What I Learned this Month

This pop quiz question on www.beTheSignal.com, was really about estimating the equivalent series inductance (ESL) of a decoupling capacitor and how low it can be engineered. Of course, the ESL is all about how the capacitor is integrated into the board and the stack up of the board.

As a rough approximation, the ESL of a capacitor is composed of three elements, the sheet inductance of the capacitor and surface traces, the via loop inductance to the top of the power and ground plane cavity and the spreading inductance in the power and ground plane cavity. Each of these can be estimated with simple approximations.

The sheet inductance of the surface traces and the capacitor body is 32 pH/mil x h1 x Len/width

where

h1 = distance from top surface to top of the power-gnd plane cavity, in mils
Len = the total length of surface traces and capacitor body, in mils
width = width of the surface traces, in mils

The ratio of Len/width is really the number of squares of surface trace, and 32 pH/mil x h1 is the sheet inductance per square between the board surface and the top of the power-gnd cavity. If h1 = 5 mils, the sheet inductance of the top layer is 160 pH/square. If there are 5 squares of surface traces, this is a total loop inductance from the surface traces of about 800 pH.

The loop inductance of the vias to the top cavity is about 15 pH/mil. For a total of 5 mils, this is about 75 pH.

Finally, the spreading inductance in the planes is about 20 pH/mil x h2 x ln(B/D), where
h2 = the distance between the power and ground planes, in mils
B = the distance between the capacitor and the BGA package pins, in mils
D = via diameter in mils.

If h2 = 3 mils, a common minimum thickness in all fab houses, and B = 500 mils and D = 13 mils, the spreading inductance is roughly 20 x 3 x 3.6 = 220 pH

Without doing anything special, the typical ESL of an 0603 multi layer ceramic capacitor (MLCC) might be on the order of 800 pH + 75 pH + 220 pH = 1.1 nH. The choices were 0.2 nH, 1.5 nH and 5 nH. the closest to our simple estimate is 1.5 nH.

Of course, if you do everything right, bring the power-gnd plane cavity close to the surface, use a minimum number of squares for surface traces, use a thinner power-gnd plane cavity, the ESL can be dropped even more. If you use interdigitated capacitors, like the X2Y, the parallel combination of capacitor elements can reduce the surface trace inductance and reduce the spreading inductance in the cavity to achieve an ESL on the order of 0.2 nH.

Check www.beTheSignal for the latest online lectures on inductance and for the next pop quiz!

There is an old joke told by Henny Youngman (1906 –1998) that goes something like this,

A man goes to a doctor and says to him, “Doctor, it hurts when I raise my arm, what should I do?” the Doctor says, “Don’t raise your arm.”

Surprisingly, this is an excellent strategy to follow to design signal integrity problems out of your next product. The details of this strategy are a core part of the Essential Principles of SI (EPSI) class I teach. Here’s a brief snapshot and a glimpse at how you apply the “Youngman Principle”.

The first step in designing SI problems out of your product is to identify the signal integrity problems to avoid. The next step is to identify the root cause of the problem. If you know the root cause, it often screams out at you (in pain) the way to avoid the problem.

For example, a common problem to avoid is reflection noise. The root cause is, that when the instantaneous impedance the signal sees changes, a reflection is created. Reflections that rattle around create ringing. How do you eliminate this problem? If it hurts when the instantaneous impedance changes, don’t change the instantaneous impedance. This means use controlled impedance interconnects, manage the reflections at the ends of lines with a termination strategy and use a routing topology that is linear.

Ground bounce is the most difficult problem to eliminate because it can reach very large voltages, can be long range, is poorly understood by most engineers, and involves the return path, which is often hard to trace out. The problem is voltage noise injected on signal lines when nearby signal lines switch.

The root cause of ground bounce is two fold. First, the return path of a signal needs to be screwed up from the usual wide return path. Second, the return path of one conductor needs to share this return path of another conductor.

If it hurts when the return path is not in a wide plane and when the return paths are shared, don’t screw up the return path and don’t share return paths.

If you can figure out the root cause of a problem, it screams out at you, when you do this, (raise your arm), the problem arises. The solution is, as Henny Youngman points out, “don’t raise your arm!”

To learn about the root cause of some of the common signal integrity problems, check out the articles I have on my web site.