# Stop Relating Trace Temperature to Current Density

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Many design engineers and even many software suppliers make the significant mistake of equating changes in trace or via temperature with current density. This is incorrect at best and dangerous at worst. There is little if any correlation between temperature and current density. Current and trace dimensions (among other things) are the relevant variables, but current density is not. I hope by the end of this article you will see why. Here are four illustrations that will help you understand this.

1. Current Density Is Not an Independent Measure

We can understand that the change in trace (and via) temperatures are a function of other variables. Thus, we can formulate the following as two possible relationships (all other things equal). Let:

C = current
J = current density
w = trace width
th = trace thickness
ΔT = change in trace temperature

Then, we can suggest the following:
Equation 1: ΔT = fn(C, w, th)
Equation 2: ΔT = fn(J, w, th)

Now, the question is, “Are both of these relationships true, or, if not, is either one true?” We know from the extensive experimental evaluations reported in IPC-2152 that Equation 1 is true, so is Equation 2 also true? From Equations 1 and 2, it follows that:

Equation 1a: C = fn(ΔT, w, th)
Equation 2a: J = fn(ΔT, w, th)

To read this entire article, which appeared in the September 2020 issue of Design007 Magazine, click here.

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