[SI-LIST] Re: Decoupling Capacitor ESR/ESL

Erin, The science behind Dr Johnson's analysis is solid.  It does 
predict incremental effects of moving vias around pretty well.  For 
example if you take end mounted vias and push them further apart, his 
methods predict the incremental inductance pretty closely.  Dr 
Johnson verifies that with his 100X models.  The issue with the 
models is that capacitors are represented by solid metal blocks 
virtually at the PCB surface.  That isn't what happens with real 
capacitors.  Had he built his 100X models with additional features to 
account for the location of the capacitor plates relative to the PCB 
mounting surface there is little doubt that the results would have 
been substantially higher and much closer to what you see in Lee's 
book and real life.
The incremental inductance for via Z axis in Lee's book are not way 
off for specific cases.  In Lee's book I recall that John Zasio was 
measuring primarily 0603 capacitors.  John did not specify either 
drill size or spacing.  However, I suspect that the spacing was 
50mils to support routing grid.  Similarly, most likely he was using 
14 or 15mil drills to keep the aspect ratio under control for thick 
boards.  For 14mil drills I get 20pH / mil and for 15mil drills 
19.3pH / miil.  In that case his measurements are off by 11% or less 
for the case of a two via capacitor mount.  That's still a lot better 
than much of the information that is out there.  You just need to 
understand where those numbers come from and how to get the right 
numbers for your situation.

For big capacitors like tantalums, the capacitor body contributes a 
lot of inductance.  An ordinary tantalum construction has a wire half 
way up the body extending into the tantalum slug.  That big Z axis 
rise and little wire makes a big induction loop.  John Pymak did a 
nice presentation on this at the TF at DesignCon East 2005.  You can 
find it on Istvan's web-site. Because of the large contribution from 
the capacitor dimensions, and the large value of inductance to begin 
with the percentage error of measurements in Lee's book for big caps 
is quite low.

Where I find the book goes a bit wrong is that John offered a blanket 
metric of 35.5pH / mil / via that does not specify via diameter, 
spacing, or array density.  Four vias on an 0402 do not come close to 
halving the via inductance due to mutual coupling from + to +, and - 
to -.  Similarly, vias spaced 100mils apart have a lot higher 
inductance / mil than the same diameter vias spaced 40 mils apart.

If you have built a spreadsheet that uses one dimensional models you 
are still going to face other surprises, especially if you try to 
make very low impedance PDNs.  Those kinds of spreadsheets can be 
very handy as a starting point.  But at a minimum you will want to 
account for 2D effects of the planes.  Ultimately we are concerned 
with the power at the die and that means that you also need to 
account for what is between the planes and the die, sic what the IC 
package and die parasitics look like.  These considerations make a 
market for products from companies like Sigrity, Ansoft, and KAW.

Regards,


Steve.


At 11:00 AM 6/28/2006, Erin.McPhalen@xxxxxxxxxxxxxxxxxxxxxxxxx wrote:

>Hi Steve
>
>Thank you for your response, that website has excellent material on 
>decoupling capacitors.
>
>  I guess the issue I have using HJs model is that Lee Ritchy give 
> an inductance of 1.19 nH for a 0603 with End-to-End vias, and 0.780 
> nH for the Side-to-Side vias.   When I run the numbers for a 12 mil 
> drill hole,  5 mil distance from pad to ground plane, I get a via 
> contribution of 108 pH for 0.050 mils separation and 153 pH for 
> 0.150.   Using HJ's recommendation of treating the Pads, trace 
> stubs, and capacitor body as transmission lines to derive the 
> inductance, I end up with 647 pH for a Side-to-Side vias and 737 pH 
> for an End-to-End vias.  This takes into account the changes in pad 
> and trace lengths but keeping the capacitor "height" fixed.  My 
> only conclusion is that the via contribution is two low when 
> calculating the inductance for the region encased by the vias and 
> mounting structure.
>
>I was hoping to come up with an reasonable formula for calculating 
>the mounted inductance that was consistent with Lee Ritchey. Keeping 
>cap height constant should be able to give me something close to Lee 
>Ritchey's mounted inductances from his book.
>
>The end goal was to provide a tool for choosing decoupling 
>capacitors on new products here and to hopefully convert the Kemet 
>ESLs to mounted ESLs to provide a good source of various measured 
>ESLs for capacitors.
>
>Erin McPhalen
>
>
>
>
>steve weir <weirsi@xxxxxxxxxx>
>Sent by: si-list-bounce@xxxxxxxxxxxxx
>
>06/27/2006 10:40 AM
>Please respond to
>weirsi@xxxxxxxxxx
>
>To
>Erin.McPhalen@xxxxxxxxxxxxxxxxxxxxxxxxx, si-list@xxxxxxxxxxxxx
>cc
>Subject
>[SI-LIST] Re: Decoupling Capacitor ESR/ESL
>
>
>
>
>Erin, there are appnotes on the X2Y web site www.x2y.com that show
>measured capacitor ESL for several different types of ordinary
>capacitors and X2Ys of course for different mounting conditions.
>
>If you look closely, the formulas derived empirically for incremental
>inductance versus height in Lee's book are off a little but not way
>off from the derivation using the method of Biot-Savart that is
>behind Dr. Johnson's formula for via pair inductance within a cavity:
>
>L = H*u/pi * ln( S / R )
>
>Dr. Johnson derived a different formula for inductance outside a cavity.
>
>Otherwise known as 10.2pH / mil * ln( S/R )
>
>For 0402s using sidemount vias on 1mm centers and 10 mil drills this
>becomes 21pH / mil.  Lee's book has a value of 35.5pH/mil/via without
>specifying the via diameter or spacing which would work out to 17.8pH
>/ mil.  So, you can see that they are in spitting distance of each
>other for that specific case.
>
>In very carefully constructed test fixtures, we find that Biot-Savart
>still works.  The trouble that you may be having is the method that
>you use to measure inductance.  Please see any of Istvan's or my
>papers on that somewhat tricky subject.  It is very easy to get
>thrown off especially when trying to measure small inductances.
>
>Steve.
>At 09:02 AM 6/27/2006, Erin.McPhalen@xxxxxxxxxxxxxxxxxxxxxxxxx wrote:
> >Hi
> >I have put together a board impedance calculator in Excel that graphs the
> >impedance of a PCB based on various decoupling capacitor values(ESR, ESL,
> >C) and embedded capacitance of the board.  I am having difficulty,
> >determining the ESL in particular for MLC capacitor.  I was using the
> >"Right the First Time" book to bring in the mounting ESL and Via effects,
> >but find the results inconsistent in the book, especially in terms of
> >various measured values compared to calculated.   Howard Johnson had
> >several empirical formulas but I found poor correlation between the
> >formulas given by Howard Johnson compared to those presented by Lee
> >Ritchey, both calculated and measured.
> >
> >Is their a reasonable method of calculating ESL that is consistent with
> >measured values for determining the mounted inductance of a capacitor
> >including the inductance associated with the Vias to the power/ground
> >pairs?  I have looked at the AVX and Kemet Spice models as well.  AVXs ESR
> >values agree well with Lee Ritchey's measured but the ESL was fixed based
> >on package.  The Kemet spice models provided ESL/ESR but both were
> >excessively high compared to the calculated/measured values from Lee
> >Ritchey.   I know that voltage rating, vias separation, dialectic,
> >package, etc all effect the ESL.
> >
> >If anyone has a sound empirical formula or knows of a manufacturer who
> >publishes ESL values of standard ceramic capacitors that seem reasonably
> >close to measured values that would be a big help.   Even relative
> >magnitude would work across various values of capacitors, since the intent
> >of the spreadsheet is to help engineers here plan their decoupling
> >strategy based on a target board impedance.
> >
> >Thank you in advance,
> >
> >Erin McPhalen
> >
> >Hardware Designer
> >R&D Hardware
> >SCHNEIDER ELECTRIC
> >
> >
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