1. 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 2010 Tools, Techniques & Circuits for Low-Power Consumer Electronics

2. Outline Motivation Prior Work NanoPower Statistical Prediction Engine Statistical Prediction Engine in multi mode design Experimental results Conclusion

3. 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

4. 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

5. 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.

6. 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.

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. Thank you Questions ?