Article

Shannon Says

by Dr. Howard Johnson. First printed in EDN magazine, November 13, 2003

C.E. Shannon, pioneer of the information age, says that the ultimate information-carrying capacity of a band-limited communications channel varies in proportion to its bandwidth and also as a function of the SNR within the channel. Given signal power S, total-received-noise power N, and channel bandwidth B (hertz), Shannon's famous theorem provides this upper boundary for the capacity C of a digital channel in bits per second (Reference 1):

Shannon's theorem applies nicely to the problem of communication across a digital backplane. In a typical digital backplane, crosstalk within the connectors mostly determines the SNR, assuming you've already done an adequate job of preventing crosstalk in your transceiver package and board layout. Connector crosstalk generally gets worse at higher frequencies. As you attempt to push the system to progressively faster bit rates, when you go beyond a few gigabits per second, the increasing crosstalk soon degrades your SNR to the point at which ordinary binary signaling no longer functions. That's the point at which many backplane designs sit today: They work up to a few gigabits per second and then fall apart. Redesigning the system to use exotic, low-loss board materials and fully digital adaptive equalization helps improve the intersymbol interference, but crosstalk still gets you. If you find yourself in this situation, Shannon's equation suggests three possible options.

First, take note of one thing that doesn't work. Increasing S (talking louder) doesn't help in a crosstalk-limited system; it just raises the level of noise. The SNR remains unaffected. The same thing happens in a trendy bar-everyone shouts, but you can't understand the person next to you.

What works? Buying better connectors. Connector vendors are always coming out with connectors that work at higher speeds (more B) but with a controlled SNR. The maximum bandwidth you can pump through the connector limits the ultimate performance attainable through this method. Unfortunately, the physical dimensions of your connector pins, vias, pads, and the thickness of your pc board limit the bandwidth. And, none of those physical dimensions is likely to shrink much anytime soon-certainly not to the same degree of scaling that has been so successful for on-chip geometries. Therefore, I predict that the bandwidths of dense backplane connectors won't surge much higher than 10 Gbps without some serious redesigning of the whole approach to pc-board construction.

What comes next? Substantially lower crosstalk is the method that Shannon prescribes for extracting yourself from the bandwidth-limited mess that the physical scale of your packaging creates. His equation says that you can live with a limited amount of B as long as you have a very small amount of noise.

Connector vendors will soon realize that they can achieve great improvements in the information-carrying capacity of their products by reducing crosstalk. For example, if crosstalk were sufficiently low, you could use 16-level PAM (pulse-amplitude modulation), effectively quadrupling your current operating speed. Such a system requires considerable sophistication in the transceivers but is actually possible. The great advantage of a multilevel PAM system is that it works at today's bandwidths, with today's vias, and on today's pc boards, but it delivers tomorrow's data rate.

Communications engineers traditionally deploy multilevel coding in situations in which the cost of improving the transceiver is less than the cost of improving the channel. As a result, engineers have used multilevel transmission on practically every type of long-distance or high-speed connection. Doing so started all the way back in 1885 with the duplex telegraph and later included QAM telephone modems, radio modems, satellite modems, DSL, and LAN transceivers. Each of these interfaces started as a simple binary channel and then evolved to a more efficient (and more complex) standard. Given the plummeting cost of gates in modern silicon ASICs and the spiraling cost of backplane hardware, the time has come to make the leap to multilevel coding for digital backplanes.