RE: [SI-LIST] : Decoupling capacitors (again!)

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From: Larry Smith ([email protected])
Date: Tue Aug 15 2000 - 16:57:25 PDT

Martin has a good question on decoupling and Pat has contributed some
good comments on the subject. The most common complaint that I hear
about this decoupling methodology is that it requires the use of too
many capacitors! Please allow me to make a few comments that may

First of all, we need to carefully distinguish between a power
distribution problem and an SSN (simultaneous switch noise) problem.
Anytime there are IO or transmission lines involved, it is probably an
SSN problem. The two problems are closely related, but if we don't
make a careful distinction, we will greatly over estimate the number of
capacitors required.

To determine the number of discrete decoupling capacitors required in a
system, we first calculate the target impedance. For Martin's problem
we can get a good estimate from the clock frequency and capacitance
load. The system runs at 100 MHz and there is 1.5 nF of capacitance
that may be charged up to 3.3V or discharged to ground every clock
cycle. Q = CV, so we have 1.5nF*3.3V = 4.95 nCoulombs that may flow
every clock cycle. I = dQ/dt, so we have 4.95 nCoul/10nSec = .495 amps
average current. Most systems can tolerate a 5% supply, so the target
impedance is Zt = Vdd*5%/I = 3.3*.05/.495 = 333 mOhms. (If there is
more than just IO circuitry hanging on the 3.3V supply, the target
impedance should be lower.)

333 mOhms is much higher than the 20 mOhm target impedance calculated
below. The error has come because the power distribution problem was
mixed up with an SSN problem. SSN is concerned with edge rates, but
the power distribution target impedance is associated with average
currents. It will be easy to maintain 333 mOhm impedance out to more
than 100 MHz with about a dozen carefully chosen capacitors. This is
all that is needed for this power distribution problem and is
consistent with the intuition that experienced engineers have regarding
the number of capacitors required. The decoupling capacitor
methodology gives a good way to optimize the chosen capacitors and
guarantee there are no high impedance frequencies up to several hundred
MHz. This becomes necessary on larger systems where we really have to
maintain 10 mOhms or less up to high frequencies.

As Ray mentioned in a previous note, it is very difficult to maintain a
low target impedance above 200 MHz using discrete capacitors. The 1 nH
mounting inductance for a discrete capacitor contributes more than 1
Ohm of impedance. You have to put 50 of them in parallel to get to 20
mOhms at 200 MHz. If you want 20 mOhms at 1GHz, it takes 5x more than
that! With low ESR capacitors, it is possible to target certain
critical frequencies above 200 MHz using the resonance technique. But
the number of discrete capacitors required to maintain a flat 20 mOhm
impedance up to 1 GHz is prohibitively large, and really not necessary
on any of the systems that I work on.

The answer to the SSN problem is thin dielectric power planes. At 1
GHz, 8nF gives an impedance of 20 mOhms (1/jwC). 36 square inches (6x6
inches) of a pair of power planes separated by 4 mils of FR4 gives this
capacitance. If our SSN problem is centered within this area, this
capacitance will be available within a 1 nSec rise time. It really
does not make sense to use discrete decoupling capacitors to deal with
SSN noise associated with today's fast edge rates. Capacitance between
PCB and package power planes and capacitance embedded on chip are the
best defenses against SSN.

One more comment, target impedance is really too simplistic of a
concept to be useful for the SSN problem. To really deal with the SSN
problem, you have to know which way the driver is switching (high or
low) and whether the transmission line return current flows mostly on
the Vdd plane or Ground plane in order to make SSN calculations (yes,
it makes a big difference!). There is another paper on the same web
site as the decoupling capacitor paper. Check out "Simultaneous Switch
Noise and Power Plane Bounce for CMOS Technology" on:
Larry Smith
Sun Microsystems

> From: "Zabinski, Patrick J." <[email protected]>
> To: [email protected]
> Subject: RE: [SI-LIST] : Decoupling capacitors (again!)
> Date: Tue, 15 Aug 2000 10:40:50 -0500
> MIME-Version: 1.0
> Martin,
> I can't offer much advice, but I can possibly offer some
> comfort in that I've had the same problem. For one design
> I was recently involved in, I tried to follow the same
> approach/theory, and the end result was that I needed
> 80 decoupling capacitors per ASIC (to maintain 10%
> dV), and I had 32 ASICs per board (>2500 caps per board!).
> After having others verify
> my numbers/calculations, I took close look and realized
> the caps would consume more board space than the ASICs.
> I could not justify, believe, or afford this, so I
> ended up backing down and relying on my old rules of
> thumb (BTW: I hate rules of thumb, but I sometimes
> use them when I have no better way). The board works
> fine with only 12 caps per ASIC.
> Looking back, I can see three possible reasons why the approach you
> and I took is not quite complete:
> * component packaging effects are not taken to
> account. Not definite on this, but I believe
> a poor package would probably negate any capacitance
> you might have on the board.
> * the board's self-impedance. I believe Larry's
> approach addresses this as effective increase
> in inductance, but the ground/power plane itself
> does offer a low-impedance capacitance. Regardless
> if you have any discrete caps on or not, the planes
> offer some inherent, built-in capacitance.
> * most (all?) dI/dt effects are self-limiting.
> For the calculations you used, they assumed
> dV=0.0. However, if dV>0, then dI/dt will
> be reduced all on its own. I don't have any
> data or theories on how much, but dI/dt
> is likely to be reduced from what you
> predicted (also tied into/related to the
> first issue about packaging).
> Sound reasonable? Comments?
> Anyway, I sympathize and hope you find a solution. If you
> do, please share.
> Pat
> > -----Original Message-----
> > From: Martin J Thompson [mailto:[email protected]]
> > Sent: Tuesday, August 15, 2000 9:49 AM
> > To: <"[email protected]"
> > Subject: [SI-LIST] : Decoupling capacitors (again!)
> >
> >
> > Hi all, this is my first time posting here, although I've
> > been lurking for a while.
> >
> > My problem is figuring out the decoupling requirements for
> > this system:
> > FPGA, DSP, 6 SDRAMS, 2 flash, DPRAM, clock frequency is 100MHz.
> >
> > According to my calculations, my I/O's need to drive a total
> > of about 1.5nF of I/O and trace capacitance.
> > To achieve the 0.5ns edges that the FPGA will drive (3.3V
> > supply) it looks like I need dI=4amps. This is assuming that
> > 50% (is this typical?) of the I/O's toggle each cycle. (dI=0.5Cdv/dt)
> >
> > To achieve a dV of < 0.1V this implies a target impedance of
> > around 20mohm, flat up to 1GHz! (Z=dv/di)
> >
> > This then seems to need around 500-800 decouping caps spread
> > around, which is an order of magnitude more than I've ever
> > used in the past. This is the first time I have taken a
> > 'design' approach to the problem, but the previous boards
> > have worked, using various rules of thumb.
> >
> > Is this sort of number of caps to be expected in this sort of
> > system, or can anyone see any sillies in my understanding (or
> > even in the sums!)?
> >
> > Now, if I don't get right out to 1GHz, the edges will suffer,
> > but that wouldn't necessarily matter if they stayed below
> > 1-1.5ns. Or would this cause the supply to droop elsewhere?
> >
> > As you might gather from the analysis above I've read Larry
> > Smith and co's paper on decoupling design, which states that
> > a flat target impedance is indicated. If I can analyse my
> > application enough, can I then shape the Ztarget vs frequency
> > to make life easier?
> >
> > Many thanks for your time, any help greatly appreciated,
> >
> > Martin
> >
> >
> >
> > TRW Automotive Advanced Product Development,
> > Stratford Road, Solihull, B90 4GW. UK
> > Tel: +44 (0)121-627-3569
> > mailto:[email protected]
> >
> >
> >
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