Monday , May 29 2023

Theoretical Design and Analysis of EDFA Gain Control System Based on Two-Level EDFA Model

Seong-Ho SONG, Seop-Hyeong PARK
Hallym University,
1 Okchon, Chunchon, Gangwon 200-701, Korea,

Abstract: In this paper, a disturbance observer (DOB) based erbium-doped fiber amplifier(EDFA) gain controller is proposed. In order to stabilize an EDFA gain in wavelength-division-multiplexing (WDM) channel add/drop networks, the channel add/drop is estimated based on a mathematical EDFA model and compensated using DOB technique. The performance of the proposed control method is theoretically analyzed using Lyapunov method. The performance of the proposed DOB-based gain control algorithm was investigated through simulations. Simulation results verify the excellent performance of the proposed gain control methodology.

Keywords: Erbium-Doped Fibre Amplifier, Gain Control, Mathematical Model, Disturbance Observer, Channel Add/Drop. Theoretical Analysis.

>>Full Text
Seong-Ho SONG, Seop-Hyeong PARK, Theoretical Design and Analysis of EDFA Gain Control System Based on Two-Level EDFA Model, Studies in Informatics and Control, ISSN 1220-1766, vol. 22 (1), pp. 97-105, 2013.


Control and management of erbium-doped fiber amplifiers (EDFAs) is an important design problem in the evolution towards a dynamic optical network [1]. As wavelength- division -multiplexed networks increase in complexity, there remain a number of challenges, such as dealing with disturbances related to intrinsic network characteristics. The power level of each channel in WDM networks should be unchanged when channel add/drops or active rearrangements of network occur. Keeping the signal powers to a constant value is more important when the signals are amplified through EDFAs. At the EDFA, the change of the number of signals causes the change of the amplifier gain of each signal due to the cross gain saturation effect [2, 3, 4] which results in gain-related errors at the receivers.

To avoid this effect, several control methods have been developed [5-9]. One of them uses EDFA output as a feedback signal in an optical feedback control loop [5]. The all-optical scheme has a drawback; the frequency of channel add/drop should be less than that of the relaxation oscillation frequency of EDFA, which is several hundred Hz. On the other hand, the mostly used one is an electrical scheme which controls the pump laser output electrically according to EDFA output signal level [9, 10].

Based on image002 control theory, a systematic design approach has been introduced in [9] and some robustness has been also analyzed therein. However, most systems adopt traditional proportional, integral, derivative (PID) control, or need feed-forward perfect cancellation algorithms for gain control. As mentioned in [9], there have been no formal attempts to analyze the performance theoretically and systematically.

In this paper, theoretical performance analysis of EDFA gain control algorithm is carried out based on a mathematical EDFA model. As a nominal controller, a proportional-,integral controller is considered and a disturbance observer is considered as feed-forward control.

To our knowledge, this is the first attempt to theoretically analyze the performance of PI and feed forward control algorithm in EDFA control literature.

Singular perturbation approach [11] reduces the mathematical model to two level equation and disturbance observer technique [12,13] is adopted to compensate channel add/drop effects in this two-level model. The asymptotic performance is proven theoretically using Lyapunov method and through simulation results, the feasibility of the proposed algorithm is verified.


  1. PAVEL, L., Dynamics and Stability in Optical Communication Networks: A System Theoretic Framework, Automatica, vol. 40, no. 8, 2004, pp. 1361-1370.
  2. ZYSKIND, J. L., et al., Fast Power Transients in Optically Amplified Multiwavelength Optical Networks, Proceedings of OFC’96, 1996, Paper PD31.
  3. SRIVASTAVA, A. K., Y. SUN, J. L. ZYSKIND, J. W. SULHOFF, EDFA Transient Response to Channel Loss in WDM Transmission System, IEEE Photonics Technology Letters, vol. 9, no. 3, Mar. 1997, pp. 386-388.
  4. SUN, Y., et al., Fast Power Transients in WDM Optical Networks with Cascaded EDFAs, Electronics Letters, vol. 33, no. 4, 1997, pp. 313-314.
  5. ZIRNGIBL, M., Gain Control in Erbium-doped Fiber Amplifiers by All-optical Feedback Loop, Electronics Letters, vol. 27, no.7, 1991, pp. 560-561.
  6. DESURVIRE, E., Erbium Doped Fiber Amplifiers: Principles and Applications. New York, Wiley, 1994.
  7. TRAN, A. V., C. J. CHAE, R. S. TUCKER, Y. J. WEN, EDFA Transient Control based on Envelope Detection for Optical Burst Switched Networks, IEEE Photonics Technology Letters, vol. 17, no. 1, January 2005, pp. 226-228.
  8. SRIVASTAVA, A. K. et al., Fast-link Control Protection of Surviving Channels in Multi-wavelength Optical Networks, IEEE Photonics Technology Letters, vol. 9, no. 12, Dec. 1997, pp. 1667-1669.
  9. TAING, Y., L. PAVEL, An EDFA H Controller for Suppression of Power Excursions Due to Pilot Tones and Network Traffic, IEEE Photonics Technology Letters, vol. 18, no. 18, September 15, 2006, pp. 1916-1918.
  10. SHIN, S., D. KIM, S. KIM, S. LEE, S. SONG, A Novel Technique to Minimize Gain-transient Time of WDM Signals in EDFA, Journal of the Optical Society, Korea, vol. 10, no. 4, 2006, pp. 174-177.
  11. KOKOTOVIC, K. K., H. KHALIL, J. ORELLY, Singular Perturbation Method in Control, SIAM, 1987.
  12. CHOI, Y., W. K. CHUNG, Y. YOUM, Disturbance Observer in Framework, IEEE IECON, 1996, pp. 1394-1400.
  13. KIM, K., H. T. CHOI, W. K. CHUNG, I. H. SUH, Analysis and Design of Robust Motion Controllers in the Unified Framework, Journal of Dynamic Systems, Measurement, and Control, vol. 124, 2002, pp. 313-321.
  14. DESURVIRE, E., Erbium-doped Fiber Amplifiers, John Wiley & Sons, New York, 1994.
  15. KHALIL, H. K. Nonlinear Systems, 2nd Ed., Prentice-Hall, 2002.