Via temperature is determined by the temperature of the trace associated with the via, not the current itself.

Many designers and some EDA design tools place heavy emphasis on current density when sizing traces for a given current. Current density is current/unit area. Thus, it does make some intuitive sense that trace temperature might be proportional to current density: the higher the current, the higher the current density, and therefore the higher the temperature. But it is much more complicated. Following this design rule blindly may lead to significant design errors, especially when designing vias for allowable current. And a few examples will illustrate why.

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