basics of low power circuit and logic design · pdf filebasics of low power circuit and logic...

Basics of Low Power Circuit and Logic Design

Anantha Chandrakasan

Massachusetts Institute of Technology

Basics of Low Power Circuit and Logic Design © Anantha Chandrakasan 1997 2

High Performance Processors

75 80 85 90 95Year

0

10

20

30

Pow

er (W

att)

Microprocessor Power (source ISSCC)


Portable Devices

(40+ lbs)Battery

• Radio transceiver

• Modem • Voice I/O • Pen Input• Text/Graphics Processing• Text/Graphics display• Video decompression• Full-motion video display

Portable FunctionsRequired

How to get 8 hours of operation ???


Battery Trends

Year

Nom

inal

Cap

acity

(Wat

t-ho

urs /

lb)

Nickel-Cadmium

Ni-Metal Hydride

(from Jon Eager, Gates Inc. , S. Watanabe, Sony Inc.)

65 70 75 80 85 90 95 0

10

20

30

40

50 Rechargable Lithium


Where Does Power Go in CMOS?

Short-circuit or direct-path currents

Leakage currents

- Charging and discharging parasitic capacitors

- Sub-threshold conduction- Reverse bias diode leakage

Dynamic or switching currents

- Direct path between supply rails during switching

Static currents


Dynamic Power of a CMOS GateVdd

Vout

isupply

CL

E0->1 = CLVdd2

PMOSNETWORK

NMOS

A1

AN

NETWORK

E0 1→ P t( )dt0

T∫ Vdd isupply t( )dt

0

T∫ Vdd CLdVout

0

Vdd

∫ CL Vdd• 2= = = =

Ecap Pcap t( )dt0

T∫ Vouticap t( )dt

0

T∫ CLVoutdVout

0

Vdd∫

12---CL Vdd• 2= = = =


Modification for Circuits with Reduced Swing

CL

Vdd

Vdd

Vdd -Vt

E0 1→ CL Vdd Vdd Vt–( )••=

Can exploit reduced swing to lower power(e.g., reduced bit-line swing in memory)


Physical Capacitance of an Inverter

0.8 1.0 1.2 1.4 1.6 1.80.0

10.0

20.0

30.0

40.0

50.0

Cgate

Cjunction

Cjunction + CgateC

apac

itanc

e, fF

2.0

VDD

Important to account for capacitive non-linearitiesin power estimation


Node Capacitance is a Function of Voltage

0.8 0.9 1.0 1.1 1.2 1.3 1.450

60

70

80

90

100

110 Sw

itche

d C

apac

itanc

e, fF

C2MOS

TSPCR

1.5

LCLR

VDD, V


Node Transition Activity and Power

Consider switching a CMOS gate for N clock cycles

EN CL Vdd• 2 n N( )•=

n(N): the number of 0->1 transition in N clock cycles

EN : the energy consumed for N clock cycles

Pavg N ∞→lim

ENN-------- fclk•= n N( )

N------------N ∞→

lim⎝ ⎠⎛ ⎞ C•

LVdd• 2 fclk•=

α0 1→n N( )

N------------N ∞→

lim=

Pavg = α0 1→ C•L

Vdd• 2 fclk•


Factors Affecting Transition Activity, α0->1

“Dynamic” or timing dependent component

→ Type of Logic Function (NOR vs. XOR)“Static” component (does not account for timing)

→ Circuit Topology

→ Type of Logic Style (Static vs. Dynamic)

→ Signal Statistics→ Inter-signal Correlations

→ Signal Statistics and Correlations


Type of Logic Function: NOR vs. XOR

A B Out0 0 10 1 01 0 01 1 0

Truth Table of a 2 input NOR gate

Example: Static 2 Input NOR Gate

Assume:p(A=1) = 1/2p(B=1) = 1/2

p(Out=1) = 1/4p(0→1)

= 3/4 × 1/4 = 3/16

Then:

= p(Out=0).p(Out=1)

α0->1 = 3/16


Type of Logic Function: NOR vs. XOR

A B Out0 0 00 1 11 0 11 1 0

Truth Table of a 2 input XOR gate

Example: Static 2 Input XOR Gate

Assume:p(A=1) = 1/2p(B=1) = 1/2

p(Out=1) = 1/2p(0→1)

= 1/2 × 1/2 = 1/4

Then:

= p(Out=0).p(Out=1)

α0->1 = 1/4


Type of Logic Style: Static vs. DynamicVdd

CL

CLK

A B

CL

A

B

A B

Vdd

CLK

STATIC NOR DYNAMIC NOR

α0->1 = 3/16 α0 1→N0

2N------- 34---= =

Power is only dissipated when Out=0!


Another Logic Style: Dynamic DCVSL

Vdd

I

I

Vdd

IN

INB

OUTB OUT

Guaranteed transition for every operation!

α0->1 = 1


Influence of Signal Statistics on α0->1

00.2

0.40.6

0.8

1

PA

0

0.2

0.4

0.6

0.8

1

PB

0

.1

2

00.2

0.40.6

0.8

1

PA

0

0.2

0.4

0.6

0.8

1

PB

0

.1

2

B

B

A

A CLpb

0

1

0

1pa

p0->1

α0->1 is a strong function of signal statistics

p1 = (1-pa) (1-pb)

p0->1 = p0 p1 = (1-(1-pa) (1-pb)) (1-pa) (1-pb)


Inter-signal Correlations

(a) Logic circuit withoutreconvergent fanout

(b) Logic circuit withreconvergent fanout

A

BZ

CA

Z

C

B

p0->1 = (1- pa pb) pa pb = 3/16p0->1 = 0

pZ = p(C=1|B=1) • p(B=1)

Need to use conditional probabilities to modelinter-signal correlations!CAD tools required for such analysis


0 5 100.0

2.0

4.0

Time, ns

Sum

Out

put V

olta

ge, V

olts

Cin

S15

S10

6

5

4

3

2S1

Add0 Add1 Add2 Add14 Add15

S0 S1 S2 S14 S15

Cin

α0->1 can be > 1 due to glitching!

“Dynamic” or Glitching Activity in CMOS


Glitch Reduction Using Balanced Paths

A7

F

A6A5A4A3A2A1

A0

A0A1

A2A3

A4A5

A6A7

F

Ripple

Lookahead


Comparison of Adder Topologies

from [Callaway92]

16 bit 32 bit 64 bit

Ripple Carry 3.09 0.81 0.27Carry Lookahead 10.0 3.54 1.76Carry Bypass 5.45 2.39 0.99Carry Select 4.44 2.08 1.00Conditional Sum 3.82 1.23 0.42

Power-Delay-Product-1

Logic Transition Histogram

(VLSI Signal Processing, V)


Glitching at the Datapath Level

Tree vs. Chain

A B

C

D+ +

+

A B C D+

++

+

(A + B) + C + D(A + B) + (C + D)

Can be reduced by reducing the logic depth and balancing

ChainTreeInputs

4

8

1.45

2.5

1

1

Normalized # of Transitions

signal paths


Short-circuit Component of Power

Vin Vout

CL

Vdd

I VD

D (m

A)

0.15

0.10

0.05

Vin (V)5.04.03.02.01.00.0


Short-Circuit Current vs. Load Capacitance

from [Veendrick84] (IEEE Journal of Solid-State Circuits, August 1984)


Minimizing Short-circuit Power

Keep the input and output rise/fall times the same (< 10% of Total Consumption)

If Vdd < Vtn + |Vtp| then short-circuit power can be eliminated!

0.0 0.5 1.0 1.5 2.00.0

0.1

0.2

0.3

0.4

0.5

Vdd = 5V

Vdd = 3V

W/LP = 7.2µm/1.2µmW/LN = 2.4µm/1.2µm

Device Sizes:

∆E /

E(t R

in=

0)

tRin/tRout

from [Veendrick84] (IEEE Journal of Solid-State Circuits, August 1984)


Reverse Biased Diode Leakage

Np+ p+

Reverse Leakage Current

+

-Vdd

GATE

IDL = JS × A

JS = 1-5pA/µm2 for a 1.2µm CMOS technology

Js double with every 9oC increase in temperature


Subthreshold Leakage Component

Leakage control is critical for low-voltage operation

VDS=1VID

+-VGS

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.010-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

I D, A

VGS, V

VT = 0.4 VVT = 0.1V


Static Power

Vin=5V

Vout

CL

Vdd

Istat

Pstatic = p(In=1).Vdd . Istat

• Not a function of switching frequency


Ultra Low Power System Design

Technology

Circuit/Logic

Architecture

Algorithm

System

Threshold Reduction,

Transistor Sizing, Logic optimization,

Concurrency, Instruction set selection,

Complexity, Concurrency, Locality,

Design partitioning, Power Down

Lower Supply Voltage and Switched Capacitance

Activity Driven Power Down,

Advanced packaging

Signal correlations, Data Representation

Regularity, Data representation

low-swing logic, adiabatic switching


Signal Processing Attributes

0 5 10 15 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Bit Number

Tran

sitio

n P

roba

bilit

ySign-extension

Spe

ech

Dat

a

-4000

-2000

0

2000

4000

Time

Throughput constrained computing

Knowledge of signal statistics

“water all year”

- Optimize power supply voltages

Time-varying computational requirements- Adaptive signal processing techniques

- 30ms refresh rate requirement for video


Energy Efficiency Metric: Fixed Throughput

For this mode (most DSP applications), minimizing energy/sample is both Energy and Power Efficient

Example: Video Compression

P = (Σ (NiCiVdd2)) fsample

fsample is fixed

Energy/Sample


Energy Efficiency Metric: Max Throughput

ETR Energy/operationThroughput-------------------------------------------≡ Power

Throughput2-----------------------------------=

Process Queue

A lower ETR (higher efficiency) indicates lower energyfor constant throughput, or higher throughput forconstant energy

Other metrics such as E x D, see [Horowitz94],

(1994 Symposium on Low-power Electronics)

from [Burd95](HICSS 95)


Supply Voltage Scaling

Lowering Vdd reduces energy but increases delays

CL • VddI

=Td

Td(Vdd=5)

Td(Vdd=1.5)=

(1.5) • (5 - 0.7)2

(5) • (1.5 - 0.7)2

≈ 8

I ~ (Vdd - Vt)2

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

2.0 4.0 6.0 Vdd (volts)

NO

RM

AL

IZE

D D

EL

AY

adder (SPICE)

microcoded DSP chip

multiplier

adder

ring oscillator

clock generator2.0µm technology


Vin

Vdd

Vout

CL 0.9Vdd0.1Vdd

VDSATVout

time

Vin

Technology Based Voltage Scaling

Exploit velocity saturated sub-micron devices to lower

τ1∼ const.

Power Supply Voltage: Vdd(V)

Fall

Tim

e: τ

τ2 ∝ Vdd -1

τ = τ1 + τ2

voltage without significant loss in device speed

from [Kakumu90]

Technology based “Optimal” Vdd: 2.43V for 0.3µm CMOS

(IEEE Tran. on Electron Devices)


Supply Voltage Scaling Using VT Reduction

0.05 0.15 0.25 0.35 0.450.0

0.25

0.5

0.75

1.0

1.25

1.5V D

D,V

VT, V

tpd=840pS

tpd=645pStpd=420pS

Threshold voltage reduction enables voltage scaling without performance loss


also see [Burr94]

Optimizing Continuous Mode Circuits

Optimum VDD/VT point trades-off switching andleakage power and is a strong function of activity

0.05 0.15 0.25 0.35 0.450.0

0.25

0.50

0.75

1.00

1.25En

ergy

(pJ)

VT (V)

VDD=1.4V

VDD=1V

VDD=0.34V

VDD=0.55V

VDD=1.02V

VDD=0.67V

tpd=840pS

tpd=420pS


Limits of Supply Voltage Scaling

0.6

0.5

0.4

0.3

0.20.15

0.1

0.2 0.3 0.4 0.5 0.6 0.70.20

Input Voltage (V) Vin

Vout 0.7

0.6

0.5

0.4

0.3

0.2

0.1

Ou

tpu

t Vo

ltag

e (V

)

0.7 V = Vs

Experiment

Calculation

CMOS Inverter Transfer Curves

Vsmin ≥ 2-4 kT / q

from [Swanson72](IEEE JSSC, April 1972)


Burst Mode or “Event Driven”Computation

Trace1

Trace2

Trace3

Trace Length (sec) 5182.48 26859.9 995.16Toff (sec) 5047.47 26427.4 960.82Ton (sec) 135.01 432.5 34.34Toff/(Toff+Ton) 0.9739 0.9839 0.9655

BLOCKED(waiting for

hardware eventsand client requests)

RUNNING(doing actualcomputation)

Tblocked

Trunning

“On”“Off”

For an X-server application, processor spends most of thetime in the blocked or off state.

from [Srivastava95](IEEE Trans. on VLSI Systems)


Techniques for Burst Mode Computation

Low VT

SLEEP High VT

SLEEP High VT

Multiple VT Technology

(Disable high VT devices during idle periods)

High VT transistor sizing issuesPreserving state requires extra transistors

e.g., [Sakata93] (Symposium on VLSI Circuits),[Mutoh93] (International ASIC Conference)


Latch Design in MTCMOS

SLEEP High VT

SLEEP High VT

CLK

JSSC, August 1995From S. Mutoh, et. al.

SLEEP High VT

SLEEP High VT


Vin Vout

VDD

Substrate Bias ControlledVariable VT Devices -

(Increase VT during idle periods)

-+ VN < 0

standby

ON

-+ VP > 0ON

standby

Techniques for Burst Mode Computation

Needs large body factors - large well capacitancesTriple well process needed

from [Seta95] (ISSCC 1995)


SOI with Active Substrate (SOIAS)

n+ n+p np+ p+

p+ n+i-poly

SiO2

SiO2

SiO2

Silicon Substrate

tfox tt

sibox

Loverlap

Backgate Control Enables Dynamically Varying Threshold Voltages

from [Yang95]


NMOS Device Characteristics

-0.2 0 0.2 0.4 0.6 0.8 1

Vgf (V)

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

Id (

mA

/um

)

0

0.01

0.02

0.03

Id (

mA

/um

)

~ 4 Dec

1.8x

VDS=1.0 Vtbox=100 nmtfox=9 nmtsi=4.5 nmLeff=0.44 um

Vt=0.448 V (Vgb=0.0 V)Vt=0.184 V (Vgb=3 V)


Ring Oscillator Characteristics

Varied VTP onlyVTN = 0.512V

Varied VTN onlyVTP= - 0.2V

Processor speed is adjustable on demand

0.0 0.1 0.2 0.3 0.4 0.5 0.66

8

10

12

0.7Rin

g O

scill

ator

Fre

quen

cy (M

Hz)

Backgate Controlled Variable |VT| (V)


Architectural Model & Activity Parameters for SOIAS

ADD ON ADD ONADD OFF

fga = Module Activity Factor

CLK ADD

CLK BACKGATE

LOW VT HIGH VT LOW VT

bga = Backgate Switching Activity

Add15

00.2

0.40.6

0.8

1

PA

0

0.2

0.4

0.6

0.8

1

PB

0

.2

4

00.2

0.40.6

0.8

1

PA

0

0.2

0.4

0.6

0.8

1

PB

0

.2

4 1αx

CLK ADD CLK BACKGATE

Add1

01pa

0 pb

Circuit Node Transition Activity

ab

x


Generic Architecture Model for All Technologies

TechnologyLeakage Control

Mechanism(hence affecting bga)

Multiple Threshold Technology Switching the High VT devices ON/OFF

Substrate Bias Control Controlling the Substrate Voltages

Silicon On Insulator Active Substrate Switching the Backgate Voltage

Hierarchy of Profilers and Statistical ModelsRequired for “Virtual Prototyping”


Energy Estimation Models for SOI and SOIAS

ESOI = α fga CfgVdd2

ESOIAS = α fga CfgVdd2

fga = Module Activity Factorbga = Backgate Switching Activityα = Node Transition Activity Factor

+ fga Ileak_lowVT Vdd Tcycle + (1-fga)Ileak_highVT Vdd Tcycle + bgaCbgVbg

2

+ Ileak_lowVT Vdd Tcycle


Architectural Profiling to Determine fga and bga

Table 1. SPEC benchmark espresso

Number fga bgaTotal Instructions 900158847 - -

Additions 543616709 0.6039 0.1954 Shifts 57000715 0.0633 0.0541

Multiplications 172883 0.0002 0.0002Table 2. SPEC benchmark Li

Number fga bgaTotal Instructions 1737729538 - -Total Additions 661236960 0.6023 0.2233

Total Shifts 52224367 0.0087 0.0086Multiplications 7088 0.0000 0.0000

Table 3. Data Encryption (IDEA)

Number fga bgaTotal Instructions 2125 - -

Additions 1250 0.5882 0.2635 Shifts 186 0.0875 0.0753

Multiplications 3 0.0014 0.0014


SOI vs. SOIAS Technology Evaluation

−4−3.5

−3−2.5

−2−1.5

−1−0.5 −4

−3.5

−3

−2.5

−2

−1.5

−1

−2

−1

0

1

o*

.

o

.

*

Adder

log(

back

-gat

e ac

tivity

fact

or)

*

*

Shifter

Mult.0.0

-0.5

-1.0

0.5

log(front-gate activity factor)

log

(ES

OIA

S/E

SO

I)


Transistor Sizing for Low-Power

Minimum sized devices are usually optimal for low-power

Small W/L’s

Large W/L’s

Higher Voltage

Lower Voltage

Lower Capacitance

Higher Capacitance

Larger sized devices are useful only when interconnect dominated


Transistor Sizing for Fixed Throughput

α = 0

adder

0.5

0.7

1.0

1.52

345

7

10

1 3 10

α = 0.5

α = 1

α = 1.5

α = 2

W/L

NO

RM

AL

IZE

D E

NE

RG

Y

CP = Cwiring + CDF

Cg = W/L CMIN I ∝ W/L CMIN

CMIN = Minimum sized gate (W/L=1) W /L after sizing

HIGH PERFORMANCE

W/L >> CP / (K CMIN)

LOW POWER

W/L = 2 CP / (K CMIN) (if CP ≥ K CMIN)

W/L = 1 ELSE

α = CP / (K CMIN)

from [Chandrakasan92](IEEE JSSC, 1992)


Capacitance Breakdown

MODULE LEVEL

DATAPATH LEVEL

MODULE GATE DIFFUSION INTERCONNECT

ADDER (Conventional Static) 30% 45% 25%

ADDER (Carry Select) 37% 31% 32%

TSPC COUNTER 32% 26% 36%

LOG SHIFTER (8 bit shift by 4) 15% 42% 43%

COMPARATOR 33% 38% 29%

MODULE GATE DIFFUSION INTERCONNECT

ADDER CHAIN ( 7 adders ) 38% 38% 24%

WAVE DIGITAL FILTER 31% 29% 40%

ADDRESS GENERATION (STD CELL) 56% 24% 20%

VIDEO SYNC GENERATOR (STD CELL)

45% 25% 30%


Choice of Logic Style

A

B

A

B

B

CIN CIN

B

VDD VDDPRE

CO CO

A

CIN

ACIN

CIN

B B

CIN

VDD VDDPRE

SUMSUM BB

CONVENTIONAL CMOS Adder

CPL AdderDCVSL Adder

GND

AA BB

P

CIN GEN

CIN PROP

GEN

VDDGND

A

B

A B

VDD

GEN

CINSUM

CIN

CIN

P

PB

P

B

A

PA

B

COUT

GND

CIN

P GEN

CIN P

GEN

VDD

COUT

OPTIMIZED static Adder

A

A

B

B

C C

GND

VDD

A

A

B

B

AB

AB

AB

AB

Sum

B

C

AB

A

VDD

A

B

A

B

VDD

CoutA B C

AA

B B

CC

Sum Sum

ACC

B

CoutCout

B

AA

A A


Choice of Logic Style

Power-delay product improves as voltage decreases.

The “best” logic style minimizes power-delay for a given delay constraint.

3

5

7

10

1520

30

50

70

100

150200

10 30 100

8-bit adders in 2.0µm

POW

ER

-DE

LAY

PR

OD

UC

T (p

J)

DELAY (ns)

Decreasing Vdd

CPL - LOW Vt

Optimized

Standard Cell

CSA

DCVSL

ConventionalStatic

Static


Reducing the Energy/Operation at a Fixed Vdd

oo 6/2 3/9

7/29/2

4/2

< >

o

Vdd (=1.5V)

Ceff = 5pF

ϕ

ϕ

Vin

Vout

HeavilyLoadedBit-line

0 20 40 60 80 1000

0.5

1.0

1.5

v(line)

v(out)v(out)v(ϕ)

t (ns)

Volts

SignalAmplification

M1 M2

M3M4

M5

V(out)

Reduced Signal Swing Example: FIFO Memory

Power Reduction Over Rail-to-Rail Swing = Vdd/(Vdd-Vt)


R

Ctr

E = (RC/tr)CV2 (for tr >> RC)

Applying slow input slopes reduces E below CV2

Useful for driving large capacitors (Buffers)Power reduction > 4 for pad drivers (1 MHz) ISI

ADIABATIC CHARGING

Reducing the Energy/Operation at a Fixed Vdd


Example: Stepwise Adiabatic Driver

CLV1 1

2

N

V2

VN

0

Estep Q Vavg• CLVdd

N----------Vdd2N----------⋅•

12--- CL Vdd

2••

N2---------------------------------= = =

Etotal N

12--- CL Vdd

2••

N2---------------------------------•Econventional

N----------------------------------------= =

RC charging steps

from [Svensson94]

Vi = (i/N) V(IEEE Symposium on Low Power Design, 1994)


Activity Driven Logic Level Power Down

MSBREG

REG

CLK

COMPARATOR

forbits

0->N-2

MSBA[N-1]B[N-1]

COMPARATOR

forbits 0->N-2

REGforbits

0->N-2

GATED_CLK

A > B

A[N-2:0]

B[N-2:0]

A > B

REG

CLK

MODIFIED REGISTER

COMBINATIONAL

LOGIC

CONDITIONALLYSWITCHED

BLOCK

50% reduction possible for random inputs

from [Alidina94](1994 International Workshop on Low-power Design)


Activity Reduction in Shift Registers

fCLK

Data In Data Out

fCLK/2

Data In Data Out

N Length Shift Register

N/2 Length Shift Register

Pserial = NCreg V2 fclk

Pparallel= 2 x (N/2 Creg V2 fclk/2) + Poverhead


Shift Register Power for Various Lengths

0 8 16 24 32 Degree of Parallelism

0.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

Pow

er D

issi

patio

n

32-bit

64-bit

128-bit

256-bit


Summary

• Power dissipation is a prime design constraint for portable systems

• Low Power design requires optimization at all Levels

• Sources of power dissipation have been analyzed

• Technology, circuit, and logic design techniques havebeen described

References[Alidina94] M. Alidina, J. Monteiro, S. Devadas, A. Ghosh, and M. Papaefthymiou, “Precomputation-Based Sequential Logic

Optimization for Low Power,” 1994 International Workshop on Low-power Design, pp. 57-62, April 1994.[Burd95] T. Burd, R. Brodersen, “Energy Efficient CMOS Microprocessor Design,” Proceedings of the 28th Annual HICSS Con-

ference, Vol. I, pp. 288-297 Jan. 1995. [Burr94] J. Burr, J. Shott, “A 200mV Self-Testing Encoder/Decoder using Stanford Ultra-low Power CMOS,” IEEE ISSCC, pp.

84-85, 1994. [Callaway92] T. Callaway and E. Swartzlander, Jr., “Optimizing Arithmetic Elements for Signal Processing,” VLSI Signal Pro-

cessing V, pp. 91-100, IEEE Special Publications, 1992.[Chandrakasan92] A. P. Chandrakasan, S. Sheng, and R. W. Brodersen, “Low-power Digital CMOS Design,” IEEE Journal of

Solid State Circuits, pp. 473-484, April 1992.[Horowitz94] M. Horowitz, T. Indermaur, R. Gonzalez, “Low-Power Digital Design,” Proceedings of the Symposium on Low

Power Electronics, 1994.[Kakumu90] M. Kakumu and M Kinugawa, “Power-Supply Voltage Impact on Circuit Performance for Half and Lower Submi-

crometer CMOS LSI,” IEEE Transactions on Electron Devices, Vol 37, No. 8, pp. 1902-1908, August 1990.[Mutoh93] S. Mutoh, T. Douseki. Y. Matsuya, T. Aoki, and J. Yamada, “1-V High-speed Digital Circuit Technology with 0.5µm

Multi Threshold CMOS,” IEEE Int. ASIC Conf., pp. 186-189, 1993.[Sakata93] T. Sakata, M. Horiguchi, K. Itoh, “Subthreshold-Current Reduction Circuits for Multi-GIGABIT DRAM’s,” 1993

Symposium on VLSI Circuits, pp. 45-46.[Seta95] K. Seta, H. Hara, T. Kuroda, M. Kakumu, T. Sakurai, “50% Active-Power Saving Without Speed Degradation Using

Standby Power Reduction (SPR) Circuit,” IEEE ISSCC 95, pp. 318-319.[Srivastava95] M. Srivastava, A.P. Chandrakasan, R. Brodersen, “Predictive System Shutdown and Other Architectural Tech-

niques for Energy Efficient Programmable Computation”, to appear in the IEEE Trans. on VLSI Systems, March 1996.[Svensson94] L.“J.” Svensson and J.G. Koller, “Driving a capacitive load without dissipating fCV2,” IEEE Symposium on Low

Power Design, pp. 100–101, 1994. [Yang95] I. Yang, C. Vieri, A. P. Chandrakasan, D. Antoniadis, "Back Gated CMOS on SOIAS for Dynamic Threshold Control,"

1995 IEEE International Electron Devices Meeting, December 1995.[Veendrick84] H.J.M. Veendrick, ‘‘Short-Circuit Dissipation of Static CMOS Circuitry and Its Impact on the Design of Buffer

Circuits,’’ IEEE Journal of Solid-State Circuits, Vol. SC-19, pp. 468-473, August 1984.

basics of low power circuit and logic design · pdf filebasics of low power circuit and logic...

Documents