Vishwani D. Agrawal James J. Danaher Professor Department of Electrical and Computer Engineering

1. ELEC 5970-001/6970-001(Fall 2005)Special Topics in Electrical EngineeringLow-Power Design of Electronic CircuitsPower Analysis: High-Level 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 ELEC 5970-001/6970-001 Lecture 13

2. Key Parameters Power α Capacitance × Activity • Capacitance • Area • Complexity • Activity • Dynamic behavior • Operational characteristics ELEC 5970-001/6970-001 Lecture 13

3. Architecture-Level Power Estimation • Analytical methods • Complexity-based models • Activity-based models • Empirical methods • Fixed-activity models • Activity-sensitive models ELEC 5970-001/6970-001 Lecture 13

4. A Complexity-Based Model Power = Σ GEk (Etyp + CLkVDD2) f Ak All functional blocks k where • GEk = gate equivalent count for block k, e.g., estimated number of 2-input NANDs. • Etyp = average energy consumed by an active typical 2-input NAND. • CLk = average capacitance of a gate in block k. • f = clock freqency. • VDD = supply voltage. • Ak = average fraction of gates switching in block k. Ref.: K. Müller-Glaser, K. Kirsch and K. Neusinger, “Estimating Essential Design Characteristics to Support Project Planning for ASIC Design Management,” Proc. IEEE Int. Conf. CAD, Nov. 1991, pp. 148-151. ELEC 5970-001/6970-001 Lecture 13

5. Improving Complexity Models • Treat logic, memory, interconnects and clock tree, separately • For example, a memory array may not be modeled as equivalent NAND gates, but as a memory cell. ELEC 5970-001/6970-001 Lecture 13

6. An On-Chip SRAM 2k cells Memory array word line Six-transistor memory cell . . . . . . Address bus bit line Row decode and drivers 2n-k cells . . . Ctrl Sense and column decode . . . Data bus ELEC 5970-001/6970-001 Lecture 13

7. Power Consumed by SRAM 2k Power = ── (cint lcol +2n-k ctr) VDD Vswing f 2 Where 2k number of cells in a row cint wire capacitance per unit length lcol memory column length 2n-k number of cells in a column ctr minimum size transistor drain capacitance Vswing bitline voltage swing Ref.: D. Liu and C. Svenson, “Power Consumption Estimation in CMOS VLSI Chips,” IEEE J. Solid-State Circuits, June 1991, pp. 663-670. ELEC 5970-001/6970-001 Lecture 13

8. Activity-Based Models • Power α capacitance × activity • Capacitance α area • Both area and activity can be estimated from the entropy of a Boolean function. • Definition: Entropy of a system with m states having probabilities p1, p2, . . . , pm, is m H = - Σ pk log2 pk bits k=1 ELEC 5970-001/6970-001 Lecture 13

9. Binary Signals • Entropy of a binary signal: H(p1) = - p1 log2 p1 – (1- p1) log2(1-p1) • Entropy of an n-bit binary vector: n H(X) = Σ H(p1k) k=1 ELEC 5970-001/6970-001 Lecture 13

10. Entropy and Activity 1.0 0.75 0.50 0.25 0.0 4 p1k(1-p1k) Entropy 0.0 0.25 0.5 0.75 1.0 p1k ELEC 5970-001/6970-001 Lecture 13

11. Entropy of a Circuit Combinational Logic Y1 Y2 Ym X1 X2 Xn . . . . . . ELEC 5970-001/6970-001 Lecture 13

12. Input and Output Entropy 2n Hi = Σ pk log2 pk k=1 where pk = probability of kth input vector 2m Ho = Σ pj log2 pj j=1 where pj = probability of jth output vector ELEC 5970-001/6970-001 Lecture 13

13. Average Acrivity 2/3 Average entropy ≈ ─── (Hi + 2Ho) n+m Quadratic decay Hi Hi ≥ Ho Ho PI PO Circuit depth → ELEC 5970-001/6970-001 Lecture 13

14. Area Estimate • K.-T. Cheng and V. D. Agrawal, “An Entropy Measure for the Complexity of Multi-Output Boolean Functions,” Proc. 17th DAC, 1990, pp. 302-305. • M. Nemani and F. Najm, “Towards a High-Level Power Estimation Capability,” IEEE Trans. CAD, vol. 15, no. 6, pp. 588-598, June 1996. Area = 2n Ho/n for large n = 2n Ho for n ≤ 10 ELEC 5970-001/6970-001 Lecture 13

15. Power N Power = K1 × Av. Activity × Σ Ck = K2 × Av. Activity × Area k=1 where Ck is the capacitance of kth node in a circuit with N nodes 2n+1 Power = K3 ────── Ho (Hi + Ho) 3n(n+m) Constant K3 is determined by simulation of gate-level circuits. ELEC 5970-001/6970-001 Lecture 13

16. Sequential Circuit Combinational Logic PI PO Ho Hi Flip-flops Hi and Ho are determined from high-level simulation. ELEC 5970-001/6970-001 Lecture 13

17. Empirical Methods • Functional blocks are characterized for power consumption in active and inactive (standby) modes by • Analytical methods, or • Simulation, or • Measurement • A software simulator determined which blocks become active and adds their power consumption. ELEC 5970-001/6970-001 Lecture 13

18. Example: RISC Microprocessor Clock cycles 1 2 3 4 5 6 . . . add R1←R2+R3 IF ID EX MEM WB mem rfile ALU rfile pcadd bradd lw R4←4(R5) IF ID EX MEM WB mem rfile ALU mem rfile pcadd bradd ALU mem ALU Power profile mem mem ALU ALU rfile rfile ALU ALU rfile rfile time ELEC 5970-001/6970-001 Lecture 13

19. Additional References • P. E. Landman, “A Survey of High-Level Power Estimation Techniques,” in Low-Power CMOS Design, A. Chandrakasan and R. Brodersen (Editors), New York: IEEE Press, 1998. • P. E. Landman and J. M. Rabaey, “Activity-Sensitive Architectural Power Analysis,” IEEE Trans. CAD, vol. 15, no. 6, pp. 571-587, June 1996. ELEC 5970-001/6970-001 Lecture 13