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I understand that higher-speed optical links require a stronger signal. For example, 16 Gbps Fibre Channel transceivers have to transmit at -1.3 dBm and receive at -10.3 dBm. If it falls below that, they will fall back to transmitting at 8 Gbps. That speed requires a transmit power of -8.2 dBm. Why is that?

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You can visualize a high-speed pulse signal by using an eye pattern. The "eye" opening is the measure of distinction between levels (vertical) and pulse sequence (horizontal). The larger the eye, the clearer the signal. enter image description here

Now, if you increase the signal frequency, the eye pattern becomes narrower and the signal levels may become less distinct, up to a point when they can't be properly recognized any more. Raising the amplitude increases the level distance and usually helps making them more distinct.

I'm not sure about FC but some higher-rate standards use multi-level signaling like PAM-4 (four levels for two simultaneous bits) which in turn requires more power to open the eyes.

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