Equation 5 · When the Substrate Became the Product
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol E_b
is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol C_fix
ix is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
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Its accuracy depends on the assumptions and range of use described in the article.
What the article says around this equation
Here is the physical core. To first order, a short parallel die-to-die link is a driven capacitive wire, and the energy spent per bit is set by the capacitance that must be charged and discharged: . where collects driver, receiver, bump and pad capacitance, is capacitance per unit length of the conductor, is the reach, and is the signalling swing. Two assumptions are doing the work and both deserve stating. First, this treats the link as a lumped capacitance rather than a transmission line — reasonable for a few millimetres of on-package wire at moderate rates, wrong once the link is long or fast enough to need equalisation,…
Read the full surrounding passage
Here is the physical core. To first order, a short parallel die-to-die link is a driven capacitive wire, and the energy spent per bit is set by the capacitance that must be charged and discharged: . where collects driver, receiver, bump and pad capacitance, is capacitance per unit length of the conductor, is the reach, and is the signalling swing. Two assumptions are doing the work and both deserve stating. First, this treats the link as a lumped capacitance rather than a transmission line — reasonable for a few millimetres of on-package wire at moderate rates, wrong once the link is long or fast enough to need equalisation, retiming and serialisation, at which point the fixed circuit overhead dominates and the linear term stops being the whole story. Second, it ignores clocking and idle power, which for real links are not negligible.
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