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Effect of ASE on Performance of EDFA for 1479nm-1555nm Wavelength Range
Inderpreet Kaur, Neena Gupta
Deptt. of Electrical & Electronics Engg. Chandigarh University Gharuan, India
Dept. of Electronics & Communication Engg. PEC University of Technology, Chandigarh, India Email: [email protected]
Abstract—The present research is an attempt to improve the gain broadness of EDFA and to reduce its noise figure by dynamic modeling of EDFA for DWDM systems. A model of EDFA has been designed based on simulation after considering all the major parameters like noise, ASE, input pump and signal power. The present research claims to support 96 DWDM channels across 1479nm-1555nm wavelength range, with a peak gain of 23.8dB, ASE of 0.9dBm for optimum length of EDF as 6m, which has been further flattened for 1479nm-1555nm wavelength range so as to accommodate 96 DWDM channels at a channel spacing of 0.8nm. A gain over a wider bandwidth of 76nm has been obtained in the present work.
Keywords—EDFA;Gain;NoiseFigure;ASE;DWDM
I. INTRODUCTION
One of the main issues when EDFA amplifies multiwavelength signals is the gain flatness in the wavelength range used[1-2]. To ensure high gain flatness and broadness, it is necessary to retain high average value of population inversion. It can be achieved by two ways; either by using higher pump power or shorter lengths of EDF.
The aim of present work is to optimize EDFA parameters i.e. pump power and fiber length (EDF) so as to obtain sufficient metastable state population and hence the high gain (in terms of flatness and broadness) and low noise figure. Gain flatness may be defined in terms of gain variation. Gain variation is defined as the difference between the maximum and minimum gain per channel. The fiber length (EDF) is a crucial factor as shorter the fiber length (EDF)[3], lesser is the ASE and thence reduced noise and enhanced gain of the amplifier.
Keeping this in consideration, the optimum fiber length (EDF) has been computed to consequently determine the gain and noise factor. One of the main objectives of present work is to broadened the gain spectrum so as to accommodate more number of DWDM channels. Before starting the simulation of model, operating bandwidth and channel spacing have to be finalized.
II. METHODOLOGY
A. Bandwidth and Channel Selection
To start with the present research and simulation of the proposed system, two significant parameters of the system to be defined first i.e. the number of channels to be transmitted and the operating bandwidth of the system. The model of EDFA presented in [4] considered only single channel while in [5] twenty six channels and in [6] eight channels were considered. As per ITU-T- G.694.1 recommendations, 0.8nm channel spacing has been recommended for DWDM system[7]. As we already know that S-Band operates from 1460nm to 1530nm range and C-Band operates from 1530nm to 1565nm range. The purpose of the work to be carried out is to utilize the entire selected wavelength range of S-Band and C-Band effectively and efficiently (i.e.
1460nm to 1565nm). However , to ensure that there is no interference, guard bands are considered on both sides of the entire wavelength range i.e. from 1460nm to1479nm range in the start of S-Band and from 1555 to 1565 nm range at the end of C-Band (which are the guard bands normally considered as per the available literature). Hence, wavelength range from 1479nm to 1555nm(i.e. operating bandwidth is 76nm) has been used for analysis in this work.
As mentioned above 0.8nm channel spacing is recommended for DWDM systems, so 96 channels have been accomodated in 76nm operating bandwidth(i.e from 1479nm to 1555nm wavelength). With channel spacing more than 0.8nm, lesser number of channels will be accomodated in the wavelength range from 1479nm to 1555nm, which is clearly shown in the figure 1.
Figure 1: Channel Spacing Varaition for Different Channels within 76nm Bandwidth Range
B. Modeling of EDFA for Dynamic Effects
In this section modeling of EDFA has been carried out in two steps. In the first step, the modeling and analysis of EDFA has been carried out without considering the effect of ASE. During the modeling of EDFA few dynamic effects have been considered, which are fiber length and pump power. Through this analysis the optimum value of pump power and the range of fiber length (EDF) have been evaluated.
In the second step, the EDFA has been designed by remodeling and improvising the existing concept of rate equations of EDFA by considering the effect of ASE. In this section, an effort has further been made to use the least possible fiber length of EDF so as to ensure least ASE noise for maximum possible gain and in turn economical (cheaper) amplifier. The flowchart has been shown in figure 2.
C. Mathematical Modeling and Analysis of EDFA Without Amplified Spontaneous Emission
The initial steps in designing of Erbium doped fiber amplifier have been started with finding the value of the appropriate pumping power and fiber length of EDF for EDFA. In this section, the modeling and analysis of EDFA has been carried out without considering the effect of ASE[4-5].
(1) Where, Ps(0,t) and Pp(0,t) represent the time- dependent input powers for the pump and signal and Nm represents the number of erbium ions in the metastable state. The B and C are related in terms of the confinement factors Γp and Γs[8], the absorption and emission cross sections (σgm, σmg and σge), the density of the erbium atoms ρ, the length L and the effective cross- sectional area A of the erbium doped fiber. It has been inferred from the equation (1) that the population density of metastable state is dependent upon pump power, signal power, constants related to pump (i.e. Bp and Cp), constants related to signal (i.e. Bs and Cs), and emission and absorption coefficients. Since this equation has neglected the presence of ASE, so this equation is valid only in the presence of negligible ASE[9].
D. Mathematical Modeling and Analysis of EDFA With Amplified Spontaneous Emission
In order to consider the effect of ASE, mathematical modeling of EDFA has been done. This has been done by improvising the existing rate equations of EDFA.
(2) The equation (2) is the basic equation for describing the dynamic gain effects in the EDFA including ASE. ν represents operating frequency spectrum , Δν represents the frequency deviation (channel spacing) around ν, h is the Plank’s constant [10] . In the present work, the improved non- linear ordinary differential equation (2) is implemented as a mathematical model, including the impact of ASE. Simulink environment has been created by using equation (2) and is shown in figure 3.The mathematical model shown in Simulink environment represents the interdependence of system parameters on the performance of EDFA. The mathematical model shown in figure 3 depicts that amplification of input signal depends on gain of EDFA, which in turn depends on Cp, Cs (which are related to lengths of EDF) and pump power. This diagram also represents the effect of ASE on metastable population which in turn is related
Figure 3: Block Diagram of EDFA
III. RESULTS AND DISCUSSIONS
A mathematical model of EDFA has been simulated using MATLAB for investigating EDFA dynamics including the effect of ASE. The results are given in terms of gain spectrum and noise figure for optimal length of EDFA. The summarized results have been shown in Table I.
A. Variation of Gain versus Wavelength Without ASE The graph is plotted between gain and wavelength (without considering ASE) for EDF length ranges from 4m to14m as shown in figure 4[10]. This graph implies that the length 14m can be chosen as optimum length, because at this length peak gain of 32dB is obtained while for 6m its value is 26dB and for 4m its value is 18dB. As discussed in previous section that the main goal of present work is to define the optimum value of EDF length so that gain flatness is maximum in largest possible wavelength range.
Figure 4: Gain versus Wavelength for Different Lengths of EDF without ASE
B. Variation of ASE versus Length of EDF
In the present model, co-propagating ASE is taken into consideration (equation 2). The ASE has been plotted for different lengths of EDFA which has been shown in figure 5. In figure 5, it is clear that the ASE noise increases as length of EDF increases. This is because of the fact that as spontaneously emitted photons travel along the length of the fiber they get amplified and they also stimulate the emission of more photon.
Figure 5: Variation of ASE versus Fiber Length of EDF The figure 5 depicts that ASE is 10dBm for amplifier length of 14m, for amplifier length of 6m its value is 1dBm and value of ASE still lowers at shorter length of EDF.
C. Variation of Gain (with ASE) versus Wavelength To obtain the optimum fiber length, gain of EDFA is plotted as shown in figure 6 by considering the effect of co-propagating ASE for length of EDF ranges from 4m to 14m. When ASE is included the optimum length for gain is determined by maximizing the signal gain which is a function of the length. It has been observed that the gain peak is reduced from 32dB to 26dB for 14m length, from 26dB to 23.8dB for 6m length and from 18dB to 13dB for 4m length. It has been clear from figure 6 that while considering the effect of co-propagating ASE, there is a very small difference in gain peaks for 14m length and 6m length. So, it is concluded from figure 4, 5 and 6 that the fiber length of 6m is considered as the optimum length for pump power of 57mW.
Figure 6: Gain versus Wavelength for Different Fiber Lengths with ASE
The results that are presented in figure 4, 5 and 6 are summarized in Table I and shown in figure 7.
Table I: Summarized Results of EDFA Without
considering ASE
Considering ASE Length
(m)
Max.Gain (dB)
Length (m)
Max.
Gain (dB)
ASE Power (dBm)
4 18 4 13 0.7
6 26 6 23.8 1.0
8 28 8 24.5 2.5
10 30 10 25 5.0
12 31.5 12 25.5 7.5
14 32 14 26 10
Figure 7: Gain (with and without ASE), ASE Power of EDFA at different lengths of EDF
From figure 7 it is observed that as the length of EDF increases the ASE power is also increased. This is also observed that with increase in length, the gain (with ASE) of EDFA is decreased as compared to gain (without ASE). It is observed that 6m length of EDF can be the optimum length to be chosen as at 6m length the ASE is much lesser as compared to 14m length.
However at the same time it is comparable to ASE at 4m length. As also the gain at 6m is much higher as compared to 4m and comparable to gain at 14m.
The variation of gain and noise figure of EDFA has been plotted for optimum length of EDF (i.e. 6m), signal wavelength of 1530nm and pump power of 57mW and is shown in figure 8.
Figure 8: Gain and Noise Figure versus Wavelength of EDFA
ACKNOWLEDGMENT
The authors would like to thank Optical Laboratories of PEC University of Technology, Chandigarh.
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