EQUALIZATION - Advanced Signal Integrity for High-Speed Digital Design - page 511

termination, high-pass filter, and dc power-limiting filter. Termination is provided
by the single resistor R TT , which is matched to the transmission-line impedance.
The high-pass filter is composed of the parallel capacitance and resistance, C HP
and R HP , whose values are chosen to give the desired frequency response. Finally,
C L and R L prevent the system from dissipating excess power at dc while pro-
viding a high-frequency path for the termination. The transfer function for this
circuit is

Z L
R TT + Z HP

H eq (f ) = (12-15)

+ Z L

where

R L

Z L (f ) = (12-16)

1 + j 2 πf R L C L

R HP

Z HP (f ) = (12-17)

1 + j 2 πf R HP C HP

From (12-15) through (12-17) we can plot the frequency response of the
equalizer, which is shown in Figure 12-16 for R TT = 100 , R HP = 5k ,

C HP 20 fF. In addition to the equalizer, the

figure shows the transfer function for the printed circuit board interconnect from
Example 12-1 and the combined response of the PCB-equalizer system. From
the transfer function we see that compared to the PCB alone, the passive equalizer
reduces the overall loss variation between dc and 10 GHz by 5.2 dB. The signifi-
cance of this reduced variation between minimum and maximum signals becomes
apparent when we consider that 6 dB of loss at the fundamental frequency is
sufficient to close the eye completely (see Figure 12-17). This means that if the
slope of the loss curve is such that high-frequency bit patterns (101010) are
attenuated 6 dB or more relative to low-frequency bit patterns (111000111000),
the eye will close. To comprehend the benefit of equalization, consider
Figure 12-16a, which shows that the magnitude of the equalized channel is more
lossy, but the total variation in the loss decreased from

= 100 fF, R L = 2 . 5k , and C L =

− −

23 . 5
dB. The reduction in the loss variation in our example doubles the frequency
at which the eye closes completely from approximately 2 to 4 GHz. The
nonequalized eye will close at

18 . 3dBto

− 6 dB, and the equalized eye will close when

there is 7-dB peak. Thus, the equalizer provides

an increase in usable bandwidth simply by flattening the slope of the loss curve
that will allow us to extract more performance from the system by running
at a substantially higher data rate. Assuming that the noise power spectrum
is unaffected by the equalizer, the Shannon-Hartley theorem predicts that the
equalizer would allow a doubling of the maximum data rate. In terms of the
expected performance demand trend, an equalizer can extend the useful life of a
given interconnect by approximately two years. (Of course, the exact benefit for
a given system will depend on the specifics of the channel loss characteristics,
the equalizer design, and actual performance demand.)

− 6 dB of variation from the −