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34 DESIGN007 MAGAZINE I SEPTEMBER 2020 Feature by Douglas Brooks, Ph.D. Many design engineers and even many soft- ware 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 illustra- tions 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 oth- er variables. Thus, we can formulate the fol- lowing 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 rela- tionships true, or, if not, is either one true?" We know from the extensive experimental evalua- tions reported in IPC-2152 [1] that Equation 1 is true, so is Equation 2 also true? From Equa- tions 1 and 2, it follows that: Equation 1a: C = fn(ΔT, w, th) Equation 2a: J = fn(ΔT, w, th) Now, a little thought reveals that Equation 2a does not follow. C is an independent variable, but J is not. J is a derived variable equal to C divided by the cross-sectional area w times th. What Equation 2a really describes is Equation 2b: C/(w*th) = fn(ΔT, w, th) We cannot independently change w and th on each side of the relationship. We can't have one cross-sectional area on one side of the equation and a different one on the other side. If we move w and th to the right side of the relationship, we find that Equation 2b reduc- es to Equation 1a. What it means: We cannot Stop Relating Trace Temperature to Current Density

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