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ESE370:
Circuit-Level
Modeling, Design, and Optimization
for Digital Systems
Day 17: October 19, 2011
Energy and Power Basics
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Penn ESE370 Fall2011 -- DeHon
Previously
• Where capacitance arises
• What drives delay
– How to optimize
• Power as a limiting constraint
– Energy, Power Density
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Penn ESE370 Fall2011 -- DeHon
Today
Power Sources
• Static
• Capacitive Switching
• Short Circuit (Day 18)
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Penn ESE370 Fall2011 -- DeHon
Power
• P=I×V
• Where should we look at I?
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Penn ESE370 Fall2011 -- DeHon
Power
• P=IV
• What’s V?
• What is I?
– Steady-State (input fixed)?
– When input switches
• 01
• 10
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Penn ESE370 Fall2011 -- DeHon
Observe
• I changes over time
• Data dependent
• At least two components
– Istatic – no switch
– Iswitch – when switch
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Penn ESE370 Fall2011 -- DeHon
Static Power
• Where does Istatic come from?
– Subthreshold leakage
– Gate-Drain leakage
IDS
W 
 IS e
 L 
VGS VT 


nkT
/
q


 VDS 

kT / q 
1  e  1 VDS 


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Penn ESE370 Fall2011 -- DeHon
Data Dependent?
• How does value of input impact Istatic?
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Penn ESE370 Fall2011 -- DeHon
Data Dependent?
• How does value of input impact Istatic?
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Penn ESE370 Fall2011 -- DeHon
Billion Transistor Leakage
•
•
•
•
4 Billion transistors
Say 1 Billion gates
Each with one W=2 transistor leaking
How much leakage current?
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Penn ESE370 Fall2011 -- DeHon
ITRS 2009 45nm
High Performance
Isd,leak
100nA/mm
Isd,sat
1200 mA/mm
Cg,total
1fF/mm
Vth
285mV
Ileak0 = 0.045mm × Isd,leak
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Penn ESE370 Fall2010 -- DeHon
Leakage Power
• 4 Billion Transistor chip doing nothing
• Total Leakage?
• Leakage Power?
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Penn ESE370 Fall2011 -- DeHon
Reduce Leakage?
• P=VI
IDS
W 
 IS e
 L 
VGS VT 


 nkT / q 
 VDS 

kT / q 
1  e  1 VDS 


• How do we reduce leakage?
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Penn ESE370 Fall2011 -- DeHon
ITRS 2009 45nm
Low Power
Isd,leak
Isd,sat
High
Performance
100nA/mm
1200 mA/mm
Cg,total
Vth
1fF/mm
285mV
0.91fF/mm
585mV
50pA/mm
560mA/mm
Ileak0 = 0.045mm × Isd,leak
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Penn ESE370 Fall2010 -- DeHon
Low Power Process
• 4 Billion Transistor chip doing nothing
• Total Leakage?
• Leakage Power?
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Penn ESE370 Fall2011 -- DeHon
Switching
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Penn ESE370 Fall2011 -- DeHon
Switching
• Where does current go during switching?
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Penn ESE370 Fall2011 -- DeHon
Switching Currents
• Charge (discharge) output
• If both transistor on:
– Current path from Vdd to Gnd
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Penn ESE370 Fall2011 -- DeHon
Switching Currents
• Iswitch(t) = Isc(t) + Idyn(t)
• I(t) = Istatic(t)+Iswitch(t)
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Penn ESE370 Fall2011 -- DeHon
Charging
• Idyn(t) – why changing?
– Ids = f(Vds,Vgs)
– and Vgs, Vds changing
IDS
IDS

VDSAT 
  satCOX W VGS  VT 


2 
2 
W 
VDS
 mnCOX  VGS VT VDS 

 L 
2 
Penn ESE370 Fall2011 -- DeHon
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Look at Energy
E
 P(t)dt
P  E dyn /t switch
E
 I(t)V
dt
dd
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Penn ESE370 Fall2011 -- DeHon
Energy to Switch
E
 I(t)V
E  Vdd
dt
dd
 I(t)dt
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Penn ESE370 Fall2011 -- DeHon
Integrating
• Do we know what this is?
 I(t)dt
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Penn ESE370 Fall2011 -- DeHon
Capacitor Charge
• Do we know what this is?
Q
 I(t)dt
• What is Q?
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Penn ESE370 Fall2011 -- DeHon
Capacitor Charge
Q  CV 
 I(t)dt
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Penn ESE370 Fall2011 -- DeHon
Capacitor Charging Energy
E  Vdd  I(t)dt
Q  CV   I(t)dt
2
E  CVdd
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Penn ESE370 Fall2011 -- DeHon
Switching Power
• Every time switch 01 pay:
– E = CV2
• Pdyn = (# 01 trans) × CV2 / time
• # 01 trans = ½ # of transitions
• Pdyn = (# trans) × ½CV2 / time
Penn ESE370 Fall2011 -- DeHon
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Charging Power
• Pdyn = (# trans) × ½CV2 / time
• Often like to think about switching
frequency
• Useful to consider per clock cycle
– Frequency f = 1/clock-period
• Pdyn = (#trans/clock) ½CV2 f
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Penn ESE370 Fall2011 -- DeHon
Charging Power
• Pdyn = (#trans/clock) ½CV2 f
• Let a = activity factor
a = average #tran/clock
• Pdyn = a½CV2 f
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Penn ESE370 Fall2011 -- DeHon
ITRS 2009 45nm
Low Power
Isd,leak
Isd,sat
High
Performance
100nA/mm
1200 mA/mm
Cg,total
Vth
1fF/mm
285mV
0.91fF/mm
585mV
50pA/mm
560mA/mm
C0 = 0.045mm × Cg,total
C0 = 0.045 × 10-15 F
Penn ESE370 Fall2010 -- DeHon
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Switching Power
• 4 Billion Transistors
– Organized into 1 billion gates (e.g. nand2)
•
•
•
•
Cload = 22C0
a=0.2
f=1GHz
Power?
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Penn ESE370 Fall2011 -- DeHon
Switching Power
• V=1V
• Cload=22C0 ≈ 1 fF = 10-15F
• P=a(0.5×10-15)(Ngate)f
• a=0.2
• P=10-16(Ngate)f
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Penn ESE370 Fall2010 -- DeHon
Dynamic vs. Static Power
• At what speed (f) does leakage power
dominate switching power?
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Penn ESE370 Fall2011 -- DeHon
Compare
•
•
•
•
•
WN = 2  Ileak = 9×10-9 A
P=a(0.5×10-15) f + 9×10-9 W
a=0.2
P=10-16×f + 9×10-9 W
For what freqs does leakage power
dominate switching power?
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Penn ESE370 Fall2010 -- DeHon
Charging Power
• Pswitch = a(½C)V2f
• What values can a take on?
o a>1?
o a<1?
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Penn ESE370 Fall2011 -- DeHon
Data Dependent Activity
• Consider an 8b counter
– What is activity, a, for:
• Low bit?
• High bit?
• Average across all 8 output bits?
• Assuming random inputs (no glitching)
– Activity at output of nand4?
– Activity at output of xor4?
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Penn ESE370 Fall2011 -- DeHon
Glitches
• Inputs Transition from 0 1 0  1 1 1
– What does output look like?
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Penn ESE370 Fall2011 -- DeHon
Admin
• HW5 due Friday
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Penn ESE370 Fall2011 -- DeHon
Ideas
• Three components of power
– Static
– Short-circuit
– Charging
• Ptot = Pstatic + Psc + Pdyn
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Penn ESE370 Fall2011 -- DeHon