# A Comprehensive Study on EDFA Characteristics: Temperature Impact
## 3 Results and Discussion
### Saturation Signal Power Variation with Temperature  
The study of the saturation signal power P\({}_{\rm s}^{\rm sat}\) is of great importance in order to have a complete overview concerning the maximum possible input signal power that could be driven to the fiber without affecting its output gain. The saturation signal power could be defined as the input signal power at which the gain has been reduced by 3 dB of its small-signal gain. From previous studies [2,3], increasing the input signal power will push into the saturation region because, in this case, the number of photons of the input signal will be higher than the number of carriers in the meta-stable state. The saturation signal power investigation shows its dependency on the input pump power. This will be explained as follows.  
To calculate the saturation signal power, the gain versus the input signal power should be driven first for each parameter that needs to be studied. The input signal power related to a value of gain lower than the maximum gain value by 3 dB represents the saturation signal power. The gain versus the input signal power is depicted in Figure 7. The EDFA length is 2 m, and the input pump power is 200 mW.  
The effect of temperature has been studied in the range from \(-40\)\({}^{\circ}\)C to \(+80\)\({}^{\circ}\)C. It is worthy to choose the fiber length to be L\({}_{\rm opt}\). It could easily be calculated to be 6.86 m using Equation (12) in which the simulation data for P\({}_{\rm s}\), P\({}_{\rm p}\), \(\lambda_{\rm s}\) and T have the following values: 0.05 mW, 200 mW, 1530 nm, and 300 K, respectively. This choice will afford a high gain of \(\sim\)36.9 dB in the case of a very low input signal power at \(-40\)\({}^{\circ}\)C. However, this length will not provide gain saturation in the case of a low-input power signal, and hence the concept of calculating P\({}_{\rm s}^{\rm sat}\) will not be accomplished, which is why we have chosen the fiber length to be 2 m. Another important observation is that the gain versus the input signal power variation with temperature is clearer in the case of 1480-nm pumping rather than 980-nm pumping, because this last case is less sensitive to temperature variation [13]. This result led [PERSON] et al. [22] to use a laser with a wavelength of 1480 nm in their sensing application using EDFA.  
Figure 6: Variation of L\({}_{\rm opt}\) with input pump power using P\({}_{\rm s}\) = 10 μW at different temperatures with \(\lambda_{\rm p}\) = 1480 nm.  
Figure 8 represents the effect of changing the pump power on the saturation signal power variation with temperature. The fiber length is chosen to be 2 m, and the temperature is in the range from \(-40\)\({}^{\circ}\)C to \(+80\)\({}^{\circ}\)C. An increase in the value of the saturation signal power with temperature is noticeable. Hence, working at higher temperature ranges will afford higher opportunities to amplify input signals while conserving a flat output amplified signal. Also, one can notice the increase in the saturation pump power due to the temperature increase with the increase of the driven signal power in the case of the 1480-nm pumping.