Appendix B. Formal Proof of Optimum Single Via Placement
In this appendix, the Lemma used to determine the optimum via location for an interplane interconnect that includes only one via for different values of r21, c12, and l1 is stated and proved.
Lemma 1: If f(x) = Ax2+Bx+C and
(a) for xmax
[x0, x1], x1 > x0 >0,
(i) if
, f(x0) < f(x1), (ii) if
, f(x1) < f(x0),
(b) for xmax < x0, f(x0) > f(x1),
(c) for xmax > x1, f(x0) < f(x1).
Proof: (a) (i) f(x) ...
Get Three-dimensional Integrated Circuit Design now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
