scholarly journals On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

2011 ◽  
Vol 23 (2) ◽  
pp. 245-265 ◽  
Author(s):  
MARIA AGUARELES ◽  
JAUME HARO ◽  
JOSEP RIUS ◽  
J. SOLÀ-MORALES
Keyword(s):  
Integrated Circuits ◽  
Asymptotic Formula ◽  
Power Distribution ◽  
Voltage Drop ◽  
Special Functions ◽  
Distribution Networks ◽  
Power Distribution Networks ◽  
Power Distribution Network ◽  
On Chip ◽  
Solutions Of Equations

We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of the Poisson's equation in an infinite planar domain whose boundary is an array of circular pads of radius ϵ, and we deal with the singular limit ϵ → 0 case. In comparison with approximations that appear in the electronics engineering literature, our formula is more complete, since we have obtained terms up to order ϵ15. A procedure will be presented to compute all the successive terms, which can be interpreted by using multipole solutions of equations involving spatial derivatives of δ-functions. To deduce the formula, we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and the Gauss constant G.

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

2014 ◽  
Vol 25 (5) ◽  
pp. 531-551
Author(s):  
TOM CARROLL ◽  
JOAQUIM ORTEGA-CERDÀ
Keyword(s):  
Power Distribution ◽  
Complex Analysis ◽  
Voltage Drop ◽  
Elliptic Functions ◽  
Distribution Networks ◽  
Power Distribution Networks ◽  
Power Distribution Network ◽  
On Chip ◽  
Geometric Arrangements ◽  
Maximum Voltage

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.

Minimizing area of VLSI power distribution networks using river formation dynamics

2018 ◽  
Vol 20 (4) ◽  
pp. 417-429 ◽  
Author(s):  
Satyabrata Dash ◽  
Sukanta Dey ◽  
Deepak Joshi ◽  
Gaurav Trivedi
Keyword(s):  
Power Distribution ◽  
Large Scale ◽  
Distribution Network ◽  
Distribution Networks ◽  
Power Distribution Networks ◽  
Power Distribution Network ◽  
Content Type ◽  
Ir Drop ◽  
Formation Dynamics ◽  
River Formation Dynamics

Purpose The purpose of this paper is to demonstrate the application of river formation dynamics to size the widths of power distribution network for very large-scale integration designs so that the wire area required by power rails is minimized. The area minimization problem is transformed into a single objective optimization problem subject to various design constraints, such as IR drop and electromigration constraints. Design/methodology/approach The minimization process is carried out using river formation dynamics heuristic. The random probabilistic search strategy of river formation dynamics heuristic is used to advance through stringent design requirements to minimize the wire area of an over-designed power distribution network. Findings A number of experiments are performed on several power distribution benchmarks to demonstrate the effectiveness of river formation dynamics heuristic. It is observed that the river formation dynamics heuristic outperforms other standard optimization techniques in most cases, and a power distribution network having 16 million nodes is successfully designed for optimal wire area using river formation dynamics. Originality/value Although many research works are presented in the literature to minimize wire area of power distribution network, these research works convey little idea on optimizing very large-scale power distribution networks (i.e. networks having more than four million nodes) using an automated environment. The originality in this research is the illustration of an automated environment equipped with an efficient optimization technique based on random probabilistic movement of water drops in solving very large-scale power distribution networks without sacrificing accuracy and additional computational cost. Based on the computation of river formation dynamics, the knowledge of minimum area bounded by optimum IR drop value can be of significant advantage in reduction of routable space and in system performance improvement.

scholarly journals Adaptive Day-Ahead Prediction of Resilient Power Distribution Network Partitions

2021 ◽  
Author(s):  
Chinmay Shah ◽  
Richard Wies
Keyword(s):  
Power Distribution ◽  
Renewable Energy Sources ◽  
Optimization Technique ◽  
Distribution Network ◽  
Distribution Networks ◽  
Optimization Techniques ◽  
Power Distribution Networks ◽  
Power Distribution Network ◽  
High Penetration ◽  
Islanded Mode

The conventional power distribution network is being transformed drastically due to high penetration of renewable energy sources (RES) and energy storage. The optimal scheduling and dispatch is important to better harness the energy from intermittent RES. Traditional centralized optimization techniques limit the size of the problem and hence distributed techniques are adopted. The distributed optimization technique partitions the power distribution network into sub-networks which solves the local sub problem and exchanges information with the neighboring sub-networks for the global update. This paper presents an adaptive spectral graph partitioning algorithm based on vertex migration while maintaining computational load balanced for synchronization, active power balance and sub-network resiliency. The parameters that define the resiliency metrics of power distribution networks are discussed and leveraged for better operation of sub-networks in grid connected mode as well as islanded mode. The adaptive partition of the IEEE 123-bus network into resilient sub-networks is demonstrated in this paper.

Power Distribution Networks with On-Chip Decoupling Capacitors

2011 ◽  
Author(s):  
Renatas Jakushokas ◽  
Mikhail Popovich ◽  
Andrey V. Mezhiba ◽  
Selçuk Köse ◽  
Eby G. Friedman
Keyword(s):  
Power Distribution ◽  
Distribution Networks ◽  
Power Distribution Networks ◽  
Decoupling Capacitors ◽  
On Chip
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