Every multigigabit backplane, trace and cable distorts the signalspassing through it. This degradation may be slight or devastating,depending on the conductor geometry, materials, length and type ofconnectors used.
Because they spend their lives working with sine waves,communications engineers prefer to characterize this distortion in thefrequency domain. Figure 1 below shows the channel gain , alsocalled the frequencyresponse, of a perfectly terminated typical 50 ohm stripline (or100 ohm differential stripline).
|Figure1: The effective channel gain associated with a long PCB trace dependson the trace width, dielectric materials, length and type of connectorsused.|
The stripline acts like a low-pass filter, attenuatinghigh frequency sine waves more than lower-frequency waves. Figure 2 below illustrates thedegradation inherent to a digital signal passing through 0.5m of FR-4stripline.
|Figure2: Long traces reduce the amplitude of the input pulse and disperse itsrising and falling edges.|
The dielectric and skin effect losses in the trace reduce theamplitude of the incident pulse and disperse its rising and fallingedges. The received pulse, much smaller than normal, is called the runtpulse. In binary communication systems, any runt pulse that fails tocross the receiver threshold by a sufficient margin causes a bit error.
Three things degrade the amplitude of the runt pulse ina high-speed serial link: losses in the traces or cables, reflectionsdue to connectors and other signal transitions, and the limitedbandwidth of the driver and receiver. A classic test of dispersionappears in Figure 3, below .
|Figure3: This test waveform displays the worst-case runt-pulse amplitude.|
This particular waveform is adjusted so that the long, flat portionsof the test signal represent the worst-case, longest runs of ones orzeros available in your data code. This waveform displays therunt-pulse amplitude.
Without reflections, crosstalk orother noise, this single waveform (measured at the receiver) representsa worstcase test of channel dispersion. Longer traces introduce moredispersion, eventually causing receiver failure at a length of 1.5m inthis 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 thereceiver threshold at the instant sampling occurs. In a system withzero reflections, crosstalk or other noise, you could theoreticallyoperate with a very small voltage margin and still expect the system tooperate perfectly.
In a practical system, however, you must maintain a noise marginsufficient to soak up the maximum amplitude of all reflections,crosstalk and other noise in the system, while still keeping thereceived signal sufficiently above the threshold to account for thelimited bandwidth and noise inherent to the receiver.
A runt-pulse amplitude equal to 85 percent of the nominallow-frequency signal amplitude exceeds the receiver threshold by only35 percent, instead of the nominal 50 percent. A smaller runt pulsewith amplitude 75 percent of the normal size would reduce the voltagemargin by half, a huge hit to noise budget, but still workable. Forgeneric binary communication using no equalization, we would like tosee the runt pulse arrive with amplitude never smaller than 70 percentof the low-frequency pulse amplitude.
On the left side of Figure 4, below, is a sine wave with a period of two baud. To the extent that therunt-pulse pattern (101) looks somewhat like this sine wave, you shouldbe able to infer the runt-pulse amplitude from a frequency-domain plotof channel attenuation.
|Figure4: A runt-pulse amplitude equal to 85 percent of the nominallow-frequency signal amplitude reduces the voltage margin above thethreshold to only 35 percent, instead of the nominal 50 percent.|
In Figure 4 , the datawaveform has a baud rate of 2.5Gbps, and half of this frequency (theequivalent sine wave frequency) equals 1.25GHz. According to Figure 5, below, the half-metercurve gives you 4.5dB of attenuation at 1.25GHz. The same curve alsoshows 1.5dB of attenuation at one-tenth this frequency, correspondingroughly to the lowest frequency of interest in an 8B10B codeddata-transmission system.
The difference between these two numbers (-3dB) approximates theratio of runt-pulse amplitude to low-frequency signal amplitude at thereceiver. With only -3dB degradation, the system satisfies the 70percent frequency-domain criterion for solid link performance,precisely explaining why time-domain waveforms look so good at ahalf-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- domainapproximation.
This discrepancy arises partly from the harmonic construction of asquare wave, where the fundamental amplitude exceeds the amplitude ofthe square wave signal from which it is extracted, and partly from thenatural fuzziness inherent to any quick rule-of-thumb translationbetween the time and frequency domains. The simple frequency domaincriteria conservatively estimate these factors.
If your data code permits longer runs of zeros or ones than 8B10Bcoding, you must use a correspondingly lower frequency as your “lowestfrequency of interest.” In the time domain, you will see the receivedsignal creep closer to the floor or ceiling of its maximum range beforethe runt pulse occurs, making it even more difficult for the worst-caserunt pulse to cross the threshold.
|Figure5: The difference between high-frequency and low-frequency channel gainin this 2.5Gbps system equals 3dB.|
As a rule of thumb (see Figure 5,above) , we look at the difference between the channelattenuation at the highest frequency of operation (101010 pattern) andthe lowest frequency of operation (determined by your data-coding run length) toquickly estimate the degree of runt-pulse amplitude degradation at thereceiver. This simple frequency-domain method only crudely estimateslink performance. It cannot substitute for rigorous time-domainsimulation, but it can greatly improve understanding of link behavior.
A channel with less than 1dB of runt-pulse degradation works greatwith just about any ordinary CMOS logic family, assuming that you solvethe clock-skew problem either with low-skew clock distribution or byusing a clock recovery unit at the receiver. A channel with as much as3dB degradation requires nothing more sophisticated than a gooddifferential architecture with tightly placed, well-controlled receiverthresholds. A channel with 6dB of degradation requires equalization.
The Xilinx Virtex-4RocketIO transceiverincorporates three forms of equalization. The first is transmitpre-emphasis. Figure 6 below illustrates a simple binary waveform x[n] and the related firstdifference waveform x[n]-x[n-1].
|Figure6: The transmit pre-emphasis circuit creates a big kick at thebeginning of every transition.|
On every edge, the difference waveform creates a big kick. Thetransmit pre-emphasis circuit adds together a certain proportion of themain signal and the first-difference waveform to superimpose the bigkick at the beginning of every transition. As viewed by the receiver,each kick boosts the amplitude of the runt pulses without enlarging lowfrequency portions of the signal, which are already too big.
The first-difference idea helps you see how pre-emphasis works, butthat is not how it is built. The actual circuit sums three delayedterms: the pre-cursor, cursor and post-cursor. This architecture givesthe capacity to realize both first and second differences by adjustingthe coefficients associated with these three terms.
|Figure7: Over the critical range from DC to 1.25GHz, the pre-emphasisresponse rises smoothly.|
Programmable 5-bitmultiplying DACs control the three coefficients. The first and thirdamplitudes are always inverted with respect to the main center term, atrick accomplished by using the NOT-Q outputs of the first and thirdflip-flops.
As shown in Figure 7, above ,over the critical range from DC to 1.25GHz, the pre-emphasisresponse rises smoothly. The response peaks at 1.25GHz. If you clockthis pre-emphasis circuit at a higher data rate, the peak shiftscorrespondingly higher, always appearing just where you want it at afrequency equal to half the data rate.
|Figure8: Composing the pre-emphasis circuit with the channel produces aresponse much flatter than either curve.|
Figure 8, above , overlaysthe preemphasis response with the channel response at 1m, showing acomposite result (the equalized channel) that appears much flatter thaneither curve alone. In very simplistic terms, a flatter compositechannel response should make a better-looking signalin the time domain.
At shorter distances, the signal appears over-equalized. Theovershoot at each transition works fine in a binary system, assumingthat the receiver has ample headroom to avoid saturation with themaximum-sized signal. At 1m, the signal looks good, with very littlerunt-pulse degradation visible, and if you look closely, very littlejitter. The 1.5m waveform now just meets the 70 percent criteria forrunt-pulse success.
|Figure9: A pre-emphasis circuit doubles the length of channel over which youmay safely operate.|
Compared to a simple differential architecture, the pre-emphasiscircuit (Figure 9, above ) hasat leastdoubled the length of channel over which you may safely operate.
Besides the pre-emphasis circuit, the RocketIO transceiver alsoincorporates a sophisticated 6-zero, 9-pole receive-based linearequalizer. This circuitprecedes the data slicer. It comprises three cascaded stages of activeanalog equalization that may be individually enabled, turning on zero,one, two or all three stages in succession.
|Figure10: The linear equalizer in the receiver may be set to one of fourdistinct response curves preprogrammed to match the response of variouslengths of FR-4 PCB trace.|
Figure 10, above , presentsthe set of four possible frequency-response curves attainable with thisreceiver- equalization architecture. Each section of the equalizer istuned to approximate the channel response of a typical PCB channel withan attenuation of about 3dB at 2.5GHz.
With all stages on, you get a little more than 9dB of boost at2.5GHz. Because the response keeps rising all the way to 5GHz, thisequalizer is useful for data rates up to and beyond 10Gbps.
When setting up the equalizer, first select the number of sectionsof the Rx linear equalizer that best match your overall channelresponse. Then, fine-tune the overall pulse response using the 5-bitprogrammable coefficients in the transmit pre-emphasis circuit toobtain the lowest ISI, the lowest jitter or a combination of both.
After building the circuit, a clock-phase adjustment internal to thereceiver helps you map out BERbathtub curves, so you can corroborate the correctness of the equalizersettings. These two forms of equalization provide flexibility thatallows interoperation with many serial-link standards, meeting exacttransmitted signal specifications and adding receiver-basedequalization.
As a last defense against uncertain channel performance, the RocketIOtransceiver includes a manually adjustable six-tap decision feedbackequalizer (DFE) .
This device is integrated into the slicer circuit at the receiver.The DFE is particularly useful with poor-quality legacy channels notinitially designed to handle high serial data rates. It can accentuatethe incoming signal without exacerbating crosstalk.
To read a PDF version of this article, go to Extendingyour reachwith Serdes.