A Tutorial on Battery Simulation - Matching Power Source to Electronic System Manish Kulkarni and Vishwani D. Agrawal Auburn University Auburn, AL 36849, USA VDAT10, July 8, 20101Kulkarni & Agrawal

Contents Introduction Powering an electronic system Statement of the battery problem Power subsystem, components, characteristics A Design Example Circuit simulation for critical path delay and battery current Battery simulation for lifetime and efficiency Finding the smallest battery for required system performance Finding battery for lifetime requirement Finding minimum energy mode Summary VDAT10, July 8, 2010Kulkarni & Agrawal2

Introduction: Powering a System VDAT10, July 8, 2010Kulkarni & Agrawal3 VBVB +_+_ RBRB VLVL RLRL ILIL AHr (capacity) Ideal lifetime = AHr/I L = AHr.R B (1 + R L /R B ) / V B Power supplied to load, P L = I L 2 R L = (V B 2 /R B )(R L /R B ) / (1+ R L /R B ) 2 Efficiency = P L / Battery Power = (1+ R B /R L ) –1

Lifetime, Power and Efficiency VDAT10, July 8, 2010Kulkarni & Agrawal Efficiency or Power R L /R B Lifetime (x AHr.R B /V B ) Lifetime Efficiency P L x V B 2 /(4R B )

Problem Statement Battery problem Battery should be capable of supplying power (current) for required system performance. Battery should meet the lifetime (time between replacement or recharge) requirement. How to extend the lifetime of selected battery. Solution Determine minimum battery size for efficiency ≥ 85% Increase battery size over the minimum size to meet lifetime requirement. Determine a lower performance mode with maximum lifetime. VDAT10, July 8, 2010Kulkarni & Agrawal5

Power Subsystem of an Electronic System VDAT10, July 8, 2010Kulkarni & Agrawal6

Some Characteristics Lithium-ion battery Open circuit voltage: 4.2V, unit cell 400mAHr, for efficiency ≥ 85%, current ≤ 1.2A Discharged battery voltage ≤ 3.0V DC-to-DC converter Supplies VDD to circuit, VDD ≤ 1V for nanometer technologies. VDD control for energy management. Decoupling capacitor(s) provide smoothing of time varying current of the circuit. VDAT10, July 8, 2010Kulkarni & Agrawal7

DC-to-DC Buck (Step-Down) Converter Components: switch, diode, inductor, capacitor. Switch control: pulse width modulated (PWM) signal. V out = D · V in, D is duty cycle of PWM control signal. References: M. Pedram and Q. Wu, “Design Considerations for Battery-Powered Electronics,” Proc. 36th Design Automation Conference, June 1999, pp. 861–866. L. Benini, G. Castelli, A. Macii, E. Macii, M. Poncino, and R. Scarsi, “A Discrete-Time Battery Model for High-Level Power Estimation,” Proc. Conference on Design, Automation and Test in Europe, Mar. 2000, pp. 35–41. Power Supply Circuits, Application Note 2031, Maxim Integrated Products, Oct. 19, 2000, ic.com/en/an/AN2031.pdfhttp://pdfserv.maxim- ic.com/en/an/AN2031.pdf VDAT10, July 8, 2010Kulkarni & Agrawal8

A DC-to-DC Buck Converter VDAT10, July 8, 2010Kulkarni & Agrawal9 V in V out PWM control; duty cycle determines V out

A Design Example 70 million gate circuit. Critical path: 32bit ripple-carry adder (RCA) 352 NAND gates (2 or 3 inputs), 1,472 transistors. 45nm bulk CMOS technology. Three-step design procedure: Circuit characterization – current and delay vs. VDD; find average current for peak performance. Battery lifetime simulation – minimum battery size for efficiency ≥ 85% at peak performance; battery size for lifetime requirement. Minimum energy mode – maximum lifetime VDD and clock frequency. VDAT10, July 8, 2010Kulkarni & Agrawal10

Critical Path Simulation Simulation model: 45nm bulk CMOS, predictive technology model (PTM), Simulator: Synopsys HSPICE, fication/CircuitSimulation/HSPICE/Documents/ hspice ds.pdf fication/CircuitSimulation/HSPICE/Documents/ hspice ds.pdf VDAT10, July 8, 2010Kulkarni & Agrawal11

Hspice Simulation of 32-Bit RCA, VDD = 0.9V VDAT10, July 8, 2010Kulkarni & Agrawal12 Critical path vectors 2ns Average total current, I circuit = 74.32μA, Leakage current = 1.108μA 100 random vectors including critical path vectors

Hspice Simulation of 32-Bit RCA, VDD = 0.3V VDAT10, July 8, 2010Kulkarni & Agrawal13 Average total current, I circuit = μA, Leakage current = 0.092μA Critical path vectors 200ns 100 random vectors including critical path vectors

Finding Battery Current, I Batt Assume 32-bit ripple carry adder (RCA) with about 350 gates represents circuit activity for the entire system. Total current for 70 million gate circuit, I circuit = (average current for RCA) x 200,000 DC-to-DC converter translates VDD to 4.2V battery voltage; assuming 100% conversion efficiency, I Batt = I circuit x VDD/4.2 Example: Hspice simulation of RCA: 100 random vectors, VDD = 0.9V, vector period = 2ns, average current = μA, I batt = 3.18A VDAT10, July 8, 2010Kulkarni & Agrawal14

Delay and Current vs. VDD VDAT10, July 8, 2010Kulkarni & Agrawal15 ~ 2ns (500MHz) 3.18A

Battery Simulation Model VDAT10, July 8, 2010Kulkarni & Agrawal16 Lithium-ion battery, unit cell capacity: N = 1 (400mAHr) Battery sizes, N = 2 (800mAHr), N = 3 (1.2AHr), etc. M. Chen and G. A. Rincón-Mora, “Accurate Electrical Battery Model Capable of Predicting Runtime and I-V Performance,” IEEE Transactions on Energy Conversion, vol. 21, no. 2, pp. 504–511, June 2006.

Lifetime from Battery Simulation VDAT10, July 8, 2010Kulkarni & Agrawal s

Finding Battery Efficiency Consider: 1.2AHr battery I Batt = 3.6A Ideal efficiency = 1.2AHr/3.6A = 1/3 hour (1200s) Actual lifetime from simulation = 1008s Efficiency=(Actual lifetime)/(Ideal lifetime) =1008/1200 =0.84 or 84% VDAT10, July 8, 2010Kulkarni & Agrawal18

Battery Efficiency vs. Size VDAT10, July 8, 2010Kulkarni & Agrawal19

Minimum Battery Size Consider a performance requirement of 500MHz clock, critical path delay ≤ 2ns. Circuit simulation gives, VDD = 0.9V and I Batt = 3.18A. From battery efficiency simulation, for efficiency ≥ 85%, battery capacity should not be less than 1.2AHr, i.e., three-cell (N=3) Li-ion battery. VDAT10, July 8, 2010Kulkarni & Agrawal20

Battery Lifetime Requirement Suppose battery lifetime for the system is to be at least one hour. For smallest battery, size N = 3 (1.2AHr), I Batt = 3.18A, efficiency ≈ 93%, Lifetime = 0.93 x 1.2/3.18 = 0.35 hour For 1 hour lifetime, battery size N = 3/0.35 = 8.57 ≈ 9. We should use a 9 cell (3.6AHr) battery. VDAT10, July 8, 2010Kulkarni & Agrawal21

Minimum Energy Operation A meaningful measure of the work done by the battery is its lifetime in terms of clock cycles. For each VDD in the range of valid operation, i.e., VDD = 0.1V to 0.9V, we calculate lifetime using circuit delay and battery efficiency obtained from Hspice simulation. Minimum energy operation maximizes the lifetime in clock cycles. VDAT10, July 8, 2010Kulkarni & Agrawal22

Minimum Energy Operation VDAT10, July 8, 2010Kulkarni & Agrawal Lifetime (x10 12 cycles) Battery capacity 3.6AHr Battery capacity 1.2AHr VDD (volts)

Summary Battery size VDD = 0.9V, 500MHzVDD = 0.3V, 5MHz Effici. % Lifetime Effici. % Lifetime NAHr x10 3 seconds x10 11 cycles x10 6 seconds x10 11 cycles VDAT10, July 8, 2010Kulkarni & Agrawal24 seven-times 1.Battery size should match the current need and satisfy the lifetime requirement of the system: (a) Undersize battery has poor efficiency. (b) Oversize battery is bulky and expensive. 2Minimum energy mode can significantly increase battery lifetime.