Howard Johnson, Signal Consulting, and Mike Degerstrom, Xilinx
Embedded.com

Every multigigabit backplane, trace and cable distorts the signals passing through it. This degradation may be slight or devastating, depending on the conductor geometry, materials, length and type of connectors used.

Because they spend their lives working with sine waves, communications engineers prefer to characterize this distortion in the frequency domain. Figure 1 below shows the channel gain, also called the frequency response, of a perfectly terminated typical 50 ohm stripline (or 100 ohm differential stripline).

Figure 1: The effective channel gain associated with a long PCB trace depends on the trace width, dielectric materials, length and type of connectors used.

The stripline acts like a low-pass filter, attenuating high frequency sine waves more than lower-frequency waves. Figure 2 below illustrates the degradation inherent to a digital signal passing through 0.5m of FR-4 stripline.

Figure 2: Long traces reduce the amplitude of the input pulse and disperse its rising and falling edges.

The dielectric and skin effect losses in the trace reduce the amplitude of the incident pulse and disperse its rising and falling edges. The received pulse, much smaller than normal, is called the runt pulse. In binary communication systems, any runt pulse that fails to cross the receiver threshold by a sufficient margin causes a bit error.

Three things degrade the amplitude of the runt pulse in a high-speed serial link: losses in the traces or cables, reflections due to connectors and other signal transitions, and the limited bandwidth of the driver and receiver. A classic test of dispersion appears in Figure 3, below.

Figure 3: This test waveform displays the worst-case runt-pulse amplitude.

This particular waveform is adjusted so that the long, flat portions of the test signal represent the worst-case, longest runs of ones or zeros available in your data code. This waveform displays the runt-pulse amplitude.

Without reflections, crosstalk or other noise, this single waveform (measured at the receiver) represents a worstcase test of channel dispersion. Longer traces introduce more dispersion, eventually causing receiver failure at a length of 1.5m in this example.

One measure of signal quality at the receiver is voltage margin. This number equals the minimum distance in volts between the signal amplitude and the receiver threshold at the instant sampling occurs. In a system with zero reflections, crosstalk or other noise, you could theoretically operate with a very small voltage margin and still expect the system to operate perfectly.

In a practical system, however, you must maintain a noise margin sufficient to soak up the maximum amplitude of all reflections, crosstalk and other noise in the system, while still keeping the received signal sufficiently above the threshold to account for the limited bandwidth and noise inherent to the receiver.

A runt-pulse amplitude equal to 85 percent of the nominal low-frequency signal amplitude exceeds the receiver threshold by only 35 percent, instead of the nominal 50 percent. A smaller runt pulse with amplitude 75 percent of the normal size would reduce the voltage margin by half, a huge hit to noise budget, but still workable. For generic binary communication using no equalization, we would like to see the runt pulse arrive with amplitude never smaller than 70 percent of the low-frequency pulse amplitude.

Runt-pulse degradation
On the left side of Figure 4, below, is a sine wave with a period of two baud. To the extent that the runt-pulse pattern (101) looks somewhat like this sine wave, you should be able to infer the runt-pulse amplitude from a frequency-domain plot of channel attenuation.

Figure 4: A runt-pulse amplitude equal to 85 percent of the nominal low-frequency signal amplitude reduces the voltage margin above the threshold to only 35 percent, instead of the nominal 50 percent.

In Figure 4, the data waveform has a baud rate of 2.5Gbps, and half of this frequency (the equivalent sine wave frequency) equals 1.25GHz. According to Figure 5, below, the half-meter curve gives you 4.5dB of attenuation at 1.25GHz. The same curve also shows 1.5dB of attenuation at one-tenth this frequency, corresponding roughly to the lowest frequency of interest in an 8B10B coded data-transmission system.

The difference between these two numbers (-3dB) approximates the ratio of runt-pulse amplitude to low-frequency signal amplitude at the receiver. With only -3dB degradation, the system satisfies the 70 percent frequency-domain criterion for solid link performance, precisely explaining why time-domain waveforms look so good at a half-meter.

The actual runt-pulse amplitude in the time domain is 85 percent, not quite as bad as the -3dB predicted by the quick frequency- domain approximation.

This discrepancy arises partly from the harmonic construction of a square wave, where the fundamental amplitude exceeds the amplitude of the square wave signal from which it is extracted, and partly from the natural fuzziness inherent to any quick rule-of-thumb translation between the time and frequency domains. The simple frequency domain criteria conservatively estimate these factors.

If your data code permits longer runs of zeros or ones than 8B10B coding, you must use a correspondingly lower frequency as your "lowest frequency of interest." In the time domain, you will see the received signal creep closer to the floor or ceiling of its maximum range before the runt pulse occurs, making it even more difficult for the worst-case runt pulse to cross the threshold.

Figure 5: The difference between high-frequency and low-frequency channel gain in this 2.5Gbps system equals 3dB.

As a rule of thumb (see Figure 5, above), we look at the difference between the channel attenuation at the highest frequency of operation (101010 pattern) and the lowest frequency of operation (determined by your data-coding run length) to quickly estimate the degree of runt-pulse amplitude degradation at the receiver. This simple frequency-domain method only crudely estimates link performance. It cannot substitute for rigorous time-domain simulation, but it can greatly improve understanding of link behavior.

A channel with less than 1dB of runt-pulse degradation works great with just about any ordinary CMOS logic family, assuming that you solve the clock-skew problem either with low-skew clock distribution or by using a clock recovery unit at the receiver. A channel with as much as 3dB degradation requires nothing more sophisticated than a good differential architecture with tightly placed, well-controlled receiver thresholds. A channel with 6dB of degradation requires equalization.

Transmit pre-emphasis
The Xilinx Virtex-4 RocketIO transceiver incorporates three forms of equalization. The first is transmit pre-emphasis. Figure 6 below illustrates a simple binary waveform x[n] and the related first difference waveform x[n]-x[n-1].

Figure 6: The transmit pre-emphasis circuit creates a big kick at the beginning of every transition.

On every edge, the difference waveform creates a big kick. The transmit pre-emphasis circuit adds together a certain proportion of the main signal and the first-difference waveform to superimpose the big kick at the beginning of every transition. As viewed by the receiver, each kick boosts the amplitude of the runt pulses without enlarging low frequency portions of the signal, which are already too big.

The first-difference idea helps you see how pre-emphasis works, but that is not how it is built. The actual circuit sums three delayed terms: the pre-cursor, cursor and post-cursor. This architecture gives the capacity to realize both first and second differences by adjusting the coefficients associated with these three terms.

Figure 7: Over the critical range from DC to 1.25GHz, the pre-emphasis response rises smoothly.

Programmable 5-bit multiplying DACs control the three coefficients. The first and third amplitudes are always inverted with respect to the main center term, a trick accomplished by using the NOT-Q outputs of the first and third flip-flops.

As shown in Figure 7, above, over the critical range from DC to 1.25GHz, the pre-emphasis response rises smoothly. The response peaks at 1.25GHz. If you clock this pre-emphasis circuit at a higher data rate, the peak shifts correspondingly higher, always appearing just where you want it at a frequency equal to half the data rate.

Figure 8: Composing the pre-emphasis circuit with the channel produces a response much flatter than either curve.

Figure 8, above, overlays the preemphasis response with the channel response at 1m, showing a composite result (the equalized channel) that appears much flatter than either curve alone. In very simplistic terms, a flatter composite channel response should make a better-looking signal in the time domain.

At shorter distances, the signal appears over-equalized. The overshoot at each transition works fine in a binary system, assuming that the receiver has ample headroom to avoid saturation with the maximum-sized signal. At 1m, the signal looks good, with very little runt-pulse degradation visible, and if you look closely, very little jitter. The 1.5m waveform now just meets the 70 percent criteria for runt-pulse success.

Figure 9: A pre-emphasis circuit doubles the length of channel over which you may safely operate.

Compared to a simple differential architecture, the pre-emphasis circuit (Figure 9, above) has at least doubled the length of channel over which you may safely operate.

Linear-receive equalizer
Besides the pre-emphasis circuit, the RocketIO transceiver also incorporates a sophisticated 6-zero, 9-pole receive-based linear equalizer. This circuit precedes the data slicer. It comprises three cascaded stages of active analog equalization that may be individually enabled, turning on zero, one, two or all three stages in succession.

Figure 10: The linear equalizer in the receiver may be set to one of four distinct response curves preprogrammed to match the response of various lengths of FR-4 PCB trace.

Figure 10, above, presents the set of four possible frequency-response curves attainable with this receiver- equalization architecture. Each section of the equalizer is tuned to approximate the channel response of a typical PCB channel with an attenuation of about 3dB at 2.5GHz.

With all stages on, you get a little more than 9dB of boost at 2.5GHz. Because the response keeps rising all the way to 5GHz, this equalizer is useful for data rates up to and beyond 10Gbps.

When setting up the equalizer, first select the number of sections of the Rx linear equalizer that best match your overall channel response. Then, fine-tune the overall pulse response using the 5-bit programmable coefficients in the transmit pre-emphasis circuit to obtain the lowest ISI, the lowest jitter or a combination of both.

After building the circuit, a clock-phase adjustment internal to the receiver helps you map out BER bathtub curves, so you can corroborate the correctness of the equalizer settings. These two forms of equalization provide flexibility that allows interoperation with many serial-link standards, meeting exact transmitted signal specifications and adding receiver-based equalization.

Decision-feedback equalizer
As a last defense against uncertain channel performance, the RocketIO transceiver includes a manually adjustable six-tap decision feedback equalizer (DFE).

This device is integrated into the slicer circuit at the receiver. The DFE is particularly useful with poor-quality legacy channels not initially designed to handle high serial data rates. It can accentuate the incoming signal without exacerbating crosstalk.

Howard Johnson is president of Signal Consulting Inc. and Mike Degerstrom is Sr. Staff Signal Integrity Design Engineer, Xilinx Inc.

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