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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 ?