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Handbook of algorithms for physical design automation part 95

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Handbook of Algorithms for Physical Design Automation part 95 provides a detailed overview of VLSI physical design automation, emphasizing state-of-the-art techniques, trends and improvements that have emerged during the previous decade. After a brief introduction to the modern physical design problem, basic algorithmic techniques, and partitioning, the book discusses significant advances in floorplanning representations and describes recent formulations of the floorplanning problem. The text also addresses issues of placement, net layout and optimization, routing multiple signal nets, manufacturability, physical synthesis, special nets, and designing for specialized technologies. It includes a personal perspective from Ralph Otten as he looks back on. | 922 Handbook of Algorithms for Physical Design Automation 44.3 POWER GRID NOISE ANALYSIS 44.3.1 Noise Metrics For static DC analysis the maximum voltage drop among all power grid nodes is a general metric for the entire chip. In dynamic transient analysis maximum voltage drop of a node is defined as the largest voltage drop value along the period of time for simulation. The maximum voltage drop among all nodes in the power grid circuit can indicate performance of the power grid and help identify hot spots on a chip. This measurement is widely used in most power grid noise estimation tools. However such a measurement is very sensitive to the accuracy of circuit analysis and does not take the timings of the voltage violations into account 29 . An efficient metric for the performance of each node in a circuit was first introduced in Ref. 29 which is the integral of voltage waveform beyond the noise margin Zj p f max NMh - Vj t p 0 dt 0 44.10 J NMh - Vj t p dt ts where p represents the tunable circuit parameters. Su et al. in Ref. 30 initially applied this metric in transient power grid noise analysis and optimization. The transient noise in a node in the supply network is represented by the shaded area voltage integral in Figure 44.5. 44.3.2 Fast Analysis Techniques Because of the large scale millions of nodes of the power distribution network even after separating the nonlinear devices from the linear grids and modeling them using independent current sources the analysis of such a huge linear network in reasonable amount of time and memory is still a challenge. The behavior of the power distribution circuit can be described by a first-order differential equation formula using modified nodal analysis MNA 31 Gx t Cx t u t 44.11 where x is a vector of node voltages and source and inductor currents G is the conductance matrix C includes both the decoupling capacitance and package inductance terms u t includes the loads and voltage sources FIGURE 44.5 Illustration of the