Peer-Reviewed Journal Details
Mandatory Fields
Tom Carroll and Joaquim Ortega-Cerda
2014
October
The European Journal of Applied Mathematics
The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements.
Published
Optional Fields
Mathematical problems of computer architecture; Elliptic functions and integrals; Poisson's equation
25
5
531
551
A mathematical model of the voltage drop which arises in on-chip power distribution networks is used to compare the maximum voltage drop in the case of different geometric arrangements of the pads supplying power to the chip. These include the square or Manhattan power pad arrangement, which currently predominates, as well as equilateral triangular and hexagonal arrangements. In agreement with the findings in the literature and with physical and SPICE models, the equilateral triangular power pad arrangement is found to minimize the maximum voltage drop. This headline finding is a consequence of relatively simple formulas for the voltage drop, with explicit error bounds, which are established using complex analysis techniques, and elliptic functions in particular.
0956-7925
10.1017/S0956792514000114
Grant Details