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

From: Doug Brooks ([email protected])
Date: Fri Feb 04 2000 - 18:17:34 PST

>
>Then we have to space capacitors close together in value. This
>prevents the parallel resonance from getting too high. The attached
>spice deck and .pdf file shows two combinations of capacitors. The
>first set has 5 closely spaced values and the second set has just two
>values. Inductance is 1nH and ESR is 100mOhms:
>
>xcap2 vdd 0 cap C=1.0n R=100m L=1n \$npo
>xcap3 vdd 0 cap C=1.5n R=100m L=1n \$npo
>xcap4 vdd 0 cap C=2.2n R=100m L=1n \$npo
>xcap5 vdd 0 cap C=3.3n R=100m L=1n \$npo
>xcap6 vdd 0 cap C=4.7n R=100m L=1n \$npo
>
>...and...
>
>xcap2 vdd 0 cap C=1.0n R=100m L=1n \$npo
>xcap3 vdd 0 cap C=1.0n R=100m L=1n \$npo
>xcap4 vdd 0 cap C=1.0n R=100m L=1n \$npo
>xcap5 vdd 0 cap C=4.7n R=100m L=1n \$npo
>xcap6 vdd 0 cap C=4.7n R=100m L=1n \$npo
>
> >From the spice output you can readily see the parallel resonance and
>how dangerous it is when capacitors are not spaced closely in value.
>(One ac amp has been forced into the parallel circuit, so volts is
>interpreted as magnitude of impedance.) With the 5 different valued
>capacitors, we see 4 parallel 'antiresonances', growing with increasing
>frequency. The growth is because Q increases as omega increases. The
>higher the resonant frequency, the more important it is to have low
>inductance pads. The 5 capacitor-value case has a maximum impedance of
>about 150 mOhm, but the 2 capacitor-value case has a maximum of about
>600 mOhms. That is enough difference to make a product pass or fail.
>
>With 5 capacitors, we have made a nice flat 100 mOhm impedance
>between 60MHz and 200Mhz. With 50 capacitors, we could have made a
>10 mOhm impedance between those frequencies. If only we could get a
>bunch of 100 mOhm capacitors...
>
>Members of the SI community should feel free to take this generic
>spice deck and run it. Play around with ESR and inductance. You
>will quickly see the value of using low ESR capacitors on low
>inductance pads in managing a low impedance power system across
>a broad frequency range. I believe the same results will be obtained
>with Doug Brooks' simulator. Doug, please let us know.

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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Doug Brooks, President [email protected]