EQUALIZATION - Advanced Signal Integrity for High-Speed Digital Design - page 525

8000

7800

7600

7400

7200

7000

6800

6600

6400

6200

6000

− 0.34 − 0.32 − 0.3 − 0.28 − 0.26 − 0.24

C 1

Figure 12-29 Worst-case eye trend for the two-tap equalizer for Example 12-4.

In summary, the two-tap equalizer is capable of meeting the voltage and
timing specs proposed, with some room for adjustment. Addition of a precursor
improves the margins by 7.5% for eye height and 3.8% for eye width. Addition
of the additional postcursor taps provides an additional 2.4% increase in eye
width but no improvement in eye height.
The final step in this example is to use the results to decide how many taps
to include in the equalizer design. The two-tap design provides a sufficient eye
to meet the design specs, and it can be implemented with a very simple design.
In general, designers will choose the simplest equalizer design that meets the
requirements for a given application. In our case, the two-tap equalizer will work
just fine. Longer channels will typically have more attenuation, causing the ISI to
intrude on additional postcursor bit positions and may therefore require additional
equalizer taps. Higher data rates may also require more taps.

12.3.2 Coefficient Selection

At this point the question of how to determine the tap coefficients seems appropri-
ate to consider. In this section we present a method that can be used to establish
coefficient values based on specific performance criteria. The method, called a
zero forcing solution (ZFS), sets the tap coefficients to force the equalizer output
to match the values desired at all sample points. [Qureshi, 1985; Sklar, 2001].
Development of the algorithm follows.
Given a pulse response input to the equalizer, we start by extracting samples
from the input stream x i , where i runs from − n pre to n post , with n pre being

the number of precursor taps and n post the number of postcursor taps in the
equalizer. This gives a total of n pre

+ n post + 1 samples. We can express the