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Equation 5 · Part 3 · Comparing the Main Approaches to Chiplets and Advanced Packaging

Symbol i

ΔTj  =  P∑i=1NRth,i,\Delta T_j \;=\; P \sum_{i=1}^{N} R_{\mathrm{th},i},
ii

What this part means

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Its job in the formula

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

The passage around this formula

The bill for that proximity arrives as heat, and it arrives in a specific, structural way rather than as a vague “3D runs hotter” intuition. A stack has exactly one face in contact with the package’s heat-removal path — typically the topmost die, under a lid or heat spreader — so the temperature rise at a given tier depends on everything the heat has to cross to reach that face: ΔTj  =  P∑i=1NRth,i\Delta T_j \;=\; P \sum_{i=1}^{N} R_{\mathrm{th},i}. where P is the power dissipated at that tier and each Rth,iR_{\mathrm{th},i} is the thermal resistance of one layer already between that tier and the heat sink — die bulk, bonding interface, or an intervening active tier. A tier two layers from the heat-removal face inherits the resistance of…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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