# Re: [SI-LIST] : low ESR decoupling capacitors

From: Larry Smith ([email protected])
Date: Wed Jan 05 2000 - 13:46:08 PST

DC - the calculations below are just an example for one capacitor.

To build a robust power system, we need many different valued
capacitors in parallel. The list probably includes some 100nF, 10nF,
4.7nF, 3.3nF, 2.2nF, 1.5nF, 1nF, 820pF, 680pF, 470pF, as well as bulk
capacitors. Each capacitor value resonantes and presents a minimum
impedance to the power distribution system at a different frequency.

To calculate the number of each value to put in parallel, we have to
know the ESR. Then it is just a simple matter of putting enoungh
capacitors of each value in parallel to reach down to a target
impedance. We might end up with 100 capcitors in parallel, some of
each value. The impdeance over frequency becomes flat and resisitive
in phase. It is quite practical to have a flat 10 mOhm impedance out
to 100 MHz or more with 100 capacitors. The phase of the parallel
impedances does not deviate very far from being resistive.

You can hit that power system with any clock pulse or any conceivable
current load waveform and see noise similar to what you would see with
an ideal voltage source with a 10 mOhm series resistor. It is very
difficult to predict the load waveform that customer code is going to
cause the uP and ASICs to draw from the power system. Therefore, we
want to have a flat impedance across a broad frequency range.

This makes an almost ideal supply. If your system needs a 5 mOhm
supply, just double the number of capacitors (...or halve the ESR of
the capcitors you already have...). There is no voltage ringing in the
overall system because of the flat impedance profile.

There is however tremendous current ringing back and forth between
capacitors. We have not seen an EMI problem from this. In fact, the
EMI performance of the systems that we have built from this methodolgy
have always shown an EMI improvement. It seems that power planes with
bouncing voltages are more harmful than power planes that redistribute
a lot of current.

regards,
Larry Smith
Sun Microsystems

> From: "D. C. Sessions" <[email protected]>
>
> Larry Smith wrote:
> >
> > Doug - I am changing the thread title to better reflect the subject.
> > We need to take a look at inductance, resistance and capacitance
> > to determine the impedance of a capacitor at 200 MHz. If you follow
> > this through, you will see the great value of low ESR capacitors.
> >
> > Inductance is probably the most important parameter of a decoupling
> > capacitor. You have correctly calculated the inductive reactance of a
> > typical capacitor at 200 MHz if it is mounted on 5 nH pads. But with
> > careful pad and via design, we routinely reduce the mounted loop
> > inductance of 0805 size capacitors to less than 1 nH. One nH gives us
> > 1.26 Ohms of inductive reactance at 200 MHz.
> >
> > But, suppose we mount a 633pF capacitor with 100mOhms ESR on that 1 nH
> > pad. It forms a nice series RLC circuit that has a minimum impedance
> > at frequency 1/(2pi*sqrt(LC)) = 200 MHz. The impedance is:
> >
> > R + jwL + 1/jwC
> > = 100m + j 1.26 - j 1.26
> > = 100mOhm
>
> The problem is that most of us aren't trying to draw narrow-bandwidth
> sinusoidal power from the supply network. For us, the wild resonant
> swings on the capacitors aren't neatly balanced by equally wild di/dt
> swings on the inductance, and instead the local supply gets sucked
> down hard at clock edges and then swings out of safe operating area
> in between.
>
> I'm somewhat familiar with the work being done on resonant clock/power
> systems, but since our libaries and processes aren't designed with
> them in mind I really would prefer a supply net that minimized peak
> excursions from nominal over one that was nominal only at selected times.
>
> > By using a low ESR capacitor, we have presented an impedance to the
> > power distribution system that is 1/10 of the impedance from the
> > inductance.
> >
> > This is an extremely powerful concept. With low inductance mounting
> > pads and low ESR capacitors, it is possible to build a high performance
> > power distribution system with a fraction of the capacitors you might
> > have thought you needed. You just have to carefully pick the
> > capacitance value, carefully design the pads, and have a source of low
> > ESR caps. THE LOWER, the BETTER!
> >
> > We are designing power distribution systems with target impedances that
> > are less than 10 mOhms. Typical NPO and X7R capacitors in the 470 pF
> > to 10 nF range have ESR greater than 100mOhms. We could use capacitors
> > that have 1/10 the ESR of today's caps. We could reduce the number of
> > capacitors cluttering up or boards from hundreds to tens. If we only
> > had lower ESR caps...
> >
> > We do not sprinkle in capacitors like salt and pepper but rather have a
> > very deliberate design methodology. It is documented in the IEEE Journal
> > Transactions on Advance Packaging, Aug 1999, Vol 22, Number 3. The
> > paper gives much more details on power distribution and decoupling
> > capacitors than I can give in this space. A soft copy is available at:
> >
> > http://www.qsl.net/wb6tpu/si_documents/docs.html
> >
> > Parallel capacitor resonance is definitely an issue. You must have a
> > methodology that avoids the parallel resonance if you are going to use
> > low ESR capacitors. You must carefully design the power plane stackup.
> > Placement is critical for capacitors that resonate at a frequency where
> > the dimensions of the board become significant. But fortunately,
> > software tools will soon become available in the public domain to help
> > us do all of this.
> >
> > Now, all we need is low ESR caps.
> >
> > BTW, I really like your time domain method of measuring capacitor
> > parameters. You won't get any information about mounted inductance
> > from this measurement, but capacitance, ESR and fixture inductance
> > determine the shape of the observed waveform. Is there some reason
> > why you use a 100 Ohm resistor to inject energy into the cap? A 50
> > Ohm resistor might better terminate the transmission line and avoid
> > transmission line resonance issues in the measurement.
> >
> > regards,
> > Larry Smith
> > Sun Microsystems

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