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ESE370:
Circuit-Level
Modeling, Design, and Optimization
for Digital Systems
Day 18: October 13, 2014
Energy and Power Basics
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Penn ESE370 Fall2014 -- DeHon
Previously
• Where capacitance arises
• What drives delay
– How to optimize
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Penn ESE370 Fall2014 -- DeHon
Today
Power Sources
• Static
• Capacitive Switching
• Short Circuit (Day 19)
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Penn ESE370 Fall2014 -- DeHon
Power
• P=I×V
• Tricky part:
– Understanding I
– (pairing with correct V)
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Penn ESE370 Fall2014 -- DeHon
Understanding Currents
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Penn ESE370 Fall2014 -- DeHon
Preclass 1
• Vin vs. Ipwr,gnd?
– 0V
– 140mV
– 400mV
– 500mV
– 600mV
– 840mV
– 1V
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Penn ESE370 Fall2013 -- DeHon
Operating Modes
• Steady-State: What modes are the
transistors in?
– Vin=Vdd
– Vin=Gnd
• What current flows
in steady state?
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Penn ESE370 Fall2014 -- DeHon
Operating Modes
• Steady-State: Vin=Vdd
– PMOS subthreshold
– NMOS resistive
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Penn ESE370 Fall2014 -- DeHon
Static Power
• Where does Istatic come from?
– Subthreshold leakage
– (possibly) Gate-Drain leakage
Vin~=Vdd
VGS VT 
 VDS
IDSp
W 
 IS e
 L 


nkT
/
q


1  e





kT
/
q



1  VDS 


2 
W 
VDS
IDS  nCOX  VGS VT VDS 

 L 
2 
Penn ESE370 Fall2014 -- DeHon
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Data Dependent?
• How does value of input impact Istatic?
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Penn ESE370 Fall2014 -- DeHon
Data Dependent?
• How does value of input impact Istatic?
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Penn ESE370 Fall2014 -- DeHon
Static Power
• P=I×V
• What V should we use?
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Penn ESE370 Fall2014 -- DeHon
Power: During Switching
•
•
•
•
•
P=IV
Input switch 10
What’s V?
What’s I?
Where does I go?
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Penn ESE370 Fall2014 -- DeHon
Power: During Switching
• P=IV
• Input switch 10
• Where does I go?
– Vin=Gnd
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Penn ESE370 Fall2014 -- DeHon
Power: During Switching
• P=IV
• Input switch 10
• Where does I go?
– Vin=Gnd
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Penn ESE370 Fall2014 -- DeHon
Power: During Switching
• P=IV
• Where does I go?
– Vin=Vdd/2
• And Vdd>Vthn+|Vthp|
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Penn ESE370 Fall2014 -- DeHon
Power: During Switching
• P=IV
• Input switch 10
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Penn ESE370 Fall2014 -- DeHon
Power: During Switching
•
•
•
•
•
P=IV
Input switch 01
What’s V?
What’s I?
Where does current flow?
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Penn ESE370 Fall2014 -- DeHon
Power: During Switching
• P=IV
• Input switch 01
• Where does I go?
– Vin=Vdd
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Penn ESE370 Fall2014 -- DeHon
Power: During Switching
• P=IV
• Input switch 01
• Where does I go?
– Vin=Vdd
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Penn ESE370 Fall2014 -- DeHon
Switching Currents
• Charge (discharge) output
• If both transistor on:
– Current path from Vdd to Gnd
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Penn ESE370 Fall2014 -- DeHon
Observe
• I changes over time
• Data dependent
• At least two components
– Istatic – no switch
– Iswitch – when switch
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Penn ESE370 Fall2014 -- DeHon
Switching
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Penn ESE370 Fall2014 -- DeHon
Switching Currents
• Iswitch(t) = Isc(t) + Idyn(t)
• I(t) = Istatic(t)+Iswitch(t)
Idyn
Istatic
Isc
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Penn ESE370 Fall2014 -- 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
 nCOX  VGS VT VDS 

 L 
2 
Penn ESE370 Fall2014 -- DeHon
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Look at Energy
[focus on Idyn(t)]
E
 P(t)dt
P  E dyn /t switch
E
 I(t)V
dt
dd
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Penn ESE370 Fall2014 -- DeHon
Energy to Switch
E
 I(t)V
E  Vdd
dt
dd
 I(t)dt
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Penn ESE370 Fall2014 -- DeHon
Integrating
• Do we know what this is?
 I(t)dt
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Penn ESE370 Fall2014 -- DeHon
Capacitor Charge
• Do we know what this is?
Q
 I(t)dt
• What is Q?
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Penn ESE370 Fall2014 -- DeHon
Capacitor Charge
Q  CV 
 I(t)dt
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Penn ESE370 Fall2014 -- DeHon
Capacitor Charging Energy
E  Vdd  I(t)dt
Q  CV   I(t)dt
2
E  CVdd
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Penn ESE370 Fall2014 -- DeHon
Switching Power
• Every time output switches 01 pay:
– E = CV2
• Pdyn = (# 01 trans) × CV2 / time
• # 01 trans = ½ # of transitions
• Pdyn = (# trans) × ½CV2 / time
Penn ESE370 Fall2014 -- DeHon
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Short Circuit Current
(time permitting)
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Penn ESE370 Fall2014 -- DeHon
Short Circuit Power
• Between VTN and Vdd-VTP
– Both N and P devices conducting
• Roughly:
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Penn ESE370 Fall2013 -- DeHon
Peak Current
• Ipeak around Vdd/2
– If |VTN|=|VTP| and sized equal rise/fall
IDS

VDSAT 
  satCOX W VGS  VT 


2 

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Penn ESE370 Fall2013 -- DeHon
Short-Circuit Energy
E  Vdd
 I(t)dt 
1
 I(t)dt  I peak  tsc  2 
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Penn ESE370 Fall2013 -- 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 Fall2013 -- 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 Fall2013 -- 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
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Penn ESE370 Fall2013 -- DeHon
Ideas
• Three components of power
– Static
– Short-circuit
– Charging
• Ptot = Pstatic + Psc + Pdyn
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Penn ESE370 Fall2014 -- DeHon
Admin
• HW6 due Thursday
– 4def dynamic switching energy
• Tuesday 11am Talk by Herman Schmit
Subversive Innovation
• Normal lecture Wednesday and Friday
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Penn ESE370 Fall2014 -- DeHon