EQUALIZATION - Advanced Signal Integrity for High-Speed Digital Design - page 495

ISI-induced timing jitter and voltage margin loss by compensating for nonideal
aspects, in particular the loss of interconnects at high speed.
In this chapter we adopt a communications channel-based approach to analyz-
ing our signaling interfaces. Communications engineers view the I/O circuits and
the interconnect (also known as the channel )asfilters, as shown in Figure 12-1.
In previous chapters we noted the low-pass filtering effect of the I/O and inter-
connect. By viewing the system as a series of filters, including the equalizer, we
can determine the desired characteristics for a given equalizer.

12.1 ANALYSIS AND DESIGN BACKGROUND

Before considering equalization analysis and design, we must cover some
necessary background material. We first offer some motivation for employing
equalizers in high-speed signaling systems by examining the requirements for
maximizing data transfer rates. We then present the notion of linear time-invariant
(LTI) systems and show how to use their characteristics to analyze the behavior
of high-speed signals. Finally, we contrast the characteristics of an ideal
interconnect with that of a physically realizable interconnect.

12.1.1 Maximum Data Transfer Capacity

Shannon's capacity theorem [Shannon, 1949] describes the upper limit on the
information rate that can be transmitted over a communications channel. The
theorem is widely accepted in the scientific community and has never been
exceeded in practice. We provide a heuristic derivation of the capacity equation
with the motivation of developing an understanding of how closely we can
approach the theoretical maximum with conventional interconnects, and we then
demonstrate how equalization techniques allow us to come closer to achieving
the maximum rates.
We start by defining the data transfer rate in bits per second as the product
of the number of symbols transmitted per second ( S ) and the number of bits per
symbol ( B ):

D = SB (12-1)

The symbol transfer rate is related directly to the channel bandwidth by the
Nyquist rate [Nyquist, 1928]:

S = 2BW (12-2)

where BW is the bandwidth in hertz. To develop an intuitive feeling for
(12-2), consider a simple binary nonreturn-to-zero (NRZ) signaling scheme. In
Figure 12-2 we show a periodic pulse train with a repetition frequency f and a
random data sequence with the same fundamental frequency. A single symbol is
contained within successive edge positions, each positioned a width of T symbol
apart, and the full cycle is twice the symbol width. For the periodic signal, the