IEEE Solid-State Circuits Magazine - Fall 2017 - 13

A C IRCU IT FOR ALL SEA SONS

Behzad Razavi

The Decision-Feedback Equalizer

The Need for Equalization
As high-speed random data propagates through a medium with a limited bandwidth (also called a "lossy"
medium), it is dispersed. That is, the
data edges become slower, possibly disallowing full transition if a
010 or 101 sequence occurs [Figure 1(a)]. This sluggishness of the
channel also makes the zero crossing
times of the data a function of the bit
amplitudes, causing significant jitter.
Both degradations increase the bitdetection error rate. In the frequency
domain, the channel attenuates the
high-frequency content of the data
[Figure 1(b)].
The frequency-dependent channel loss depicted in Figure 1(b) can
be undone by means of a circuit
having the inverse response, i.e., a
high-pass filter (HPF). As illustrated
in Figure 1(c), if subjected to such a
response, the received data assumes
its original, undispersed shape and
more easily lends itself to detection. This HPF exemplifies a "linear"
equalizer as it can be approximated
by a finite impulse response filter
incorporating only linear stages (delay
units and scaling coefficients). We
Digital Object Identifier 10.1109/MSSC.2017.2745939
Date of publication: 16 November 2017

say the equalizer provides a highfrequency "boost" to compensate for
the channel loss.

izer does not suffice in most practical cases. Specifically, a typical
channel introduces, in the signal
path, i mp e d a n ce discontinuities
(mismatches) resulting from connectors and other physical interfaces
between boards, cables, etc. Such
discontinuities manifest themselves
as deep notches in the channel's frequency response (Figure 2) that would
be difficult to compensate by a linear equalizer.
To appreciate the beauty of DFEs,
we first return to the time domain and
view the data waveform as the superposition of random steps shifted in time by
integer multiples of Tb [Figure 3(a)].

The Need for Decision-Feedback
Equalization
While intuitively appealing, linear
equalization faces three issues. First,
since it requires a large amount of
boost for very lossy channels, it significantly amplifies high-frequency
noise, corrupting the data. Second,
a high boost demands multiple
stages, each one inevitably limiting
the bandwidth and consuming considerable power. Third, the inverse
response provided by a linear equal-

Din

Dispersive
Channel
t

Dout
t

(a)
Spectrum of
Random Data

Channel Response

The decision-feedback equalizer (DFE)
dates back to the 1960s [1] and began
to appear in high-speed wireline communication systems in the early 2000s.
In this article, we study the properties
of this circuit and describe its "analog" implementations.

(b)
Dispersive
Channel

HPF

t
(c)

FIGURE 1: (a) The dispersion of random data in a lossy channel, (b) the channel frequency
response showing attenuation of high-frequency components, and (c) the use of an HPF to
equalize the channel.

IEEE SOLID-STATE CIRCUITS MAGAZINE

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Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Fall 2017