EQUALIZATION - Advanced Signal Integrity for High-Speed Digital Design - page 520

x k

T T T T

C
− N

C C N − 1 C N

− N + 1

S

y k

Figure 12-25 Finite impulse response filter.

12.3.1 Transmitter Equalization

The basic architecture of a discrete linear equalizer is the transversal filter , also
known as a finite impulse response (FIR) filter , which is shown in Figure 12-25.
In the figure the rectangles represent delay elements, such as the stages of a
shift register. The circles represent the filter taps . In this filter, input samples
(typically, voltage samples), x k , propagate through the delay elements, each of
which has a delay value of T , which is also known as the tap spacing . At each
stage, the input samples are multiplied by the filter tap coefficient, C i , where
i is simply the index into the tap subscripts. With each cycle the outputs from
the taps are then summed to provide the filter output, y k . In effect, the current
and past values of the signal are linearly weighted with the equalizer coefficients
(also known as tap weights ) and then summed to produce the output.
The figure shows a total of 2 N taps in the filter, numbered from − N to N .

The main contribution comes from the cursor tap , C 0 . This tap is intended to
amplify the main portion of the signal. Filter taps with negative coefficients are
known as precursor taps ; those with positive coefficients are called postcursor
taps . Figure 12-25 shows symmetry in the number of precursor and postcursor
taps, but equalizers are typically designed with unequal numbers of precursor and
postcursor taps. Precursor taps compensate for dispersion-induced phase distor-
tion, which typically requires only a single tap. Postcursor taps compensate for
the ISI caused by amplitude distortion and may require multiple taps, depending
on the length of the channel with respect to the width of a data bit.
The output of the equalizer, y(k) , is expressed as the discrete convolution of
the input signal, x(k) , with the equalizer filter coefficients:

N

y(k) =

x(k − n)c n (12-21)

k =− N

where k is the sample number of the discretely sampled signal (i.e., the time
position of a given sample is t k = kT , where T is the tap spacing of the equalizer).