[SI-LIST] Re: [Bulk] Re: PCB Impedance Failure
- From: "Dr. Edward P. Sayre" <esayre@xxxxxxxx>
- To: erdinih@xxxxxxxxx, si-list@xxxxxxxxxxxxx
- Date: Fri, 13 Jan 2006 18:05:24 -0500
Folks:
Just another way to look at differential impedance. Use the not so well
known exact formula:
Zdiff = (2*Zo)*(1-Kb)/1+Kb)
where: Zo is the uncoupled single ended trace impedance and Kb is the
backward coupling coefficient between the two coupled traces and (0 <= Kb
<= 1). One sees that Zdiff is always <= 2*Zo
A similar formula form is also convenient for defining the common mode
impedance:
Zcm = (Zo/2)*(1+Kb)/1-Kb)
and Zcm is always >= Zo/2.
All the interaction between traces is embodied in the coupling
coefficient. Real simple to think about, at least far simpler than even
and odd mode impedance ala the microwave theory route.
Thanks -
ed
=============================
At 01:10 PM 1/13/2006 -0500, Ihsan Erdin wrote:
>At the risk of deviating from the original topic, I'd like to make some
>comments on the calculation of differential impedance I've seen in this
>thread. I guess sqrt(L_mutual/C_mutual) is meant by the term "coupling
>impedance" but I doubt it has any meaningful value. The differential
>impedance can be found by decomposing the coupled transmission line circuit
>into its odd and even mode components and multiplying the odd-mode impedance
>by 2. That results in sqrt( 2*(L_self-L_mutual)/( 0.5*C_self +C_mutual) ).
>The formulation assumes the elements of the pair are identical.
>Regards.
>
>Ihsan
>
>
>
>On 1/12/06, Ken Cantrell <Ken.Cantrell@xxxxxxxxxxxxxxxx > wrote:
> >
> > Ludwig,
> > Re: "I don't think anyone was claiming that one can achieve 100 Ohm
> > differential impedance using 50 Ohm SE traces."
> > I use 50 ohm SE, 100 ohm diff all the time. Example: stripline, trace and
> > plane thicknesses 0.64 mils, permittivity 4.0, dielectric thicknesses 4
> > mils, trace width 3.25 mils, run the pair on 15 mil centers. SE is 49.5,
> > Diff is 98.5. If I get 97 - 100 ohm diff, things work great, and I'm sure
> > it could be looser than that and still work fine for standard LVDS type
> > implementations. As someone else stated, this type of geometry (loosely
> > coupled spacing), although it yields a lower routing density, allows for a
> > smooth impedance transition in the pin field escape area since the
> > increased
> > trace separation has little effect on the diff impedance.
> > If you need to go to higher routing densities, then the SE impedance must
> > be
> > increased as you have pointed out.
> >
> > Clayton,
> > If the board house can't produce a good cupon, I would get a re-spin soley
> > on those grounds. Be patient though, stuff happens.
> >
> > Ken
> >
> > -----Original Message-----
> > From: si-list-bounce@xxxxxxxxxxxxx
> > [mailto: si-list-bounce@xxxxxxxxxxxxx ]On Behalf Of Stefan Ludwig
> > Sent: Thursday, January 12, 2006 8:08 AM
> > To: tom@xxxxxxxxxxxxx
> > Cc: si-list@xxxxxxxxxxxxx
> > Subject: [SI-LIST] Re: [Bulk] Re: PCB Impedance Failure
> >
> >
> > Hi Tom,
> >
> > Just a clarification: I don't think anyone was claiming that one can
> > achieve 100 Ohm differential impedance using 50 Ohm SE traces. Given a
> > constant distance to the reference plane(s), your differential pairs of
> > 100 Ohm will be built using, say, 60 Ohm SE traces of a certain width
> > and of a certain separation.
> >
> > Your 50 Ohm SE traces on the same layer will have a different width
> > (wider) than the 60 Ohm SE traces. If you'd calculate the differential
> > impedance of two such 50 Ohm SE traces, given the same separation, you'd
> > end up with less than 100 Ohms.
> >
> > Zdiff = 2*Z0*(1-a*exp(-b*D/H))
> > with a, b = positive constants, D = trace separation, H = height
> > over/between reference plane.
> >
> > The exponential term of trace separation is what you refer to as
> > coupling impedance. But the point is that you can achieve Zdiff = 2*Z0
> > only if the distance between the traces goes to infinity.
> >
> > In any case, the board house didn't deliver the goods and Clayton should
> > either ask for a refund or a respin of the board. The message, however,
> > sounded like there was no time for a respin, hence his request for
> > information.
> >
> > Cheers,
> >
> > Stefan Ludwig
> >
> > Tom Dagostino wrote:
> >
> > >Kai
> > >
> > >I think you are missing the point. The board was designed to have 50 Ohm
> > SE
> > >traces and at the same time 100 Ohm differential traces. What was
> > received
> > >was 59 Ohm SE traces and 86 Ohm differential traces. When the impedance
> > of
> > >the SE traces increases the differential impedance should also increase.
> > >The differential impedance is 2*SE - coupling impedance. If we assume
> > the
> > >coupling did not change significantly since the original was no coupling
> > the
> > >as fabricated board's impedance should have been 118 Ohms.
> > >
> > >Tom Dagostino
> > >Teraspeed(R) Labs
> > >13610 SW Harness Lane
> > >Beaverton, OR 97008
> > >503-430-1065
> > >tom@xxxxxxxxxxxxx
> > > www.teraspeed.com
> > >
> > >Teraspeed Consulting Group LLC
> > >121 North River Drive
> > >Narragansett, RI 02882
> > >401-284-1827
> > >
> > >-----Original Message-----
> > >From: si-list-bounce@xxxxxxxxxxxxx
> > >[mailto: si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Kai Keskinen
> > >Sent: Wednesday, January 11, 2006 2:47 PM
> > >To: Aubrey_Sparkman@xxxxxxxx ; a.ingraham@xxxxxxxx; si-list@xxxxxxxxxxxxx
> > >Subject: [SI-LIST] Re: [Bulk] Re: PCB Impedance Failure
> > >
> > >
> > >Aubrey:
> > >
> > >That is really easy. Just closely couple the diff pairs and you can go
> > from
> > >60 Ohms single ended to 90 Ohms differential with very little effort. It
> > is
> > >not really what you want to do if you have complicated routing through
> > pin
> > >fields since you then get a huge impedance hit if you have to separate
> > the
> > >pairs. Just use any field solver that handles diff pairs and try it. Set
> > up
> > >a 60 Ohm single ended line. Use the same cross-section and add the second
> >
> > >line and move them closer together. You will get a lot lower than 2x
> > single
> > >ended impedance.
> > >
> > >Cheers,
> > >
> > >-----Original Message-----
> > >From: si-list-bounce@xxxxxxxxxxxxx
> > >[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of
> > > Aubrey_Sparkman@xxxxxxxx
> > >Sent: Wednesday, January 11, 2006 1:45 PM
> > >To: a.ingraham@xxxxxxxx; si-list@xxxxxxxxxxxxx
> > >Subject: [Bulk] [SI-LIST] Re: PCB Impedance Failure
> > >
> > >
> > >I'm a little puzzled about something else. Did you really get the diff
> > >impedance to be on the low side (100->86) on the same board / layer
> > >where the single ended impedance is on the high side (50->59)? Please
> > >explain how that was done!
> > >
> > >
> > >Aubrey Sparkman=20
> > >Enterprise Engineering Signal Integrity Team
> > >Dell, Inc.=20
> > >Aubrey_Sparkman@xxxxxxxx=20
> > >(512) 723-3592
> > >
> > >-----Original Message-----
> > >From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
> > >On Behalf Of Andrew Ingraham
> > >Sent: Wednesday, January 11, 2006 11:40 AM
> > >To: si-list@xxxxxxxxxxxxx
> > >Subject: [SI-LIST] Re: PCB Impedance Failure
> > >
> > >Clayton,
> > >
> > >I was a little puzzled about two things you stated.
> > >
> > >One, that the specified differential impedance was exactly twice the
> > >specified single trace impedance. That requires no coupling between
> > >traces of a differential pair (if they are routed on the same layers
> > >with the same trace widths). Is that what you really intended? Since
> > >you got 86 ohms diff. and 59 ohms s.e., your differential pairs must not
> > >have been routed with nearly enough isolation.
> > >
> > >The other is about the error on the test coupon. Can you trust any
> > >measurements on those coupons?
> > >
> > >Did your company actually specify 50 +/- 10%, or was that only a
> > >recommendation? If it was in the spec, then I wouldn't even bother
> > >asking about the risk; I'd send the boards back to the board vendor and
> > >tell them to make new ones that satisfy what you paid them to do. The
> > >fact that they were made wrong, is reason enough to be concerned.
> > >
> > >Regarding the question of the impact on SI, that depends entirely on the
> > >application, on how long the traces are (vs. risetimes and/or frequency
> > >content), on the types of signals, on the chips used, and if and how
> > >lines are terminated. Sometimes it makes little difference whether the
> > >actual impedances are even close to the target. Sometimes it makes all
> > >the difference. 59 ohms isn't that far from 50 ohms, but if you were
> > >using leading edge technologies and pushing all the margins (which you
> > >probably aren't, since you didn't use SI tools), it could indeed be
> > >significant.
> > >
> > >Regards,
> > >Andy Ingraham
> > >
> > >
> > >
> > >>A board we just had fabricated failed the impedance test coupon. 59=20
> > >>ohm vs 50+/- 10%. They could not measure the diffferential pairs=20
> > >>because of an error on the coupon, but calculated 86 ohm impedance vs=20
> >
> > >>100 +/- 10%
> > >>
> > >>
> > >
> > >
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> > --
> >
> > Ludwig Systems Engineering Consulting - Design - Implementation
> > WWW: www.ludwigsystems.com System Architectures - FPGAs - PCBs
> > Ph/Fx: +41-43-355-58-73/74 Hardware - Firmware - Software
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