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

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> 
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06/27/2006 10:40 AM
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[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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