[SI-LIST] Re: Estimating Crosstalk
- From: "Howard Johnson" <howie03@xxxxxxxxxx>
- To: <si-list@xxxxxxxxxxxxx>
- Date: Fri, 9 Dec 2011 14:44:13 -0800
Dear Dudi Tash,
If you configure two long parallel lines, with an end-termination on the
aggressor, and terminations at *both* ends of the victim, what you will see
in response to a step-voltage on the aggressor is the following.
1) Start the agressor step at time zero.
2) At time zero you will immediately see a step on the near end of the
victim.
3) The near-end step has the same rise time as the aggressive signal, where
rise-time is interpreted to mean the rise or fall time between 10 and 90% of
a signal's peak-to-peak signal swing.
4) The near-end amplitude, compared to the amplitude of the step on the
aggressor, is given by the coefficient of "NEAR-END CROSSTALK", or NEXT.
5) The NEXT coefficient is what the 1/(1+(d/h)^2)) expression is all about.
6) The near-end step at the victim abruptly ends after time 2*T, where T is
the one-way transit delay of the length of parallelism you have configured
between your two traces.
7) At the far end of the victim at time T you receive one of two signals. In
the case of two perfect striplines you receive nothing. In the case of two
microstrips, you usually receive a short, negative pulse with a duration
comparable to the rise time of the aggressor's step and an amplitude that
varies in proportion to the length of parallelism. Unless your lines are
quite long, you may not see this small effect.
8) Whatever happens, the two crosstalk signals (near-end and far-end)
usually bounce off the endpoints of the victim structure, ending up all over
the place, making a fairly complex result. A crosstalk simulator will show
you that effect.
9) In the event that your victim line is perfectly-terminated at both ends,
the near-end crosstalk waveform makes what is known to linear system
theorists as a "boxcar" shape (i.e., a rectangle with the same rise and fall
time). The "frequency response" of the near-end crosstalk effect would be
the ratio of the Fourier transform of the near-end boxcar signal, divided
(at each frequency) by the Fourier transform of the aggressor's step
waveform. That result equals NEXT*(1 - exp(-jw2T)), where NEXT is the
near-end crosstalk coefficient, exp is the exponential funtion, "j" is the
imaginary square root of (-1), w is the frequency in rad/sec (equal to two
pi times the frequency in Hz), and T is the one-way transit delay of the
length of parallelism you have configured between your two traces. This
expression works correctly even if the lines are not "long", meaning that
the length of parallelism is shorter than the signal rise and/or fall time.
Hope that helps.
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
_____
From: Dudi Tash [mailto:dudi@xxxxxxxxxxxxxxxxx]
Sent: Wednesday, December 07, 2011 11:03 AM
To: Howard Johnson; si-list@xxxxxxxxxxxxx
Subject: Re: [SI-LIST] Re: Estimating Crosstalk
First, thanks for the elaborate answer.
Second, is there an equation relating to the frequency?
Please advise
Thanks in advance
David
_____
From: Howard Johnson
Sent: éåí ã×, ãöî 7, 2011 8:21 PM
To: "si-list@xxxxxxxxxxxxx"
CC:
Subject: [SI-LIST] Re: Estimating Crosstalk
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<
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 > >> 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 >>
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
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