Published by Eric Bogatin on 16 Feb 2009
In preparing the content for our new course on Power Distribution Network Design (PDN), I’ve been reviewing many of the capacitor vendor web sites to see how they describe the electrical properties of their capacitors.
I have found in measuring many capacitors that an RLC model is a pretty good approximation to the actual, measured impedance of a capacitor, even into the GHz range. The C is based on the internal design of the capacitor, the number of plates, their spacing and the ceramic used. The value I measure usually does meet the specified value to within the typical 20% tolerance.
The R is also intrinsic to the capacitor inner design and depends on the series resistance of the metallization in the plates. The higher the C, the more plates in parallel and the lower the R. I typically measure the R to be within 30% of the specified value.
However, the most important quality of a capacitor for use in decoupling applications is its equivalent series inductance or ESL. The ESL is not intrinsic to the capacitor, but depends on how it is mounted to the circuit board.
Yet, every capacitor vendor site I visited lists a value for the ESL of their capacitors. AVX uses a value of 0.4 nH while Kemet uses a value of 0.7 nH. When pressed, they say this is the “intrinsic” ESL of their capacitors. This has as much meaning as the sound of one hand clapping, and for basically the same reason.
While it is perfectly correct to say the “partial self inductance” of a capacitor is 0.4 nH, unless you also know the partial self and mutual inductances of the rest of the elements that make up the loop the capacitor is part of, you can’t do anything with this term, and I doubt that AVX or Kemet mean to present their inductance as a partial self inductance.
From a user’s perspective, what is important is the ESL when the capacitor is on a board. Unfortunately, this really does depend on the rest of the loop the capacitor sees. The ESL of the same capacitor can change by more than a factor of 20, depending on how it is mounted on a board. It can vary from less than 0.3 nH to more than 8 nH.
Without knowing the rest of the loop- the other hand- the ESL cannot be known. Once the other hand starts to interact, you can easily estimate the ESL of a mounted capacitor, and here’s how.
The inductance of the loop composed of the bottom of the capacitor and the top of the pwr/gnd cavity in the board make up most of the mounted ESL of a capacitor. A good approximation to the loop inductance of this structure is the sheet inductance x the number of squares.
The sheet inductance is 32 pH/mil x h, where h is the depth of the top of the cavity from the top of the board. This can vary from 1 mil in HDI boards to more than 20 mils in cheap four layer boards. If h = 10 mils, the sheet inductance is 320 pH per square of the surface trace and capacitor body.
The number of squares of surface trace is just the length of the surface traces and capacitor body, from via to via, divided by its width. The wider the trace and shorter the length, the fewer the squares.
In a typical 0603 or 0402 capacitor, the body of the capacitor is 2 squares. For via-in-pad mounting, the ESL would be about 2 squares worth of sheet inductance. When h is 1 mils, the ESL would be about 0.032 x 2 = 0.07 nH. When h is 20 mils, the ESL would be about 0.64 nH x 2 = 1.3 nH.
Of course with surface traces from the capacitor pads to the vias that could be 4-10 squares, the mounted ESL of the same capacitor could be as high as 5x these values- ranging from 0.3 nH to 8 nH.
What does it mean for a capacitor vendor to supply an ESL value of 0.4 nH, when the actual mounted ESL depends so much on the rest of the loop the capacitor is part of? It is less than worthless, as it gives the impression you have a real value, when in fact, it is meaningless.
The intrinsic ESL of a capacitor is as meaningful as the sound of one hand clapping.
For more information about signal integrity topics, check out my web site, www.beTheSignal.com