12 Replies Latest reply on Jul 19, 2013 3:26 PM by michael.weinberg

# Formula for length-matching a HS diff pair?

Hello All,

Can someone educate me on length-matching HS pairs? I have heard that, at the very minimum, the pair should be matched to within 1/4 wavelength of the highest transmission rate. I have also heard that electrons traveling through a copper wire, move at nearly the speed of light. I have run the math for a 10GHz pair and I am coming up with 0.295" for 1/4 wavelength. I don't think I believe this. It seems it should be quite a bit tighter than this. I usually match to within 0.001" just to be safe, but this is time-consuming and I'd like to know how to calculate the requirement for any given frequency of transmission.

Many thanks,

Lou Rossi

• ###### 1. Re: Formula for length-matching a HS diff pair?

Hi Lou:

I think that I would be spending more time looking at the receiver spec for the time window for which the two signals need to arrive and not the quarter wave of the first through seventh harmonics. I would try to be less and 10 mil difference in length.  My answer is to spend the time routing.

Have you looked at the board material?  Standard FR-4 has its surface chemically roughened to better hold on to the copper.  But that means the copper will also have a rough surface.  This will give you higher transmission loss. Depending on how far the signal has to travel you may want to look at better board material.  Definitely a flat weave for the glass.

Lastly, you can't wait for the electrons to move down the piece of copper.  Electron migration in copper is only about 13,000 feet per second.  Electron movement is a secondary event.  The signal is made up of photons whether you look at them as a wave front or particles.  Although I am sure the your practices for layout topology are great for these connections, you are past the point of worrying about current return paths as some bicycle chain of electron movement.  What your copper topology is doing now is ensuring that there is an induced wave front generated at all points along the signal path that will null the effects of the original signal's wave front.

Have fun

Dwain

• ###### 2. Re: Formula for length-matching a HS diff pair?

Hi Dwain,

Thank you for your reply. Being a musician, I know a thing or two about harmonics. But I hadn't really thought about harmonics in this setting. I realize a square wave is rich in harmonics and this is what gives it its crisp right-angular shape. But apparently, there is more to it than having a single square wave shape? Are you saying that some of the upper harmonics (whose frequencies are higher than the fundamental) can cause the receiver to false trigger? When I look at a square wave on a scope (mind you, I have never looked at a 10GHz square wave), I see one cohesive wave shape - I do see anything that looks like it might arrive "before" or out of sync with the fundamental. What am I missing?

To be honest, your last paragraph about particles, wave fronts, and bicycle chains of electron movement pretty much flew right over my head. But the gist of your dissertation seems to be - there is no simple or formulaic way to approach my conundrum.

But let's say I follow your advice and look at the data sheet for the receiver to find the allowable window for the pair. And let's say the data sheet says the signal and its compliment need to arrive within 10pS of each other. Then what? Aren't we sort of back to my original question regarding a difference in trace length equalling a time shift? So, what is the maximum allowable difference in trace length to a 10pS difference in time?

Also, you had suggested a 10-mil maximum difference for a 10GHz pair. Does this translate linearly to other frequencies as follows?

3GHz = 33-mils max

625MHz = 160-mils max

Many thanks,

Lou

• ###### 3. Re: Formula for length-matching a HS diff pair?

Lou:

The distance that a a signal can move down a trace is not the same for all board material.  For the most part the dielectric is viewed as having the greatest effect on signal propagation speed. For 1ns if the board dielectric constant is a little over 2, then the distance traveled is around 11 inches and if the dielectric constant of cheap material is round 5, then that distance can approach 6.5 inches. When I don't have control of board material I use 1 ns = 8 inches and divide down from there.

There are more than one or two formulae out there. And you can dig up the one that you like best.  Are you running micro strip, co-planner, strip line, or some combination?  What kind of crystal structure does the copper have?  How much of the trace is plated and with what? (Really! How much moisture is in the board?) What coatings are on top of the board?  Just how constant is your dielectic constant across the board?  I don't run the formula any more. I just make the lengths match to a few mil and spend more time on the board material, copper layout topologies and propagation losses. I do RF and High Speed.

Good luck

Dwain

• ###### 4. Re: Formula for length-matching a HS diff pair?

Hi Dwain,

Thank you for all your help. This stuff makes a little more sense now. The company I am consulting for makes internet backbone switch gear. The principal engineer, who knew his way around hi-speed design as well as anyone, passed away a few years ago. He was a good friend and mentor, whom I miss every day. I have done several layouts based on my friend's original design for the company in the last two years. I don't remember his length-matching requirement for 10GHz, but it was less restrictive than the 1-mil paradigm I have adopted. I am getting good reports on my layouts, so they seem to be working. And at the end of the day, I seem to spend the bulk of my length-matching time just getting into the ballpark - going from there to 1-mil really isn't where all my time is spent. I have done many layouts with 625MHz to 3GHz, 16-bit differential busses where all 32 wires need to be the same length. Many times, each wire has a series cap in-line and so I need to add the wire length on both sides of the cap to get the actual trace length for each bit.

I have attached a screen shot of the layout I am currently working on. In the center of the screen is a crossbar switch chip, and you can see 16 differential pairs egressing away from it - eight on the component side (red) and eight on the solder side (blue - layer 8). Layers 2 and 7 are GND planes. Top and bottom layers were originally chosen so that there would not be a stubs associated with vias. You will notice that when length-matching "humps" are required, I place one at each end of the wire, of equal size - another request of the original design engineer. Anything above 3GHz, I use curved rather than 45-degree mitered corners.

Thanks again,

Lou

• ###### 5. Re: Formula for length-matching a HS diff pair?

Good day Lou:

I just took a quick look at the layout.  I did not expect to see any glaring routing mistakes.  The humps are not much different than what I have used in the past.  The diff pairs are a tight coupled routing which I prefer but does have more loss than loosely coupled routing.  You have sticking vias between your reference planes.

From afar, the match length spreads for your earlier busses look reasonable.  It is my preference not to use the MHz buss descriptors but the rise times of the signals.  The next time there is a die shrinkage it may still be a 6 GHz SAS bus but the rise times have all gained speed.  This is when your taking the little extra time to balance the routing will pay off.  It will also go completely un-noticed by the product design company.

Although I carry a license for PADS, I do all of this routing in Expedition.  The diff pair router will grow the radius of the outer curve to add length and reduce the need for the humps.  The advanced constraints editor will lump together nets into an electrical net to make match lengths a little easier.

Dwain

• ###### 7. Re: Formula for length-matching a HS diff pair?

Here's a PCI Express PHY PCB Layout Guideline of PCI-express differential pairs which runs at 2.5ghz:

AN10373_1.pdf

From the screenshot I see that the serpentines are rather big in some places, in the PCI-e spec there is a maximum size of the serpentine. To avoid impedance discontinuity I think.

• ###### 8. Re: Formula for length-matching a HS diff pair?

Hi Matthias,

Thank you for the link. This is useful information. And you are correct, the serpentines do cause a disturbance in impedance.

Many thanks,

Lou

• ###### 9. Re: Formula for length-matching a HS diff pair?

Hi Paul,

Thank you for the links - more good information.

Lou

• ###### 10. Re: Formula for length-matching a HS diff pair?

Hi Dwain,

Once again, thank you for your insight. From you last reply, I get the impression that Expedition has a better auto-router? Do you ever use this for HS routing, or do you do by hand? If I am understanding you correctly, it sounds like you are able to route both traces of a differential pair simultaneously? I use the pads AR for only stuff near DC - it does things which I consider to be unconscionable. I would be interested in discovering new ways to  increase my throughput. Any comments welcome, time permitting.

Many thanks,

Lou

• ###### 11. Re: Formula for length-matching a HS diff pair?

Good day Lou:

Yes, Expedition will route the full dif pairs at one time while in interactive routing mode.  Sometimes it is a pain to get it to stop wanting to route both sides of a dif pair.  But this has gotten better in recent software releases.

I have not used the multi-route interactive routing technique on dif pairs but if the interactive router does not already, it soon will, allow dif pairs and single ended multi-routing at the same time.  I saw a demo a month ago at a users' group conference.

I have not had any time to look at version 9 of PADS so I can not comment on it.  Expedition at its high end is Pinnacle and the low end is Ascent.  The underlying software engines of PADS and Expedition are very different as Mentor bought each of the products.  I do think that it is fair to say that for the most part, Expedition will get the new code for high end routing before PADS does.

You would have to compare the price of each tool's configuration that allows you to route the technology that your company uses.  I believe that Expedition is a better tool for high speed routing and I have had very good luck getting the boards designed right the first time when using it.

I do all high speed routing with the interactive router.  But other people claim to have used the auto-router.  There can be at lot of time spent setting up the constraints editor in Expedition and if you do spend the time to do a fairly complete setup and you auto-route sections of your high speed one at a time, I would have to believe that the auto-route could do a decent job.  I have used this technique but not on the stuff that is starting to act like RF.  And if the routing area is tight, you will be doing tuning clean-up by hand.

Have fun

Dwain

• ###### 12. Re: Formula for length-matching a HS diff pair?

I've just posted a basic procedure for matching diff pairs: http://communities.mentor.com/message/42175#42175

Also, check out this article from the July 2013 issue of Printed Circuit Design and Fab magazine on "Resolving Impedance Discontinuities" for tips on minimizing reflections when using serpentine routes to match lengths.

The article, titled "Techniques for Routing Differential Signals" can be found here: http://ourdigitalmags.com/publication/?i=165181