From: Doug Brooks (firstname.lastname@example.org)
Date: Fri Feb 04 2000 - 11:52:55 PST
At 11:06 AM 2/4/00 -0800, you wrote:
>Doug - Please allow me to address your comments below.
> > X-Sender: email@example.com
> > Date: Thu, 03 Feb 2000 15:38:06 -0800
> > 1. As ESR goes down, the troughs get deeper and the peaks get higher!
> > 2. The minimum impedance value is NOT NECESSARILY ESR (or ESR/n); it can
> > and is lower than that!
>I am not sure I understand this one. If we have a series RLC circuit,
>the minimum impedance will be when the positive and negative reactance
>(jwL and -1/jwC) cancel each other and you are left with R. I don't
>see how the minimum impedance can be any less than that. Are you
>considering a more complex circuit?
Well, the arithmetic in the article "proves" this point. That's why we
posted the article.
The minimum is ESR for a SINGLE RLC circuit, but not for parallel RLC
circuits unless (1) their self resonant frequencies are far apart or (2)
ESR's are very low. Intuitively we see that if two RLC circuits are very
close together, the minimum resistance will be closer to ESR/2. Of course
the whole point about bypass caps is that you have more than one!
> > 3. The minimum impedance points are not necessarily at the capacitor
> > self-resonant points.
>With typical RLC values found in the industry today, we have always
>found the minimums to be at frequency 1/(2pi*sqrt(LC)), both in the
>lab and in simulation. Again, we have assumed a simple series RLC
>model for the capacitor. This model checks out very well with all of our
Again, we thought so too. This is true for a SINGLE RLC circuit. But put
two of them in parallel and the game changes!
Again, we prove this in the arithmetic. That IS the point of all this! With
very low ESRs or self resonant frequencies far apart, the minimums are not
exactly the self resonant frequency, but close enough not to matter. But
with lower ESRs or with groups of bypass capacitors whose self resonant
frequencies can be close together, there can be noticeable shifts between
the cap SRF and the min frequency. In carefully chosen cases, it could be
that the effects on a given cap by two other caps whose SRF's are on
opposite sides of the given cap may 'cancel' and the result look like the
given caps SRF.
> > 4. For a given number of capacitors, better results can be obtained from
> > more capacitor values, with moderate ESRs, spread over a range than with a
> > smaller set of capacitor VALUES, with very low ESRs, even at well chosen
> > specific self resonant frequencies.
>I mostly agree with this.
The demonstration is in the article
>We (Ray and I) took a quick look at your
>article. We would like to see you narrow in on inductance and ESR
>values that are typical in the industry today for surface mount
>chip size capacitors mounted on pcb's with vias down to power planes.
Since there are an infinite number of ways people can select bypass caps
and their values, that is why we are making the calculator tool we
developed (with some difficulty!) available for license. With it you can
formulate ANY combination of values you want and check what happens to the
min/max frequencies and impedance values.
See our updated message re in-house seminars on our web page
Doug Brooks, President firstname.lastname@example.org
UltraCAD Design, Inc. http://www.ultracad.com
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