Equation 5 · Part 4 · When the Substrate Became the Product

Symbol V_sw^2

E_b \;\approx\; \tfrac{1}{2}\left(C_{\mathrm{fix}} + c_w \ell\right) V_{\mathrm{sw}}^{2},

V_{\mathrm{sw}}^{2}

What this part means

the square of $V_s$ w; the signalling swing.

Its job in the formula

$V_s$ $w^2$ is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

Full expressionSymbol V_sw^2Article meaning

Where the article explains it

where $C_{\mathrm{fix}}$ collects driver, receiver, bump and pad capacitance, $c_w$ is capacitance per unit length of the conductor, $\ell$ is the reach, and $V_{\mathrm{sw}}$ is the signalling swing.

The passage around this formula

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: $E_b \;\approx\; \tfrac{1}{2}\left(C_{\mathrm{fix}} + c_w \ell\right) V_{\mathrm{sw}}^{2}$ . where $C_{\mathrm{fix}}$ collects driver, receiver, bump and pad capacitance, $c_w$ is capacitance per unit length of the conductor, $\ell$ is the reach, and $V_{\mathrm{sw}}$ 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,…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

[5] Bunch of Wires PHY Specification ↗

These citations provide research context; check each source for the exact claim it supports.