A realistic early-stage power grid verification algorithm based on hierarchical constraints

Power grid verification has become an indispensable step to guarantee a functional and robust chip design. Vectorless power grid verification methods, by solving linear programming (LP) problems under current constraints, enable worst-case voltage drop predictions at an early stage of design when the specific waveforms of current drains are unknown. In this paper, a novel power grid verification algorithm based on hierarchical constraints is proposed. By introducing novel power constraints, the proposed algorithm generates more realistic current patterns and provides less pessimistic voltage drop predictions. The model order reduction-based coefficient computation algorithm reduces the complexity of formulating the LP problems from being proportional to steps to being independent of steps. Utilizing the special hierarchical constraint structure, the submodular polyhedron greedy algorithm dramatically reduces the complexity of solving the LP problems from over O(k 3 m) to roughly O(k k m), where k m is the number of variables. Numerical results have shown that the proposed algorithm provides less pessimistic voltage drop prediction while at the same time achieves dramatic speedup. © 2011 IEEE.published_or_final_versio

Design and Analysis of Power Distribution Networks in VLSI Circuits.

Rapidly switching currents of the on-chip devices can cause fluctuations in the supply voltage which can be classified as IR and Ldi/dt drops. The voltage fluctuations in a supply network can inject noise in a circuit which may lead to functional failures of the design. Power supply integrity verification is, therefore, a critical concern in high-performance designs. Also, with decreasing supply voltages, gate-delay is becoming increasingly sensitive to supply voltage variation. With ever-diminishing clock periods, accurate analysis of the impact of supply voltage on circuit performance has also become critical. Increasing power consumption and clock frequency have exacerbated the Ldi/dt drop in every new technology generation. The Ldi/dt drop has become the dominant portion of the overall supply-drop in high performance designs. On-die passive decap, which has traditionally been used for suppressing Ldi/dt, has become expensive due to its area and leakage power overhead. This has created an urgent need for novel circuit techniques to suppress the Ldi/dt drop in power distribution networks. We provide accurate algorithmic solutions for determining the worst-case supply-drop and the impact of supply noise on circuit performance. We propose a path-based and a block-based approach for computing the maximum circuit delay under power supply fluctuations. We also propose an early-mode supply-drop estimation approach and a statistical approach for power grid analysis. All the proposed approaches are vectorless and account for both IR and Ldi/dt drops. We also propose a performance-aware decoupling capacitance allocation technique which uses timing slacks to drive the optimization. Finally, we present analog as well as all-digital circuit techniques for inductive supply noise suppression. The proposed all-digital circuit techniques were implemented in a test-chip, fabricated in a 0.13µm CMOS process. Measurements on the test-chip demonstrate a reduction in the supply fluctuations by 57% for a ramp loads and by 75% during resonance. We also present a low-power, all-digital on-chip oscilloscope for accurate measurement of supply noise. Supply noise measurements obtained from the on-chip oscilloscope were validated to conform well to those obtained from a traditional supply-drop monitor and direct on-chip probing.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58508/1/spant_1.pd

On-Chip Power Supply Noise: Scaling, Suppression and Detection

Design metrics such as area, timing and power are generally considered as the primary criteria in the design of modern day circuits, however, the minimization of power supply noise, among other noise sources, is appreciably more important since not only can it cause a degradation in these parameters but can cause entire chips to fail. Ensuring the integrity of the power supply voltage in the power distribution network of a chip is therefore crucial to both building reliable circuits as well as preventing circuit performance degradation. Power supply noise concerns, predicted over two decades ago, continue to draw significant attention, and with present CMOS technology projected to keep on scaling, it is shown in this work that these issues are not expected to diminish. This research also considers the management and on-chip detection of power supply noise. There are various methods of managing power supply noise, with the use of decoupling capacitors being the most common technique for suppressing the noise. An in-depth analysis of decap structures including scaling effects is presented in this work with corroborating silicon results. The applicability of various decaps for given design constraints is provided. It is shown that MOS-metal hybrid structures can provide a significant increase in capacitance per unit area compared to traditional structures and will continue to be an important structure as technology continues to scale. Noise suppression by means of current shifting within the clock period of an ALU block is further shown to be an additional method of reducing the minimum voltage observed on its associated supply. A simple, and area and power efficient technique for on-chip supply noise detection is also proposed