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where CDcMax = maximum tolerable chromatic dispersion coefficient, s/(m m) CDMax = maximum tolerable chromatic dispersion limit, s/m = epsilon value = 03 for 1 dB power penalty and 048 for 2 dB power penalty at BER 10 12 for NRZ modulated signals z = transmission distance, m
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Chromatic Dispersion
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R = transmission rate, bps fc = optical carrier RMS spectral width, Hz c = speed of light in a vacuum, m/s c = carrier center wavelength, m This result estimates4 the maximum tolerable chromatic dispersion for an input Gaussian NRZ modulated optical signal at transmission distance z If the fiber link chromatic dispersion coefficient is known the result estimates the maximum transmission distance Often the laser spectral width is given as the 20 dB full width, and therefore Eq (436) can be used to convert to the RMS spectral width assuming a Gaussian spectral shape f 20dB = 6 0697 fc
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For very narrow optical sources, such as a DFB laser with a spectral width of 100 MHz, and a high transmission rate where the carrier unmodulated spectral width is f 20dB < R/10, Eq (434) is simplified to Eq (437) CD cMax z c 2 c R2
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For other optical sources where the carrier width is much wider than the modulating signal width, where f 20dB > 14R, Eq (434) is simplified to Eq (438) CD cMax z c 2 c R fc
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ITU-T GSup39 epsilon values for specific optical power penalties for BER of 10 12 due to chromatic dispersion pulse spreading using NRZ modulation and DFB lasers are shown in Table 41 Using epsilon values shown in Table 41, Eq (437) can be written as Eq (439) for 1 dB power penalty Assume high bit rate transmission systems, narrow spectrum lasers (DFB), no chirp in the signal, and initial launch Gaussian NRZ pulse
Optical Power Penalty (dB) 05 1 2
Epsilon Value 02 03 048
TABLE 41 Epsilon and Power Penalty Values for NRZ Modulation for BER 10 12
Four
Bit Rate (Gbps) 25 10 40 100
Protocol (NRZ) OC-48 & STM-16 OC-192 & STM-64 OC-768 & STM-256 100G Ethernet
Chromatic Dispersion Limit 1 dB Penalty (ps/nm) 18800 1176 735 118
Distance Limit G652 Fiber (km) 1100 69 43 069
TABLE 42 Estimated Chromatic Dispersion Limits for Externally Modulated Chirp-Free DFB Laser over G652 Fiber with a 1 dB Power Penalty
CD cMax z
2 8255 108 2 c R2
(439)
For a 2 dB optical budget power penalty, see Eq (440) CD cMax z 4 5208 108 2 c R2
(440)
Table 42 shows estimated chromatic dispersion pulse propagation limits for a 1 dB optical power penalty calculated using Eq (439), assuming G652 fiber with CDc at 17 ps/(nm km) at 1550 nm, externally modulated DFB laser with chirp free ideal NRZ Gaussian pulse transmissions The actual pulse shape may be more rectangular (super Gaussian), which may reduce these limits Note, dispersion limits vary greatly between different manufacturer equipment and this table should be used only for general reference for possible maximum reach under ideal conditions Directly modulated DFB lasers experience frequency chirp, which greatly reduces these limits For accurate dispersion limit values, equipment manufacturer specifications should be consulted For a 2 dB optical power penalty see Table 43 For broad spectrum lasers such as Fabry-Perot or light emitting diodes (LED), lower transmission rates and a 1 dB optical budget, Eq (438) can be shown as Eq (441) CD cMax z 8 9938 107 2 c R fc
(441)
For example, if an LED source has an RMS spectral width of 1870 GHz (15 nm) at 1550 nm and is modulated at 1 Gbps it would have an estimated dispersion limit of 20 ps/nm or 12 km using G652 fiber To see the effect of laser chirp we can keep the chirp parameter C0 in Eq (420) and keep the assumption that the carrier wavelength is
Chromatic Dispersion
Bit Rate (Gbps) 25 10 40 100
Protocol (NRZ) OC-48 & STM-16 OC-192 & STM-64 OC-768 & STM-256 100G Ethernet
Chromatic Dispersion Limit 2 dB Penalty (ps/nm) 30100 1880 117 188
Distance Limit G652 Fiber (km) 1770 111 69 11
TABLE 43 Estimated Chromatic Dispersion Limits for Externally Modulated Chirp- Free DFB Laser over G652 Fiber with a 2 dB Power Penalty
far away from the zero dispersion wavelength; therefore, 3 can be assumed to be zero, and we get Eq (442)
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