compensation method is proposed to decrease the dispersion-induced jitter. Simulations are performed and the results show the validity of the proposed compensation method. An experimental demonstration is carried out to verify the theoretical expression derived.

© 2009 OSA

## 1. Introduction

1. J. U. Kang and R. D. Esman, “Demonstration of time interweaved photonic four-channel WDM sampler for hybrid analogue-digital converter,” Electron. Lett. **35**(1), 60–61 (1999). [CrossRef]

3. T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a Time- and Wavelength-Interleaved Photonic Sampler for Analog–Digital Conversion,” IEEE Photon. Technol. Lett. **11**(9), 1168–1170 (1999). [CrossRef]

1. J. U. Kang and R. D. Esman, “Demonstration of time interweaved photonic four-channel WDM sampler for hybrid analogue-digital converter,” Electron. Lett. **35**(1), 60–61 (1999). [CrossRef]

4. G. C. Valley, J. P. Hurrell, and G. A. Sefler, “Photonic analog-to-digital converters: fundamental and practical limits,” Proc. SPIE **5618**, 96–106 (2004). [CrossRef]

## 2. Theory

*R*. The WDM part has

_{S}*M*wavelength channels, which are arranged at different time slot so as to form a pulse group by using

*M*fiber delay lines. The OTDM part has

*N*paths, which replicate the pulse group by

*N*times. The repetition rate of the output pulse train is thus

*MNR*.

_{S}*j*th wavelength and its delay,

*i*th delay unit,

*1/NR*and the ideal time delay for the wavelength

_{S}*j*through path

*i*should be:

*j=1,2…M*, differs from each other due to fiber dispersion. The actual time delay of the wavelength

*j*through path

*i*is:where

*j*th channel. Suppose there is a wavelength,

*1/NR*(in fact, what we concern is the relative delay, so the assumption is valid which will be seen in Section 3). We regard this channel as the ideal channel and rewrite the

_{S}*j*th wavelength using

*j*th wavelength through

*i*th path,

## 3. Compensation method and analysis

*fs*. The WDM part has 16 channels with channel spacing of 200GHz (1.6nm) and

*f*=10GHz. The dispersion coefficient,

*c*is the speed of light in vacuum,

*s=M/2*, then stretch the

*j*th (

*j=1,2,…,M*) fiber in WDM part so that it produces an extra compensation

*C*is a constant. The relative delay to the “ideal wavelength channel”,

*C*is effectively equal to each other, we will not include it in the equations of the following analysis. The term “effectively equal” indicates that the dispersion induced delay for each wavelength, i.e., (

*C*. After compensation, the sampling error becomes:

*k*. Figure 3 shows the relationship between the effective bits and

*k*when

*s=M/2*. We can find that when

*k=N/2*, the impact of the timing jitter is the lowest. Therefore, Eq. (15) gives the amount of compensation of the

*j*th wavelength in the WDM part for the compensation strategy mentioned above, where

*k=N/2*.

*fs*) and very noisy (

*fs*). The results still show effectiveness of the compensation scheme.

*j*th wavelength and the reference wavelength. Then measure the time interval again after the pulse train passes through the

*N/2*th path of the OTDM as shown in Fig. 6 (a) .

*ps*and 62.7

*ps*, respectively. After passing through the OTDM, these values changed to 66.8

*ps*and 63.2

*ps*, respectively, as shown in Fig. 6(a). Hence

*C*values are equal to −0.4

*ps*and 0.5

*ps*, respectively. From Eq. (15), one can calculate the theoretic values are −0.36

*ps*and 0.51

*ps*, respectively, which are in good agreement with the test result.

9. www.generalphotonics.com, Fiber Stretcher-FST-001-B, General Photonics Corp.

10. www.optiphase.com, PZ1-Low-profile Fiber Stretcher, Optiphase, Inc.

11. X. Li, L. Peng, S. Wang, Y.-C. Kim, and J. Chen, “A novel kind of programmable 3(n) feed-forward optical fiber true delay line based on SOA,” Opt. Express **15**(25), 16760–16766 (2007). [CrossRef] [PubMed]

## 4. Conclusion

## Acknowledgments

## References and links

1. | J. U. Kang and R. D. Esman, “Demonstration of time interweaved photonic four-channel WDM sampler for hybrid analogue-digital converter,” Electron. Lett. |

2. | G. Wu, M. Li, and B. Wang, at al., “An Approach to Generate Multi-wavelength Sampling Clock for Photonic A/D Converters,” The 14th OptoElectronics and Communications Conference (OECC 2009), Hong Kong, July 13–17, 2009. |

3. | T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a Time- and Wavelength-Interleaved Photonic Sampler for Analog–Digital Conversion,” IEEE Photon. Technol. Lett. |

4. | G. C. Valley, J. P. Hurrell, and G. A. Sefler, “Photonic analog-to-digital converters: fundamental and practical limits,” Proc. SPIE |

5. | H. F. Taylor, “An optical analog-to-digital converter—design and analysis,” IEEE J. Quantum Electron. |

6. | Gerd Kerser, Optical Fiber Communications, (Third Edition). (MCGraw-Hill Companies, New York, 2000). |

7. | R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. |

8. | P. G Agrawal, Nonlinear Fiber Optics (Third Edition). (Academic Press, San Diego, 2001). |

9. | www.generalphotonics.com, Fiber Stretcher-FST-001-B, General Photonics Corp. |

10. | www.optiphase.com, PZ1-Low-profile Fiber Stretcher, Optiphase, Inc. |

11. | X. Li, L. Peng, S. Wang, Y.-C. Kim, and J. Chen, “A novel kind of programmable 3(n) feed-forward optical fiber true delay line based on SOA,” Opt. Express |

**OCIS Codes**

(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems

(230.0250) Optical devices : Optoelectronics

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: June 15, 2009

Revised Manuscript: August 7, 2009

Manuscript Accepted: August 26, 2009

Published: September 18, 2009

**Citation**

Ming Li, Guiling Wu, Pan Guo, Xinwan Li, and Jianping Chen, "Analysis and compensation of dispersion-induced bit loss in a photonic A/D converter using time-wavelength interweaved sampling clock," Opt. Express **17**, 17764-17771 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-17764

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### References

- J. U. Kang and R. D. Esman, “Demonstration of time interweaved photonic four-channel WDM sampler for hybrid analogue-digital converter,” Electron. Lett. 35(1), 60–61 (1999). [CrossRef]
- G. Wu, M. Li, and B. Wang, at al., “An Approach to Generate Multi-wavelength Sampling Clock for Photonic A/D Converters,” The 14th OptoElectronics and Communications Conference (OECC 2009), Hong Kong, July 13–17, 2009.
- T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a Time- and Wavelength-Interleaved Photonic Sampler for Analog–Digital Conversion,” IEEE Photon. Technol. Lett. 11(9), 1168–1170 (1999). [CrossRef]
- G. C. Valley, J. P. Hurrell, and G. A. Sefler, “Photonic analog-to-digital converters: fundamental and practical limits,” Proc. SPIE 5618, 96–106 (2004). [CrossRef]
- H. F. Taylor, “An optical analog-to-digital converter—design and analysis,” IEEE J. Quantum Electron. 15(4), 210–216 (1979). [CrossRef]
- Gerd Kerser, Optical Fiber Communications, (Third Edition). (MCGraw-Hill Companies, New York, 2000).
- R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm. 17(4), 539–550 (1999). [CrossRef]
- P. G Agrawal, Nonlinear Fiber Optics (Third Edition). (Academic Press, San Diego, 2001).
- www.generalphotonics.com , Fiber Stretcher-FST-001-B, General Photonics Corp.
- www.optiphase.com , PZ1-Low-profile Fiber Stretcher, Optiphase, Inc.
- X. Li, L. Peng, S. Wang, Y.-C. Kim, and J. Chen, “A novel kind of programmable 3(n) feed-forward optical fiber true delay line based on SOA,” Opt. Express 15(25), 16760–16766 (2007). [CrossRef] [PubMed]

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