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Example at 5 Gb/s
When the SNR slope exceeds -40 dB/decade at the operating frequency, 4-level
signaling is almost always superior.
Let's work an example.
Here we start with a binary system operating at 5 Gb/s. (This is still over a PCB
stripline 48 inches long, 7 mils wide, in FR-4.) Let's reduce the operating frequency
by a factor of two, and plan to use four-level coding (two bits per baud).
B=2, so we gain a factor of log(2)*40=13.6 dB in SNR due to the lower operating frequency.
N=4 (four levels, with three spaces), so we have cut our slicing threshold spacing by a
factor of three, which penalizes us by 20*log(3)=9.5 dB.
Looks like the multilevel system will have an SNR ADVANTAGE of about 4.1 dB.
Of course, there's a lot more to the analysis than that, as we need to include other improvements
due to adaptive equalization, error-coding, and so forth. The net result I'd like you to remember
is this:
When facing a brick-wall deterioration in SNR (like that produced by dielectric loss effects
in PCB's), consider multilevel signaling.
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