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Rule of thumb: Total inductance in return path

03 Apr 2014  | Eric Bogatin

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In this instalment of rule of thumb series, we estimate the total inductance in the return path of a flat, wide conductor.


Ltotal ~ 10 nH/inch x Len


Inductance is probably the most confusing and incorrectly applied concept in signal integrity.

There are two schools of thought about inductance: those who will only talk about a loop inductance and those who are brave enough to look under the hood and leverage the powerful, and dangerous, principles of partial inductance. It's dangerous because there are a lot more ways of making mistakes using partial inductance. It's powerful because if you really know how to use it, partial inductance can often help guide you in design decisions, especially about ground bounce.

Ground bounce is the voltage noise generated across the return path of an interconnect as a dI/dt of switching return current passes through its total inductance.

The next rule of thumb covers how to estimate the amount of ground bounce in a connector. But, before we can estimate the ground bounce expected, we have to be able to estimate the total inductance in the return path. The problem is this is generally really hard.

The total inductance of a return path depends not only on the geometry of the return path, but also on the geometry and location of the signal path. Change the location of the signal path, and the total inductance in the return path changes.

We are faced with the fundamental trade-off of simplifying the problem enough to make the calculation easy, and at the same time keeping it close enough to real situations to be useful.

There are two geometries where the total inductance in the return path has a simple form and for which we can develop a simple estimate: when the two conductors are two parallel round rods, like a pair of wire bonds, or a pair of vias, and when the conductors are two wide, parallel, flat leads, side by side. Surprisingly, the result is just about the same.

In this rule of thumb, we will consider the very special geometry of two flat conductors, like adjacent leads in a lead frame package. An example of the geometry we analyse is shown in figure 1.


Figure 1: Geometry considered in this rule of thumb.


There are no good analytical approximations for the total inductance in one leg of these conductors, but we can use a 2D field solver to calculate it. We take two long conductors, send current down one, let it return down the other and calculate the total inductance in each leg. If the two conductors are symmetrical, the total inductance in either leg is just half the loop inductance.

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