A Power Grid Analysis and Verification Tool Based on a Statistical Prediction Engine

M.K. Tsiampas, D. Bountas, P. Merakos, N.E. Evmorfopoulos,S. Bantas and G.I. Stamoulis

ICECS 2010Tools, Techniques & Circuits for Low-

Power Consumer Electronics

Outline

• Motivation• Prior Work• NanoPower• Statistical Prediction Engine• Statistical Prediction Engine in multi mode design• Experimental results• Conclusion

Motivation• Voltage-drop on the power supply network

• Ground bounce respectively on the ground network – Cells do not operate with the nominal power/ground supply – Signal integrity issues – Timing

• Which is the worst case voltage drop ?– Designer would have to check the voltage drops that occur

from the simulation of all possible input vector pairs . . .– Prohibitive amount of simulations for modern ICs that have

hundreds of inputs

Prior Work• Vector-less pseudo dynamic methods.

– Cannot determine with accuracy relationships between different sinks and formulate them as constraints .

– Current constraints have the form of vague upper bounds and thus will only generate a pessimistic upper bound of voltage drop rather than a tight approximation .

– These constraints only involve linear relationships between sink currents .

• Vector-based methods .– Accurate in calculating voltage drop for this particular vector

sequence – Prohibitively large number of all possible input vectors to simulate– No formal methods that provide a set of vectors which is

guaranteed to excite the worst-case voltage drops

NanoPower (1/2)

• Fast, accurate and reliable prediction of the worst case voltage waveforms over each tap-point of the power supply net of the IC.

• Three lynchpin technologies (modules):– An accurate RLCK extraction engine to model the

power supply network .– A high capacity digital (gate level) simulation engine

with grid awareness .– A statistical prediction engine to estimate the worst

case voltage waveforms .

NanoPower (2/2)• NanoPower works internally in an iteration loop between the digital simulator and the linear solver that simulates the power supply network .

• 3-5 iterations between the two simulators are enough to converge to within 2-3% of SPICE .

Statistical Prediction Engine (1/3)• Independent approaches so far :

– Mostly heuristic or over-simplified – Could not provide the accuracy needed for the design of deep-submicron ICs

• A Statistical Prediction Engine based on the Extreme Value Theory– No need to identify and simulate the vector pairs that generate the worst-

case voltage drop– Simulate the design for ~2500 random input vectors – Locate the maximal among the points of the sample space S resulted by the

2500 vectors– Shift the maximal points of the sample space S by a computed difference vector d

and generate the excitation space D y2

y1

ω(y)-max(y1,…,yl)

D

S

Statistical Prediction Engine (2/3)• Confidence interval :– Define the interval of the voltage values for each time

value in a period where the true worst-case voltage will fall into

– Depend on the size of the input vectors set

Statistical Prediction Engine (3/3)• At each via correspond 3 waveforms :

– 1 waveform giving the true worst case voltage– 2 waveforms determining the confidence interval

Statistical Engine in Multi Mode Designs• Modern ICs function in multiple modes of operation

– The set of all possible input vectors is separated into subsets – Each vector subset forces the design operate in a specific mode – Each mode corresponds to a specific average current

consumption

• Solution :– A sufficient number of the input vectors for simulation to be

part of the right most lobe

Experimental Test and Results• Design : H264 (~ 107000 standard cells ) • Technology : 65nm CMOS technology (TSMC) • Simulation vectors : 3000 (random) • Iterations : 3 • Nominal voltage : 1.0 V

Conclusion• Complete methodology encapsulated in a tool

called NanoPower, for power grid analysis and verification – Able to calculate the voltage waveforms for all the

vias in a placed and routed design – Predicts the worst case voltage waveforms at each via

of the power supply network – Uses a very small, internally generated, subset of the

overall possible input vectors set – The Statistical Prediction Engine used by NanoPower

is based on solid mathematical foundation

Thank you

Questions ?