EMC Question of the Week: November 26, 2018

What is the inductance of a 2-cm wide, 10-cm long ground strap that is 2 mm thick?

1. 100 nH
2. 55 nH
3. 50 nH
4. undefined

Answer

The correct answer is "d". 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.

Nevertheless, it is sometimes 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,
$$L\approx 0.002\times L\times \ln \left(\frac{\text{2}\times L}{W}\right)\text{μH}$$
where L and W are the length and width of the strap in centimeters, respectively. This formula would yield an approximate value of 46 nH (or 50 nH, expressed to one significant figure) for the ground strap in this example.

Another well-known equation for the inductance of a ground strap can be found in the Radio Engineers Handbook (F.E. Terman, 1945). That equation looks like this,
$$L=0.002\times L\left[\ln \left(\frac{2L}{W+t}\right)+0.5+0.2235\left(\frac{W+t}{L}\right)\right]\text{μH}$$
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 nH.

Finally, it is important to remember that none of the equations above can be applied if the ground strap is folded, or if it is located alongside any of the conductors that form the rest of the current loop. In these situations, the branch inductance of the strap will be less (perhaps significantly less) than the values determined from these equations. Without knowing the geometry of the current loop, it is not possible to define (much less accurately calculate) the inductance of a ground strap.

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