Filter Induced Signal Distortion

So far we have considered linear crosstalk from a single device. In a realistic optical network, an optical signal may pass through many nodes before reaching its final destination, while suffering from crosstalk at each node. As a result, crosstalk can accumulate to a large level by the time signal reaches its destination. At the same time, signal may become distorted as it passes through many optical filters. In this section we address the filter-concatenation problem [35]—[37].

All filters in an optical network are designed to be wide enough to pass the signal spectrum without any distortion. However, if the signal passes through a large number of optical filters during its transmission, one must study the effects of filter concatenation. Consider a filter with the transfer function H(co). Even when a signal passes through this filter twice, the effective filter bandwidth becomes narrower than the original value because H2(co) is a sharper function of frequency than H(co). A cascade of many filters may narrow the effective bandwidth enough to produce clipping of the signal spectrum. This effect is shown schematically in Figure 9.6, where transmissivity of the signal is plotted after 12 third-order Butterworth filters of 36-GHz bandwidth. Since it may be difficult to align the passband of filters precisely at all locations, the response function is also shown when filters are misaligned within the range of ±5 GHz. Clearly, the effective transfer function after 12 filters is considerably narrower and its effective bandwidth is reduced further when individual filters are misaligned even by a relatively small amount.

To see how such bandwidth narrowing affects an optical signal, the spectrum of a 10-Gb/s signal is also shown in Figure 9.6 in the cases of the NRZ format and the RZ format with 50% duty cycle. Although the NRZ signal remains relatively unaffected, the RZ spectrum will be significantly clipped even after 12 filters, although the 36GHz bandwidth of each filter exceeds the bit rate by a factor of 3.6. A second effect produced by optical filters is related to the phase of the transfer function. As discussed

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Number of filters

Figure 9.7: Eye-closure penalty as a function of the number of filters for a 10-Gb/s RZ signal with 50% duty cycle. The bandwidth of filters is varied in the range of 32 to 50 GHz. (After Ref. [16]; ©2003 IEEE.)

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Number of filters

Figure 9.7: Eye-closure penalty as a function of the number of filters for a 10-Gb/s RZ signal with 50% duty cycle. The bandwidth of filters is varied in the range of 32 to 50 GHz. (After Ref. [16]; ©2003 IEEE.)

in Section 7.3, a frequency-dependent phase associated with the transfer function can produce a relatively large dispersion. The concatenation of many filters will enhance the total dispersion and may lead to considerable signal distortion [38],

The penalty induced by cascaded filters is quantified through the extent of eye closure at the receiver. Among other things, it depends on the shape and bandwidth of the filter passband. It also depends on whether the RZ or the NRZ format is employed for the signal and is generally larger for the RZ format. As an example, Figure 9.7 shows the increase in eye-closure penalty as the number of cascaded filters increases for a 10-Gb/s RZ signal with 50% duty cycle [16], The transfer function of all filters corresponds to a third-order Butterworth filter. Although a negligible penalty occurs when the filter bandwidth is 50 GHz, it increases rapidly as the bandwidth is reduced below 40 GHz. The penalty exceeds 4 dB when the signal passes through 30 filters with 32-GHz bandwidth.

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