[SI-LIST] Re: Importance of Package Height
- From: "Abe Riazi" <ARIAZI@xxxxxxxxxxx>
- To: <si-list@xxxxxxxxxxxxx>
- Date: Thu, 14 Mar 2002 21:49:16 -0800
Larry Smith Wrote:
> The total mounted inductance determines the series resonant frequency
> of the capacitor. The equivalent series inductance (ESL) of the mounted
> capacitor is found from the capacitance value and the resonant
> frequency and the relationship: f0 = 1/(2pi*sqrt(ESL*C)) where f0 is
> the frequency of the impedance dip, C is capacitance. There are four
> factors that contribute to the mounted inductance (ESL) of a capacitor:
>
> 1) Power plane spreading inductance - This is the inductance (energy
> stored in the B field between the power and ground planes) as current
> escapes from the decoupling capacitor location. Some people like to
> refer this inductance to the via between the planes but the inductance
> is really associated with the planes themselves because there is B
> field between the planes even if planes are connected together by a
> perfect, zero inductance connection. This can be demonstrated in most
> power plane simulation tools. The spreading inductance for power
> planes is likely to be 50pH to 1000pH, depending upon the thickness of
> the dielectric and the location of the capacitor on the PCB (center,
> edge or corner).
>
> 2) Via and pad inductance - The capacitor is generally connected to
> power planes through a pair of vias, one for power and one for ground.
> There is an inductance associated with the vias that is determined by
> via length, diameter and spacing. B field accumulates in this loop
> indicating stored energy in a magnetic field and therefor inductance.
> The inductance associated with the via and mounting pads is 50 pH to
> 3000 pH, depending on geometries.
>
> 3) There are two inductances associated with the capacitor itself. We
> call the first inductance L_bottom. It is associated with the filler
> plate at bottom of the capacitor. The filler plate fills up the area
> between the bottom of the physical capacitor and first conductive plates.
> B field stored in this physical region contributes to L_bottom. It is
> between 10 and several hundred pH, depending on the design of the
> capacitor.
>
> 4) Finally, there is an inductance associated with the capacitor
> plates themselves. A good way of looking at this is from a
> transmission line perspective. As we move up the physical stack of
> capacitor plates, we uncover more and more capacitance (plates). We
> also uncover more and more loop area which contributes inductance.
> Hmmm, sounds like a transmission line. It is possible to establish a
> capacitance and inductance per unit length of this short little
> transmission line and therefor an impedance and delay. It turns out
> that the series resonant frequency for the capacitor occurs at the
> quarter wavelenth frequency of this transmission line, including
> inductances described in 1), 2) and 3). Those "weird little bumps" (I
> believe that was terminology used in a previous posting on this
> subject) in the measured impedance vs frequency curve are multiples of
> quarter and half wavelength frequencies in the capacitor
> transmission line. You have to mount the capacitor on a fixture or
> product with very small inductance in order to see these transmission
> line effects. If you mount the capacitor sideways, with the plates
> sticking straight up rather than parallel to the PCB power planes, you
> will not see the transmission line effects at all. You will see a very
> different impedance vs frequency profile. The inductance associated
> with the capacitor plates is between 10 and 500 pH, depending on the
> design (capacitance value and height) of the capacitor.
>
Dear Larry:
In order to explore certain details of your interesting post, I have
formulated below a practical example.
Using the Kemet Spice Simulation Software (available at their Web site),
I specified a ceramic capacitor:
Chip Style: 0805
Dielectric Type: X7R
Capacitance: 100 nF
Rated Voltage: 50 WVDC
Tolerance: +/- 10%
The program determined the Kemet part number (e.g. C0805C104K5RAC ),
Impedance and ESR (as functions of frequency), series self resonance, and
also
following equivalent series inductance:
ESL = 1.94 nH
Here I assumed this ESL value includes what you have described by factors 3
and 4,
but it needs to be increased (when mounted on PCB) by:
1) 50 pH to 1000 pH (e.g. about 0.5 nH) to account for power plane spreading
capacitance.
2) 50 pH to 3000 pH (nominal value ~ 1.5 nH ) due to via and pad inductance.
Therefore, a value for total mounted equivalent series inductance (under
typical mounting conditions) is:
ESL = 1.94 nH + 0.5 nH + 1.5 nH = 3.94 nH
which yields series resonant frequency of:
f0 = 1/(2pi*sqrt(ESL*C)) = 1/{2pi * sqrt [( 3.94E-9) * ( 100E-9 )}
f0 ~ 8.02 MHz
Are my numbers and assumptions OK?
Thanks for sharing your expertise.
Abe Riazi
ServerWorks
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