EMC Question of the Week: July 22, 2019
What is the inductance of a 2-cm wide, 10-cm long ground strap that is 2 mm thick?
- 5.0 nH
- 46.05 nH
- 50 nH
- 55.13 nH
Answer
The best answer is "c". Some of you may recognize this question as being identical to the November 26, 2018 EMC Question of the Week. The correct answer to the question at that time was "undefined." That was because Inductance is a property of current loops. Assigning an inductance to a component that is a minor part of a unknown current loop can be both confusing and misleading.
But "undefined" was not one of the options this week. And, as we pointed out in November, it is often possible to convey useful information about a component's contribution to the overall inductance of a loop (i.e. its branch inductance), even when the loop geometry is not completely specified. For example, a general rule-of-thumb for estimating the contribution of one segment of a relatively open wire loop is that the inductance is "on the order of 1 nH/mm." In the case of this ground strap, the rule estimates a ground strap inductance on the order of 100 nH. While this number may not be particularly precise, it can be useful for determining whether or not a strap's inductance might be an issue that needs to be dealt with in the design.
Another, slightly more accurate means for estimating the branch inductance of a relatively open loop is to assume the loop geometry is a circle or square constructed using 4 of the components in question. This yields the following simple formula for the approximate branch inductance of a ground strap,
where L and W are the length and width of the strap in centimeters, respectively. This formula would yield a value of 46.05 nH. This is option (a), but it is not the best answer.
Another well-known equation for the inductance of a ground strap can be found in the
where L, W and t are the length, width and thickness of the strap in centimeters, respectively. This is actually a formula for the "self partial inductance" of the strap. The self and mutual partial inductances of the components of a loop can be summed to calculate the total inductance of a loop. The self partial inductance alone does not represent the inductance of the ground strap. However, since the self partial inductance is always higher than the actual branch inductance, it can sometimes be used to provide a rough worst-case estimate of the branch inductance. For the ground strap in this problem, the formula above yields a partial self inductance of 55.13 nH. This is option (d), but it is not the best answer.
Without knowing the geometry of the current loop, it is not possible to define (much less accurately calculate) the inductance of a ground strap. (e.g. if the ground strap were folded on itself, the branch inductance could be as low as 5 nH.)
The inductance is definitely "undefined," but that answer is not very helpful. In typical applications, we know from the calculations above that the contribution of a ground strap to the loop inductance is likely to be on the order of 50 nH. This is the best answer.
So what's wrong with 46.05 nH or 55.13 nH? Those answers, imply an accuracy to the solution that can't be justified. Even if the equations were accurate to 4 significant figures (which they aren't), the dimensions of the ground strap were provided with 1 significant figure. In the world of EMC, where most measurements and calculations are good to 1 or 2 significant figures at best, it is important not to convey a false sense of precision. Many of the most useful EMC modeling tools and techniques (including assigning inductances to ground straps, traces and wire bonds) don't yield precise values, but they get us "close enough" to make good design decisions.
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