1. 10/13/05ELEC 5970-001/6970-001 Lecture 131 ELEC 5970-001/6970-001(Fall 2005) Special Topics in Electrical Engineering Low-Power Design of Electronic Circuits Power 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

2. 10/13/05ELEC 5970-001/6970-001 Lecture 132 Key Parameters Capacitance –Area –Complexity Activity –Dynamic behavior –Operational characteristics Power α Capacitance × Activity

3. 10/13/05ELEC 5970-001/6970-001 Lecture 133 Architecture-Level Power Estimation Analytical methods –Complexity-based models –Activity-based models Empirical methods –Fixed-activity models –Activity-sensitive models

4. 10/13/05ELEC 5970-001/6970-001 Lecture 134 A Complexity-Based Model where GE k = gate equivalent count for block k, e.g., estimated number of 2-input NANDs. E typ = average energy consumed by an active typical 2-input NAND. C Lk = average capacitance of a gate in block k. f = clock freqency. V DD = supply voltage. A k = average fraction of gates switching in block k. Power =ΣGE k (E typ + C Lk V DD 2 ) f A k All functional blocks 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.

5. 10/13/05ELEC 5970-001/6970-001 Lecture 135 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.

6. 10/13/05ELEC 5970-001/6970-001 Lecture 136 Memory array An On-Chip SRAM Sense and column decode Row decode and drivers Ctrl Address bus... Data bus word line bit line Six-transistor memory cell 2 k cells 2 n-k cells

7. 10/13/05ELEC 5970-001/6970-001 Lecture 137 Power Consumed by SRAM 2 k Power = ── (c int l col +2 n-k c tr ) V DD V swing f 2 Where2 k number of cells in a row c int wire capacitance per unit length l col memory column length 2 n-k number of cells in a column c tr minimum size transistor drain capacitance V swing 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.

8. 10/13/05ELEC 5970-001/6970-001 Lecture 138 Activity-Based Models Powerαcapacitance × activity Capacitanceα 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 log 2 pkbits k=1

9. 10/13/05ELEC 5970-001/6970-001 Lecture 139 Binary Signals Entropy of a binary signal: H(p1) = - p1 log 2 p1 – (1- p1) log 2 (1-p1) Entropy of an n-bit binary vector: n H(X)=ΣH(p1k) k=1

10. 10/13/05ELEC 5970-001/6970-001 Lecture 1310 Entropy and Activity p1k 0.00.250.50.751.0 1.0 0.75 0.50 0.25 0.0 Entropy 4 p1k(1-p1k)

11. 10/13/05ELEC 5970-001/6970-001 Lecture 1311 Entropy of a Circuit Combinational Logic...... X1 X2 Xn...... Y1 Y2 Ym

12. 10/13/05ELEC 5970-001/6970-001 Lecture 1312 Input and Output Entropy 2 n Hi=Σpk log 2 pk k=1 where pk = probability of kth input vector 2 m Ho=Σpj log 2 pj j=1 where pj = probability of jth output vector

13. 10/13/05ELEC 5970-001/6970-001 Lecture 1313 Average Acrivity Hi Ho Circuit depth → PIPO 2/3 Average entropy ≈ ─── (Hi + 2Ho) n+m Quadratic decay Hi ≥ Ho

14. 10/13/05ELEC 5970-001/6970-001 Lecture 1314 Area Estimate K.-T. Cheng and V. D. Agrawal, “An Entropy Measure for the Complexity of Multi-Output Boolean Functions,” Proc. 17 th 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=2 n Ho/nfor large n =2 n Hofor n ≤ 10

15. 10/13/05ELEC 5970-001/6970-001 Lecture 1315 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 2 n+1 Power = K3 ────── Ho (Hi + Ho) 3n(n+m) Constant K3 is determined by simulation of gate-level circuits.

16. 10/13/05ELEC 5970-001/6970-001 Lecture 1316 Sequential Circuit Combinational Logic Flip-flops PIPO Hi Ho Hi and Ho are determined from high-level simulation.

17. 10/13/05ELEC 5970-001/6970-001 Lecture 1317 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.

18. 10/13/05ELEC 5970-001/6970-001 Lecture 1318 Example: RISC Microprocessor IF ID EXMEM WB add R1←R2+R3 lw R4←4(R5) Clock cycles123456... memrfileALUrfile pcaddbradd memrfileALUmemrfile pcaddbradd mem ALU rfile mem ALU rfile ALU rfile mem time Power profile

19. 10/13/05ELEC 5970-001/6970-001 Lecture 1319 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.