**From:** Ray Anderson (*[email protected]*)

**Date:** Fri Jan 28 2000 - 10:41:14 PST

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Issac Cheng <[email protected]> wrote:

*> Raymond Anderson,
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*>
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*> I've read your paper on Power Distribution System Design Methodology and
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*> Capacitor selection for Modern CMOS technology. I found it excellent and
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*> well written. I hv some questions here regarding to the topic.
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*>
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*> 1. From figure 12(showing the anti-resonance of parallel caps), how do you
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*> add up two Z-Freq response graphs to get the anti-resonance?
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*> 2. Say I got the R and X values of a cap for various freq(100, 1K, 10K,
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*> 100K, 1MHz), say, how can I plot out the Z vs Freq graph for 2 caps(same
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*> question as above, but it's actually asking how to calculate it and put it
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*> on a graph)?
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*> 3. For the formula in estimating the needed decoupling capacitance for a
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*> PDS, ie. C=I(dt/dv), how do you estimate I and dt here? I is the transient
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*> current, is it the Imax in the system? dt is the VRM respond time, how do
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*> you get dt? Is it from the VRM spec or somewhere else?
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*> 4. Do you do a 'anti-resonance' and Ztarget check at then end of your
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*> simulation for PDS?
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*>
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*> Isaac Chang
*

Issac, thank you for your kind comments on our paper. The lion's share of the

compliments should go to my colleague Larry Smith who was primarily responsible

for spearheading our group's work that led to the paper.

1.

As Istvan has pointed out (3 time zones ahead of me), the anti-resonances

plotted in Figure 12 are numerically the result of a parallel combination of

the impedances of the two series RLC circuits. This can be calculated by summing

the admittances of the circuits and then taking the reciprocal of the result

(parallel impedances are similar to parallel resistances, EE101 stuff). The

actual plots included in the paper are a result of a simple Hspice

simulation. The same plots could have been produced with numerical

calculations in Matlab, in a spreadsheet, or by hand as Istvan pointed out.

2.

If you have tabulated R and X values I guess you could curve fit those values to

and expression of Z for each RLC ckt. and then parallel the combination as described

above. You could even do it in spice if you figure out how to represent a ckt as

a table of values.

3.

The current we are interested in is the delta current. Suppose you have a system

that draws 40 amps DC. You also know that its current consumption varies between

40 amps maximum when it is running at full speed and executing code, and it draws

30 amps when idling in the sleep mode. It is the 10 amp delta (40-30) or transient

current that you are interested in. The dt value is determined by the dynamic response

of the VRM (which is determined by the loop response of the VRM). The dt number can be

estimated by looking at a plot of the transient current response of the VRM and noting

how long it takes the supply to ramp the transient current up or down. It can be

extracted from the spec, measurement, or simulation (if you have enough time...).

4.

After a simulation run, the resulting Z profile is compared to the target impedance

determined for the system. The goal is to produce a decoupling solution that lies

below the target-Z. Anti-resonances, if not managed can exceed the target Z and may

be problematic in that they represent high impedances at specific frequencies that may

cause system malfunctions if the system needs to draw appreciable current at those frequencies

and also may spell bad news for EMI radiation at those frequencies as well. It is the

job of the designer to manage the number, value and position of the decaps to produce

a broadband, flat, low impedance response profile that keeps below the calculated target-z.

-Ray Anderson

Sun Microsystems

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**Next message:**Bob Ross: "[SI-LIST] : EUROPEAN IBIS SUMMIT MEETING ANNOUNCEMENT"**Previous message:**Istvan NOVAK: "Re: [SI-LIST] : Questions abt Power Distribution System"**Maybe in reply to:**Chang, Isaac Yew Beng: "[SI-LIST] : Questions abt Power Distribution System"

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