ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems

Lec 15: October 7, 2019 Energy and Power Basics

Penn ESE 370 Fall 2019 - Khanna

Previously

!  Where capacitance arises "  Device materials

!  What drives delay "  Equivalent drive resistance and load capacitance

!  Optimize delay "  τ-estimate "  Transistor sizing "  Fanin/fanout "  Drive in stages

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Today

!  Power Sources "  Static power "  Switching power

"  Dynamic switching power "  Short circuit power

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Power

!  P = I×V

!  Tricky part: "  Understanding I "  (pairing with correct V)

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Inverter Current Simplification

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!  What is Ipwr,gnd? "  0V "  140mV "  400mV "  500mV "  600mV "  860mV "  1V

"  From preclass – see next two slides

Preclass (1/2)

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Preclass (2/2)

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Inverter Current Simplification

!  What is Ipwr,gnd? "  0V "  140mV "  400mV "  500mV "  600mV "  860mV "  1V

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Understanding Currents

Static Power

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Operating Modes

!  Steady-State: What modes are the transistors in? "  Vin=Vdd

"  Vin=Gnd

!  What current flows in steady state?

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Operating Modes

!  Steady-State: Vin=Vdd

"  PMOS: subthreshold "  NMOS: resistive

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Operating Modes

!  Steady-State: Vin=Vdd

"  PMOS: subthreshold "  NMOS: resistive

12

€

IDSp = −IS#WL

$

% &

'

( ) e

−VGS −VTnkT / q

$

% &

'

( )

1− eVDSkT / q$

% &

'

( )

$

% & &

'

( ) ) 1− λVDS( )

IDSn = µnCOXWL

!

"#

$

%& VGS −VT( )VDS −

VDS2

2(

)*

+

,-

Penn ESE 370 Fall 2019 - Khanna

Operating Modes

!  Steady-State: Vin=Vdd

"  PMOS: subthreshold "  NMOS: resistive

13

€

IDSp = −IS#WL

$

% &

'

( ) e

−VGS −VTnkT / q

$

% &

'

( )

1− eVDSkT / q$

% &

'

( )

$

% & &

'

( ) ) 1− λVDS( )

IDSn = µnCOXWL

!

"#

$

%& VGS −VT( )VDS −

VDS2

2(

)*

+

,-

Which current determines Istatic ?

Penn ESE 370 Fall 2019 - Khanna

Operating Modes

!  Steady-State: Vin=Vdd

"  PMOS: subthreshold "  NMOS: resistive

14

€

IDSp = −IS#WL

$

% &

'

( ) e

−VGS −VTnkT / q

$

% &

'

( )

1− eVDSkT / q$

% &

'

( )

$

% & &

'

( ) ) 1− λVDS( )

IDSn = µnCOXWL

!

"#

$

%& VGS −VT( )VDS −

VDS2

2(

)*

+

,-

Which current determines Istatic ?

Penn ESE 370 Fall 2019 - Khanna

Static Power

!  P = I×V !  What V should we use?

"  Where is the static current flowing?

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Data Dependent?

!  How does the binary value of the input impact Istatic?

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Data Dependent?

!  How does the binary value of input impact Istatic?

17

€

IDS = IS"WL

#

$ %

&

' ( e

VGS −VTnkT / q

#

$ %

&

' (

1− e−VDSkT / q#

$ %

&

' (

#

$ %

&

' ( 1+ λVDS( )

Penn ESE 370 Fall 2018 - Khanna

Out

1

2

1

2

1

2

1

2

A

B

Data Dependent Leakage Current

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ACM Great Lakes Symposium on VLSI Stresa, I. (n.d.). Analysis of data dependence of leakage current in CMOS cryptographic hardware. In GLSVLSI ’07 proceedings of the 2007 ACM Great Lakes Symposium

on VLSI : Stresa - Lago Maggiore, Italy, March 11-13, 2007 /. New York, N.Y. :: Association for Computing Machinery. https://doi.org/10.1145/1228784.1228808

Understanding Currents

Dynamic Switching Currents

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Power: During Switching

!  P = IV !  Input switch: 1#0 !  Where does I go?

"  Vin=Gnd

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Power: During Switching

!  P = IV !  Input switch: 1#0 !  Where does I go?

"  Vin=Gnd

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Power: During Switching

!  P = IV !  Input switch: 1#0 !  Where does I go?

"  Vin=Gnd

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Subtheshold Leakage

Idyn (Saturation/Linear)

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Power: During Switching

!  P = IV !  Input switch 0#1 !  Where does I go?

"  Vin=Vdd

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Power: During Switching

!  P = IV !  Input switch 0#1 !  Where does I go?

"  Vin=Vdd

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Power: During Switching

!  P = IV !  Input switch 0#1 !  Where does I go?

"  Vin=Vdd

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Subtheshold Leakage

Idyn (Saturation/Linear)

Penn ESE 370 Fall 2019 - Khanna

Switching Currents

!  Dynamic current flow:

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Understanding Currents

Short Circuit Currents

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Power: During Switching

!  P = IV !  Where does I go?

"  Vin=Vdd/2 "  And Vdd>Vthn+|Vthp|

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Power: During Switching

!  P = IV !  Where does I go?

"  Vin=Vdd/2 "  And Vdd>Vthn+|Vthp|

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Vou

t

Vin

CMOS Inverter DC Transfer

Linear/Saturation

Penn ESE 370 Fall 2019 - Khanna

Linear/Saturation

Switching Currents

!  Dynamic current flow:

!  If both transistor on: "  Current path from Vdd

to Gnd "  Short circuit current

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Currents Summary

!  Current (I) changes over time !  At least two components

"  Istatic – no switching "  Iswitch – when switching

"  Idyn and Isc

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Currents Summary

!  Current (I) changes over time !  At least two components

"  Istatic – no switching "  Iswitch – when switching

"  Idyn and Isc

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VRAMP

CLK

φ

ramp_enable

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Switching

Dynamic Power

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Switching Currents

!  Itotal(t) = Istatic(t)+Iswitch(t)

!  Iswitch(t) = Isc(t) + Idyn(t)

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Isc

Istatic

Idyn

Penn ESE 370 Fall 2019 - Khanna

Charging

!  Idyn(t) – why is it changing? "  Ids = f(Vds,Vgs) "  and Vgs, Vds changing

35

€

IDS = µnCOXWL

"

# $

%

& ' VGS −VT( )VDS −

VDS2

2)

* +

,

- .

€

IDS ≈νsatCOXW VGS −VT −VDSAT

2%

& '

(

) *

Penn ESE 370 Fall 2019 - Khanna

Switching Energy – focus on Idyn(t)

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Isc

Istatic

Idyn

Switching Energy – focus on Idyn(t)

E = P(t)dt∫= I(t)Vdd dt∫=Vdd I(t)dt∫

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Idyn

Penn ESE 370 Fall 2019 - Khanna

Switching Energy

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!  Do we know what this is?

Idyn

Idyn (t)dt∫

E = P(t)dt∫= I(t)Vdd dt∫=Vdd I(t)dt∫

Penn ESE 370 Fall 2019 - Khanna

Switching Energy

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!  Do we know what this is?

Idyn

E = P(t)dt∫= I(t)Vdd dt∫=Vdd I(t)dt∫

Penn ESE 370 Fall 2019 - Khanna

Q = Idyn (t)dt∫

Switching Energy

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!  Do we know what this is?

!  What is Q? Idyn

E = P(t)dt∫= I(t)Vdd dt∫=Vdd I(t)dt∫

Penn ESE 370 Fall 2019 - Khanna

Q = Idyn (t)dt∫

Switching Energy

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!  Do we know what this is?

!  What is Q? Idyn

E = P(t)dt∫= I(t)Vdd dt∫=Vdd I(t)dt∫

Penn ESE 370 Fall 2019 - Khanna

Q = Idyn (t)dt∫=CV

Switching Energy

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!  Do we know what this is?

!  What is Q? Idyn

E = P(t)dt∫= I(t)Vdd dt∫=Vdd I(t)dt∫

Penn ESE 370 Fall 2019 - Khanna

Q = Idyn (t)dt∫=CV

€

E = CVdd2

Capacitor charging energy

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

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Data Dependent Activity

!  Consider an 8b counter "  How often do each of the following switch?

"  Low bit? "  High bit?

!  Assuming random inputs "  Activity at output of nand2? "  Activity at output of xor2?

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Gate Output Switching (random inputs)

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0

1

P(outi!=outi+1)=P(outi=0)*P(outi+1=1)+P(outi=1)*P(outi+1=0)

i i+1

Output states

Probablity of output switch of nand4? Probablity of output switch of xor4?

Penn ESE 370 Fall 2018 - Khanna

Charging Power

!  Pdyn = (# trans) × ½CV2 / time !  Often like to think about switching frequency !  Useful to consider per clock cycle

"  Frequency f = 1/clock-period = clock-cycles/time

!  Pdyn = (#trans/clock-cycle) ½CV2 f

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Charging Power

!  Pdyn = (#0#1 trans) × CV2 / time !  Often like to think about switching frequency !  Useful to consider per clock cycle

"  Frequency f = 1/clock-period = clock-cycles/time

!  Pdyn = (#0#1 trans/clock-cycle) CV2 f

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Dynamic Power

!  Pdyn = (#0#1 trans/clock-cycle) CV2 f !  Let a = activity factor

a = average #tran0#1/clock a = probability of #tran0#1

!  Pdyn = aCV2 f

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Activity Factor

!  Let a = activity factor "  a = average #tran0#1/clock "  a = probability of #tran0#1

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a = p(outi = 0)p(outi+1 =1)

a = N0

2NN12N

=N0 (2

N − N0 )22N

Switching

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Short Circuit Power

Short Circuit Power

!  Between VTN and Vdd - VTP

"  Both N and P devices conducting

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Short Circuit Power

!  Between VTN and Vdd - VTP

"  Both N and P devices conducting

!  Roughly:

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Isc

Penn ESE 370 Fall 2019 - Khanna

Vin

time

Vout

Isdp

time

time

time

Vthn

Vdd

Vdd

Vdd-Vthp

Isc

tsc tsc

Peak Current

!  Ipeak around Vdd/2 "  If |VTN|=|VTP| and sized equal rise/fall

53

€

IDS ≈νsatCOXW VGS −VT −VDSAT

2%

& '

(

) *

Penn ESE 370 Fall 2019 - Khanna

Vin

time

Vout

Isdp

time

time

time

Vthn

Vdd

Vdd

Vdd-Vthp

Isc

tsc tsc

Peak Current

!  Ipeak around Vdd/2 "  If |VTN|=|VTP| and sized equal rise/fall

54

€

IDS ≈νsatCOXW VGS −VT −VDSAT

2%

& '

(

) *

€

I(t)dt∫ ≈ Ipeak × tsc ×12%

& ' (

) *

Penn ESE 370 Fall 2019 - Khanna

Vin

time

Vout

Isdp

time

time

time

Vthn

Vdd

Vdd

Vdd-Vthp

Isc

tsc tsc

Vin

time

Vout

Isdp

time

time

time

Vthn

Vdd

Vdd

Vdd-Vthp

Isc

tsc tsc

Peak Current

!  Ipeak around Vdd/2 "  If |VTN|=|VTP| and sized equal rise/fall

55

€

IDS ≈νsatCOXW VGS −VT −VDSAT

2%

& '

(

) *

€

I(t)dt∫ ≈ Ipeak × tsc ×12%

& ' (

) *

€

E =Vdd × Ipeak × tsc ×12#

$ % &

' (

Penn ESE 370 Fall 2019 - Khanna

Short Circuit Energy

!  Make it look like switching an equivalent capacitance, CSC

"  Q=I×t "  Q=CV

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E =Vdd × I peak × tsc ×12"

#$%

&'

"

#$

%

&'

E =Vdd ×QSC

E =Vdd × (CSCVdd ) =CSCV2dd

Penn ESE 370 Fall 2019 - Khanna

Short Circuit Energy

!  Make it look like switching an equivalent capacitance, CSC

"  Q=I×t "  Q=CV

57

E =Vdd × I peak × tsc ×12"

#$%

&'

"

#$

%

&'

E =Vdd ×QSC

E =Vdd × (CSCVdd ) =CSCV2dd

Penn ESE 370 Fall 2019 - Khanna

CSC =I peaktsc2Vdd

Short Circuit Energy

!  Every time switch (0#1 and 1#0) "  Also dissipate short-circuit energy: E = CscV2

"  Ccs “fake” capacitance (for accounting)

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Total Power

!  Ptot = Pstatic + Psc + Pdyn

!  Pdyn + Psc = aCloadV2f+2aCscV2f

!  Ptot ≈ a(Cload+2Csc)V2f+VI’s(W/L)e-Vt/(nkT/q)

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Switching Waveforms

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Switching Waveforms

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Switching Waveforms

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Switching Waveforms

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Switching Waveforms

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Ideas

!  Three components of power "  Static "  Dynamic "  Short-circuit

!  Ptot = Pstatic + Pdyn+ Psc

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Admin

!  HW6 due Friday

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