MICROELECTRONIC TECHNIQUES FOR FREQUENCY TUNING OF PIEZO-ELECTRIC (PZ) ENERGY HARVESTING

DEVICES (EHDs)Interim Report

Jianying Zhao: Tianjin UniversityYogesh Ramadass: Texas Instruments

Dennis Buss: Texas Instruments and MITProf Jianguo Ma: Tianjin University

Summary• Piezo-electric (PZ) Energy Harvesting Devices

(EHDs): Background

• Four key elements of frequency tuning1. High load resistance => high E-field in the PZ material

=> enables PZ coupling2. Inductor in output => Coupled oscillators => Pole

Splitting 3. Variable inductor => Frequency tuning4. Bias Flip to approximate large variable inductor

• Simulation results

• Conclusions

External Circuits for Extracting Power from EHDs

Energy Management

CircuitD3

D4

D1

D2

CRECTEHD

Rectification Circuit for DC Energy Storage

RL

+

-

V

is

Linear Circuit for Extracting AC Power

EHD L

cond.circuit

The focus of this talk will be this

conditioning circuit

Energy Management

CircuitD3

D4

D1

D2

CRECTEHD

Rectification Circuit for DC Energy Storage

RL

+

-

V

is

Liner Circuit for Extracting AC Power

EHD L

cond.circuit

External Circuits for Extracting Power from EHDs

PZ EHDs: Background

Strain

Strain

+– Voltage

Mass

IP RPCP

Current Source Model

F

+

-

V

t

X

E, Dδ, σ

dEY

dED

maFext

sidt

dQ

NOTE: In the open circuit case, D=0, and the effective Young’s modulus is

12 )1( YYeff Y

d 22 2

22

1

moc

2

222

oc

moc

Voltage

Definition of Key ParametersMechanical spring constant

Mechanical resonance frequency

Open circuit (Q=0) spring constant

Open circuit resonance frequency

Electrical capacitance

Mechanically constrained capacitance

t

AYkm

22 11

1

m

oc

k

t

AYk

m

kmm 2

t

ACe

)1(1

22

22

mmoc

oc m

k

)1(1 22 emc C

t

AC

Normalized parameters mcNLm wYQ

/ 1

2mc mmcmc

mcmcm

LNLm

mcm

inNin w

LCC

YYQ

C

YY

2

2

22

1

Y

d

0.90 0.95 1.00 1.05 1.10 1.15 1.20-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

095.11/

mococw

Voltage is normalized to the open circuit voltage at mechanical resonance

Log 10

(Nor

mal

ized

Vol

tage

Mag

nitu

de)

𝒘=𝝎 /𝝎𝒎

=0

=0.1

=1

=10

=50

10)/( 0 50 2.0

mmmcinNin

mcm

QCYYwQ

dZVoc /

Electrical Frequency TuningOutput Voltage in the Case of No Inductor

0.7 0.8 0.9 1.0 1.1 1.2 1.3-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

Power is normalized to the max power with matched load atmechanical resonance

Log 10

(Nor

mal

ized

Ave

rage

Pow

er)

𝒘=𝝎 /𝝎𝒎

=0.1

=1

=10

=50

10)/(0 50 2.0

mmmcinNin

mcm

QCYYwQ

inav Y

d

ZP

2

max 8

1

Electrical Frequency TuningOutput Power in the Case of No Inductor

Wpeak=1.095

0.70 0.80 0.90 1.00 1.10 1.20 1.30-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Log 10

(Nor

mal

ized

Vol

tage

Mag

nitu

de)

𝒘=𝝎 /𝝎𝒎

=0

=0.1

=1

=10

=50

12 )( mcmCL

10)/( 1 50 2.0

mmmcin

Nin

mcm

QCYYwQ

Pole SplittingOutput voltage in the case of an impedance matchinginductor of value

Wpeak=1.247Wpeak=0.805

0.70 0.80 0.90 1.00 1.10 1.20 1.30-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Log 10

(Nor

mal

ized

Vol

tage

Mag

nitu

de)

𝒘=𝝎 /𝝎𝒎

=0

=0.1

=1

=10

=50

12 )( mcmCL

10)/( 1 50 2.0

mmmcin

Nin

mcm

QCYYwQ

Pole SplittingOutput voltage in the case of an impedance matchinginductor of value

Pole

Fre

quen

cies

𝒘𝒎𝒄

ρ = 0.2

0.2

0.6

1.0

1.4

1.8

1.41.00.60.2

Wpeak=0.805Wpeak=1.247

𝑤𝑚𝑐=1

𝜔𝑚√𝐿𝐶𝑚𝑐

0.7 0.8 0.9 1.0 1.1 1.2 1.3-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

w=ω/ωm

=0.1

=1

=10

=50

Normalized Power in the Case of an Impedance Matching Inductor of Value 12 )( mcmCL

10)/( 1 50 2.0

mmmcin

Nin

mcm

QCYYwQ

Log 10

(Nor

mal

ized

Ave

rage

Pow

er)

0.7 0.8 0.9 1.0 1.1 1.2 1.3-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

Log 10

(Nor

mal

ized

Ave

rage

Pow

er)

𝒘=𝝎 /𝝎𝒎

=0.1

=1

=10

=50

2222

22222

)1(

)1(

wQw

Qwwww

m

mmc

10)/( optimized 50 2.0

mmmcinNin

mcm

QCYYwQ

Inductor value is optimized at each frequency to maximize power delivered to the load

Output Power in the Case ofOptimized, Tunable Inductor

0.7005 0.7941 0.8877 0.9813 1.0749 1.1685 1.2621-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

Log 10

(Nor

mal

ized

Ave

rage

Pow

er)

𝒘=𝝎 /𝝎𝒎

𝑇𝑢𝑛𝑎𝑏𝑙𝑒 𝐼𝑛𝑑𝑢𝑐𝑡𝑜𝑟

10)/(1.0 50 2.0

mmmcin

Nin

NLm

QCYYYQ

Output Power for the case YLN = 0.1

Optimized tunable inductor compared to no inductor

𝑁𝑜 𝐼𝑛𝑑𝑢𝑐𝑡𝑜𝑟

0.7005 0.7941 0.8877 0.9813 1.0749 1.1685 1.2621-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

Log 10

(Nor

mal

ized

Ave

rage

Pow

er)

𝒘=𝝎 /𝝎𝒎

𝑇𝑢𝑛𝑎𝑏𝑙𝑒 𝐼𝑛𝑑𝑢𝑐𝑡𝑜𝑟

𝑁𝑜 𝐼𝑛𝑑𝑢𝑐𝑡𝑜𝑟𝐵𝑖𝑎𝑠 𝐹𝑙𝑖𝑝

Output Power for the Case YLN = 0.1

10)/( 0.1 50 2.0

mmmcin

Nin

NLm

QCYYYQ

L RLIP

RinCmc

+

-

V(t)

iP(t)

v(t)

Close Switch

Open Switch

½ Period

v(t)

Operation of the Bias Flip Technique

Volta

ge

t

Volta

ge

t

DC Rectification and Storage

ton toff

IP RinCmc Energy

Manage Circuit

D3

D4

D1

D2 CRECT

VRECT

BiasFlip

Circuitυ (t )

Volta

ge

t

Cmc = 0

Large Cmc

No BF

Large Cmc

With BFNegBias

Biasflip

VRECT

VRECT

ton toff

VRECT

ton toff

Log 10

(Nor

mal

ized

Pow

er)

Rectified DC Power as a Function of Cmc

Log10(Capacitance )

-8.0 -7.5 -7.0 -6.5 -6.0 -5.5 -5.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

No Bias Flip

Using Bias Flip

kYR

Hz

inin

m

10

1002

1

8% gap

Conclusions1. Frequency tuning of a PZ EHD can be achieved when the

Electric field in the PZ material is high, and PZ coupling is strong.

2. When an inductor is added to the output circuit, we have two coupled resonant circuits. When the coupling between them is high, pole-splitting determines the frequencies of max output power.

3. By varying the inductor value, the device can be “tuned” for max output power at frequencies different from the mechanical resonant frequency.

4. The Bias Flip technique has been proposed to approximate the effect of a large, tunable inductor.

Using a physical model for the PZ EHD, a generalization of the impedance matching concept has been shown to obtain high output power over an extended frequency range.

THANK-YOU