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Published equation contexts

BA  ≈  fbp2B_A \;\approx\; \frac{f_b}{p^{2}}

Why this formula appears here

Shortening the electrical path this way has a direct, quantifiable effect on how much bandwidth a given joint area can carry. Treating the joint as a grid of independent connections at pitch p , each connection occupying roughly p2p^2 of area, gives a first-order areal bandwidth density BA  ≈  fbp2B_A \;\approx\; \frac{f_b}{p^{2}}. where fbf_b is the data rate carried by a single connection. The relationship is quadratic in pitch, not linear: halving the pitch alone — with no change to the per-connection data rate — quadruples the number of connections available in the same area, and therefore roughly quadruples aggregate bandwidth density. That is why the packaging industry has spent so much engineering effort on pitch…

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BAB_A

Symbol B_A

BAB_A is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Its accuracy depends on the assumptions and range of use described in the article.

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Published contexts (1)

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BA  ≈  fbp2,B_A \;\approx\; \frac{f_b}{p^{2}},

Equation 3 · AI Hardware & Semiconductors

Comparing the Main Approaches to Chiplets and Advanced Packaging

This equation gives an approximation: it relates the quantities while allowing an approximation.

Shortening the electrical path this way has a direct, quantifiable effect on how much bandwidth a given joint area can carry. Treating the joint as a grid of independent connections at pitch p , each connection occupying roughly p2p^2 of area, gives a first-order areal bandwidth density BA  ≈  fbp2B_A \;\approx\; \frac{f_b}{p^{2}}. where fbf_b is the data rate carried by a single connection. The relationship is quadratic in pitch, not linear: halving the pitch alone — with no change to the per-connection data rate — quadruples the number of connections available in the same area, and therefore roughly quadruples aggregate bandwidth density. That is why the packaging industry has spent so much engineering effort on pitch…

Meanings in this article

  • fbf_b: the data rate carried by a single connection.
  • p2p^{2}: the square of p; the pitch.
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