ee141 © digital integrated circuits 2nd arithmetic circuits 1 low power design in cmos [adapted...
TRANSCRIPT
![Page 1: EE141 © Digital Integrated Circuits 2nd Arithmetic Circuits 1 Low Power Design in CMOS [Adapted from Rabaey’s Digital Integrated Circuits, ©2002, J. Rabaey](https://reader035.vdocuments.site/reader035/viewer/2022062221/56649f505503460f94c7342e/html5/thumbnails/1.jpg)
EE1411
© Digital Integrated Circuits2ndArithmetic Circuits
Low Power DesignLow Power Design in CMOS in CMOS
[Adapted from Rabaey’s Digital Integrated Circuits, ©2002, J. Rabaey et al.]
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EE1412
© Digital Integrated Circuits2ndArithmetic Circuits
Why Power MattersWhy Power Matters
Packaging costs Power supply rail design Chip and system cooling costs Noise immunity and system reliability Battery life (in portable systems) Environmental concerns
Office equipment accounted for 5% of total US commercial energy usage in 1993
Energy Star compliant systems
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EE1413
© Digital Integrated Circuits2ndArithmetic Circuits
Why worry about power? -- Why worry about power? -- ChipChip Power DensityPower Density
40048008
80808085
8086
286386
486Pentium®
P6
1
10
100
1000
10000
1970 1980 1990 2000 2010
Year
Po
wer
Den
sity
(W
/cm
2)
Hot Plate
NuclearReactor
RocketNozzle
Sun’sSurface
…chips might become hot…
Source: Borkar, De Intel
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EE1414
© Digital Integrated Circuits2ndArithmetic Circuits
Why worry about power?Why worry about power?-- -- Heat DissipationHeat Dissipation
DEC 21164
source : arpa-esto
microprocessor power dissipation
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EE1415
© Digital Integrated Circuits2ndArithmetic Circuits
Why worry about power ? -- Why worry about power ? -- Battery Size/WeightBattery Size/Weight
Expected battery lifetime increase over the next 5 years: 30 to 40%
From Rabaey, 1995From Rabaey, 1995
65 70 75 80 85 90 95
0
10
20
30
40
50
Rechargable Lithium
Year
Nickel-Cadmium
Ni-Metal Hydride
Nom
inal
Cap
acity
(W
-hr/
lb)
Battery(40+ lbs)
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EE1416
© Digital Integrated Circuits2ndArithmetic Circuits
Why worry about power? -- Why worry about power? -- Standby PowerStandby Power
Drain leakage will increase as VT decreases to maintain noise margins and meet frequency demands, leading to excessive battery draining standby power consumption.
8KW
1.7KW
400W
88W 12W
0%
10%
20%
30%
40%
50%
2000 2002 2004 2006 2008
Sta
nd
by
Po
wer
Source: Borkar, De Intel
Year 2002 2005 2008 2011 2014
Power supply Vdd (V) 1.5 1.2 0.9 0.7 0.6
Threshold VT (V) 0.4 0.4 0.35 0.3 0.25
…and phones leaky!
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EE1417
© Digital Integrated Circuits2ndArithmetic Circuits
Problem IllustrationProblem Illustration
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EE1418
© Digital Integrated Circuits2ndArithmetic Circuits
Power and Energy Figures of MeritPower and Energy Figures of Merit Power consumption in Watts
determines battery life in hours Peak power
determines power ground wiring designs sets packaging limits impacts signal noise margin and reliability analysis
Energy efficiency in Joules rate at which power is consumed over time
Energy = power * delay Joules = Watts * seconds lower energy number means less power to perform a
computation at the same frequency
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EE1419
© Digital Integrated Circuits2ndArithmetic Circuits
Power versus EnergyPower versus Energy
Watts
time
Power is height of curve
Watts
time
Approach 1
Approach 2
Approach 2
Approach 1
Energy is area under curve
Lower power design could simply be slower
Two approaches require the same energy
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EE14110
© Digital Integrated Circuits2ndArithmetic Circuits
PDP and EDPPDP and EDP Power-delay product (PDP) = Pav * tp = (CLVDD
2)/2 PDP is the average energy consumed per switching event
(Watts * sec = Joule) lower power design could simply be a slower design
allows one to understand tradeoffs better
0
5
10
15
0.5 1 1.5 2 2.5
Vdd (V)
Energ
y-Dela
y (no
rmali
zed)
energy-delay
energy
delay
Energy-delay product (EDP) = PDP * tp = Pav * tp2
EDP is the average energy consumed multiplied by the computation time required
takes into account that one can trade increased delay for lower energy/operation (e.g., via supply voltage scaling that increases delay, but decreases energy consumption)
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EE14112
© Digital Integrated Circuits2ndArithmetic Circuits
Understanding TradeoffsUnderstanding Tradeoffs
Ene
rgy
1/Delay
a
b
c
d
Lower EDP
Which design is the “best” (fastest, coolest, both) ?
bett
er
better
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EE14113
© Digital Integrated Circuits2ndArithmetic Circuits
CMOS Energy & Power EquationsCMOS Energy & Power Equations
E = CL VDD2 P01 + tsc VDD Ipeak P01 + VDD Ileakage
P = CL VDD2 f01 + tscVDD Ipeak f01 + VDD Ileakage
Dynamic power
Short-circuit power
Leakage power
f01 = P01 * fclock
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EE14114
© Digital Integrated Circuits2ndArithmetic Circuits
Dynamic Power ConsumptionDynamic Power Consumption
Energy/transition = CL * VDD2 * P01
Pdyn = Energy/transition * f = CL * VDD2 * P01 * f
Pdyn = CEFF * VDD2 * f where CEFF = P01 CL
Not a function of transistor sizes!Data dependent - a function of switching activity!
Vin Vout
CL
Vdd
f01
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EE14116
© Digital Integrated Circuits2ndArithmetic Circuits
Lowering Dynamic PowerLowering Dynamic Power
Pdyn = CL VDD2 P01 f
Capacitance:Function of fan-out, wire length, transistor sizes
Supply Voltage:Has been dropping with successive generations
Clock frequency:Increasing…
Activity factor:How often, on average, do wires switch?
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EE14117
© Digital Integrated Circuits2ndArithmetic Circuits
Short Circuit Power ConsumptionShort Circuit Power Consumption
Finite slope of the input signal causes a direct current path between VDD and GND for a short period of time during switching when both the NMOS and PMOS transistors are conducting.
Vin Vout
CL
Isc
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EE14118
© Digital Integrated Circuits2ndArithmetic Circuits
Short Circuit Currents DeterminatesShort Circuit Currents Determinates
Duration and slope of the input signal, tsc
Ipeak determined by the saturation current of the P and N transistors which
depend on their sizes, process technology, temperature, etc. strong function of the ratio between input and output slopes
– a function of CL
Esc = tsc VDD Ipeak P01
Psc = tsc VDD Ipeak f01
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EE14119
© Digital Integrated Circuits2ndArithmetic Circuits
Impact of CImpact of CLL on P on Pscsc
Vin Vout
CL
Isc 0
Vin Vout
CL
Isc Imax
Large capacitive load
Output fall time significantly larger than input rise time.
Small capacitive load
Output fall time substantially smaller than the input rise
time.
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EE14120
© Digital Integrated Circuits2ndArithmetic Circuits
IIpeakpeak as a Function of C as a Function of CLL
-0.5
0
0.5
1
1.5
2
2.5
0 2 4 6
I pea
k (A
)
time (sec)
x 10-10
x 10-4
CL = 20 fF
CL = 100 fF
CL = 500 fF
500 psec input slope
Short circuit dissipation is minimized by matching the rise/fall times of the input and output signals - slope engineering.
When load capacitance is small, Ipeak is large.
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EE14121
© Digital Integrated Circuits2ndArithmetic Circuits
PPscsc as a Function of Rise/Fall Times as a Function of Rise/Fall Times
0
1
2
3
4
5
6
7
8
0 2 4
P n
orm
aliz
ed
tsin/tsout
VDD= 3.3 V
VDD = 2.5 V
VDD = 1.5V
normalized wrt zero input rise-time dissipation
When load capacitance is small (tsin/tsout > 2 for VDD > 2V) the power is dominated by Psc
If VDD < VTn + |VTp| then Psc is eliminated since both devices are never on at the same time.
W/Lp = 1.125 m/0.25 mW/Ln = 0.375 m/0.25 mCL = 30 fF
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EE14122
© Digital Integrated Circuits2ndArithmetic Circuits
Leakage (Static) Power ConsumptionLeakage (Static) Power Consumption
Sub-threshold current is the dominant factor.
All increase exponentially with temperature!
VDD Ileakage
Vout
Drain junction leakage
Sub-threshold currentGate leakage
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EE14123
© Digital Integrated Circuits2ndArithmetic Circuits
Leakage as a Function of VLeakage as a Function of VTT
0 0.2 0.4 0.6 0.8 1
VGS (V)
ID (A
)
VT=0.4V
VT=0.1V
10-2
10-12
10-7
Continued scaling of supply voltage and the subsequent scaling of threshold voltage will make subthreshold conduction a dominate component of power dissipation.
An 90mV/decade VT roll-off - so each 255mV increase in VT gives 3 orders of magnitude reduction in leakage (but adversely affects performance)
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EE14124
© Digital Integrated Circuits2ndArithmetic Circuits
TSMC Processes Leakage and VTSMC Processes Leakage and VTT
80
0.25 V
13,000
920/400
0.08 m
24 Å
1.2 V
CL013 HS
52
0.29 V
1,800
860/370
0.11 m
29 Å
1.5 V
CL015 HS
42 Å42 Å42 Å42 ÅTox (effective)
43142230FET Perf. (GHz)
0.40 V0.73 V0.63 V0.42 VVTn
3000.151.6020Ioff (leakage) (A/m)
780/360320/130500/180600/260IDSat (n/p) (A/m)
0.13 m 0.18 m 0.16 m 0.16 m Lgate
2 V1.8 V1.8 V1.8 VVdd
CL018 HS
CL018 ULP
CL018 LP
CL018 G
From MPR, 2000
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EE14125
© Digital Integrated Circuits2ndArithmetic Circuits
Exponential Increase in Leakage CurrentsExponential Increase in Leakage Currents
1
10
100
1000
10000
30 40 50 60 70 80 90 100 110
0.25
0.18
0.13
0.1
Temp(C)
I leak
age(n
A/
m)
From De,1999
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EE14126
© Digital Integrated Circuits2ndArithmetic Circuits
Review: Energy & Power EquationsReview: Energy & Power Equations
E = CL VDD2 P01 + tsc VDD Ipeak P01 + VDD
Ileakage
P = CL VDD2 f01 + tscVDD Ipeak f01 + VDD Ileakage
Dynamic power(~90% today and
decreasing relatively)
Short-circuit power(~8% today and
decreasing absolutely)
Leakage power(~2% today and
increasing)
f01 = P01 * fclock
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EE14127
© Digital Integrated Circuits2ndArithmetic Circuits
Power and Energy Design SpacePower and Energy Design Space
Constant Throughput/Latency
Variable Throughput/Latency
Energy Design TimeNon-active Modules
Run Time
Active
Logic Design
Reduced Vdd
Sizing
Multi-Vdd
Clock Gating
DFS, DVS
(Dynamic Freq,
Voltage Scaling)
Leakage + Multi-VT
Sleep Transistors
Multi-Vdd
Variable VT
+ Variable VT
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EE14128
© Digital Integrated Circuits2ndArithmetic Circuits
Dynamic Power as a Function of Device SizeDynamic Power as a Function of Device Size Device sizing affects dynamic energy consumption
gain is largest for networks with large overall effective fan-outs (F = CL/Cg,1)
The optimal gate sizing factor (f) for dynamic energy is smaller than the one for performance, especially for large F’s e.g., for F=20,
fopt(energy) = 3.53 while fopt(performance) = 4.47
If energy is a concern avoid oversizing beyond the optimal
1 2 3 4 5 6 70
0.5
1
1.5
f
norm
aliz
ed e
nerg
y
F=1
F=2
F=5
F=10
F=20
From Nikolic, UCB
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EE14129
© Digital Integrated Circuits2ndArithmetic Circuits
Dynamic Power Consumption is Data DependentDynamic Power Consumption is Data Dependent
A B Out
0 0 1
0 1 0
1 0 0
1 1 0
2-input NOR Gate
With input signal probabilities PA=1 = 1/2 PB=1 = 1/2
Static transition probability P01 = Pout=0 x Pout=1
= P0 x (1-P0)
Switching activity, P01, has two components
A static component – function of the logic topology A dynamic component – function of the timing behavior
(glitching)
NOR static transition probability = 3/4 x 1/4 = 3/16
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EE14130
© Digital Integrated Circuits2ndArithmetic Circuits
NOR Gate Transition ProbabilitiesNOR Gate Transition Probabilities
CL
A
B
BA
P01 = P0 x P1 = (1-(1-PA)(1-PB)) (1-PA)(1-PB)
PA
PB
0
1 0 1
Switching activity is a strong function of the input signal statistics PA and PB are the probabilities that inputs A and B are one
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EE14132
© Digital Integrated Circuits2ndArithmetic Circuits
Transition Probabilities for Some Basic GatesTransition Probabilities for Some Basic Gates
P01 = Pout=0 x Pout=1
NOR (1 - (1 - PA)(1 - PB)) x (1 - PA)(1 - PB)
OR (1 - PA)(1 - PB) x (1 - (1 - PA)(1 - PB))
NAND PAPB x (1 - PAPB)
AND (1 - PAPB) x PAPB
XOR (1 - (PA + PB- 2PAPB)) x (PA + PB- 2PAPB)
B
AZ
X0.5
0.5
For Z: P01 = P0 x P1 = (1-PXPB) PXPB
For X: P01 = P0 x P1 = (1-PA) PA
= 0.5 x 0.5 = 0.25
= (1 – (0.5 x 0.5)) x (0.5 x 0.5) = 3/16
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EE14134
© Digital Integrated Circuits2ndArithmetic Circuits
Inter-signal CorrelationsInter-signal Correlations
B
A
Z
X
P(Z=1) = P(B=1) & P(A=1 | B=1)
0.5
0.5
(1-0.5)(1-0.5)x(1-(1-0.5)(1-0.5)) = 3/16
(1- 3/16 x 0.5) x (3/16 x 0.5) = 0.085Reconvergent
Determining switching activity is complicated by the fact that signals exhibit correlation in space and time reconvergent fan-out
Have to use conditional probabilities
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EE14135
© Digital Integrated Circuits2ndArithmetic Circuits
Logic RestructuringLogic Restructuring
Chain implementation has a lower overall switching activity than the tree implementation for random inputs
Ignores glitching effects
Logic restructuring: changing the topology of a logic network to reduce transitions
A
BC
D F
AB
CD Z
FW
X
Y0.5
0.5
(1-0.25)*0.25 = 3/16
0.50.5
0.5
0.5
0.5
0.5
7/64
15/256
3/16
3/16
15/256
AND: P01 = P0 x P1 = (1 - PAPB) x PAPB
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EE14137
© Digital Integrated Circuits2ndArithmetic Circuits
Input OrderingInput Ordering
Beneficial to postpone the introduction of signals with a high transition rate (signals with signal probability close to 0.5)
A
BC
X
F
0.5
0.20.1
B
CA
X
F
0.2
0.10.5
(1-0.5x0.2)x(0.5x0.2)=0.09 (1-0.2x0.1)x(0.2x0.1)=0.0196
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EE14139
© Digital Integrated Circuits2ndArithmetic Circuits
Glitching in Static CMOS NetworksGlitching in Static CMOS Networks
ABC
X
Z
101 000
Unit Delay
AB
X
ZC
Gates have a nonzero propagation delay resulting in spurious transitions or glitches (dynamic hazards) glitch: node exhibits multiple transitions in a single
cycle before settling to the correct logic value
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EE14140
© Digital Integrated Circuits2ndArithmetic Circuits
Glitching in an RCAGlitching in an RCA
S0S1S2S14S15
Cin
0
1
2
3
0 2 4 6 8 10 12
Time (ps)
S O
utp
ut
Vo
ltag
e (
V)
Cin
S0
S1
S2
S3
S4
S5S10
S15
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EE14141
© Digital Integrated Circuits2ndArithmetic Circuits
How to Cope with Glitching?How to Cope with Glitching?
F1
F2
F3
F1
F3
F2
0
0
0
0
1
2
0
0
0
01
1
Equalize Lengths of Timing Paths Through Design
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EE14142
© Digital Integrated Circuits2ndArithmetic Circuits
Power Analysis in SPICEPower Analysis in SPICE
RC
k iDDCircuitUnder Test
+
-
VDD
iDD
Pav
Equivalent Circuit for Measuring Power in SPICE
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EE14143
© Digital Integrated Circuits2ndArithmetic Circuits
Reducing Reducing VVdddd
P x td = Et = CL * Vdd2
E(Vdd=2)=
(CL) * (2)2
(CL) * (5)2E(Vdd=5)
Strong function of voltage (V2 dependence).
Relatively independent of logic function and style.
E(Vdd=2) 0.16 E(Vdd =5)
0.03
0.05
0.07
0.1
0.15
0.20
0.30
0.50
0.70
1.00
1.5
1 2 5
51 stage ring oscillator
8-bit adder
Vdd (volts)
quadratic dependence
NO
RM
AL
IZE
D P
OW
ER
-DE
LA
Y P
RO
DU
CT
Power Delay Product Improves with lowering VDD.
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EE14144
© Digital Integrated Circuits2ndArithmetic Circuits
Lower VLower Vdddd Increases DelayIncreases Delay
CL * Vdd
I=Td
Td(Vdd=5)
Td(Vdd=2)=
(2) * (5 - 0.7)2
(5) * (2 - 0.7)2
4
I ~ (Vdd - Vt)2
Relatively independent of logic function and style.
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
6.50
7.00
7.50
2.00 4.00 6.00Vdd (volts)
NO
RM
AL
IZE
D D
EL
AY
adder (SPICE)
microcoded DSP chip
multiplier
adder
ring oscillator
clock generator2.0m technology
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EE14145
© Digital Integrated Circuits2ndArithmetic Circuits
Lowering the ThresholdLowering the Threshold
DESIGN FOR PLeakage == PDynamic
Vt = 0.2Vt = 0
ID
VGS
Reduces the Speed Loss, But Increases Leakage
Vdd
Delay
2Vt
Interesting Design Approach:
Reduced threshold
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EE14146
© Digital Integrated Circuits2ndArithmetic Circuits
Transistor Sizing for Power MinimizationTransistor Sizing for Power Minimization
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.
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EE14147
© Digital Integrated Circuits2ndArithmetic Circuits
Balanced Delay Paths to Reduce GlitchingBalanced Delay Paths to Reduce Glitching
So equalize the lengths of timing paths through logic
F1
F2
F3
0
0
0
0
1
2
F1
F2
F3
0
0
0
0
1
1
Glitching is due to a mismatch in the path lengths in the logic network; if all input signals of a gate change simultaneously, no glitching occurs
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EE14148
© Digital Integrated Circuits2ndArithmetic Circuits
Power and Energy Design SpacePower and Energy Design Space
Constant Throughput/Latency
Variable Throughput/Latency
Energy Design TimeNon-active Modules
Run Time
Active
Logic Design
Reduced Vdd
Sizing
Multi-Vdd
Clock Gating
DFS, DVS
(Dynamic Freq,
Voltage Scaling)
Leakage + Multi-VT
Sleep Transistors
Multi-Vdd
Variable VT
+ Variable VT
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EE14149
© Digital Integrated Circuits2ndArithmetic Circuits
Dynamic Power as a Function of VDynamic Power as a Function of VDDDD
Decreasing the VDD
decreases dynamic energy consumption (quadratically)
But, increases gate delay (decreases performance)
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
VDD (V) t p
( no
r ma
l ize
d)
Determine the critical path(s) at design time and use high VDD for the transistors on those paths for speed. Use a lower VDD on the other gates, especially those that drive large capacitances (as this yields the largest energy benefits).
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EE14150
© Digital Integrated Circuits2ndArithmetic Circuits
Multiple VMultiple VDDDD Considerations Considerations
How many VDD? – Two is becoming common Many chips already have two supplies (one for core and one for
I/O) When combining multiple supplies, level converters are required
whenever a module at the lower supply drives a gate at the higher supply (step-up) If a gate supplied with VDDL drives a gate at VDDH, the PMOS never
turns off– The cross-coupled PMOS transistors
do the level conversion– The NMOS transistor operate on a
reduced supply Level converters are not needed
for a step-down change in voltage Overhead of level converters can be mitigated by doing
conversions at register boundaries and embedding the level conversion inside the flipflop (see Figure 11.47)
VDDH
Vin
VoutVDDL
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EE14151
© Digital Integrated Circuits2ndArithmetic Circuits
Dual-Supply Inside a Logic BlockDual-Supply Inside a Logic Block Minimum energy consumption is achieved if all logic paths are
critical (have the same delay) Clustered voltage-scaling
Each path starts with VDDH and switches to VDDL (gray logic gates) when delay slack is available
Level conversion is done in the flipflops at the end of the paths
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EE14152
© Digital Integrated Circuits2ndArithmetic Circuits
Power and Energy Design SpacePower and Energy Design Space
Constant Throughput/Latency
Variable Throughput/Latency
Energy Design Time Non-active Modules Run Time
Active
Logic Design
Reduced Vdd
Sizing
Multi-Vdd
Clock Gating
DFS, DVS
(Dynamic Freq, Voltage
Scaling)
Leakage + Multi-VT
Sleep Transistors
Multi-Vdd
Variable VT
+ Variable VT
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EE14153
© Digital Integrated Circuits2ndArithmetic Circuits
Stack EffectStack Effect Leakage is a function of the circuit topology and the value of the
inputs
VT = VT0 + (|-2F + VSB| - |-2F|)where VT0 is the threshold voltage at VSB = 0; VSB is the source- bulk
(substrate) voltage; is the body-effect coefficient
A B
B
A
Out
VX
A B VX ISUB
0 0 VT ln(1+n) VGS=VBS= -VX
0 1 0 VGS=VBS=0
1 0 VDD-VT VGS=VBS=0
1 1 0 VSG=VSB=0 Leakage is least when A = B = 0 Leakage reduction due to stacked
transistors is called the stack effect
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EE14154
© Digital Integrated Circuits2ndArithmetic Circuits
Short Channel Factors and Stack EffectShort Channel Factors and Stack Effect
In short-channel devices, the subthreshold leakage current depends on VGS,VBS and VDS. The VT of a short-channel device decreases with increasing VDS due to DIBL (drain-induced barrier loading). Typical values for DIBL are 20 to 150mV change in VT per voltage
change in VDS so the stack effect is even more significant for short-channel devices.
VX reduces the drain-source voltage of the top nfet, increasing its VT and lowering its leakage
For our 0.25 micron technology, VX settles to ~100mV in steady state so VBS = -100mV and VDS = VDD -100mV which is 20 times smaller than the leakage of a device with VBS = 0mV and VDS = VDD
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EE14155
© Digital Integrated Circuits2ndArithmetic Circuits
Leakage as a Function of Design Time VLeakage as a Function of Design Time VTT
Reducing the VT increases the sub-threshold leakage current (exponentially) 90mV reduction in VT
increases leakage by an order of magnitude
But, reducing VT decreases gate delay (increases performance)
0 0.2 0.4 0.6 0.8 1
VGS (V)ID
(A)
VT=0.4V
VT=0.1V
Determine the critical path(s) at design time and use low VT devices on the transistors on those paths for speed. Use a high VT on the other logic for leakage control. A careful assignment of VT’s can reduce the leakage by as much
as 80%
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EE14156
© Digital Integrated Circuits2ndArithmetic Circuits
Dual-Thresholds Inside a Logic BlockDual-Thresholds Inside a Logic Block
Minimum energy consumption is achieved if all logic paths are critical (have the same delay)
Use lower threshold on timing-critical paths Assignment can be done on a per gate or transistor basis;
no clustering of the logic is needed No level converters are needed
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EE14157
© Digital Integrated Circuits2ndArithmetic Circuits
Variable VVariable VTT (ABB) at Run Time (ABB) at Run Time
VT = VT0 + (|-2F + VSB| - |-2F|)
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
-2.5 -2 -1.5 -1 -0.5 0
VSB (V)
VT (
V)
A negative bias on VSB causes VT to increase
Adjusting the substrate bias at run time is called adaptive body-biasing (ABB)
Requires a dual well fab process
For an n-channel device, the substrate is normally tied to ground (VSB = 0)
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EE14158
© Digital Integrated Circuits2ndArithmetic Circuits
SummarySummary
• Power Dissipation is becoming Prime DesignConstraint
• Low Power Design requires Optimization at all Levels
• Sources of Power Dissipation are well characterized
• Low Power Design requires operation at lowest
possible voltage and clock speed