**From:** Howard Johnson (*howiej@sigcon.com*)

**Date:** Wed Nov 03 1999 - 15:26:36 PST

**Next message:**Larry Smith: "Re: [SI-LIST] : Comment on Johnson's article"**Previous message:**Jim Freeman: "Re: [SI-LIST] : Micro Noise"**Next in thread:**Larry Smith: "Re: [SI-LIST] : Comment on Johnson's article"

I think the original question that started this

thread has been adequately addressed, but there

is one thing I'd like to say about Larry's note below.

Although I USUALLY agree with him, I'll have to differ

this time.

My quibble has to do with the

precise value of capacitance in a bypass capacitor.

For ordinary, inexpensive dielectrics (like Z5U) in

small packages the value of capacitance (after

discounting for the initial tolerance, temperature,

and aging) can vary by a factor of 3:1. With

that large a swing in the value of capacitance

you can't really assume much about the precise

location of the series resonant frequency. If you

want to precisely control the SRF you need to use

a more stable dielectric (which therefore has

a lower dielectric constant, and comes in a LARGER

package). I don't think that's such a good tradeoff.

I'd rather see Larry just put enough capacitors

on the board to make it work purely from consideration

of the inductance alone, without have to make assumptions

about the precise location and depth of the SRF null.

Also, as a general rule, as you lower the series resistance

of a capacitor the notch at the SRF deepens, but

unfortunately at the same time the (parallel) resonance

between the (inductance of the) discrete capacitor package

and the (idealized) capacitance of the Vcc-Gnd planes

becomes more pronounced. For this reason I don't usually

seek capacitors with a super-low value of ESR. I stick

with the cheap, cruddy, non-resonant kind of regular

bypass capacitors (Z5U or equivalent) that don't harbor

any resonant surprises.

Best regards,

Dr. Howard Johnson

At 01:00 PM 11/1/99 -0800, you wrote:

*>[KEVEN--MORE FROM THE SI LIST]
*

*>---------------------------
*

*>Content-Type: TEXT/plain; charset=us-ascii
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*>Content-MD5: HxKGAo37SqiDXilkosOhLQ==
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*>
*

*>Arrigo - It is true that inductance is an extremely important parameter
*

*>for decoupling capacitors and a low inductive impedance between the
*

*>power rails is useful in reducing noise.
*

*>
*

*>But to get a complete picture, we need to consider the L, C and R of
*

*>the decoupling capacitors. A good model for ceramic decoupling
*

*>capacitors is a series RLC circuit. If we had perfect (lossless) L and
*

*>C, the decoupling capacitor would be zero impedance(!) at the series
*

*>resonant frequency which is 1/sqrt(LC). But, all capacitors have loss
*

*>which is usually represented as equivalent series resistance, ESR. For
*

*>many ceramic decoupling capacitors, the ESR is a lower impedance than
*

*>jwL or 1/jwc, leading to nice minimum impedance at resonant frequency.
*

*>A gif file is attached that shows frequency domain spice analysis of a
*

*>small menu of individual 0805 size decoupling capacitors:
*

*>
*

*>
*

*> 3.3nF 0.7nH 142mOhms
*

*> 2.2nF 0.7nH 155mOhms
*

*> 1.5nF 0.7nH 168mOhms
*

*> 1.0nF 0.7nH 158mOhms
*

*>
*

*>Suppose we have a system that requires a power supply with an impedance
*

*>of 100 mOhms between 100 and 200 MHz. We have room for just 5
*

*>capacitors that are 0805 size. What are the best 5 capacitors that we
*

*>can choose?
*

*>
*

*>None of the capacitors on the menu have 100 mOhms of impedance, but if
*

*>we parallel them up we can get less than 100 mOhms of impedance.
*

*>First, try using 5x3.3nF. The spice analysis in the lower panel of the
*

*>.gif file shows that at 100 MHz, we are far below 100 mOhms, but do
*

*>not meet requirements at 200 MHz.
*

*>
*

*>We might try using 2x3.3nF in parallel with 3x1.0 nF. This combination
*

*>works well at 100MHz and 200MHz, but leaves a bad 'anti-resonance' at
*

*>150MHz. The anti resonance occurs when one capacitor has gone
*

*>inductive and another capacitor is still capacitive. It forms a
*

*>parallel RLC circuit that has a dangerous high impedance at some
*

*>frequency.
*

*>
*

*>The best choice is to use one of each of the above capacitors and double
*

*>up on the 1nF, for a total of 5 capacitors. The five capacitors in
*

*>parallel make a nice flat impedance between 100MHz and 200MHz. The ESR
*

*>for lower value capacitors tends to be higher because fewer plates are
*

*>used in the construction.
*

*>
*

*>A word of warning: Power planes have very high quality (low inductance,
*

*>low ESR) capacitance. Four mil thick FR4 has a capacitance of 225 pF
*

*>per square inch. If we use discrete capacitors to decouple a set of
*

*>FR4 power planes, there will be a large antiresonance at some higher
*

*>frequency. The lower panel shows the antiresonance at about 500 MHz
*

*>when 4 square inches of power plane are decoupled with 5x3.3nF. The
*

*>high Q circuit formed by low ESR capacitors attached to power planes
*

*>through inductive vias/pads can result in EMI problems.
*

*>
*

*>Several of us at Sun have published a paper in the IEEE Transactions on
*

*>Advance Packaging, Aug 1999, Vol 22, Number 3. The paper gives much
*

*>more details on power distribution and decoupling capacitors. A soft
*

*>copy is available at:
*

*>
*

*> http://www.qsl.net/wb6tpu/si_documents/docs.html
*

*>
*

*>regards,
*

*>Larry Smith
*

*>Sun Microsystems
*

*>
*

*>
*

*>
*

*>> Date: Sun, 31 Oct 1999 23:56:05 -0800
*

*>>
*

*>> Dear SI experts,
*

*>>
*

*>> I have a question on the article posted on Dr. Johnson's web site at
*

*>>
*

*>> http://www.sigcon.com/news/2_3.htm
*

*>>
*

*>> entitled `Bypass Capacitor Layout'. At the end of the article
*

*>> Dr. Johnson's states that since the only parameter that affects the
*

*>> performance of bypass capacitors at high frequency is their parasitic
*

*>> inductance, there is no point in using many small capacitors, rather
*

*>> the highest value capacitor in the chosen package should be used.
*

*>>
*

*>> Isn't this in contraddiction with the principle, also stated in the
*

*>> book, that many small capacitors are a better choice since the total
*

*>> parasitic inductance is lower? After the series resonant frequency
*

*>> of 1/sqrt(LC) the impedance goes up with 20 dB/decade slope so the
*

*>> only way to decrease it is by lowering either L or C, so both L and C
*

*>> are important.
*

*>>
*

*>> Am I missing something?
*

*>>
*

*>> Thanks in advance,
*

*>>
*

*>> -Arrigo
*

*>Content-Type: IMAGE/gif; name="caps.gif"; x-unix-mode=0644
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*>
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*>Content-Description: caps.gif
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*>Content-MD5: eHrQrybJNhhShCRCXssW9g==
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*>
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*>
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*>
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*>Attachment Converted: "C:\Eudo_twisp\attach\caps.gif"
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*>
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_________________________________________________

Dr. Howard Johnson, Signal Consulting, Inc.

tel 425.556.0800 fax 425.881.6149 email howiej@sigcon.com

Upcoming High-Speed Digital Design seminars:

S E E - - - >>> WWW.sigcon.com

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