評估光纖色散之數學方法

Abstract

本論文由已知的Gaussian pulse色散方程式著手，推導出一群連續的Gaussian pulse色散後彼此間互相影響的關係，再藉由適當的組合這些Gaussian pulse成為方波訊號，以得到方波訊號色散後的波形。利用此結果，除計算色散後pulse展開的寬度外，亦可細估色散後訊號本身的大小及訊號間彼此的干擾量。 接著利用上述方法組成不同pulse length ratio的方波，以評估在特定速率的系統，不同傳輸距離下，訊號寬度與ISIR ( inverse signal to noise ratio )之關係，以找出最佳的pulse length ratio及傳輸距離的限制。以10G bps，色散常數D為17 ps/km•ns之系統為例，我們發現在傳輸距離拉長時，NRZ的訊號比RZ的訊號更適合在光纖中傳遞，其傳輸限制大約為100㎞。 最後論文中考量雜訊的影響下之錯碼率。我們可計算出訊號色散干擾量後，適當的移動threshold點以得到較佳的錯碼率。

In this thesis, we analyze the relationship of a group of Gaussian pulses under the affect of fiber dispersion form the time domain dispersion equation. By Constituting these Gaussian pulses suitably, we can find the time domain dispersion equation of a rectangular pulse. By employing this equation, we can calculate the magnitude of the signal and the magnitude of the interference of the other pulses after dispersion. Next we use the method to generate rectangular pulses, which have different pulse length ratios. We can evaluate the relationship between pulse width and ISIR (inverse signal to noise ratio) at different transmission rate and distance. Afterward we can find out the optimum pulse length ratio and the transmission limit. For example, in the 10G bps system, we find that when the distance is long, the NRZ signal is more suitable than the RZ signal, and the transmission limit is around 100km . Finally, we consider the affect of noise and calculate the resultant BER. We can move the threshold point properly and get the minimum BER by the means of calculating the magnitude of the interference, generated form fiber dispersion.