The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements

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.

An overview of the proposal for a new Package Travel Directive

After an endless wait, a proposal for a new Package Travel Directive repealing Directive 90/314/EEC1 was presented on 9 July 2013 (hereafter, the Proposal).This article is aimed at providing an overall view of the Proposal. I will address the following issues: The concept of traveller; online package holidays and assisted travel arrangements; information requirements; a new particular right of withdrawal for package travel; other changes to the contract before the start of the package; performance of the Package; and insolvency protection. Some early concluding remarks are made as to when a future Package Travel Directive might take place at some future date