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Equation 1 · Part 9 · Chiplets and Advanced Packaging in Practice: Floorplanning, UCIe, and Thermal Co-Design

=

Cost(P)  =  α⋅WL(P)  +  β⋅Tmax⁡(P)  +  γ⋅σmax⁡(P),\text{Cost}(\mathcal{P}) \;=\; \alpha \cdot WL(\mathcal{P}) \;+\; \beta \cdot T_{\max}(\mathcal{P}) \;+\; \gamma \cdot \sigma_{\max}(\mathcal{P}),
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

A floorplanning objective built to hold all three properties at once is naturally written as a weighted combination rather than a single term: Cost(P)  =  α⋅WL(P)  +  β⋅Tmax⁡(P)  +  γ⋅σmax⁡(P)\text{Cost}(\mathcal{P}) \;=\; \alpha \cdot WL(\mathcal{P}) \;+\; \beta \cdot T_{\max}(\mathcal{P}) \;+\; \gamma \cdot \sigma_{\max}(\mathcal{P}). where P\mathcal{P} is a candidate placement of dies on the carrier, WL is total interconnect wirelength, Tmax⁡T_{\max} is peak steady-state junction temperature anywhere in the assembly, and σmax⁡\sigma_{\max} is peak mechanical stress at any bonded interface. This is a schematic statement of the shape these tools optimize, not a reproduction of any one paper’s exact formula, but it makes the practitioner point concrete: whichever of α\alpha , β\beta , and γ\gamma a design team weights most heavily determines where dies actually land, and a…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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