# Re: [SI-LIST] : Comment on Johnson's article

From: Larry Smith ([email protected])
Date: Wed Nov 03 1999 - 18:09:50 PST

Dr Johnson - Thank you for the comments. Please see my response in
the text:

> Date: Wed, 03 Nov 1999 15:26:36 -0800
> From: Howard Johnson <[email protected]>
>
> I think the original question that started this
> is one thing I'd like to say about Larry's note below.
> Although I USUALLY agree with him, I'll have to differ
> this time.
>
> My quibble has to do with the
> precise value of capacitance in a bypass capacitor.
> For ordinary, inexpensive dielectrics (like Z5U) in
> small packages the value of capacitance (after
> discounting for the initial tolerance, temperature,
> and aging) can vary by a factor of 3:1. With
> that large a swing in the value of capacitance
> you can't really assume much about the precise
> location of the series resonant frequency. If you
> want to precisely control the SRF you need to use
> a more stable dielectric (which therefore has
> a lower dielectric constant, and comes in a LARGER
> package). I don't think that's such a good tradeoff.
> I'd rather see Larry just put enough capacitors
> on the board to make it work purely from consideration
> of the inductance alone, without have to make assumptions
> about the precise location and depth of the SRF null.

We are using about 100 decoupling capacitors now. One hundred times 1
nH in parallel gives an impedance of 628 mOhms at 100 MHz (jwL =
2*pi*1E8*1E-9), far more than we can tolerate. To achieve a target
impedance of 10 mOhms, we would need 6280 inductances in parallel! And
the impedance would be purely inductive, which would resonate badly
with the pure capacitance of the power planes. By using carefully
chosen capacitors and careful PCB layout, it is possible to achieve a
resistive 10 mOhm impedance with about 100 capacitors to well over 100
MHz.

There are several different capacitor dielectric types, each with
different characteristics. I don't like to use Z5U and Y5V capacitors
for decoupling because they have such poor voltage and temperature
coefficients, just as you have said. The tolerance is usually given
as +20% and -80%. The -80% comes at high temperature. In other words,
just when your system needs decoupling the most, during high power
(high heat) conditions, the capacitor has only 20% of it's rated
value. No thanks!

X7R capacitors have much better temperature and voltage coefficients
(about 10%). They are available between 4.7nF and 1uF in 0603 and 0805
package sizes. X5R dielectric is has similar voltage and temperature
coefficients but a little less reliability. Aggressive vendors can
push X5R ceramic capacitors up to 100 uF in larger package sizes. They
are cost competitive after derating the Z5U and Y5V capacitors. But
the ESR of X7R capacitors becomes unacceptably high below 4.7nF.

We use NPO capacitors for 3.3nF and all lower capacitor values.
Voltage and temperature coefficients are 5% or better. The ESR is much
lower than X7R because many plates in parallel are required to achieve
nF values. We routinely target EMI problem frequencies and solve
compliance problems by working with the capacitance and mounted
inductance to achieve a low impedance resonance at the problem
frequency. At resonance, it is possible to achieve an impedance that
is 1/5 or maybe even 1/10 of the impedance of the inductance at that
frequency, depending on the ESR of the capacitor. And, the impedance
is resistive rather than inductive. With careful design, it does not
cause anti-resonance problems with the 'pure' capacitance of the PCB
power planes.

The analysis given in the previous note involved 3.3, 2.2, 1.5 and 1.0
nF NPO dielectric capacitors. Those are best for decoupling between
100 and 200MHz. Our processors are capable of putting tremendous (20
amp) transients on the power planes at those frequencies. The 5%
tolerance in capacitance actually smoothes out the impedance curve --
if you can count on the capacitance values having a nice statistical
distribution.

> Also, as a general rule, as you lower the series resistance
> of a capacitor the notch at the SRF deepens, but
> unfortunately at the same time the (parallel) resonance
> between the (inductance of the) discrete capacitor package
> and the (idealized) capacitance of the Vcc-Gnd planes
> becomes more pronounced. For this reason I don't usually
> seek capacitors with a super-low value of ESR. I stick
> with the cheap, cruddy, non-resonant kind of regular
> bypass capacitors (Z5U or equivalent) that don't harbor
> any resonant surprises.

Yes! As you lower the series resistance, the dips (series RLC)
resonances get deeper and the peaks (parallel RLC) anti-resonances get
higher. Kind of like playing with fire... But by using many different
values of capacitors on low inductance pads and careful placement on
the power planes, we achieve a flat (resistive) impedance across a
broad frequency range, as demonstrated in the previous analysis.

If you can tolerate a power supply impedance of several hundred mOhms
in the 30 to 300 MHz region, cheap, cruddy, resistive Z5U capacitors
will do fine. But modern busses run at 66 and 133MHz and we are
running some faster than that. I have seen computers consistently
crash when running customer code because the code stimulates
the power planes in the 100 MHz region. With careful decoupling
capacitor design, it is possible maintain a power distribution
impedance less than 10 mOhms to several hundred MHz, and beyond that
with careful power plane design. Low power distribution impedance at
high frequency is also very effective in solving EMI problems.

best regards,
Larry Smith
Sun Microsystems

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