Transcript ppt

ESE370:
Circuit-Level
Modeling, Design, and Optimization
for Digital Systems
Day 16: September 15, 2010
Energy and Power
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Penn ESE370 Fall2010 -- DeHon
Previously
• Where capacitance arises
• What drives delay
– How to optimize
• Power as a limiting constraint
– Energy, Power Density
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Today
Power Sources and Design Options
• Static
• Capacitive Switching
• Short Circuit
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Power
• P=I×V
• Where should we look at I?
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Power
• P=IV
• What’s V?
• What is I?
– Steady-State (input fixed)?
– When input switches
• 01
• 10
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Observe
• I changes over time
• Data dependent
• At least two components
– Istatic – no switch
– Iswitch – when switch
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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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Data Dependent?
• How does value of input impact Istatic?
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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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Switching
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Switching
• Where does current go during switching?
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Switching Currents
• Charge (discharge) output
• If both transistor on:
– Current path from Vdd to Gnd
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Switching Currents
• Iswitch(t) = Isc(t) + Idyn(t)
• I(t) = Istatic(t)+Iswitch(t)
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Charging
• Idyn(t) – why changing?
– Ids = f(Vds,Vgs)
– andVgs, Vds changing
IDS
2 
W 
VDS
 nCOX  VGS VT VDS 

 L 
2 
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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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Energy to Switch
E
 I(t)V
E  Vdd
dt
dd
 I(t)dt
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Integrating
• Do we know what this is?
 I(t)dt
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Capacitor Charge
• Do we know what this is?
Q
 I(t)dt
• What is Q?
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Capacitor Charge
Q  CV 
 I(t)dt
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Capacitor Charging Energy
E  Vdd  I(t)dt
Q  CV   I(t)dt
2
E  CVdd
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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 Fall2010 -- DeHon
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Reduce Dynamic Power?
• Pdyn = (# trans) × ½CV2 / time
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Charging Power
• Pdyn = (# trans) × ½CV2 / time
• Often like to think about switching
frequency
• Ideally, switch per clock cycle
– Frequency f = 1/clock-period
• Pdyn = (#trans/clock) ½CV2 f
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Penn ESE370 Fall2010 -- DeHon
Charging Power
• Pdyn = (#trans/clock) ½CV2 f
• Let a = activity factor
a = average #tran/clock
• Pdyn = a½CV2 f
• Get back to talking about a….
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Short Circuit Power
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Short Circuit Power
• Between VTN and Vdd-VTP
– Both N and P devices conducting
• Roughly:
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Peak Current
• Ipeak around Vdd/2
– If |VTN|=|VTP| and sized equal rise/fall
IDS
2 
W 
VDS
 nCOX  VGS VT VDS 

 L 
2 
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Penn ESE370 Fall2010 -- DeHon
Short-Circuit Energy
E  Vdd
 I(t)dt 
1
 I(t)dt  I peak  tsc  2 
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Penn ESE370 Fall2010 -- DeHon
Short-Circuit Energy
E  Vdd
 I(t)dt 
1
 I(t)dt  I peak  tsc  2 
1 
E  Vdd  I peak  t sc   
2 
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Penn ESE370 Fall2010 -- DeHon
Short Circuit Energy
• Looks like a capacitance
– Q=I×t
– Q=CV

1 
E  Vdd  I peak  t sc   
2 

E  Vdd  Qsc

E  CscV dd
2
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Penn ESE370 Fall2010 -- DeHon
Short Circuit Energy and
Power
• Every time switch
– Also dissipate short-circuit energy: E = CV2
– Different C = Csc
– Ccs “fake” capacitance (for accounting)
• Largely same dependence as charging
Psc = aCscV2 f
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Penn ESE370 Fall2010 -- DeHon
Reduce Short-Circuit Power?
• Psc = aCscV2 f

1 
E  Vdd  I peak  t sc   
2 


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Charging Power
• Pswitch = Pdyn + Psc = a(½Cload+Csc)V2f
• What values can a take on?
o a>1?
o a<1?
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Glitches
• Inputs Transition from 0 1 0  1 1 1
– What does output look like?
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Class ended here
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Data Dependent Activity
• Consider an 8b counter
– What is activity, a, for:
• Low bit?
• High bit?
• Assuming random inputs (no glitching)
– Activity at output of nand4?
– Activity at output of xor4?
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Total Power
• Ptot = Pdyn + Psc + Pdyn
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Slow Down
• What happens to power contributions as
reduce clock frequency?
• What suggest about Vth?
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Reduce V
• What happens as reduce V?
– Delay?
– Energy?
• Static
• Switching
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Reduce V (no physical scale)
 tgd=Q/I=(CV)/I
 V S×V
 Id=(COX/2)(W/L)(Vgs-VTH)2
 Id  S2×Id
 tgd  tgd /S
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Penn ESE370 Fall 2010 -- DeHon
Observe
• Ignoring leakage
Et  Const
2
E V
2
t V
1
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Energy vs. Power?
• What do we care about?
– Battery operated devices?
– Desktops?
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Admin
• Project
– Baseline done
– SPICE Power Measurement 5.5.4
– List of ideas to accelerate done?
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Ideas
• Three components of power
– Static
– Short-circuit
– Charging
• aCV2f dependence for short-circuit,
charging
• Energy-Delay tradeoff: Et2
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