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EDFA Simulink Model for Analyzing Gain Spectrum and ASE by Stephen Pinter

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Presentation Overview Project objectives Project objectives Gain characteristics of EDFA Gain characteristics of EDFA wavelength dependant gain wavelength dependant gain Gain flattening Gain flattening non-uniform gain over the spectrum non-uniform gain over the spectrum implications implications

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Project Objectives Determine the optimum length for simulations Determine the optimum length for simulations ASE not considered – optimum length is shorter when ASE taken into account ASE not considered – optimum length is shorter when ASE taken into account Expand the current EDFA Simulink model to show the gain over the entire 1550nm window Expand the current EDFA Simulink model to show the gain over the entire 1550nm window important to know gain in range 1530nm – 1560nm important to know gain in range 1530nm – 1560nm Consider gain flattening, and Consider gain flattening, and Integrate forward ASE into the EDFA model Integrate forward ASE into the EDFA model Why Simulink? Why Simulink?

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Why use Simulink when an EDFA can be simulated using simulation tools such as OASIX or PTDS? Why use Simulink when an EDFA can be simulated using simulation tools such as OASIX or PTDS? OASIX or PTDS OASIX or PTDS static model static model input pump power is a static input internal to the EDFA module input pump power is a static input internal to the EDFA module Simulink Simulink dynamic model dynamic model input pump power as well as other EDFA parameters can be easily modified input pump power as well as other EDFA parameters can be easily modified

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EDFA Gain characteristics Significant equations governing EDFA dynamics Significant equations governing EDFA dynamics Output pump and signal power: Output pump and signal power: Quantities B and C characterize the physical EDFA and are given by: Quantities B and C characterize the physical EDFA and are given by: To handle multiple signal wavelengths, B s and C s as well as the input signal must be multidimensional To handle multiple signal wavelengths, B s and C s as well as the input signal must be multidimensional Why? Why?

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and are wavelength dependant as shown in the figure and are wavelength dependant as shown in the figure and are the absorption and emission coefficients, respectively and are the absorption and emission coefficients, respectively so, the quantities B and C are wavelength dependant so, the quantities B and C are wavelength dependant this relationship is how the wavelength dependency of the gain arises this relationship is how the wavelength dependency of the gain arises EDFA gain ratio between the absorption and emission at a particular wavelength is critical in determining the gain EDFA gain ratio between the absorption and emission at a particular wavelength is critical in determining the gain O. Mermer, “EDFA Gain Flattening By Using Optical Fiber Grating Techniques,” [Online Adobe Acrobat Document], Available at

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when performing simulations on the EDFA model it is important to simulate all the wavelengths simultaneously instead of one at a time when performing simulations on the EDFA model it is important to simulate all the wavelengths simultaneously instead of one at a time EDFAs work in the nonlinear regime, so properties like linear superposition don’t hold true EDFAs work in the nonlinear regime, so properties like linear superposition don’t hold true when there are several channels in an EDFA there is an effect called gain stealing when there are several channels in an EDFA there is an effect called gain stealing the energy that each of the channels takes from the pump depends on the details of the emission and absorption spectra the energy that each of the channels takes from the pump depends on the details of the emission and absorption spectra before simulating the gain, the optimum length was determined before simulating the gain, the optimum length was determined Note on Aspects of Simulation

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Optimum Length gain varies significantly over wavelength gain varies significantly over wavelength two distinct peaks two distinct peaks 12m and 30m 12m and 30m first peak first peak nm nm choose L opt = 12m choose L opt = 12m

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Simulink Models implementation of the ordinary nonlinear differential equation used for studying EDFA gain dynamics implementation of the ordinary nonlinear differential equation used for studying EDFA gain dynamics rate equation rate equation input/output input/output

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EDFA Gain significant gain variation is visible significant gain variation is visible about 11dB gain difference in the range 1530nm-1560nm about 11dB gain difference in the range 1530nm-1560nm How do we flatten the gain? How do we flatten the gain?

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Gain Flattening using the equations shown earlier, I derived an equation relating the pump gain (G P ) to the signal gain (G S ) using the equations shown earlier, I derived an equation relating the pump gain (G P ) to the signal gain (G S ) the resultant equation is: the resultant equation is: B P and C P are fixed, and B S and C S vary with wavelength B P and C P are fixed, and B S and C S vary with wavelength now G S can be fixed and G P for gain flatness can be obtained now G S can be fixed and G P for gain flatness can be obtained

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for a G S of 30dB, G P should follow the curve shown in the figure for a G S of 30dB, G P should follow the curve shown in the figure theoretical view of what the pump should be theoretical view of what the pump should be practically, in order to get a different power at each wavelength might be difficult practically, in order to get a different power at each wavelength might be difficult something to be further analyzed something to be further analyzed

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Thank You

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