EQUALIZATION - Advanced Signal Integrity for High-Speed Digital Design - page 532

to 15 in. in length [Coleman et al., 2004; PCI-Sig 2005]. However, effectively
equalizing channels that may exhibit wide variation in frequency-dependent loss
(e.g., a range of PCB lengths) requires that the equalizer design contain the
flexibility to set the equalizer coefficients adaptively to minimize the ISI. Such
an equalizer, called an adaptive equalizer , was invented by Lucky in 1964 to
improve data transmission rates over telephone lines from 1200 b/s (using non-
adaptive equalizers based on average channel characteristics) to 9600 b/s [Lucky,
2006].
The benefit of adaptive equalization is the flexibility to accommodate a range
of interconnect lengths and/or data rates. It does, however, add significant com-
plexity to the design and consumes more power and chip real estate. A high-level
schematic of the adaptive equalizer structure is shown in Figure 12-35. The intent
of the adaptation is illustrated in Figure 12-36. The figure depicts the deviation
of the equalized signal from desired value as a function of equalizer coefficients.
The deviation is plotted as a set of error contours in which the error is the dif-
ference in the equalized output, y(t) , from the training data, y(t) . The error is a

convex function of the equalizer coefficients, so that it has a global minimum.
The goal of the adaptive algorithm is to converge on a set of coefficient values
that minimize the error in a small number of iterations. The general approach of
an adaptive equalizer to updating the equalizer tap coefficient is

c new = c old + ( step size )( error function )( input function ) (12-28)

The error function is typically based on the difference between the actual equal-
ized signal y . The input function is based

on the signal at the input to the equalizer, and step size is a design parameter.
Designers have many options for implementing adaptive equalizers, the range of
which extends beyond our scope. However, we present a pair of examples to
provide some insight into the operation of adaptive equalizers.
The first example is the adaptive implementation of the zero forcing equalizer.
In this approach a known data pattern (a.k.a. training sequence ) of equal or larger
length than that of the equalizer is transmitted and equalized. The coefficients
are updated from the equalized results using

y and the desired equalizer output

c k (n + 1 ) = c k (n) + k [

y(n) − y(n) ] x(n − k)

(12-29)

x ( t ) y ( t )

i n

Linear
Equalizer

y ( t )

Coefficient
Update

+

Training Data

Figure 12-35 Adaptive linear equalizer.