as the square of the bit rate, at least in a first approximation. This is a confirmation of the rough evaluation carried out in the previous section on the ground of the pulse widening. It is clear from the aforementioned results that in order to obtain long-reach systems, dispersion has to be compensated. Penalty (dB) 40 Gbit/s 10 Gbit/s 10 Gbit/s Link length (km) FIGURE 6.8 Chromatic dispersion penalty for an IM-DD system using NRZ modulation. System parameters are reported Table 6.1 but for fibers parameters that are reported in the suitable table of Chapter 4. Telecommunication Networks Several methods have been conceived to compensate dispersion and the most used is the adoption of dispersion compensating fibers (DCFs). It is interesting however to analyze the effect of several different methods. 6.2.4.1 Dispersion-Compensated NRZ IM-DD Systems Since dispersion is a linear and deterministic phenomenon, in line of principle perfect pas- sive compensation with optical dispersion elements should be possible. Two kinds of in-line dispersion elements exist: DCF and dispersion compensating gratings. The DCF can be placed either at the transmitter or at the receiver, even if the receiver position seems advantageous since at the receiver it could be integrated with other devices. The only real disadvantage in using DCFs is their high loss that in a system without opti- cal amplifiers can be a limitation. Besides the use of DCF or fiber gratings, electronic compensation or pulse pre-chirp can be used. The basic idea of the pre-chirp method is to inject into the fiber a signal whose pulses have already a phase modulation exactly opposite to that caused by the fiber dispersion. During propagation, dispersion compensates this pre-distortion and the pulse arrives at the receiver without any ISI [14-16]. This is a type of pre-distortion similar to that adopted through some electronic devices, but for the fact that it is performed optically. An important advantage of pre-chirping is that no specific device is needed to app