Power Consumption by Integrated Circuits

Lin ZhongELEC518, Spring 2011

Power consumption of processing

• Dynamic power

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Busy power vs. delay vs. energy

fVCaP dddyn 2

)( Tdd

dd

VVV

t

Analysis and Design of Digital ICs, Hodges et al

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Core 2 Duo for example• Intel® Core™2 Duo processor

– T7800 at 2.6GHz– T7700 at 2.4GHz available on Thinkpad T61p– 0.75-1.35V, 35Watts

• Intel® Core™2 Duo Low Voltage– L7500 at 1.6GHz available on Thinkpad X61– 0.75-1.3V, 17Watts

• Intel® Core™2 Duo Ultra Low Voltage– U7500 at 1.06GHz available on Dell D430– 0.75-0.975V, 10Watts

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Switching energy

e=1/2 C V∙ ∙ 2

Switching power

P= b C V∙ ∙ 2= a C V∙ ∙ 2 f∙

Higher integration• Selling the chipset (or solution or platform)

– Intel Centrino• Centrino Duo includes Core 2 Duo processor, 9XX Express-series chipset,

and Wi-Fi adapter– TI TCS2600 chipset

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System-on-a-chip (SoC)

• TI OMAP

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SiP: Multiple-chip product (MCP)

Siemens SX66 PDA PhoneAudiovox PPC6601KIT

32MB

400MHz

Source: Intel.com

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SiP: Stacked-die approachQualcomm 3G CDMA2000 chip

Seven power regimes 100 clock regimes

ISSCC 20049

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Moore’s Law

known

Exciting Unknown

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MOSFET at nanoscale

Sunlin Chou, “Extending Moore’s Law in the Nanotechnology Era” (www.intel.com).

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Given workload L and deadline T

• L measured by # of CPU cycles• Clock speed f ≥ L/T

• Time to finish: t = L/f

• Energy to finish: P t= a C V∙ ∙ ∙ 2 f t= a C ∙ ∙ ∙V∙ 2 L∙

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Effect of lower clock speed (f)

Power consumption

P= a C V∙ ∙ 2 f∙

Energy consumption

E=P t= a C V∙ ∙ ∙ 2 f t= a C V∙ ∙ ∙ ∙ 2

L∙

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Effect of lower supply voltage (V)

Power consumption

P= a C V∙ ∙ 2 f=k V∙ ∙ 3=x f∙ 3

Energy consumption

E=P t= a C V∙ ∙ ∙ 2 f t= a C V∙ ∙ ∙ ∙ 2

L∙

Maximum clock speed

f= b V∙

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Given workload L and deadline Tsingle processor

• The processor can run at any frequency (voltage)– f= b V∙

• The processor can be complete off when work is done (zero power when idle)

• To minimize energy consumption, at which frequency should the processor run?– f ≥ L/T (in order to meet the deadline)– E=P t= a C V∙ ∙ ∙ 2 f t= a C V∙ ∙ ∙ ∙ 2 L∙– f=????

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time

f

T

f1=L/T

f2=L/(T/2)=2f1

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time

P

T

P1=x f∙ 3

P2=23P1

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Given workload L and deadline TM processors

• The workload can be divided without overhead: L = L1+L2+…+LM (L ≥ Li≥0)

• To minimize energy consumption, at which frequency should processor i run?– f i= Li/T and V = u L∙ i

– Ei= a C V∙ ∙ 2 L∙ i=w L∙ i3

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Given workload L and deadline TM processors

• The workload can be divided without overhead: L = L1+L2+…+LM (L ≥ Li≥0)

• To minimize the TOTAL energy consumption, how should the workload be allocated?– E= E1+E2+…+EM= w L∙ 1

3+w L∙ 23+…+w L∙ M

3

– = w(L13+L2

3+…+LM3)

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From high school

• [(a+b)/2]2≤ (a2+b2)/2

≥ ≥ ≥

Quadratic mean Arithmetic mean Geometric mean harmonic mean

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From high school (Contd.)

• [(a+b)/2]3≤ (a3+b3)/2 ( for a, b ≥0)

– E= w(L13+L2

3+…+LM3) ??? (L1+L2+…+LM)3

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From college: Convex (Concave)

By definition of “convex”

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Jensen’s Inequality (finite form)

• ϕ (x) is convex– ϕ (t x∙ 1+(1-t) x∙ 2)≤ t ∙ ϕ (x1)+(1-t) ∙ϕ (x2)

http://en.wikipedia.org/wiki/Jensen%27s_inequality#Proof_1_.28finite_form.29

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• ai=1/n• ϕ (x) =x2 (Convex)

• ϕ (x) =x3(Convex for x≥0)– E= w(L1

3+L23+…+LM

3)=w M (L∙ ∙ 13+L2

3+…+LM3)/M

– ≥ w M [(L∙ ∙ 1+L2+…+LM)/M] 3=w L∙ 3/M2

≥

More about ConvexityCost

Return

Example Cost Return

Workload distribution Energy Workload finished within T

Eating Price of apples Pleasure from eating apples

Helicopter engine Price of engine Engine thrust

Law of diminishing marginal returns

Cost of production Increase in production

More about Convexity

• Greedy optimization works• Combine simpler/cheaper components

Cost

Return

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Check the assumptions

• Power consumption is zero when the processor is not active

Idle power (Static power)

Tstatic eTP

2 ddVddstatic eVP

When IC is idle but not powered off, e.g. SRAM28

Leakage power

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Scaling down

Scaling down (Contd.)

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Thermodynamics: Gas

Quantum dynamics: Individual molecules

Uniform (central limit theorem)

High variation and likely defectivel

Scaling: Not that simple (Contd.)

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Tunneling effect

33time

f

T

f1=L/T

f2=L/(T/2)=2f1

34time

P

T

P1=x f∙ 3

35time

P

T

P1=x f∙ 3+Pstatic

36time

P

T

P1=x f∙ 3+Pstatic

P2=23x f∙ 3+Pstatic

Why is static power important?

ITRS, 2009

Pentium II (Klamath) and III (Coppermine)

7.5M Transistors28M Transistors 38

Core 2 Duo (Conroe)

64KB L1 cache, 4MB L2 cache, 291M Transistors

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Core 1

Core 2

Solutions to “never-enough” challenge

234M transistors

24M go to L2 cache

8 SPE, each 20.9M transistors (167M transistors)

Each has 4 64KB SRAM (12M transistors)

SRAM takes 122M transistors (>50%)40

Multiple power/clock domains

TI OMAP 2 architecture, ISSCC 2005

Multimedia phone: NTT DoCoMo 3G FOMA 902i to be released with OMAP2420

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Given workload L and deadline Tsingle processor

• One processor can run at any frequency (voltage)– f= b V∙

• The processor can be complete off when work is done (zero power when idle) Given Pstatic

– Given energy overhead of shutting down the processor (Eoverhead)

• To minimize energy consumption, at which frequency should the processor run?

43time

P

T

P1=x f∙ 3+Pstatic

P2=23x f∙ 3+Pstatic

Why is there overhead to power off circuit?

Clock generator

• Resonant circuit + amplifier

• Resonant circuit (Oscillator)– Crystal oscillator (>2x109/yr)

• ~10KHz to ~10MHz• Quartz, ceramics (low cost, low accuracy), surface acoustic

wave (SAW) quartz crystal (expensive, accurate)• Real-time clocks

– 32.768KHz (215), 4.194304MHz (222)• Application-specific

– 4.9152MHz (4 x 1.2288MHz, CDMA baseband frequency)……

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ResA

• LC/RLC circuit• Ring oscillator

– Application other than oscillator?• Voltage-controlled oscillator (VCO)

– Varicap: variable capacitance diode (tuning diode)– Phase-locked loop for high-speed clock (next slide)– Frequency scaling of IC for energy saving

Oscillator (Contd.)

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• High-speed clock from a master oscillator• Digital PLL

• Clock generation, recovery, synchronization– Digital computing, RF communication

Phase-locked loop (PLL)

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Phase-frequency detector

Master oscillator VCO

Frequency divider (N)

voltage

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Given workload L and deadline Tsingle processor

• The processor can run at any frequency (voltage)– f= b V∙

• The processor can be complete off when work is done (zero power when idle)

• To minimize energy consumption, at which frequency should the processor run?– f ≥ L/T (in order to meet the deadline)– E=P t= a C V∙ ∙ ∙ 2 f t= a C V∙ ∙ ∙ ∙ 2 L∙– f=????

Threshold voltage

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Vdd scales slow & Vth scales slower• Vth is limited by the

thermal voltage

• Vdd needs to stay considerable higher than Vth to curb leakage current

• End up with destroying the scaling rules– low channel mobility

Plummer and Griffin, 2001 (Data from ITRS/NTRS)

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Check the assumptions (Contd.)

• The workload can be divided without overhead: L = L1+L2+…+LM (L ≥ Li≥0)

• Communication cost between processors!!!

Quadrotor vs. Helicopter

Quadrotor vs. Helicopter

De Bothezat Quadrotor, 1923.

Quadrotor vs. Helicopter

A.R. Drone, 2010

Wire power consumption

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Wire power consumption

Inter-processor communication