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36 DESIGN007 MAGAZINE I SEPTEMBER 2020 determine the desired width and thickness of a trace (or via) by assigning a value to J, which itself already depends on an implied value for w and th. Equation 2 is not the correct rela- tionship. 2. IPC-2152 Curves Can Yield an Answer It is intuitive that the form factor of the trace impacts its temperature. That is, wider, thinner traces are cooler than narrower, thicker traces with the same cross-sectional area. The reason is that wider, thinner traces have more surface area for conducting the heat away and, there- fore, cool more efficiently. Two traces with the same cross-sectional area, carrying the same current (and therefore having the same current density), will have different temperatures de- pending on their form factor. This can be seen in the IPC data. IPC-2152 contains a very large set of graphs of the relationship between trace current, trace size, and trace temperature. The gray lines in Figure 1 are derived from the data contained in Figures A-48, A-49, and A-50 (pages 57 and 57) in that publication [1] . The data are simply redrawn on a different set of axes. The green lines are lines of con- stant current density (J). It is clear, even from the IPC data, that even though the current density is con- stant, the trace temperature can vary widely because of the form factor. 3. Modeling Form Factor We can use TRM [3] to model a trace with changing form factor and con- stant current density. We modeled a trace with three segments, as shown in Figure 2. The model parameters are as shown in Table 1. Although a trace with these dimen- sions may be difficult (but not im- possible) to actually build, the TRM model can easily simulate it. Figure 2 shows the model results for both tem- perature and for current density. It is clear that the simulation model shows Figure 1: Relationship between current and temperature change for 2-oz. traces of various widths. Constant current density lines are in green. (Black numbers are trace width in mils. Green numbers are current density in amps/mil 2 .) (Source: IPC-2152 [1] and Figure 6.10, page 61 [2] ) Figure 2: Temperature (a) and current density (b) profiles of our thermal model. The temperatures shown are temperatures at a specific point on the segment and will vary from point to point.

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