Dear Mark et. al., For those of you interested in the fine details, here are a few notes about the "crosstalk estimation" formula 1/(1+(d/h)^2)) [Eq. 1]. Before I jump into the details, let me say that the greatest strength of [Eq. 1], and the reason I included it in my first book, is that it depicts crosstalk as a very steep function of lateral separation. As soon as the separation distance d exceeds h, the term "1" in the denominator becomes insignificant, and the whole distribution simplifies to 1/(d^^2). That means that a 10% increase in d produces a 20% reduction in crosstalk. Doubling d cuts crosstalk by a factor of four. That's terrific! Lateral separation over a solid reference plane is an extremely effective means of combating crosstalk. A little more spacing means a lot less crosstalk. This rule cuts the other way, too. Place your traces a little too close, and crosstalk skyrockets. Designers interested in maximum layout density (= fewest layers) should use a 2-D field solver to estimate crosstalk. That's more accurate than any simple, order-of-magnitude approximation. DETAILED NOTES: 1) The *shape* of the crosstalk function given in Equation 1 is asymptotically exact only for a very small, skinny wire (W<<H) in a microstrip configuration. 2) Equation 1 works for an offset stripline only if the stripline height h (=height above the lower plane) is much smaller than the total stripline cavity height b (=total height between upper and lower reference planes). In that case, [Eq. 1] kind of works when separation d lies between h and b, but after that, for d larger than b, the crosstalk plummets exponentially, as reported by other commentors. 2) To the extent that [Eq. 1] works, it does so because it models (partially) the distribution of returning signal current underneath a skinny microstrip trace. 3) A more complete model of the distribution of returning signal current underneath a skinny microstrip trace includes a constant of proportionality. That constant equals (I0/(pi*h)), where I0 is the trace current, pi equals 3.1415926... and h is the trace height above the plane. Integrate that expression over all values of d and you should (hopefully) get the total returning signal current, I0. 4) The distribution of current generally underneath a trace, including the constant of proportionality, is discussed in this article: "Proximity Effect III", www.sigcon.com/Pubs/news/4_8.htm , and in this writeup: http://www.sigcon.com/vault/pdf/4_8_Proximity3.pdf 5) The connection between return-current distribution and crosstalk works like this, a) a signal trace carries signal current, b) that creates magnetic fields, c) which interact with the reference plane, d) causing eddy currents, e) whose strength is determined by Maxwell's equations, f) and which are modelled reasonably well, for microstrips, by [Eq. 1]. The distribution of eddy currents (that's what returning signal current is) gives the distribution of magnetic field strength at all points near the reference plane, and the local magnetic field strength determines crosstalk. This is another way of saying that [Eq. 1] models the mutual indutance between two microstrip traces. 6) There is also a mutual capacitive crosstalk, due to electric-field effects. If the traces are long compared to the signal rise or fall time (that's what Istvan calls "fully saturated"), and if they are embedded in a homogeneous dielectric material (microstrips aren't quite like this, but they are close), then the mutual inductive and mutual capacitance terms have the same magnitude. Therefore, you needn't model both -- you can just look at one or the other. I chose to look at the inductive effect because, mathematically, I was able to figure out how it worked. 7) In a practical microstrip, the mutual inductive and mutual capacitance terms have nearly the same magnitude, but may have opposite polarities. In the forward direction (far-end crosstalk) the two terms nearly cancel each other. In the reverse direction (near-end crosstalk) the two terms reinforce. Whichever direction crosstalk gets started, it may bounce off one or more endpoints, creating a complex waveform. Obviously, [Eq. 1] models none of this. That's another good reason to use a crosstalk simulator. 8) When a trace is short compared to the signal risetime, crosstalk is less. When the trace length is less than 1/2 of the signal rise or fall time the derating factor equals (2)*(trace length)/(signal rise time) -- always less than one. When the trace length exceeds 1/2 of the signal rise or fall time, the derating factor equals one (that's the "fully saturated" case). 9) A full mathematical analysis of crosstalk must first determine the signal current, then estimate the complete distribution of return current underneath a trace, and then properly convert that to a magnetic-field intensity, and convert the magnetic field intensity into a received crosstalk signal. That's a lot of steps, and at each stage there are *assumptions* built into a good model. When I created the simple model [Eq. 1] I short-circuited all the calculations by simply reasoning that, in the worst case, the crosstalk is not likely to exceed the size of the source signal. That established a coefficient of one ("1") in the numerator of [Eq. 1]. 10) Here's a wonderful experiment. Configure two long, 50-ohm traces side-by-side. Measure the crosstalk. Now, change the width of the aggressor trace, making it 100 ohms. With long traces, given the same driver, the initial signal current is now only HALF as strong as before, reducing mutual-inductive crosstalk by a factor of two. NOTE THAT [EQ. 1] DOES NOT MODEL THE TRACE IMPEDANCES. 11) This time, configure two short, 50-ohm traces side-by-side. Drive the aggressor with a powerful, low-impedance driver and load the far end of the trace with a huge capacitive load. This circuit draws a gigantic surge of current on each edge, making crosstalk to other traces wildly exceed the limit suggested by [Eq. 1] and the de-rating factor. NOTE THAT [EQ. 1] DOES NOT MODEL SOURCE AND LOAD IMPEDANCE EFFECTS, OR DIRECTIONALITY. So, with all these foibles, what is the value of [Eq. 1]? I like it because it reminds me, in a simple and straightforward way, that crosstalk varies strongly with distance, approximately quadratically for microstrips and even faster for striplines. If you want accuracy, get a crosstalk simulator. Best regards, Dr. Howard Johnson, Signal Consulting Inc., tel +1 509-997-0750, howie03@xxxxxxxxxx www.sigcon.com -- High-Speed Digital Design seminars, publications and films -----Original Message----- From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On Behalf Of Istvan Novak Sent: Wednesday, December 07, 2011 5:50 AM To: markfilipov81@xxxxxxxxx Cc: SI LIST Subject: [SI-LIST] Re: Estimating Crosstalk Mark, The xtalk ~ 1/(1+(d/h)^2)) formula gives you the the estimated near-end inherent crosstalk in microstrip in the saturated case. This assumes matched terminations on the connections. In striplines the decay of crosstalk (near-end, saturated) rolls off with the fourth power of distance, which can be approximated with exponential in a certain range if you wish. In perfectly homogeneous striplines there is no inherent far-end crosstalk in matched case. When the connections are mismatched, the total crosstalk noise goes up in both microstrip and stripline due to the reflections. In the frequency domain the crosstalk response varies sinusoidally with frequency and if you transform the time-domain crosstalk waveform properly into the frequency domain, you get this response, and vice versa. As a first approximation, for crosstalk, differential traces can be looked at as two single-ended traces, and relying on the linearity of the coupled structure, you can work out the result as a superposition of single-ended responses. You will have four permutations though creating the interaction among common-mode and differential-mode excitations and responses. Regards, Istvan Novak Oracle Mark Filipov wrote: > Thank you all, for your valuable comments and advices! > So, to conclude about this formula, xtalk ~ 1/(1+(d/h)^2)). This gives > fairly accurate (electric) field distribution of the surface (single-ended) > microstrip traces, from trace to trace. It also gives the worst case > scenario for the crosstalk. > However which xtalk does it give? Total xtalk? Since for microstrips, the > FEXT increases with the lenght of traces. For striplines traces > the xtalk (NEXT?) decreases exponentially when we increase the spacing, > i.e. xtalk ~ e^(-d). > To see how much xtalk is created on the victim line by the aggressors > line, it depends on the frequency of the data stream and on the data > pattern of the aggressor line. Higher the switching frequency, more > crosstalk is to be expected, since it's proportional to the switching speed > (we know that for FEXT). > > How about the NEXT? How is NEXT dependent of the switching speed (rise > time/fall time). > > Which data pattern should create most xtalk for digital circuits, > 0101010.... or "1" in a long pattern of "0" or something else? > > How well does this equation hold when we have differential pair traces > (surface microstrips)? Or is there any other equations for predicting > worstcase xtalk for diff pairs traces? > > Best regards, > Mark > > > 2011/12/6 <Vittal.Balasubramanian@xxxxxxx> > >> Keep in mind that any empirical equation gets less and less accurate as >> your frequency of interest goes higher and higher. So make sure you know >> what your frequencies of interest are and the range of accuracy of any >> equations. >> >> Best regards, >> Vittal Balasubramanian >> Staff Signal Integrity Engineer >> FCI USA LLC >> (717) 938-7368 >> -----Original Message----- >> From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] >> On Behalf Of Wolfgang.Maichen@xxxxxxxxxxxx >> Sent: Tuesday, December 06, 2011 2:49 AM >> To: dbrooks9@xxxxxxxxxxxxxxx; markfilipov81@xxxxxxxxx; >> si-list@xxxxxxxxxxxxx >> Subject: [SI-LIST] Re: Estimating Crosstalk >> >> Yes, this is what I saw when experimenting with a 2D solver. Microstrip >> follows this behavior. The problem is using this for stripline - the >> trend is VERY different - whereas Microstrip has a 1/d^2 behavior for >> large spacings (see formula), striplines follow an exponential (e^-d) >> behavior, which drops of very fast - much faster than 1/d^2 - for larger >> line-to-line spacings. >> >> Wolfgang >> >> >> >> -----Original Message----- >> From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] >> On Behalf Of Doug Brooks >> Sent: Monday, December 05, 2011 6:25 PM >> To: Mark Filipov; si-list@xxxxxxxxxxxxx >> Subject: [SI-LIST] Re: Estimating Crosstalk >> >> In studies I have done (see especially >> <http://www.ultracad.com/mentor/crosstalk_coupling.pdf>Crosstalk >> Coupling: Single-ended vs. Differential on our website, >> www.ultracad.com) This formula (1/(1+(d/h)^2)) works pretty well >> for Microstrip. It is a worst-case formula for stripline, depending >> on conditions. This is shown with Hyperlynx simulations in the article. >> There is a freeware calculator, also on our website, that is based on >> this formula (taken from Howard Johnson's first book and an interview >> with him.) >> >> Doug Brooks >> >> >> >> >> At 07:39 AM 12/5/2011, Mark Filipov wrote: >>> In many books dealing with SI & PCB's, (Brooks, Johnson&Graham, >> Khandpur, >>> ..) there is a simple equation for estimating crosstalk. >>> >>> >>> Crosstalk between two traces separated by distance D, and which both >> are at >>> distance, H, from their reference plane is proportional to >>> >>> >>> >>> K / (1 + (D/H)^2 ), where K < 1. Usually, I have seen that K is set >> equal >>> to 1. >>> >>> >>> In book "Grounds for Grounding" recently published by IEEE Press (Joffe >> & >>> Sang Lock), on page 835 (which can be seen online in Google Books), >> there >>> is stated "... Assuming a trace width of 10 mils placed above the >> return >>> plane with separation, h, of 10 mils, the crosstalk between the traces >>> (where the traces are separated by 40 mils) will have an upper bound of >>> 1/(1+(d/h)^2) = 1/(1+4^2) = 0.06 = -25 dB "... >>> >>> How well does this equation agree with empirical data? Is it an upper >> bound >>> for estimating crosstalk? >>> Does this equation give only the amount of coupling between the traces, >>> since crosstalk is also data pattern dependent? >>> How does this equation relate for estimating crosstalk between >> differential >>> pair traces, separated by distance D? >>> >>> I have seen an similar expression K/(1+(D/H)^2)), when estimating how >> far >>> the return current will spread underneath the traces, so I guess this >>> formula is derived on basis of that?? >>> >>> BR /Mark ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List technical documents are available at: http://www.si-list.net List archives are viewable at: //www.freelists.org/archives/si-list Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List technical documents are available at: http://www.si-list.net List archives are viewable at: //www.freelists.org/archives/si-list Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu