Re: [questio]what relations between data rate and spectrum w
The best way to get the most accurate result is to transform the time-domain signal into frequency domain using discrete fourier transform(DFT) and take a look at its power spectrum.
If a good guess is needed, why don't we start from a simple case, the 1010 pattern? The 1010 pattern with 50% duty cycle is a typical pattern contains the "hightest frequency components" as compared to signal patterns such as PRBS7/23/31. The bandwidth of the ideal 1010 pattern is infinite since it has a rise/fall time of 0. In the real life, due to different kinds of losses and due to the fact that higher frequency components contained in the 1010 pattern subjects to higher degree losses, at certain harmonics, the higher frequency components contained in the 1010 pattern will become very small and can be neglect, where, that frequency point can be regarded as the bandwidth of the signal.
In order to relate time-domain signal to its frequency-domain counterparts, a lot of terms are used and most of which are very confusing in the definition. You must be careful when interpret their meanings. e.g.
The fundamental frequency of a 1010 pattern with a bit rate of X Gbps is 0.5X GHz due to the fact that it repeats itself 0.5XG times in one second. However, after performe the DFT to the signal and look at its spectrum, you will find that the bandwidth of the signal is not directly related to this "fundamental frequency" but relate to the fastest signal edges: rise/fall time. As a rule of thumb, the signal bandwidth(BW) relates to its Tr/Tf by BW=0.35/Tr. Someone prefer BW=0.5/Tr. Actually both of them has some assumptions behind regarding the rise/fall time(whether 80% or 90%) and the power losses that tolerated (70%-->3dB or 90%). Again, the most accurate results requires the DFT and the examination of the harmonics of its spectrum.
Another rule of thumb assuming a 7% rise/fall time of the signal period of a 1010 pattern is: BW=5th harmonic=2.5X GHz (for BR=XGbps) for clock signal, if the signal propagate down a long interconnect, the BW is roughtly 0.5X GHz (for BR=X Gbps) due to the fact that most of the high frequency components subjected to very large losses, thus is negligible.
For all the theory behind the above-comments, please refer to the following two SI books for details:
1. Signal Integrity - Simplified
2. High-Speed Digital Design: A Handbook of Black Magic
Author: Howard Johnson Graham Martin Graham
ISBN: 0133957241