1. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 1 ELEC 5770-001/6770-001 (Fall 2004) ELEC 7770-001 (Spring 2005) (Prof. A. D. Singh) Low-Power Design of CMOS Circuits Vishwani D. Agrawal James J. Danaher Professor Department of Electrical and Computer Engineering Auburn University http://www.eng.auburn.edu/~vagrawal vagrawal@eng.auburn.edu

2. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 2 Motivation Low power applications – Remote systems (e.g., satellite) – Portable systems (e.g., mobile phone) Methods of low power design – Reduced supply voltage – Adiabatic switching – Clock suppression – Logic design for reduced activity – Reduce Hazards (40% in arithmetic logic) – Software techniques Reference: Chandrakasan and Brodersen

3. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 3 Low-Power Design Design practices that reduce power consumption at least by one order of magnitude; in practice 50% reduction is often acceptable. General topics –High-level and software techniques –Gate and circuit-level methods –Power estimation techniques –Test power

4. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 4 VLSI Chip Power Density 4004 8008 8080 8085 8086 286 386 486 Pentium® P6 1 10 100 1000 10000 19701980199020002010 Year Power Density (W/cm 2 ) Hot Plate Nuclear Reactor Rocket Nozzle Sun’s Surface Source: Intel 

5. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 5 Specific Topics on Low-Power Power dissipation in CMOS circuits Low-power CMOS technologies Dynamic reduction techniques Leakage power Power estimation

6. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 6 Components of Power Dynamic –Signal transitions Logic activity Glitches –Short-circuit Static –Leakage

7. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 7 Power of a Transition V DD Ground CLCL R R Power = C L V DD 2 /2 + P sc ViVi VoVo i sc

8. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 8 Short Circuit Current, i sc (t) Time (ns) 0 1 Amp Volt V DD i sc (t) 45μA 0 V i (t) V o (t) V DD - V Tp V Tn tBtB tEtE i scmaxr

9. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 9 Peak Short Circuit Current Increases with the size (or gain, β) of transistors Decreases with load capacitance, C L Largest when C L = 0 Reference: M. A. Ortega and J. Figueras, “Short Circuit Power Modeling in Submicron CMOS,” PATMOS’96, Aug. 1996, pp. 147-166.

10. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 10 Short-Circuit Energy per Transition E scr = ∫ t B t E V DD i sc (t)dt = (t E – t B ) I scmaxr V DD /2 E scr = t r (V DD + V Tp -V Tn ) I scmaxr /2 E scf = t f (V DD + V Tp -V Tn ) I scmaxf /2 E scf = 0, when V DD = |V Tp | + V Tn

11. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 11 Short-Circuit Energy Increases with rise and fall times of input Decreases for larger output load capacitance Decreases and eventually becomes zero when V DD is scaled down but the threshold voltages are not scaled down

12. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 12 Short-Circuit Power Calculation Assume equal rise and fall times Model input-output capacitive coupling (Miller capacitance) Use a spice model for transistors –T. Sakurai and A. Newton, “Alpha-power Law MOSFET model and Its Application to a CMOS Inverter,” IEEE J. Solid State Circuits, vol. 25, April 1990, pp. 584-594.

13. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 13 P sc vs. C C (fF) Input rise time 3ns 0% 45% 0.5ns P sc /P total 0.7μ CMOS 3575

14. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 14 Technology Scaling Scale down by factors of 2 and 4, i.e., model 0.7, 0.35 and 0.17 micron technologies Constant electric field assumed Capacitance scaled down by the technology scale down factor

15. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 15 Technology Scaling Results t r (ns) 0% 70% P sc /P total L=0.7μ, C=40fF 0.41.6 10% L=0.35μ, C=20fF L=0.17μ, C=10fF

16. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 16 Effects of Scaling Down 1-16% short-circuit power at 0.7 micron 4-37% at 0.35 micron 12-60% at 0.17 micron Reference: S. R. Vemuru and N. Steinberg, “Short Circuit Power Dissipation Estimation for CMOS Logic Gates,” IEEE Trans. on Circuits and Systems I, vol. 41, Nov. 1994, pp. 762-765.

17. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 17 Summary: Short-Circuit Power Short-circuit power is consumed by each transition (increases with input transition time). Reduction requires that gate output transition should not be slower than the input transition (faster gates can consume more short-circuit power). Scaling down of supply voltage with respect to threshold voltages reduces short-circuit power.

18. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 18 Components of Power Dynamic –Signal transitions Logic activity Glitches –Short-circuit Static –Leakage

19. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 19 Leakage Power IGIG IDID I sub I PT I GIDL n+ Ground V DD R

20. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 20 Leakage Current Components Subthreshold conduction, I sub Reverse bias pn junction conduction, I D Gate induced drain leakage, I GIDL due to tunneling at the gate-drain overlap Drain source punchthrough, I PT due to short channel and high drain-source voltage Gate tunneling, I G through thin oxide

21. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 21 Subthreshold Current I sub = μ 0 C ox (W/L) V t 2 exp{(V GS -V TH )/nV t } μ 0 : carrier surface mobility C ox : gate oxide capacitance per unit area L: channel length W: gate width V t = kT/q: thermal voltage n: a technology parameter

22. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 22 I DS for Short Channel Device I DS = μ 0 C ox (W/L) V t 2 exp{(V GS -V TH +ηV DS )/nV t } V DS = drain to source voltage η: a proportionality factor

23. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 23 Increased Subthreshold Leakage 0V TH ’V TH Log I sub Gate voltage Scaled device IcIc

24. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 24 Summary: Leakage Power Leakage power as a fraction of the total power increases as clock frequency drops. Turning supply off in unused parts can save power. For a gate it is a small fraction of the total power; it can be significant for very large circuits. Scaling down features requires lowering the threshold voltage, which increases leakage power; roughly doubles with each shrinking. Multiple-threshold devices are used to reduce leakage power.

25. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 25 Components of Power Dynamic –Signal transitions Logic activity Glitches –Short-circuit Static –Leakage

26. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 26 Power of a Transition V DD Ground CLCL R R Power = C L V DD 2 /2 + P sc ViVi VoVo i sc

27. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 27 Dynamic Power Each transition of a gate consumes CV 2 /2. Methods of power saving: –Minimize load capacitances Transistor sizing Library-based gate selection –Reduce transitions Logic design Glitch reduction

28. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 28 Glitch Power Reduction Design a digital circuit for minimum transient energy consumption by eliminating hazards

29. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 29 Theorem 1 For correct operation with minimum energy consumption, a Boolean gate must produce no more than one event per transition

30. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 30 Given that events occur at the input of a gate (inertial delay = d ) at times t 1 <... < t n, the number of events at the gate output cannot exceed Theorem 2 min ( n, 1 + ) t n – t 1 --------d t n - t 1 t n - t 1 t 1 t 2 t 3 t n t 1 t 2 t 3 t n time time

31. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 31 Minimum Transient Design Minimum transient energy condition for a Boolean gate: | t i - t j | < d Where t i and t j are arrival times of input events and d is the inertial delay of gate

32. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 32 Balanced Delay Method All input events arrive simultaneously Overall circuit delay not increased Delay buffers may have to be inserted 1 1 1 1 1 1 1 1 3 1 1 4?

33. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 33 Hazard Filter Method Gate delay is made greater than maximum input path delay difference No delay buffers needed (least transient energy) Overall circuit delay may increase 2 1 1 1 1 2 1 1 1 1 1? 3?

34. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 34 Linear Program Variables: gate and buffer delays Objective: minimize number of buffers Subject to: overall circuit delay Subject to: minimum transient condition for multi-input gates AMPL, MINOS 5.5 (Fourer, Gay and Kernighan)

35. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 35 Variables: Full Adder add1b 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0

36. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 36 Objective Function Ideal: minimize the number of non-zero delay buffers Actual: sum of buffer delays

37. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 37 Specify Critical Path Delay 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 Sum of delays on each I/O path ≤ maxdel

38. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 38 Multi-Input Gate Condition 1 1 1 1 0 0 0 0 0 0 d1 d2 d d1 - d2 ≤ d d2 - d1 ≤ d d d

39. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 39 AMPL Solution: maxdel = 6 2 1 1 1 1 1 2 1 2 2 1

40. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 40 AMPL Solution: maxdel = 7 2 2 1 1 1 1 1 1 3 2

41. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 41 AMPL Solution: maxdel ≥ 11 2 3 1 1 1 1 4 3 5

42. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 42 Power Estimates for add1b maxdel No.ofbuf. Power* with respect to Ref. Ref: model del. Ref: unit del. PeakAve.PeakAve. 67≥11 2100.600.560.520.890.850.800.600.560.520.900.860.81 * Hsiao et al., ICCAD-97

43. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 43 A Limitation Constraints are written by path enumeration. Since number of paths in a circuit can be exponential in circuit size, the formulation is infeasible for large circuits. Example: c880 has 6.96M constraints.

44. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 44 Timing Window Define two timing window variables per gate output: –t i Earliest time of signal transition at gate i. –T i Latest time of signal transition at gate i. t 1, T 1 t n, T n...... t i, T i Ref: T. Raja, Master’s Thesis, Rutgers Univ., 2002 i

45. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 45 Linear Program Gate variables d 4... d 12 Buffer Variables d 15... d 29 Corresponding window variables t 4... t 29 and T 4... T 29.

46. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 46 Multiple-Input Gate Constraints For Gate 7: T 7 > T 5 + d 7 ; t 7 T 7 - t 7 ; T 7 > T 6 + d 7 ; t 7 < t 6 + d 7 ;

47. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 47 Single-Input Gate Constraints T 16 + d 19 = T 19 ; t 16 + d 19 = t 19 ; Buffer 19:

48. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 48 Overall Delay Constraints T 11 < maxdelay T 12 < maxdelay

49. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 49 Advantage of Timing Window Path constraints (exponential in n): 2 × 2 × … 2 = 2 n paths between I/O pair A single variable specifies I/O delay. Total variables, O(n). LP constraint set is linear in the size of circuit.

50. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 50 Comparison of Constraints Number of gates in circuit Number of constraints

51. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 51 Results: 1-Bit Adder

52. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 52 Estimation of Power Circuit is simulated by an event-driven simulator for both optimized and un- optimized gate delays. All transitions at a gate are counted as Events[gate]. Power consumed  Events[gate] x # of fanouts. Ref: “Effects of delay model on peak power estimation of VLSI circuits,” Hsiao, et al. (ICCAD`97).

53. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 53 Original 1-Bit Adder Color codes for number of transitions

54. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 54 Optimized 1-Bit Adder Color codes for number of transitions

55. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 55 1-Bit Adder Design Simulation over all possible vector transitions Average power = optimized/unit delay = 244 / 308 = 0.792 Peak power = optimized/unit delay = 6 / 10 = 0.60 Power Savings : Peak = 40 % Average = 21 %

56. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 56 Results: 4-Bit ALU maxdelayBuffers inserted 75 102 121 150 Power Savings : Peak = 33 %, Average = 21 %

57. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 57 Physical Design Gate l/w Gate l/w Gate l/w Gate l/w Gate delay modeled as a linear function of gate size, total load capacitance, and fanout gate sizes (Berkelaar and Jacobs, 1996). Layout circuit with some nominal gate sizes. Enter extracted routing delays in LP as constants and solve for gate delays. Change gate sizes as determined from a linear system of equations. Iterate if routing delays change.

58. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 58 Physical Level Verification Assumptions in the logic level power analysis –Leakage and short circuit power are a small portion of the entire power consumption of the circuit. –Area overhead is tolerable for the achieved power savings. –Glitches are a major portion of the power consumption of the chip.

59. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 59 Power Calculation in Spice VDD Ground Circuit Large C Open at t = 0 Ref.: M. Shoji, CMOS Digital Circuit Technology, Prentice Hall, 1988, p. 172. t Energy, E(t) E(t) = -- C VDD 2 - -- C V 2 ~ C VDD ( VDD - V ) 11 22 V

60. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 60 Power Dissipation of ALU4

61. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 61 F0 Output of ALU4 Signal Amplitude, Volts 0 5 040 80 120 160 nanoseconds Original ALU, delay = 7 units (~3.5ns) Minimum energy ALU, delay = 21 units (~10ns) 5 0

62. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 62 Benchmark Circuits Circuit C432 C880 C6288 c7552 Maxdel. (gates) 17 34 24 48 47 94 43 86 No. of Buffers 95 66 62 34 294 120 366 111 Average 0.72 0.62 0.68 0.40 0.36 0.38 0.36 Peak 0.67 0.60 0.54 0.52 0.36 0.34 0.32 Normalized Power

63. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 63 Bufferless Design Buffered optimization 4 5 7 6 1 2 3 d=2 d=1 4 5 7 6 1 2 3 d=2 d=1 d=2 d=1 4 5 7 6 1 2 3 d=2 d=1 d=2 d=1 Unoptimized Circuit Bufferless optimization

64. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 64 Example Circuit – Spectre Results time Unoptimized Circuit Buffer optimized Circuit nMOS optimized Circuit

65. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 65 Example Circuit – Energy Consumption

66. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 66 Example Circuit – Leakage Analysis

67. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 67 Physical Level Verification AMPL Technology Mapping Create Cells using Prolific Standard Cell Place and Route Extract Routing Capacitance Analog Power simulations Delays Transistor Sizes Standard Cell Library Layout Routing load Energy Consumption Routing Acceptable ? No Yes Optimized Layout

68. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 68 Design of Benchmark C7552 c7552 Un-optimized Gate Count= 3827 Transistor Count ≈ 40,000 Critical Delay = 2.15 ns Area= 710 x 710 um 2 c7552 optimized Gate Count= 3828 Transistor Count ≈ 45,000 Critical Delay = 2.15 ns Area= 760 x 760 um 2 (1.14)

69. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 69 Instantaneous Power Savings Peak Power Savings = 68%

70. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 70 Average Energy Savings Average Energy Saving = 58%

71. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 71 Patents and Dissertations Patents –V. D. Agrawal, “Low Power Circuits Through Hazard Pulse Suppression,” U.S. Patent 5,983,007, November 1999. –T. Raja, V. D. Agrawal and M. L. Bushnell, “Variable Input Delay CMOS Logic and Its Application to Low Power Design,” to be submitted to USPTO through Rutgers Univ., May 2004. Dissertations –T. Raja, Minimum Dynamic Power Design of CMOS Circuits using a Reduced Constraint Set Linear Program, MS Thesis, Dept. of ECE, Rutgers University, May 2002. –T. Raja, Minimum Dynamic Power CMOS Design with Variable Input Delay Logic, PhD Thesis, Dept. of ECE, Rutgers University, May 2004. –S. Uppalapati, Low Power Design of Standard Cell Digital VLSI Circuits, MS. Thesis, Dept. of ECE, Rutgers University, October 2004.

72. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 72 Papers V. D. Agrawal, “Low-Power Design by Hazard Filtering,” Proc. 10th Int. Conf. VLSI Design, Jan. 1997, pp. 193-197. V. D. Agrawal, M. L. Bushnell, G. Parthasarathy, and R. Ramadoss, “Digital Circuit Design for Minimum Transient Energy and a Linear Programming Method,” Proc. 12th Int. Conf. VLSI Design, Jan. 1999, pp. 434-439. T. Raja, V. D. Agrawal, and M. L. Bushnell, “Minimum Dynamic Power CMOS Circuit Design by a Reduced Constraint Set Linear Program,” Proc. 16th Int. Conf. VLSI Design, Jan. 2003, pp. 527-532. T. Raja, V. D. Agrawal, and M. L. Bushnell, “CMOS Circuit Design for Minimum Dynamic Power and Highest Speed,” Proc. 17th Int. Conf. VLSI Design, Jan. 2004, pp. 1035-1040. T. Raja, V. D. Agrawal, and M. L. Bushnell, “Variable Input Delay CMOS Logic for Low Power Design,” Proc. 18th Int. Conf. VLSI Design, Jan. 2005, pp. 598-605.

73. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 73 Other References R. Fourer, D. M. Gay and B. W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, South San Francisco: The Scientific Press, 1993. M. Berkelaar and E. Jacobs, “Using Gate Sizing to Reduce Glitch Power,” Proc. ProRISC Workshop, Mierlo, The Netherlands, Nov. 1996, pp. 183-188. M. Hsiao, E. M. Rudnick and J. H. Patel, “Effects of Delay Model in Peak Power Estimation of VLSI Circuits,” Proc. ICCAD, Nov. 1997, pp. 45-51.

74. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 74 Books on Low-Power Design A. Chandrakasan and R. Brodersen, Low-Power Digital CMOS Design, Boston: Kluwer Academic Publishers, 1995. A. Chandrakasan and R. Brodersen, Low-Power CMOS Design, New York: IEEE Press, 1998 L. Benini and G. De Micheli, Dynamic Power Management Design Techniques and CAD Tools, Boston: Kluwer Academic Publishers, 1998. T. D. Burd and R. A. Brodersen, Energy Efficient Microprocessor Design, Boston: Kluwer Academic Publishers, 2002. M. S. Elrabaa, I. S. Abu-Khater and M. I. Elmasry, Advanced Low-Power Digital Circuit Techniques, Boston: Kluwer Academic Publishers, 1997. R. Graybill and R. Melhem, Power Aware Computing, New York: Plenum Publishers, 2002. J. B. Kuo and J.-H. Lou, Low-Voltage CMOS VLSI Circuits, New York: Wiley-Interscience, 1999. J. Monteiro and S. Devadas, Computer-Aided Design Techniques for Low Power Sequential Logic Circuits, Boston: Kluwer Academic Publishers, 1997. W. Nebel and J. Mermet, Low Power Design in Deep Submicron Electronics, Boston: Kluwer Academic Publishers, 1997. N. Nicolici and B. M. Al-Hashimi, Power-Constrained Testing of VLSI Circuits, Boston: Kluwer Academic Publishers, 2003. J. M. Rabaey and M. Pedram, Low Power Design Methodologies, Boston: Kluwer Academic Publishers, 1996. K. Roy and S. C. Prasad, Low-Power CMOS VLSI Circuit Design, New York: Wiley-Interscience, 2000. E. Sánchez-Sinencio and A. G. Andreaou, Low-Voltage/Low-Power Integrated Circuits and Systems – Low-Voltage Mixed-Signal Circuits, New York: IEEE Press, 1999. W. A. Serdijn, Low-Voltage Low-Power Analog Integrated Circuits, Boston: Kluwer Academic Publishers, 1995. G. K. Yeap, Practical Low Power Digital VLSI Design, Boston: Kluwer Academic Publishers, 1998.

75. 9/30/04, 10/7/04, 1/20/05 ELEC 5770-001/6770-001/7770- 001, Guest Lecture, Low-Power Design 75 Conclusion Minimum dynamic power high speed circuits can be designed if gates with variable input delays are used. It is possible to suppresses all glitches without any delay buffers. Power is reduced without reduction in speed and with very little increase in area. Linear program provides an effective design. Technique is scalable for large circuits. Experimental result show average power savings up to 58% Future directions: Reduction of leakage power.