8/17/08 Simple Rule of Thumb for Total Inductance

I was revising my lecture on ground bounce in the Essential Principles of SI class and found a very simple rule of thumb for describing the total inductance of the return path of a conductor. Ground bounce is all about the voltage created across the return path conductor when the return current of a signal line passes through it.

Of course, if there is no other conductor sharing this same return path, then the ground bounce noise generated may be a “who cares”. However, if another signal path also uses the same conductor for its return path- shared return paths- then the ground bounce noise created by the first signal switching will be seen as noise by the innocent victim line.

The amount of ground bounce generated depends on the total inductance of the signal path and the dI/dt of the switching current. This can be on the order of 20 mA/nsec for a 1 nsec rise time signal, or even 60 mA/nsec, for a 300 psec rise time signal, such as found in DDR3 signals.

But what is a good estimate for the total inductance of the return path? Is it 0.1 nH, 1 nH, or even 10 nH? Of course, the most common answer to all signal integrity questions- and most others- is “it depends”. However, sometimes, an OK answer NOW! is better than a good answer late. If you want a rough estimate NOW!, a rule of thumb is the tool to use.

For other than a few simple geometries, inductance is really hard to calculate. The approximations available are pretty complicated. I used the built in 2D field solver, and integrated circuit simulator in Agilent’s ADS to calculate for me the total inductance for a simple geometry of two adjacent, rectangular signal lines, such as might be found in a leaded package. Each line has the same line width and there is some spacing between the two lines.

I then fixed the spacing and swept the line width. The total inductance per length of one of the lines is what is plotted in the figure. It has the features expected. As the width of the return path increases, its total inductance decreases. As the spacing between them decrease, the total inductance also decreases.

What is interesting is that for the case of the line width equal to the spacing, independent of the line width, the total inductance is pretty darn close to 10 nH/inch. This makes for a simple, easy to remember rule of thumb.

When the signal and return path conductors are of the same size and the spacing between them is on the order of their line width, the total inductance of the return path is 10 nH/inch.

If the lead lengthis 0.5 inches, this is 5 nH of total inductance. One DDR3 signal line switching through this will generate 5 nH x 60 mA/nsec = 300 mV of ground bounce. Let three signals switch throug the same common lead and you get almost 1 v of ground bounce. That’s a lot! and not so uncommon.

If you want to learn more about inductance, check out more of the content on our web site relating to inductance, cross talk, switching noise and ground bounce at www.beTheSignal.com.

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