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ELEC 5270/6270 Spring 2009 Low-Power Design of Electronic Circuits Power Analysis: High-Level

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### ELEC 5270/6270 Spring 2009Low-Power Design of Electronic CircuitsPower Analysis: High-Level

Vishwani D. Agrawal

James J. Danaher Professor

Dept. of Electrical and Computer Engineering

Auburn University, Auburn, AL 36849

http://www.eng.auburn.edu/~vagrawal/COURSE/E6270_Spr09/course.html

ELEC6270 Spring 09, Lecture 7

Key Parameters

Power α Capacitance × Activity

- Capacitance
- Area
- Complexity
- Activity
- Dynamic behavior
- Operational characteristics

ELEC6270 Spring 09, Lecture 7

Architecture-Level Power Estimation

- Analytical methods
- Complexity-based models
- Activity-based models
- Empirical methods
- Fixed-activity models
- Activity-sensitive models

ELEC6270 Spring 09, Lecture 7

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 per clock cycle 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 per cycle 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.

ELEC6270 Spring 09, Lecture 7

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 memory cells.

ELEC6270 Spring 09, Lecture 7

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

. . .

Data

Ctrl

Sense and column decode

. . .

Address bus

ELEC6270 Spring 09, Lecture 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.

ELEC6270 Spring 09, Lecture 7

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

ELEC6270 Spring 09, Lecture 7

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

ELEC6270 Spring 09, Lecture 7

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

ELEC6270 Spring 09, Lecture 7

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

ELEC6270 Spring 09, Lecture 7

Average Acrivity

2/3

Average entropy ≈ ─── (Hi + 2Ho)

n+m

Quadratic decay

Hi

Hi ≥ Ho

Ho

PI

PO

Circuit depth →

ELEC6270 Spring 09, Lecture 7

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

ELEC6270 Spring 09, Lecture 7

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 + 2Ho)

3n(n+m)

Constant K3 is determined by simulation of gate-level circuits.

ELEC6270 Spring 09, Lecture 7

Sequential Circuit

Combinational

Logic

PI

PO

Ho

Hi

Flip-flops

Hi and Ho are determined from high-level simulation.

ELEC6270 Spring 09, Lecture 7

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 determines which blocks become active and adds their power consumption.

ELEC6270 Spring 09, Lecture 7

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

ELEC6270 Spring 09, Lecture 7

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.
- A. Raghunathan, N. K. Jha, and S. Dey, High-level power analysis and optimization, Boston: Springer, 1997.

ELEC6270 Spring 09, Lecture 7

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