TAILIEUCHUNG - Handbook of algorithms for physical design automation part 90

Handbook of Algorithms for Physical Design Automation part 90 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. | 872 Handbook of Algorithms for Physical Design Automation Effects of Inductance on Delay and Signal Rise Time A general expression for the propagation delay from the input to the output of an RLC line of length l with an ideal power supply and an open circuit load is given by 18 tpd VLC e yl l where aasym R C l aasym is the asymptotic value at high frequencies of the attenuation per unit length of the signals as the signals propagate across a lossy transmission line as shown in Figure . For the limiting case where L 0 Equation reduces to illustrating the square dependence on the length of an RC wire as aforementioned. For the other limiting case where R 0 the propagation delay is given by LtCt ls LC. Note the linear dependence on the length of the line. Note also that inductance always increases the delay as compared to an RC model . if inductance is neglected the delay is underestimated by the incomplete RC model. The rise time of signals propagating across RLC lines improves as the inductance effects of the line increase. This behavior can be explained by referring to Figure which depicts the attenuation of signals as they travel across an RLC line as a function of frequency. Higher frequency components at the edges of a pulse suffer greater attenuation as compared to low frequency components. The shape of a signal degrades as the signal travels across a lossy transmission line because of the loss of these high-frequency components. The attenuation constant becomes less frequency dependent as inductance effects increase or as R rnL decreases as shown in Figure . In the limiting case of a lossless line representing maximum inductance effects the attenuation constant a is 0. Thus as inductance effects increase a pulse propagating across an RLC line maintains the high-frequency components in the edges improving the signal rise and fall times. FIGURE Attenuation constant versus frequency. L 10 nH cm

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