USC Low Power CAD

Battery-Powered Digital CMOS Design Massoud Pedram Department of EE-Systems University of Southern California Los Angeles CA 90064 [email protected]

Massoud Pedram

USC Low Power CAD

Motivation Extending the battery service life of battery-powered microelectronic devices is a primary design objective

Massoud Pedram

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USC Low Power CAD

Conventional System Model

Y Existing low power design methodologies and approaches target power consumption in the VLSI circuit Y The battery system is assumed to be an ideal source that delivers a fixed amount of energy Y Common perception is that the battery discharge rate (i.e., the inverse of the battery service life) is linearly related to the average power consumption in the VLSI circuit Battery Discharge Rate (1/sec)

Vdd

VLSI Circuit

Battery System

GND Average Circuit Power (W)

Massoud Pedram

USC Low Power CAD

Integrated Battery-Hardware Model

Y In reality, the battery discharge rate is super-linearly related to the average power consumption in the VLSI circuit

Battery Discharge Rate (1/sec)

DC/DC Converter

VLSI Circuit Average Circuit Power (W)

Massoud Pedram

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USC Low Power CAD

Common Battery Types Type

Energy

Applications

Miniature

100 mWh~2 Wh

Electric watches, calculators, implanted medical devices

Batteries for portable equipment

2~100 Wh

Flashlights, toys, power tools, portable radio and television, mobile phones, camcorders, lap-top computers

SLI Batteries (starting, lighting and ignition)

100~600 Wh

Vehicle traction 20~630 kWh batteries Stationary 250 Wh~5 MWh batteries Load leveling batteries

5~100 MWh

Cars, trucks, buses, tractors, lawn mowers Fork-lift trucks, milk floats, locomotives (submarines) Emergency power supplies, local energy storage, remote relay stations Spinning reserve, peak shaving, load leveling

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USC Low Power CAD

How Batteries Work: An Example

A Galvanic Cell:

Discharge:

Zn(s)|Zn2+(aq),m1||Cu2+(aq),m2|Cu(s)

Zn(s)+Cu2+(aq),m2 → Zn2+(aq),m1+Cu(s)

Charge:

Cu(s)|Cu2+(aq),m2|| Zn2+(aq),m1|Zn(s)

Zn2+(aq),m1+Cu(s) → Zn(s)+Cu2+(aq),m2 Massoud Pedram

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USC Low Power CAD

Battery Characteristics

Y Electrochemical capacity

Ö Practical capacity Qp is lower than the theoretical electrochemical capacity

Ö Mass-based specific capacity (Ah/Kg) and Volume-based specific capacity (Ah/dm3)

Y Energy (rated capacity)

Ö The practical available energy Ep is dependent on the

manner in which the cell is discharged (I.e., the discharge current)

Y Power (rated power)

Ö Specifies whether or not a battery is capable of sustaining a large current drain without undue polarization

Ö Cells employing the same chemical system can be designed for either high power or high energy

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USC Low Power CAD

Battery Polarization Typical polarization curve for an electrochemical cell

Region (i): Electrode polarization overvoltage, usually associated to a large extent with one of the two electrode processes Region (ii): iR polarization caused by the internal resistance of the cell Region (iii): iR polarization combined with further electrode polarization caused by depletion of electroactive materials at the electrode surface Massoud Pedram

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USC Low Power CAD

Battery Performance Criteria ‰ Battery testing and specifications

Ö Useful life test (this test of a practical primary battery is determined principally by the nature of its discharge pattern)

Ö Other tests include, storage (shelf life) test, assessment under

conditions of environmental and mechanical stress, cell behavior under conditions of continuous short circuit, cell behavior after complete discharge, etc.

‰ Rechargeable systems

Ö Cycle life (the number of times a cell can undergo a

charge/discharge sequence before its performance is degraded to below some specified threshold)

Ö Battery must have a satisfactory rate of charge acceptance

‰ Thermal management

Ö Maximum working temperature, above which corrosion and other Ö

irreversible destructive processes are very rapid Minimum working temperature, below which the electrolyte has too high a resistance or may undergo a phase change

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USC Low Power CAD

Typical Battery Structures High-energy structure

High-power structure

Spiral wound (‘jelly roll’) structure

Discharge performance

Solid: High-energy structure Dashed: High-power structure Massoud Pedram

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USC Low Power CAD

Rechargeable Batteries

Comparison of gravimetric and volumetric energy density of lithium secondary cells with aqueous electrolyte-based systems

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USC Low Power CAD

Battery Discharge Diagram

discharge

xLi(s)+AzBy(s)

charge

LixAzBy(s)

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USC Low Power CAD

Typical Structure

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USC Low Power CAD

Y Y Y

Relevant Battery Characteristics The output voltage of a battery decreases as the battery is discharged A battery cell discharged at high current rate may lose capacity due to Cathode Freeze-Over; The amount of capacity loss is a function of discharge current rate A battery cell discharged at very low current rate may lose capacity due to self-discharge Delivered Capacity (%)

Unused Cathode

Nominal Rate Discharge

High Rate Discharge

Discharge Rate (mA)

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USC

Rate Capacity of Commercial NiMH Batteries

Battery Efficiency (Utilization)

Low Power CAD

Normalized Discharge Current Massoud Pedram

USC

Rate Capacity of Commercial Lithium Batteries

Low Power CAD

Tadiran Batteries 120%

100%

100%

Battery Efficiency

Battery Efficiency

Battery Engineering 120% 80% 60% 40% 20%

TL-2150 TL-2135

80% 60% 40% 20%

0% 0

5 10 Discharge Rate (mA/cm^2)

15

0% 0

5 10 Discharge Rate (mA)

15

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USC Low Power CAD

DC/DC Converter Vo Vdd

Idd

(a) Buck Converter

V0 : Battery output voltage I0 : Average battery output current (over time N.T)

Vdd

Vdd : VLSI circuit supply voltage Idd : Average VLSI circuit supply current (over time N·T)

(b) Control Circuit

η : Efficiency of DC/DC converter

η ⋅V0 ⋅ I 0 = Vdd ⋅ I dd Massoud Pedram

USC Low Power CAD

Actual Current

The actual discharge current of the battery, after considering the capacity-rate effect, is: I 0act = I 0 μ , 0 ≤ μ ≤ 1

μ : the battery efficiency, is a function of I0 :

μ = f (I 0 ) We can approximate f by using a: Linear Approximation (LA):

μ

μ = 1 − β ⋅ I0 Quadratic Approximation (QA):

μ = 1 − γ ⋅ I 02

LA QA I0

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USC Low Power CAD

Ideal and Actual Power Dissipation

Given a fixed supply voltage Vdd, power extracted from the battery is: V ⋅I P ide = V0 ⋅ I 0 = dd dd η When we consider the electro-chemical characteristics of the battery, we have: I Vdd ⋅ I dd P act = V0 ⋅ 0 = μ ( I 0 ) η ⋅ μ (Vdd ⋅ I dd ) Actual case η ⋅V0 with QA Power extracted Actual case with LA

from the battery

Ideal case

Idd

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USC Low Power CAD

Observation I

For the same voltage level, the actual power dissipation is a super-linear function of the current consumed in the VLSI circuit.

Massoud Pedram

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USC Low Power CAD

The Actual Power Dissipation

p1 : The profile (probability density function) of Idd p2 : The profile (probability density function) of I0 p1 and p2 have the same form, but different scale Ideal power extracted from the battery: I 0 ,MAX P ide = V ⋅ I ⋅ p2 ( I 0 )dI 0 I 0 ,MIN 0 0

∫

= V0 ⋅ ∫

I 0 ,MAX

I 0 ,MIN

I 0 ⋅ p2 ( I 0 )dI 0 = V0 ⋅ I 0ave

Actual power extracted from the battery:

P act = V0 ⋅ ∫

I 0 ,MAX

I 0 ,MIN

I0 ⋅ p2 ( I 0 )dI 0 μ (I0 )

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USC Low Power CAD

Actual Power Using LA and QA

Linear Approximation (LA):

P act = V0 ⋅ ∫

I0 ⋅ p2 ( I 0 )dI 0 1 − β ⋅ I0

I 0 ,MAX

I 0 ,MIN

Quadratic Approximation (QA):

I 0 ,MAX

I0

I 0 ,MIN

1 − γ ⋅ I 02

P act = V0 ⋅ ∫

⋅ p2 ( I 0 ) dI 0

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USC Low Power CAD

Two Distributions with the Same Mean

Uniform Distribution: maximizes the actual power

1 ⎧ , ⎪ p2 ( I 0 ) = ⎨ I 0, MAX − I 0, MIN ⎪⎩ 0, I 0, MIN + I 0, MAX 2

δ-function Distribution: minimizes the actual power

I 0, MIN ≤ I 0 ≤ I 0,MAX otherwise = I 0ave p2

p2 ( I 0 ) = δ ( I 0 − I 0ave ) I 0ave

I 0, MIN

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I 0, MAX

I0

USC Low Power CAD

MAX and MIN Actual Power Using LA

act = PMAX

V0 ⋅ ( I 0,MAX − I 0, MIN )

act = V0 ⋅ ∫ PMIN

I 0 ,MAX

I 0 ,MIN

1 − β ⋅ I 0, MIN ) β ( I 0, MIN − I 0,MAX ) + ln( 1 − β ⋅ I 0, MAX

β2

I0 V ⋅ I ave ⋅ δ ( I 0 − I 0ave )dI 0 = 0 0 ave 1 − β ⋅ I0 1 − β ⋅ I0

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USC Low Power CAD

MAX and MIN Actual Power Using QA 1 − γ ⋅ I 02, MIN

act PMAX

act PMIN

V0 = ⋅ ( I 0, MAX − I 0,MIN )

=

ln( ) 1 − γ ⋅ I 02,MAX 2γ

V0 ⋅ I 0ave 1 − γ ⋅ ( I 0ave ) 2

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USC Low Power CAD

Battery Service Life and Discharge Rate

Battery Service Life (BSL):

BSL =

CAP0 P act

Battery Discharge Rate (BDR):

BDR =

1 BSL

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USC Low Power CAD

A Quantitative Example

Consider a battery with 36KJ nominal capacity and a 4-volt nominal output voltage:

Parameter V0 I0,MIN I0, MAX β γ CAP0

Value 4V 0A 5A 0.12 (1/A) 0.024 (1/A2) 36KJ (2.5AH) 2.5A

I 0ave

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USC Low Power CAD

Current Profiles for Uni-Modal Operation p2(I0)

p2(I0)

0 1.25 2.5 3.75 5 I0 (1) Pulse

0 1.25 2.5 3.75 5 I0 (2) Normal (σ=0.1)

p2(I0)

p2(I0)

0 1.25 2.5 3.75 5 I0 (3) Normal (σ=0.5)

0 1.25 2.5 3.75 5 I0 (4) Uniform

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USC Low Power CAD

BSL for Uni-Modal Current Profiles Profile (1) Profile (2) Profile (3) Profile (4)

BSL For Uni-Modal Profiles 1 0.8 BSL 0.6 (Hour) 0.4 0.2 0 LA

QA

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USC Low Power CAD

Current Profiles for Bi-Modal Operation p2(I0)

p2(I0)

0 1.25 2.5 3.75 5 I0 (1) p2(I0)

0

1.25 2.5 3.75 5 I0

0 1.25 2.5 3.75 5 I0 (2) p2(I0)

0

1.25 2.5 3.75 5 I0

(3)

(4)

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USC Low Power CAD

BSL for Bi-Modal Current Profiles BSL For Bi-Modal Profiles 1

Profile (1) Profile (2) Profile (3) Profile (4)

0.8 BSL 0.6 (Hour) 0.4 0.2 0 LA

QA

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USC Low Power CAD

Conclusions from the Example

Y The maximum BSL occurs by using the δ-function distribution Y The minimum BSL occurs by using the uniform distribution Y There is a significant increase (20%-30%) in BSL from the worst case to the best case Y Comparing uni-modal and bi-modal power distributions, we observe that:

gives longer BSL than

gives longer BSL than

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USC Low Power CAD

Observation II

Even with identical mean value, different current profiles (i.e., current density functions) may result in very different actual power dissipations.

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USC Low Power CAD

Battery Discharge (BD) Definition:

BD =

E act CAP0

Actual battery energy dissipation per operation:

E act =

E ide μ (I0 )

The circuit energy dissipation per operation: 2 E ide = 12 Csw ⋅ Vdd

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USC Low Power CAD

Battery Discharge (cont.)

The average circuit current per operation:

I

ide

E ide C ⋅V = = sw dd Vdd ⋅ T 2T

The average battery current per operation:

I0 =

2 2 Csw ⋅ Vdd k ⋅ Vdd = 2T ⋅ η ⋅ V0 T

The Battery Discharge as a function of Vdd (using the Linear Approximation for μ(I0)):

BD =

2 Csw Vdd ⋅ 2 2 ⋅ CAP0 (1 − β ⋅ k ⋅ Vdd T)

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USC Low Power CAD

BD-Delay Product Using LA

Delay equation for today’s CMOS technology

td = m

Vdd

(Vdd − Vth )α

,

1< ¡ ≤ 2

The BD-Delay Product is:

BD D =

3 m ⋅ C sw Vdd ⋅ 2 2 ⋅ CAP0 (1 − β ⋅ k ⋅ Vdd T ) ⋅ (Vdd − Vth )α

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USC Low Power CAD

Case 1: Fixed Operation Latency Assume T is fixed for all Vdd values. Consider a VLSI circuit which consumes 13.5W power at a supply voltage level of Vdd=1.5V

Parameter V0 η K/T α Vth mCsw/(2CAP0)

Value 4V 0.9 1.7 1.5 0.6V Normalized to 1

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USC Low Power CAD

BD-D Product Curves for Different β `s (fixed latency) β=0.14

β=0.13 β=0.12

BD-D product

β=0.11 β=0.10 β=0.09 β=0.08 β=0.07

β=0 3 0.7

Vdd (V) Massoud Pedram

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USC Low Power CAD

Optimal Vdd for Minimum BD-D Product (fixed latency) Optimal Vdd 1.25 1.2 1.15 1.1 1.05 1 0

0.05

0.1

0.15

β Massoud Pedram

USC Low Power CAD

Case 2: Variable Operation Latency

Assume T is proportional to the circuit delay:

T ∝ td ⇒ T = m′

Vdd

α

(Vdd − Vth )

,

1