# [SI-LIST] : ESR and Bypass Caps, revisited and revised

From: Doug Brooks ([email protected])
Date: Mon Feb 21 2000 - 15:12:59 PST

About three weeks ago I called everyone's attention to an article we had
written about ESR and Bypass Cap selection. After considerable discussion,
the concensus was that the statements I made about the subject were accurate.

But I have subsequently realized that there were TWO IMPORTANT CONSEQUENCES
of what I had developed that I had NOT included in the paper. These came
clear when we added a graphical output to the calculator (the single most
requested update to it!)

(The paper has been updated with these two conclusions, graphical

Consequence 1.
I had said that the condition for a (almost) flat impedance response curve
is that, at the anti-resonant frequencies, the following relationship hold
true:

ESR = -X1 = X2

where X1 and X2 are the reactance terms of the (in this case) two parallel
capacitors.

What I did NOT expand on is that, this being the case:

If ESR goes down, then
X1 and X2 must also go down, and
therefore the self resonant frequencies of the two capacitors must move
closer,
therefore more capacitors must be used to cover a given frequency range!

That is: The lower is ESR, the more bypass capacitors are required to
achieve a given impedance response with frequency.

This point is developed and demonstrated in the revised Appendix 4.

Consequence 2.
Another point made in the paper is that the minimum impedance is less than
ESR for all practical cases. A point NOT made originally, is:

As the self resonant points of the parallel capacitors get closer together,
without changing ESR, the minimum impedance value decreases. Revised
Appendix 3 in the paper illustrates the case of 100 bypass caps with
self-resonant frequencies spread over the range of 5 to 500 MHz. The
impedance response is quite good over this range. But when the number of
capacitors is increased to 150, the impedance curve is lower AT EVERY
FREQUENCY then the 100 cap curve. That is --- the MAXIMUM impedance for the
150 caps is LESS than the MINIMUM impedance for the 100 caps! The 200
capacitor curve is lower EVERYWHERE then the 150 cap curve! (See Revised
Appendix 3)

It was noted, correctly, that this kind of analysis cannot take into
consideration the PLACEMENT of capacitors across the board. It takes a
finite amount of time for charge to propagate between locations on a board.
So, even though there may be the appearance of sufficient capacitance
available, in fact, charge may not be able to get where needed in time. For
a simplified discussion of this point, see my column in the January issue
of PC Design ("A One-Answer Quiz"), reprinted on our web page under the
title "This Month's Quiz."

Our calculator has been upgraded to include the graphical capability.

Doug Brooks

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Doug Brooks, President [email protected]