## Equalizing Cables

I would like to know more about equalization circuitry for high-speed-interconnect systems. As an example, how do you equalize LVDS signals transmitted through cables of say 10 to 50m. What is the guiding principle behind this concept, and do you tune the equalizer to optimize the signal integrity due to different cable lengths? Can you recommend a book or papers for engineers like me?

You should begin with a plot of the attenuation of your cable versus frequency, scaled for the maximum length you plan to use. You may obtain data for this plot from the cable manufacturer. At dc, cables always work well, but at higher frequencies, the response rolls off. The most important information on the plot is the total change in attenuation across the data-carrying frequency band of your signal. If the change in attenuation exceeds a couple of decibels, you need an equalizer to flatten the overall system response.

If you have a good clock-recovery subsystem that samples in the center of the received eye pattern, the data-carrying frequency band extends only to some high limit *F*_{MAX}=½*B*, where *B* is the bit-transmission rate for binary signaling. Frequencies greater than ½*B* encode subtle information about the shape of the rising and falling edges of the signal but are unnecessary for data recovery.

Lengthening your cable increases the attenuation of the high-frequency components near *F* _{MAX}, exaggerating the received signal's rise and fall time. At excessive lengths, the rise and fall time exceeds the bit interval at which point the signal cannot rise to full height during each bit before it must descend. Such a signal displays a smooth, rounded eye with considerable jitter at the transition times and highly objectionable intersymbol interference. In general, an attenuation of 3dB at *F*_{MAX} closes the eye about halfway, and 6dB closes it completely.

The low-frequency limit (*F*_{MIN}) of the data-carrying frequency band depends on the data-coding method. For example, uncoded, random digital data may contain arbitrarily long strings of ones or zeros that produce significant spectral content down to dc. Manchester coding, on the other hand, balances every up pulse with a corresponding down pulse. Manchester coding produces a low-frequency cutoff that is substantially greater than dc, perhaps at about one-quarter the data rate. Raising the low-frequency cutoff is important, because the difficulty of equalization depends on the ratio of *F*_{MIN} to *F*_{MAX}. Raising the low-frequency cutoff narrows the range of the spectrum you must flatten, making your problem less difficult.

If the change in the attenuation of your cable over *F*_{MIN} to *F*_{MAX} does not exceed 6 dB, a single-pole fixed equalizer is adequate. A simple implementation might pass your signal through a parallel *R*-*C* combination that then feeds a 50Ω load. The best values for the capacitor and resistor depend on your rise time and your tolerance for timing jitter. A reasonable starting place would be *R*=100Ω and *C*=0.0053/*B*. In this circuit, low-frequency signals suffer additional attenuation due to the series resistor, *R*, but high-frequency signals shoot directly through the *C* undisturbed. This circuit conveniently attenuates the lows while leaving the highs unchanged.

The popular 10BaseT system incorporates fixed equalization into its transmitter. The transmitter creates two copies of the transmitted signal—one regular and one delayed by some amount of time, *T*. Next, it forms the algebraic sum of one-and-a-half times the main signal minus half the delayed signal. The frequency response of such an equalizer looks like *H(f)*=1.5-0.5e* ^{-j2πfT}*.

If you plot out the frequency response of *H(f)* with *T*=½*B* you'll find unity gain at dc, sloping upward to a 6-dB peak at *f*=*B*; beyond that, the response goes nutty. The upward slope accomplishes your equalization. Beyond the peak, presumably, your receiver filter rolls off the nutty part of the response, so you never see it.

Either style of fixed equalizer can fix a 6-dB equalization problem on a binary code. The simple fixed equalizer works for any cable length from zero to the maximum length. If, however, you need to fix a more-than-6-dB problem or you are using multilevel coding, then you must implement either an adaptive equalizer or a specific equalizer circuit coded for each cable length.

Reference 1 contains my favorite introduction to adaptive equalization. Adaptive equalization is a hot topic, and there are lots of books about it.

Reference

**[1]** Bingham, John AC, "The Theory and Practice of Modem Design," John Wiley & Sons, New York, 1988.