Let's talk about crosstalk again, something that is notwell understood by many designers. Consider the trace,A-B shown in Figure 1. We call that a 'driven' line. Let'sassume that a pulse is traveling down that line from A toB and is now at the point defined by the 'X'. There is anearby trace, C-D, which we will call the 'victim' trace. Asignal may couple between the driven and victim traces atthe point 'X'.

Now let's think about what is intuitive. There islikely some capacitive coupling between the two traces.It may be small, but there is likely to be some. Sinceparallel traces sort of look like a transformer, there isprobably some inductive coupling between the traces,also. In most PCB applications, however, the materialbetween the traces is probably a very good insulator, sothere is probably no (purely) resistive coupling betweenthe traces. Since capacitive and inductive effects reducewith distance, any coupling probably reduces as theseparation between the traces increases. This leads to:

General Rule #1: If we are concerned aboutcrosstalk, greater separation between traces is better.

If a signal along trace A-B is going to couple noiseinto trace C-D, we must be looking at an AC phe-nomenon. That is, a steady state DC signal on one tracewill not couple into the other one. But if an AC signalwill, then, intuitively, the coupling will be greater (or

more efficient) the higher the frequency (or frequencycomponents of the harmonics of the underlying signal.)More about the specific effects of frequency (and risetime) next month. But this observation leads to:

General Rule #2: If we are concerned about crosstalk,lower frequency harmonics and slower rise times arebetter.

The effects of coupling can be summarized as fol-lows:

Mutual Capacitive Coupling--a signal, SC, caused bycapacitive coupling between the two traces, which travelsalong the victim trace in both the forward and backwarddirection with the same polarity.

Mutual Inductive Coupling--a signal, SL, caused byinductive coupling between the two traces, which travelsalong the victim trace in both the forward and backwarddirection with opposite polarity.

Directionality--Crosstalk goes in both the forwardand backward direction. Mutual capacitive and inductiveforward crosstalk are approximately equal and oppositeand tend to cancel. They are approximately equal andreinforcing in the reverse direction, and therefore tend tobe additive.

Magnitude--Forward crosstalk tends to look like thedriven signal, and (at least in theory) continues to growlarger the longer is the coupled length A-B (and C-D).Reverse crosstalk tends to have a rectangular shape (inresponse to a step function) that reaches a maximum andthen does not increase further regardless of coupledlength.

Environment--If the two traces are contained within ahomogeneous material (as they are in a stripline environ-ment), the inductive and capacitive forward crosstalkcomponents are almost exactly equal and cancel. There-fore, we generally don't worry about forward crosstalk instripline environments. If the surrounding material is NOThomogeneous (as it is not in a microstrip environment),the inductive component tends to be larger than the capac-itive component.

General Rule #3: Therefore, if we are concernedabout crosstalk, keep the sensitive traces in stripline envi-ronments. (Thus ends the discussion on forwardcrosstalk!)

This two-column series appeared in Printed Circuit Design, a Miller Freeman publication, November and December, 1997

1997 Miller Freeman, Inc. 1997 UltraCAD Design, Inc.

BROOKSPEAK

Crosstalk, Part 1:The Conversation We Wish Would Stop!By Douglas Brooks, PresidentUltraCAD Design, Inc.

Figure 1A signal on the driven line, A-B, at point X couples anoise signal on the "victim" line, C-D, at the samepoint.

Figure 2 helps us understand why the reversecrosstalk waveform tends to be longer than the drivenpulse. Consider a simple signal as it travels down a trace.We will take a "snapshot" of it at seven points in time,labeled t=0 through t=6. In order to simplify the analysis,we will assume the signal is a pulse with zero width, eventhough in Figure 2 it is shown with a finite width.

At time t=0 the pulse just starts down the trace. Thereverse crosstalk signal in the victim line reflects off Cwith a negative reflection coefficient (Footnote 1) andbegins traveling down the victim line towards D. At timet=1 the driven pulse causes a coupled signal in C-D totravel in the reverse direction towards C, while thecoupled pulse from time t=0 has traveled to position t=1.

Skipping to time t=4, the driven signal couples intoC-D at position t=4, but the pulses coupled at times t=3and t=2 are moving backwards (reverse direction) to-wards C. Pulses at times t=0 and t=1 have reflected offthe end at C and are now moving with a negative polaritytowards D. In this manner it can be seen that the drivensignal creates a coupled signal in the victim line that (1)travels in a reverse direction (towards C) until it reflectsoff C and then travels the length of the line towards D.

Now, instead of thinking about snapshots in time,consider the signal in real time as it travels from A to B.The "front edge" of the signal at each increment of itstravel will couple a noise signal in C-D that will traveltowards C, reflect off C, and travel towards D. Thecoupled signal will have a magnitude (to be discussednext week) and a width equal to the propagation timefrom D to C and then back to D (twice the propagationtime of the coupled length.)

The above analysis assumes that the reverse coupledsignal travels towards C and then reflects towards D. Butwhat if the end at C is terminated in the characteristicimpedance of the trace? In that case it is tempting to saythat there would be no reflection of the reverse crosstalkwaveform. Then, if points B and D were also terminatedin their characteristic impedance, there would be noreflections at that end, either. Does this mean that wewouldn't have to be concerned about reverse crosstalk.And, further, if we are in a stripline environment so thatwe don't have to worry about forward crosstalk, wouldthis mean that the entire crosstalk problem would goaway? Never say "never", but next month we will talkabout how to calculate crosstalk, taking terminations intoaccount.

Footnote 1. Remember that the reflection coefficient is (Rs-Zo)/(Rs+Zo) where Rs is the source resistance at C andZo is the characteristic impedance of the trace. Since Rs is normally much less than Zo, the reflection coefficient canapproach -1.

Figure 2:Backwards crosstalk as the driven signal propagatesdown the trace.

Last month's column focused on what crosstalk is andattempted to provide an intuitive understanding of theprinciples involved. It also concluded that forwardcrosstalk is usually not a problem in stripline environ-ments. This month I will provide a means of(approximately) quantifying backwards crosstalk.

Estimating crosstalk can be difficult. The ap-proach shown in this column depends on several sim-plifying assumptions, and will lead to results that areclose, but not necessarily precise. The reader would bewise to calibrate this technique by applying it toboards that have been designed in the past and areknown to be either "good" or "bad" with respect tocrosstalk performance. That will provide insight intohow future boards will perform, based on the results ofthese calculations.

Three concepts are involved in the measurementapproach:

1. Electromagnetic coupling between two traces.2. The parallel distance over which that coupling

occurs.3. The effectiveness of any terminations, if they exist.

Electromagnetic coupling:Howard Johnson shows in his book “High Speed

Digital Design: A Handbook of Black Magic” (page192) that the crosstalk coupling coefficient in paralleltraces is proportional to, and does not exceed, Equa-tion 1a (see Figure 1.) Equation 1a is re-expressed inEquation 1b. It is clear from Equation 1b what wealready intuitively know: to minimize crosstalk, youminimize H and maximize D.

If the parallel traces are at different heights, the H2

term really becomes the product of the two heights, asshown in Figure 2 and Equation 2. D becomes thedirect distance between the centerline of the traces.

Finally, if the traces are between two planes, asshown in Figure 3, find each H by using a parallelcombination of the heights to each plane, as shown inEquation 3.

Coupling Distance:Backwards crosstalk starts out small and increases as

the length of parallel coupling increases --- to a point. Itreaches a maximum magnitude and then stays constant at theso-called "critical length"; the length where the round trippropagation time (TRT) equals the rise time (TR) of the drivingsignal. So for short traces (TRT/TR =< 1) crosstalk is propor-tional to the ratio of TRT/TR. We calculate TRT with Equation4. For long traces, (TRT/TR > 1) calculate crosstalk indepen-dent of length.

BROOKSPEAK

Crosstalk, Part 2:How Loud Is Your Crosstalk?By Douglas Brooks, PresidentUltraCAD Design, Inc.

( )1

1 2+ D H/

H

H D

2

2 2+

( )1

1 1 22+ D H H/ *

PlaneHH

D

Trace 1 Trace 2

Figure 1Typical crosstalk configuration

PlaneH2

H1DTrace 1

Trace 2

Figure 2Trace heights are different

Plane

DTrace 1

Trace 2

H1a

H1bH2b

H2a

Plane

Figure 3Use parallel combination to calculate H in

stripline environments

H n a H n b

H n a H n b

*

+

Eq. 1a

Eq. 1b

Eq. 2

Eq. 3

Terminations:If the coupled trace is perfectly terminated at the near end

with the characteristic impedance of the trace (Zo), there willbe no reflection at the near end and no backwards crosstalkreflecting back down the line. Correspondingly, if the driventrace is perfectly terminated at the far end, there will be noreflection at the far end that will induce crosstalk in the victimtrace. Thus, if there are terminations at both ends of thetraces, crosstalk will be reduced, and will be proportional tothe reflection coefficient (measured at the end with the worstmismatch):

Assume, for example, the tolerance for Zo is 10% and thetolerance for RL is 3%. The worst case reflection coefficient,then, would be:

( )1

1 2 2++

D HT T

Tol Zo Tol RRT R

L

/( / )

( ) ( )

Plane

16

Trace 1

Trace 2

6

126

12

Plane

Figure 4 Example

Where:εr= Relative dielectric coefficienta = 1, b = 0 for Striplinea = .475, b = .67 for Microstrip

Equation 4Use this equation to calculate TRT

T = 1.017 a + b * Parallel Length * 2RT rε

ρ =−+

( )

( )

R Z

R Z

L

L

0

0

ρ =−

+=

(. . )

( . . ).

9 7 1 1

1 1 9 70 6 3

Here is a simplifying trick. For small tolerances like this,the worst case reflection coefficient can be approximatedwith [Tol(Zo) + Tol(RL)]/2. Using the illustration above, thiswould become[10 + 3]/2 =.065

Result:The final result, now, is that the backwards crosstalk

coupling coefficient can be approximated as:

Where the TRT/TR term cannot exceed 1.0, and the finalterm applies only if there are terminations at both ends of thetraces.

People sometimes like to express coupling in decibels(db's). To convert this coupling coefficient to db's, take thecommon log (log to base 10) of the coupling coefficient andmultiply it by 20.

Example:As a final example, suppose we have the configura-

tion shown in Figure 4. Let εr be 4.5, the rise time of thecoupled pulse be 1 nsec, the parallel length be 10 in. andno terminations. The calculated coupling coefficientwould be .05195 (-26 db).

Calculator:UltraCAD has written a Windows software calcula-

tor for calculating the crosstalk coefficient. It is dis-tributed as freeware and can be downloaded from ourweb site (www.ultracad.com --- follow the link to tech-nical papers). Download the file ultra_ct.zip, and unzipit in its own directory.

Acknowledgment: We are indebted to Dr. HowardJohnson (howiej@sigcon.com) for some of the conceptspresented in this column. He was kind enough to spend anhour with my staff recently, educating us on crosstalk. Dr.Howard Johnson is president of Signal Consulting, Inc.(www.sigcon.com), a high-technology consulting firm thatspecializes in solving high-speed digital design problems.He is the author of "High-Speed Digital Design: AHandbook of Black Magic" (Prentice-Hall, 1993) and afrequent guest lecturer at the University of Oxford.

Figure 5UltraCAD’s Crosstalk Calculator

crosstalk.pub