# Re: [SI-LIST] : ESR and bypass caps

From: Larry Smith ([email protected])
Date: Mon Feb 07 2000 - 10:21:52 PST

Doug - you have an interesting and useful little calculator there.

Ok, I see how your are getting minimums below the ESR of individual
capacitors. It is the parallel combinations of all impedances that add
up to both the minimum and maximum.

It is interesting to note the phase of the lower frequency minimum and
higher frequency minimum. The lower frequency minimum are capacitive
and the higher frequency minimum are inductive. That shows you the
phase of the impedances in the parallel circuit.

One of the most important features of low ESR capacitors is that it is
possible to keep the phase at least somewhat resistive across a broad
frequency range. This is shown quite nicely with your calculator. If
the phase is somewhat resistive, the Q of the circuit will not get
dangerously high.

We must not forget the power plane capacitance. The parameters for the
power planes vary greatly (depending on the pcb stackup) but try c=1nF
r=.01 L=.1nH. You end up with a major impedance peak at a frequency
where all decaps have gone inductive and the capacitance of the power
planes is still there. True, you must do a distributed plane analysis
to really understand this. But even with your calculator, you should
be able to see the dangerous effects of this resonance. The high
impedance resonance typically lands at several hundred MHz, right where
we are trying to operate our modern processors... :(

regards,
Larry Smith,
Sun Microsystems.

> My pleasure. Here is what our little calculator would come up with: (Just
> like you said.)
>
> Case 1:
>
> 2/4/2000
> 4:26:12 PM
> Initial Conditions
> Input filename = C:\POLEZERO\LSMITH1.TXT
> Output filename = C:\POLEZERO\LSMITHO1.TXT
> Number of Capacitance Values = 5
> Total Capacitance = .0127
>
> Number L nH C
> uF R Resonant F (MHz)
> 1 01.00000 .001000 .1
> 159.155
> 1 01.00000 .001500 .1
> 129.949
> 1 01.00000 .002200 .1
> 107.302
> 1 01.00000 .003300 .1
> 87.612
> 1 01.00000 .004700 .1
> 73.413
>
> Frequency (MHz) Impedance Turn PhaseAngle(Deg)
> 72.023 .0675823 Min -36.5026
> 79.716 .0789909 Max -20.0925
> 86.671 .0699806 Min -7.6151
> 97.674 .1031926 Max 2.0211
> 107.66 .0733426 Min 10.7
> 119.99 .1153441 Max 18.4003
> 131.31 .0726022 Min 26.9647
> 148.33 .1355461 Max 34.9443
> 161.9 .0699509 Min 43.9007
> 4:27:00 PM
>
>
>
> Case 2:
>
>
> 2/4/2000
> 4:28:38 PM
> Initial Conditions
> Input filename = C:\POLEZERO\LSMITH2.TXT
> Output filename = C:\POLEZERO\LSMITHO2.TXT
> Number of Capacitance Values = 2
> Total Capacitance = .0124
>
> Number L nH C
> uF R Resonant F (MHz)
> 3 01.00000 .001000 .1
> 159.155
> 2 01.00000 .004700 .1
> 73.413
>
> Frequency (MHz) Impedance Turn PhaseAngle(Deg)
> 72.771 .0493910 Min -9.489
> 115.13 .5864965 Max -1.0232
> 159.78 .0327716 Min 9.0943
> 4:29:07 PM
>
>
>
>
> .
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