Differential Impedance Measurementwith Time Domain Reflectometry Application Note 1382-5

by Eric Bogatin, Bogatin Enterprisesand Mike Resso, Agilent Technologies

Who Should Read This Application Note?

This application note is writtenfor hardware designers of high-speed digital systems, includinghigh speed backplanes (Teradyne,etc.), high speed interconnects(Molex, Amp, etc.) or laser modu-lator drive circuitry (Nortel,Lucent, JDS Uniphase, etc).

Introduction

Differential-impedance circuitboards are becoming more com-mon as low-voltage differentialsignaling (LVDS) devices prolifer-ate. Yet there is much confusionin the industry about what differ-ential impedance means, how todesign for it, and how to leverageits benefits for noise rejection.Knowing the general features of

Table of Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1

Differential Varieties . . . . . . . . . . . . . . . . 2

Differential vs. Single-Ended . . . . . . . . . 3

Time-Dependent Impedance . . . . . . . . . 4

Measuring Differential Pairs . . . . . . . . . 5

Differential Driving. . . . . . . . . . . . . . . . . . 6

Impedance Matrix . . . . . . . . . . . . . . . . . . 7

Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Even and Odd Modes . . . . . . . . . . . . . . . . . 8

Measuring Odd- and Even-Mode Impedances . . . . . . . . . . . . . 9

Simultaneous Measurements . . . . . . . 11

Crosstalk . . . . . . . . . . . . . . . . . . . . . . . . . 12

Skewed Differential Signals . . . . . . . . 13

Full Characterization . . . . . . . . . . . . . . . 14

Signals Crossing a Gap . . . . . . . . . . . . . 15

Differential Signals Crossing a Gap . . 16

Ease Dual-Channel TDR Measurements . . . . . . . . . . . . . . . . 17

Support, Services, and Assistance . . . 18

Related Literature . . . . . . . . . . . . . . . . . 18

differential-impedance transmis-sion lines and how they can becharacterized with traditionalTDR instruments can help in thedesign and testing of high-speeddigital systems.

Although differential pairs havebeen used for high-speed inter-connects since the early 1960s, itis only in the last few years thatthe introduction of LVDS technol-ogy has accelerated their use.Differential pairs have proliferat-ed into almost every high-speedapplication. In addition to theiruse in many common board-levelbuses such as SCSI, Rambus®RDRAMs™ and InfiniBand, theyare used in virtually all high-speed serial links. However, evenwith this widespread use, theproperties of differential pairsare often poorly understood or misunderstood.

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A differential pair is simply twotransmission lines that are cou-pled in some way. There are anumber of ways of distinguishingthe various types of coupledtransmission lines, based on theirmodal properties. The lines canbe strongly or weakly coupled. Apair of lines is balanced when thesignal paths have the same elec-trical properties as the returnpaths. Twisted pairs are balancedlines, while microstrip pairs are unbalanced.

When the two lines have the samecross-sectional geometry, they arecalled symmetric and have a sim-plified electrical description.Finally, when the dielectric ishomogeneous (all field lines seeexactly the same dielectric con-stant), each of the two modes willpropagate at the same speed. Thisis the case for stripline pairs.

Differential Varieties

In addition to the intrinsic funda-mental electrical properties of theinterconnects themselves, thenature of the signals on the pairof lines can be described in termsof the voltage patterns imposed.When the signal on one line isindependent of the signal on anadjacent line, the transmissionlines are not really being used aspart of a differential pair; eachline is being used as a single-ended line.

When the lines are differentiallydriven but there is no dc connec-tion to ground, the external planeacts as a virtual ground. Its volt-age reference is capacitively tiedto the midpoint of the two volt-ages on the signal lines. Alter-natively, the plane can be dc con-nected to ground, as is commonlyimplemented in high-speed differ-ential signaling.

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To understand what makes a dif-ferential pair different from a single-ended transmission line, itis useful to consider a coplanarmicrostrip with a floating planebelow it. In this configuration, thecoplanar traces compose a bal-anced single-ended transmissionline, with one trace the signalpath and the other the returnpath. The impedance of this linedepends on the line parametersof the capacitance and loopinductance per length of thecoplanar pair.

If a floating metal plane isbrought underneath this coplanarpair, the impedance of the lineswill be changed. How this thirdconductor influences the single-ended impedance is the basis ofunderstanding what differentialimpedance really means. A timedomain reflectometer (TDR) canbe used as a tool to measure theimpedance of the lines as the planeis moved into their proximity.

The equipment used for theseexamples is an Agilent 86100Infiniium DCA oscilloscope main-frame with an Agilent 54754A dif-ferential TDR plug-in module.This module can be operated as asingle- or a dual-channel TDR,with the step waveforms fromeach channel adjusted for differ-ential drive or common drive. Theaddition of an Agilent 83484A2-channel, 50-GHz module, allowsfor measurements to be taken onthe waveforms that appear at thefar end of the transmission linepair. This plug-in displays whatthe actual signal of a differentialreceiver would detect after thetransmission through the pair can be emulated.

One channel of the differentialTDR (DTDR) plug-in can be usedto perform conventional TDRanalysis. A 35 ps, fast-edge stepsignal is generated and launchedthrough a 50Ω source impedanceto the device under test (DUT).The voltage launched into theinternal 50Ω transmission lineconnecting from the internalsource to the SMA connector onthe front panel is measured witha very fast sampling scope anddisplayed. Reflected voltages(from impedance discontinuities,for example), are displayed asincreasing voltages (for higherimpedances) or decreasing volt-ages (for lower impedances). Inthis way, the TDR can act as avery fast, time-domain impedanceanalyzer. The reflected voltage isa direct measure of the imped-ance of the DUT.

Differential vs. Single-Ended

Figure 1. Probing physical layer with N1020A TDR probe kit.

Using this setup, the measuredTDR response from three differ-ent microstrip interconnects isdisplayed in the TDR plot in fig-ure 2. In the top trace, the linewidth is equal to the dielectricthickness, and the impedance isabout 70Ω. In the middle trace,the line width is twice the dielec-tric thickness. Since there isalmost no reflected voltage, theimpedance is measured as justslightly less than 50Ω. In the bot-tom trace, the fabricated linewidth is eight times the dielectricthickness. This is a very wide lineand the measured impedance isvery low, less than 20Ω.

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Time-Dependent Impedance

The time-dependent impedance ofthe DUT can be extracted directlyfrom the measured voltage. TheAgilent 86100 mainframe can per-form this analysis automatically,displaying not only the measuredvoltage but also the extractedimpedance. The calculated imped-ances of the three microstriptransmission lines are displayedin figure 2.

One interesting observation isthat each line has the same physi-cal length of nine inches, yet theirelectrical lengths are different.The highest impedance line hasthe shortest electrical length, dueto the lower effective dielectricconstant of the narrow microstripline. The narrowest line has morefringe fields in air, contributing toa lower effective dielectric con-stant and hence shorter round-trip time delay. The widest linehas the lowest impedance andleast amount of field lines in air,resulting in higher effectivedielectric constant and longestround-trip delay.

Figure 2. The impedance of microstriptransmission lines of different widths.

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Measuring Differential Pairs

The use of a second TDR channelallows analysis of the propertiesof differential transmission linepairs. The simplest way of think-ing about differential impedanceis to consider a coplanar trans-mission line composed of twotraces on an FR4 substrate. Withno metal plane beneath them,they represent a simple coplanartransmission line. The impedanceof this transmission line dependson the line parameters of thecapacitance and loop inductanceper length. What will happen tothe impedance a signal sees if thecoplanar pair passes over a float-ing metal plane?

To explore this scenario, a simpletest board was built with a copla-nar pair of traces mounted to anFR4 substrate. For the first fourinches, there is no plane on thebackside of the board. For thesecond four inches, there is a continuous plane. The front endof the coplanar pair has an SMAconnector that is interfaced tothe TDR through a 50Ω coaxcable. The TDR can drive a signalinto the coplanar pair, with onetrace acting as the signal and theother trace acting as the returnpath. Since this is a balancedpair, it doesn't matter which lineis which. The TDR allows directmeasurement of the impedancethe signal sees in propagatingdown the line (figure 3).

In the first four inches, theimpedance is rather high, about150Ω. This is due to the relativelylarge separation of the traces,with higher inductance per lengthand lower capacitance per lengththan is typical of microstrips.

In the second half of the trace,where the plane extends beneaththe traces, the impedance the sig-nal sees is dramatically reducedto about 100Ω. This drop inimpedance is due to the change in the line parameters caused bythe proximity of the plane below.The total capacitance between the two lines is dominated by theseries combination of the cou-pling capacitance from one line tothe plane and the capacitance ofthe plane up to the second line.This series capacitance is muchlarger than the direct line-to-line capacitance. In addition, the loopinductance is reduced due to theinduced eddy currents generatedin the plane by the signal edgepropagating down the transmis-sion line. This combination of factors results in a reduction ofthe impedance to only 100Ω.

Even though there is no directelectrical connection between thetwo coplanar lines and the planebelow, the electromagnetic cou-pling has a significant impact onthe impedance a signal sees mov-ing down the coplanar lines. It isnot a coincidence that the geome-try of the second half corre-sponds to two single-ended lines,each with a single-ended charac-teristic impedance of 50Ω.

This experiment leads to the sim-plest possible description of dif-ferential impedance. When thetwo coplanar lines were driven asa single-ended transmission line,the signal was the voltage differ-ence between the two lines. Theimpedance the signal saw was150Ω where there was no planeand 100Ω where there was aplane. In the region where thereis a plane below, the transmissionlines look like two coupled micro-strip lines (a differential pair).

Figure 3. The TDR allows direct measure-ment of the impedance the signal sees inpropagating down the line.

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Driving the two transmissionlines by single-ended signals thatare exactly out of phase is calleddifferential driving. As the signalspropagate down the differentialpair, there is a voltage patternbetween each signal line and thereference plane below. In addi-tion, there is a signal between thetwo signal lines. This is called thedifference signal or differentialsignal. If the differential pair isdriven symmetrically, the differ-ential signal voltage is twice thesingle-ended signal voltage.

The difference signal is the samesignal as if the two coplanartraces are driven as a single-endedline, as in the previous example.In this case, the impedance thesignal saw was 100Ω in the regionwhere there was a plane under-neath. If the two microstrips weredriven differentially, the differ-ence signal would also see animpedance of 100Ω. The imped-ance the difference signal sees iscalled the difference impedanceor differential impedance.

Differential impedance is reallythe impedance seen by the differ-ence signal that is driven betweenthe two signal lines in the differ-ential pair. The impedance the

Differential Driving

difference signal sees is the ratioof the signal voltage (differencevoltage) to the current in the line.The difference voltage is twice thevoltage of the edges driven intoeach line. The current into eachline is related to the impedance of each individual line in the pair.There is an additional currentbetween the signal lines that isdue to the coupling between thetraces themselves. This is general-ly a small amount, but cannot be neglected.

In this simple perspective, differ-ential impedance is the imped-ance the difference signal seeswhen opposite-polarity edges arelaunched in a differential pair oftransmission lines. And, as illus-trated before, this is also theimpedance a signal would see if itwere launched between the twosignal lines, keeping the externalplane as a floating plane.

To quantify the concepts of differ-ential impedance, it is importantto introduce the formalism ofdescribing the nature of the cou-pling between transmission lines.This allows any arbitrary pair ofcoupled lines to be analyzed withthe same methods.

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Impedance Matrix

⊗ ⊗I I1 2

V1 V2

V1 = Z11 I1 + Z12 I2

V2 = Z22 I2 + Z21 I1

Example:Characteristic Impedance Matrix (Ω): 1 21 49.6 6.42 6.4 49.6

If there were no coupling betweentransmission lines, the imped-ance of a line, as defined by theratio of the voltage across thepaths and the current throughthem, would depend only on theline parameters of that one line.However, as soon as coupling isintroduced, the voltage on oneline may be affected by the cur-rent in an adjacent line. Toinclude these effects, the conceptof impedance or characteristicimpedance must be expanded toallow for one trace interactingwith another. This is handled byexpanding the impedance into animpedance matrix (figure 4).

Any two transmission lines, eachwith a signal path and a returnpath, can be modeled using animpedance matrix. The diagonalelements are the impedances ofeach line when there is no cur-rent in the adjacent line. This issometimes called self-impedance.The off-diagonal elements repre-sent the amount of voltage noiseinduced on the adjacent tracewhen current flows on the activeline. If there were little or no cou-pling, the off-diagonal impedancewould be near zero.

As the coupling between the linesincreases, the off-diagonal termswill increase. If the microstriptraces are moved closer together,the diagonal impedance (self-impedance) will not change verymuch, but the off-diagonal

elements will increase. Alterna-tively, if the plane is lowered, thediagonal elements will increaseand the off-diagonal elements willincrease. When the off-diagonalimpedance elements are a largefraction of the diagonal elements,the lines are very strongly coupled.

The definition of the characteris-tic impedance matrix betweenany two transmission lines doesnot in any way depend on theirsize, shape, material composition,or the signals imposed. Of course,the values of the matrix elementsthemselves strongly depend onthe geometry and material prop-erties. The matrix is symmetricfor identical transmission lines,so they are often called sym-metric lines.

Figure 4. The characteristic impedancematrix of a coupled differential pair.

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Modes

Any arbitrary voltage patternmay be imposed on a pair oftransmission lines. However, cer-tain patterns have special proper-ties in that they will propagatedown the line undistorted. Thesepatterns are called modes. Whenthe dielectric is inhomogeneousand the conductors are identical,the mode patterns that propagateundistorted are the same voltagepatterns as when the pair is driv-en differentially, with oppositeedges; or driven in common, withthe same voltage edge polarity.These two modes have the specialnames of odd and even modes(figure 5).

When the impedance matrix issymmetric, the odd mode is excit-ed when the pair is driven with adifferential signal. The even modeis excited when the pair is drivenwith a common signal. Thesemodes are intrinsic features ofthe transmission lines, anddepend on their precise geometryand material properties. The volt-ages imposed on the lines dependon how the drivers are configured.

Based on the definition of theimpedance matrix, and the defini-tion of odd and even modes, theimpedance of each mode can becalculated. The odd-mode imped-ance is the impedance a driverwould see, looking into one of thelines, when the pair of lines isdriven in the odd mode, or with adifferential signal. Likewise, theeven-mode impedance is the im-pedance a driver would see, look-

ing into one of the lines, when thepair of lines is driven in the evenmode, or by a common signal.

Even and Odd Modes

If there were no coupling, boththe odd- and even-mode imped-ances would be equal, and equalto the impedance of just one iso-lated line, as expected. However,with coupling, there are addition-al current paths between the sig-nal lines in odd mode, and theodd-mode impedance decreases.Some current flows not only fromthe first signal line to the returnpath, but through to the secondsignal line and then into thereturn path. This increased cur-rent through the coupling pathwith increasing coupling resultsin a decrease in the odd-modeimpedance of one line.

The even mode is also affected bycoupling. When two signal tracesare driven with a common signal,there is no voltage differencebetween them. There is thus nocoupled current between the sig-nal lines and the even-modeimpedance is higher than theodd-mode impedance.

From this analysis, it is clear thatwhen there is coupling betweentransmission lines, as in a differ-ential pair, referring to the“impedance” of one line is mean-ingless. The impedance variesdepending on how the adjacentline is driven. When both linesare driven in common, the impedance of one line is the even-mode impedance. When bothlines are driven differentially, theimpedance of one line is the odd-mode impedance.

Mode: odd, or 1, or a Corresponds todifferential driven

Mode: even, or 2, or b Corresponds tocommon driven

VCC VCC

+1v -1v +1v +1v

Figure 5. The even and odd modes.

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Measuring Odd- and Even-Mode Impedances

To measure the odd- and even-mode impedances requires apply-ing simultaneous signals to eachof the two lines. This requiresusing a dual-channel TDR thatcan be configured for differentialdrive and common drive. Withthis instrument, the even- andodd-mode impedances can bemeasured and the characteristicimpedance matrix elementsextracted.

In figure 6, the TDR response ofone trace of a closely-coupled differential pair of microstrips is measured. The other trace is driven by channel 2 of theAgilent 54754 differential TDRmodule. The TDR response hasbeen converted from a voltage

scale directly into an impedancescale to facilitate direct readoutof impedance.

When channel 2 is driven inphase with channel 1, the differ-ential pair is driven with a com-mon signal. The impedance meas-ured by the TDR for one of themicrostrip traces is the even-mode impedance of that line andis about 52Ω. Merely by changingthe signal on the second trace toout of phase, thereby driving thepair with a differential signal, theimpedance of the line under testdecreases. The odd-mode imped-ance is about 45Ω. Finally, whenthe second channel is turned off,and the voltage on line 2 is zero,the impedance of line 1 is meas-

ured as the self-impedance, whichis the diagonal matrix element,about 48.5Ω. Using the measure-ments of the odd- and even-modeimpedances, the off-diagonalimpedance matrix elements canbe extracted, as shown in figure 6.

When the differential pair is driv-en differentially by the DTDRmodule, the impedance measuredby each channel is the odd-modeimpedance of each line. These canboth be displayed directly on thescreen. For symmetric lines, theodd-mode impedance of each lineis nominally the same, but in thereal world there are always someasymmetries. These show up asslightly different odd-modeimpedances for line 1 and line 2.

Figure 6. Measuring odd and evenimpedance of tightly coupled lines.

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In figure 7, one of two microstriplines has an odd-mode impedanceof 46Ω and the other has one of47Ω. There is some variationacross the length of the trace dueto line-width variations in thetape used to fabricate the trace.When the two traces have differ-ent odd-mode impedances, thedifferential impedance is just thesum of the two different odd-mode impedances. After all, thedifference signal sees the seriescombination of the impedances ofeach line to the plane below.

The differential impedance can bedisplayed directly on the screenas the sum of the two odd-modeimpedances. In this example, it isabout 93Ω, with some variationacross the length.

Differential TDR is useful formeasuring the odd- and even-mode impedances of a coupledpair of transmission lines,enabling calculation of its charac-teristic impedance matrix ele-ments and thus the differentialimpedance. With coupled trans-mission lines, the impedance ofone line depends on how the adjacent line is driven.

Dual-channel TDR can be used toanalyze features and real-worldeffects of high-speed differentialtransmission lines under a vari-ety of conditions such as a gap inthe return path. Dual-channelTDR can be hooked up in a vari-ety of ways to maximize theamount of information obtained

Measuring Odd- and Even-Mode Impedances (continued)

Figure 7. Direct measurement ofdifferential impedance.

about a differential-pair transmis-sion line. When the second chan-nel is just used for input, it canmeasure either the transmittedresponse of a single line, as inconventional time domain trans-mission (TDT), or the response of an adjacent quiet trace due to crosstalk.

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Simultaneous Measurements

In TDT, the first channel gener-ates the exciting source into oneend of the transmission line andthe second TDR channel is thereceiver at the other end. In thisway, the TDR and TDT responseof the device under test (DUT)can be measured simultaneously.The TDR response gives informa-tion about the impedance of theDUT, and the TDT gives informa-tion about the signal propagationtime, signal quality, and rise-timedegradation. In this mode, theTDT is emulating what a receivermight see at the far end (figure 8).

One limitation of TDR/TDT is thatthe source and receiver haveimpedances of 50Ω. This may notmatch the impedance of the actu-al end-use application. However,many of the commonly encoun-tered signal-integrity effects can

Figure 8. A dual-channel TDR can provideboth the TDR and TDT response.

be illustrated with this 50Ωimpedance, and these measure-ments can be used to create orverify interconnect models, whichcan then be used in simulationswith real device models as thesources and loads.

The configuration of dual-channelTDR can also be used to measurecrosstalk between two adjacenttraces. The first TDR channel canbe used to generate the excitingwaveform for the active line. Thevoltage induced on the quiet lineis then measured with the secondchannel by alternately connectingone end and then the other tothis second channel. During thisprocedure, the unattached endsof the two transmission linesshould be terminated in 50Ω tokeep the loads the same as whenthe cables are attached.

12

Figure 9. Using a dual-channel TDR tomeasure the near-end crosstalk (NEXT)and far-end crosstalk (FEXT).

Crosstalk

In the example displayed infigure 9, the near-end crosstalk(NEXT) and far-end crosstalk(FEXT) of two closely spacedmicrostrip lines are measured.The line width is 2xh and thespace is equal to the line width.The saturated NEXT is about7 mV, which is 3.5 percent. TheFEXT shows a peak of 63 mV,strongly dependent on the risetime and coupled length.

A dual-channel TDR moduleallows the measurement of theimpedance characteristics of anycoupled differential pair. With theaddition of an Agilent 83484A2-channel, 50-GHz plug-in module, the signals propagated to the end of the differential paircan be measured. This emulateswhat the actual far-end receiversmight see, given the caveat of 50Ω termination.

In the example shown in figure 10,the signal at the far end when thepairs are driven differentially ismeasured. In the upper leftscreen shot, the TDR responsewithout the DUT connected isshown. This highlights that onechannel is driving a signal of 0 to400 mV, while the other channelis driving a signal of 0 to -400 mV.What gets launched into a 50Ωload is 0 to 200 mV in channel 1and 0 to -200 mV in channel 2.

At the far end of the roughly 50Ωdifferential pair, the two channelsof the Agilent 83484A measurethe received voltage into a 50Ωload. This shows the roughly100 ps rise time from propagatingdown eight inches of FR4. The

individual channels are displayedas directly measured. In addition,the common signal (being theaverage of these two) and the differential signal can be auto-matically displayed. All receivedsignals are displayed on the same

Figure 10. Measuring the impedance char-acteristics of a coupled differential pair.

scale. When driven differentially,very little common signal is created by the transmission down the pair. When the pair isdriven with a well balanced dif-ferential signal, the common signal is virtually nonexistent.

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Skewed Differential Signals

A common problem with differen-tial drivers for differential-pairlines is skew between the twochannels. This arises due to driv-er mismatch, different rise andfall times, different interconnectdelays due to routing differences,or different loads on the two linesof the differential pair. Any signalimbalance at the receivers willcreate a common signal.

A variable skew can be intro-duced between the two drivenTDR step generators, emulatingwhat would happen if there werea skew in the drivers. In theexample shown in figure 11, thecommon signal increases steadilyas the skew increases from zeroto 100 ps, comparable to the risetime. If the skew is longer than100 ps, the common signal at thereceiver is basically constant.This suggests that to minimize thecommon signal, the skew shouldbe kept to just a small fraction ofthe rise time.

Figure 11. Emulation of a skewed differen-tial pair by introducing a skew betweenthe two TDR step generators.

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Full Characterization

Figure 12. The measured response of awell balanced signal shows a very smallcommon signal.

Figure 13. The same pair from figure 6when one line is driven single ended.

The full characterization of theperformance of a differentiallydriven differential pair includesthe TDR response of each chan-nel, which relates to the odd-mode impedance of each line, andthe received signals of the twochannels at the far end, combinedas the differential and commonsignals. In the example shown infigure 12, the measured responseof a uniform differential pair isshown, illustrating all six meas-urements. In this example, thecommon signal is very smallbecause the differential driversare well balanced.

This response should be com-pared to the behavior of the samepair when one line is driven sin-gle ended while the other line isheld low, as shown in figure 13. Inthis case, TDR channel 2 is meas-uring the NEXT and the channel 4receiver is measuring the FEXT.When a signal is launched intoonly one line of a symmetric pairof lines, there are equal partsodd-mode and even-mode signalcreated. These propagate downthe line and are received at theend, where they are calculatedfrom the voltages in the tworeceiver channels and displayedas the differential signal and com-mon signal. The differential sig-nal, corresponding to the oddmode, arrives at the receiverbefore the common signal, corre-sponding to the even mode.

This is a direct measure of thedifference in velocity of the oddand even modes. The odd mode,having more fringe fields in theair, has a lower effective dielectricconstant and hence higher propa-gation speed. The even mode hasmore fields in the dielectric and a

higher effective dielectric con-stant, and takes longer to reachthe receiver. From this measure-ment, the connection betweencrosstalk and modes is also ap-parent. The common-mode signalis delayed due to the FEXT.

In this example, the differentialand common signals are dis-played using the Math function ofthe Agilent 86100A mainframe, sothat the TDR response can beswitched between single outputand dual output.

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Signals Crossing a Gap

With this perspective, theresponse of a differential pairthat crosses a gap in the returnpath can be examined. The tracesare about eight inches long with a50Ω load, and with weak couplingbetween them. The gap in thereturn path is about one inchwide. The time delay across thisgap is comparable to the rise timeof about 100 ps. As before, theresponse at the near end and farend of each line can be measuredwhen one line is driven singleended and also when both linesare driven differentially, as shownin figure 14.

As expected, the TDR response ofchannel 1 shows the uniformtransmission line until the gap isreached. Electrically, the gaplooks like a large inductive dis-continuity and the reflection is alarge positive value. The secondTDR channel is measuring thereflected NEXT noise. Initiallythere is the saturated near-endnoise, until the gap is reached.The mutual inductance betweenthe two traces in the vicinity ofthe gap is almost as large as theself-inductance that causes thereflection of channel 1. Thisresults in induced noise generat-ed in trace 2 that is almost aslarge as the reflected signal in trace 1.

Figure 14. The response of a differentialpair that crosses a gap in the return pathwhen driven single ended.

The inductively generated noisein trace 2 propagates down thetrace 2 transmission line in bothdirections, and appears at the farend as much-enhanced far-endnoise. From the time constant ofroughly 400 ps, the inductance ofthe discontinuity can be extract-ed as roughly 40 nH. This corre-sponds to the self-inductance ofthe perimeter of the current patharound the gap, which is about3 1/2 inches, or roughly 15 nH/in.

The enhanced crosstalk, bothnear and far, between the two

adjacent traces, due to high mutu-al inductance of the return pathsaround the gap, is a primary rea-son to carefully route returnpaths over continuous planes andavoid crossing gaps. Also, thecommon and differential signalsare greatly distorted compared toif there were no gap in the returnpath. This sort of discontinuitywould cause major problems formost single-ended-driven trans-mission lines, and is another rea-son why design rules recommendrouting adjacent traces over con-tinuous return paths.

Figure 15. The response of the differentialpair from figure 8 driven differentially,showing the robustness of differentialsignals to imperfections in the propagation path.

16

Differential Signals Crossing a Gap

However, when both lines aredriven with a differential signalbetween the pair of traces, thereflected noise from each line isin the opposite direction and theresulting reflection is reducedconsiderably (figure 15).Likewise, since the gap offers anearly balanced discontinuity toeach of the two signal lines, theeffect on the common signal isalmost negligible. This illustratesa chief advantage of transmittingsignals on differential pairs—dif-ferential signals are much morerobust to imperfections in thepropagation paths that are com-mon to both lines. The effects oneach line are better balanced,with less common-signal noisegenerated, as the lines are routedcloser to each other and the coupling is larger.

Another way to look at the gap inthe return path is in terms ofwhat impedance the differentialsignal sees. This can be measureddirectly with the differential TDR(DTDR) module. The differentialpair is driven differentially, andthe DTDR measures the odd-modeimpedance of each line. Theirsum is the differential impedance.

Before and after the gap, the dif-ferential impedance is about 97Ω.In the region of the gap, the dif-ferential impedance is about150Ω. This corresponds to theimpedance that was measured fortwo coplanar transmission lines

with no conducting plane beneaththem, which is exactly what theregion of the gap appears as. Thegap acts as a high-impedanceregion for the differential signal,which will create a reflection.However, if the lines are termin-ated at both ends, this reflectionmight not cause signal-integrityproblems.

These examples show that if sig-nals must cross gaps in the returnpath, routing the signals as differ-ential signals on closely coupleddifferential pairs is the way to do

it. This method may result insome increase in the differentialimpedance, but there is very littledistortion of the differential signal and very little common voltage created.

DTDR and a dual-channel amplifi-er module provide full characteri-zation of differential pairs oftransmission lines, enabling engi-neers to better determine howtheir designs are working at theelectrical level and suggestingideas for how to improve them.

17

Ease Dual-Channel TDR Measurements

As differential signals become amore important part of high-speed systems, it is essential thatyou have the tools to properlydesign and verify the impedanceof differential signal paths. Usingmultiple-channel time domainreflectometry (TDR) simplifiesthe process as you can makesimultaneous measurements andthen use math functions to pres-ent the data in the engineeringunits you need.

The Agilent 86100 Infiniium DCAoscilloscope provides a 50 GHzbandwidth and plug-in modulesthat ease the task of characteriz-ing a differential-pair transmis-sion line. Additional modulesspecifically for the 86100 arebeing created, but the new oscillo-scope can still use modules fromthe Agilent 83480A digital com-munications analyzer and theAgilent 54750A high-bandwidthdigitizing oscilloscope.

When used with the Agilent54754A plug-in module, the 86100 oscilloscope becomes a differential time-domain reflec-tometer. The module has twoindependent step generators thatcan be synchronized, and theresponse from each channel ismeasured independently of theother channel. To further easeyour measurements, the instru-ment has the ability to convertthe voltage measured into animpedance scale. This allows youto directly read the impedance onthe display.

The Agilent 83484A module isalso used to provide multiple50 GHz inputs. Each module hastwo 50 GHz electrical channelsand one trigger input port. Thisallows measurements of thewaveforms that appear at the far end of the transmission-linepair, thereby emulating the actualsignal a differential receiver woulddetect after transmission throughthe pair.

When used with the Agilent 54754A plug-in module,the 86100 Infiniium DCA oscilloscope becomes adifferential time-domain reflectometer.

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Related Literature

Publication Title Publication Type Publication Number

Test Tools for InfiniBand Color brochure 5988-2424EN

Infiniium DCA: Agilent 86100 Color brochure 5988-3666ENWide Bandwidth Oscilloscope

Infiniium DCA: Agilent 86100 Technical specs 5968-8546EWide Bandwidth Oscilloscope

40 Gb/s and Return-to-Zero Measurements Product note 5988-2039ENUsing the Agilent 86100 Infiniium DCA

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