Piezoelectric Sensor

Gurkan Erdogan

March 28, 2008

Content

• Piezoelectric Sensor Design– Strain to Voltage Equation (-6V +6V)

• Interface Circuit for

– Decreasing HP Filter Cut-off Frequency (-3V +3V)

– Adding Offset Voltage (0V +6V)

• Wireless Transmission• Wireless Transmission– Voltage to Frequency Conversion (expects 0V 8V)

– Antenna Transmission (what is the loss here?)

– Frequency to Voltage Conversion

• S626 Data Acquisition

Piezoelectric Sensor

GeometryGeometry

Strain to Voltage Equations

Sensor Equation

( ) ( ) ( )166313 ××× = σddD

( )

( )

( )2

16

63

2

13

meterNewtonVectorStress

VoltmeterorNewtonCoulombMatrixtCoefficienricPiezoelectDirectd

meterCoulombntDisplacemeElectricDd

×

×

×

σ

Why do we need to use double layer?

• When force is applied to a

long piezoelectric cantilever

beam, one side is in tension

while the other side will be

in compression. No

electrical output can be

obtained from this obtained from this

homogenous body by

bending.

Bimorphs• Bimorphs made with two halves of

separate beams with electrodes in between, on the top and bottom surfaces

a) series connection: If the beams are poled in the oppositedirection then on the application of a force 'F' the voltage generated on the outer electrodes generated on the outer electrodes will be additive

b) parallel connection:If the beams are poled in the same direction, the additive output can be obtained by connecting the outer electrodes and the center electrode

Approximation of Normal Stress

• There are two ways to approximate the

stress distribution.

– Calculate an average stress

– Maximum stress at the root of the cantilever – Maximum stress at the root of the cantilever

beam is assumed to be the same throughout

the beam surface.

1st Way: From Strain to Voltage

c

cccq

c

cp

ccc

c

p

cc

cc

p

cp

d

bYdS

dC

bYd

dC

bYd

dbdC

Ydv

c

c

l&l

&

l

l&l

l

l&

l&&

l

l

=

=

=

=

=

∫∫

∫

∫∫

1111

31

1131

1131

1131

11

εεε

ε

ε

∫∫ ===

=

pinCvqdADqi

dD

&&

&&

33

11313 σ

p

q

p

p

q

ccp

vS

C

C

S

c

c

&&

&

ll

l

=

=

∫

11

11

ε

ε

∫∫

∫∫

=

=

==

ccc

c

c

ccpp

dbdYd

Y

sdbddCv

l&

l&&

1131

1131

ε

σεσε

σ

Real Values for Piezo-Crystal[ ]

[ ][ ]

( )[ ][ ]

[ ]mmb

GPaY

NCpicod

nFC

mt

dielectricmpF

c

c

p

c

12

42

23

38.1

40

113106

31

0

=

−=

=

=

=

−=

µ

ε

=×=

=

− Cmm

N

N

CS

bYdS

q

cccq

1048.2 2

2

6

31 l

c

op

t

AkC

ε=

[ ][ ]

[ ]

[ ] voltC

SVstrainm

voltC

SVstrainm

S

mm

mmb

p

q

p

c

p

q

p

c

q

c

c

6100001030

10100100

6.01001030

1011

...

30

12

max

max

3

6

maxmaxmax

min

min

3

6

minminmin

≅=−=××

=∆

==∆

≅=−=×

×=

∆==∆

=

=

=

−

−

−

−

εµεµ

εµεµ

l

ll

l

ll

l

==×=××

= −−

−

VC

VC

C

F

S

C

q

p 11056.

1048.2

1038.1 3

6

9

2st Way: Maximum Stress

( ) ( ) ( )

( ) ( ) ( )

( ) ( )

3max

3

max

2

0max

3

33

6

I

yxMx

L

EIwF

EI

LFxwwxL

EI

Fxxw

FLxMMxLFxM

Lx

x

=

===−=

==−=

=

=

σ

max2max

3max

maxmax

maxmax

2

3

2

13

2

1

2

wL

ET

T

IL

L

EIw

T

IFL

Ty

I

yM

I x

=

=

=

==

σ

σ

4

6

2

12

2

1

max

2max

3

σσσ ==

=

=

avrFWT

L

T

TWFL

T

IFL

OR

2st Way: Max Stress

dD 11313 = σhttp://piezo.com/tech2intropiezotrans.html

( )

( )F

WT

Lg

WLk

TF

T

Ld

T

LWkC

C

QV

FT

LdLWF

WT

Ld

dAddADQ

dD

o

o

2

3

2

3

2

3

4

6

312

2

31

2

2

312

2

31

11313

11313

=

=

′==

=′=

==

=

∫∫∫∫

ε

ε

σ

σhttp://www.morganelectroceramics.com/capacitors/index.html

Interface Circuit

Why do we use Interface Circuit?

Two Main Parts for Two Main Reasons;

• Extra Capacitor for Decreasing the Cut-off Freq.

– Piezo Sensor coupled with a load resistor acts like a

high pass filter. In order to read low frequency signal

we need to decrease the cutoff frequency.we need to decrease the cutoff frequency.

• Voltage Divider for Adding Offset Voltage

– We can only transmit positive voltage signal so we

need to add an offset voltage to the circuit. Maybe we

could have done this with an OpAmp.

Elements of the Circuits

• Vp : Voltage Generated in Piezo Sensor

• Cp : Piezoelectric Strip Capacitor

• RL : Load Resistor• RL : Load Resistor

• Ce : Extra Capacitor

• Vos : Offset Voltage

• R1,R2 : Resistors of Voltage Divider

Simple Connection with a Load Resistor

( ) ( )

( ) ( )[ ] ( )

( ) ( ) ( )( ) ( ) ( )=+

==+

=−

=

tvtvtv

RCtvRCtvtvRC

R

tvtvtvC

titi

LpHPPLpLLLp

L

LLPp

RC

ττ

τ

&&

&&

&&

Time Domain

[ ][ ]

[ ]Hzf

MR

nFC

HP

HP

c

L

p

8.22

1

22

6.2

≅×

=

Ω=

=

τπ

( ) ( ) ( )

( ) ( ) ( )( )( ) ( )

( ) ( )( ) 1

1

+==

=+

=+

=+

s

s

sV

sVsH

ssVssV

ssVsVssV

tvtvtv

HP

HP

P

L

PHPHPL

PHPLLHP

PHPLLHP

ττ

ττ

ττ

ττ &&

Frequency Domain

Connecting an External Capacitor - 1

( ) ( ) ( )

( ) ( )[ ] ( ) ( )

( ) ( ) ( ) ( )( ) ( ) ( )ˆ =+

=++

+=−

+=

tvtvtv

tvCRtvtvRCC

R

tvtvCtvtvC

tititi

PpLLLLep

L

LLeLPp

RCC Lep

ττ &&

&&

&&&

Time Domain

[ ][ ][ ]

( )

[ ]Hzf

RCC

MR

nFC

nFC

HP

HP

c

LepHP

L

e

p

3.0ˆ2

1ˆ

ˆ

22

22

6.2

≅×

=

+=

Ω=

=

=

τπ

τ

( ) ( ) ( )

( ) ( ) ( )( )( ) ( )

( ) ( )( ) 1ˆ

1ˆ

ˆ

ˆ

+==

=+

=+

=+

s

s

sV

sVsH

ssVssV

ssVsVssV

tvtvtv

HP

HP

P

L

PHPHPL

PHPLLHP

PHPLLHP

ττ

ττ

ττ

ττ &&

Frequency Domain

Connecting an External Capacitor - 2

10

5.1910log20

20

5.19

PL

P

L

VV

V

VH

=

−=

=

−

10

10

P

PL

V

VV

≅

=

Adding an Off-Set Voltage - 1

( ) ( )[ ] ( )( ) ( )( ) ( )

( ) ( ) ( )

( ) ( ) ( ) ( )titititi

Rtitvtv

Rtitv

titvC

titvtvC

RCRC

RLos

RL

CLe

CLpp

ep

e

p

21

1

2

1

2

+=+

×=−

×=

=

=−

&

&& [ ]

21

1

2

1

2

RCRC

RLos

RL

CLe

CLpp

IIII

RIVV

RIV

IsVC

IVVsC

ep

e

p

+=+

×=−

×=

=

=−

Time Domain Frequency Domain

Adding an Off-Set Voltage - 2

[ ]

LLeLosLppp

LLe

LosLpp

RCRC

VsVCVsCsC

VR

sVCVR

VR

sVCsVC

R

VsVC

R

VVVVsC

IIIIep

111

111

211

21

21

+=

+++

+=−+−

+=−

+−

+=+Cont. in Frequency Domain

( )

( )( )

( )

( ) ( ) os

HP

Lp

HP

HPL

osL

pHPLHP

osL

ppLLepL

osppL

L

ep

osppLep

VsR

RV

s

sV

VR

RsVVs

VR

RsVCRVsCCR

VR

sVCVR

sCC

VR

sVCVR

sCR

sC

1ˆ

1

1ˆ

1ˆ

1

11

111

1

1

1

1

121

++

+=

+=+

+=++

+=

++

+=

+++

τττ

ττ

Adding an Off-Set Voltage – 3

RR111

AC Equivalent

( )

( ) p

HP

HPL

LepHP

L

L

Vs

sV

RCC

RR

RRR

RRR

1ˆ

ˆ

111

21

21

21

+=

+=

+=+=

ττ

τ

Exact same thing

as back in slide 11

Wireless Transmitter

pF1000

Ω390

G

G G

G

G

V12+

Ωk250

Ω1000

V6.3 G

ΩM100

GG

G

ΩM100

pF1000

piezoV

G

+ parallel180k

Voltage to Frequency

ConversionConversion

AD 654

Voltage to Frequency Conversion

• Output Frequency Range – pin 1:

• Digital Ground – pin 2:

• Timer Resistor – pin 3:

• Input Voltage Range – pin 4:

• Positive Voltage Supply – pin 5:

[ ]kHzf 50 −=

[ ]voltVDGND 0=

[ ]Ω= kRT 250

( )[ ]volt

V

VVV

s

in

8~0~

4:1.0

: maxmin

−=

−=

=+

• Positive Voltage Supply – pin 5:

• Timer Capacitor – pin 6&7: (see below)

• Positive Voltage Supply – pin 8:

[ ]voltVs 0=−

[ ]nFCT 64.0=

[ ]voltVs 12=+

Conversion Equation

10=

==T

inT

C

T

VV

R

VI

V

QC

T

in

TCoutT

TCoutout

TC

CVfV

CVfI

CVfQf

CVQ

T

T

T

==

=

=

=

sec250

1000

250

10

µτ ==

=

Ω=

=

TT

T

T

C

CR

pFC

kR

VVT

TT

inout

TTC

inout

TCout

T

in

CR

Vf

CRV

Vf

CVfR

T

T

1

10

1

+

=

=

==

AD654 Block DiagramCT = 1 picoFarad

VIN = + 5 Volt

VS = +12 Volt

RPU = 980 Ohm

VLOGIC = + 4.9 Volt

R1 + R2 = RT = 250 kiloOhm

( ) ( ) inin

out VV

f ×=×××

= − 40010110250

1

10 93

VS = 0 Volt

FOUT vs. VIN(piezo)

Wireless Receiver

+

Frequency to Voltage Frequency to Voltage

Conversion AD 650

F/V Converter

Complete Circuit

F/V Converter Equations

3

7

108.6

103

××−

=−

osos

tC

V max

INTR Constants Time of #

Time Response Mechanical

×=INTC

osin

outINT

tf

VR

××=

αmax

max

F/V Conversion – Ripples (1)

( )( )

( ) ( ) ( )

( ) ( )C

ti

CR

tvtv

CRs

C

sI

sV

INTINTINT

outout

INTINT

INT

IN

out

=+

+=

1

1

&

( ) ( ) ( )

( ) ( )( )

( )

( )

( ) ( ) ( ) ( ) ( ) ττ

ττα

τ

ττ

τ

ττ

τ

duBetxetx

Tt

ti

diC

evetv

C

ti

CR

tvtv

CCR

t

t

tA

o

ttA

os

os

INT

t tt

INTINTINT

outout

INTINTINT

o

o

INTINT

∫

∫

−−

−−−

+=

≤<

≤≤=

+=

+−=

0

0

10

0

&

F/V Conversion – Ripples (2)

( ) ( )( )

( )

( )

INTINT

os

INT

t tt

ti

diC

evetvτ

ττ

τατ

ττ−

−−

≤≤=

+= ∫0

0

10

( )

+=

+=

+=

−−

−−

−−−

∫

∫

∫

os

INTINT

os

INT

os

os

INTINT

os

INT

os

os

INT

os

INT

os

ttt

t

INT

tt

INT

t tt

deeve

deC

eve

dC

evev

ττ

ττ

ττ

ττ

ττ

τ

τα

τα

τα1

0

min

0

minmax

( )

( )INT

ostT

os

os

evv

Tt

ti

τ

ττα

τ

−−

=

≤<

≤≤=

maxmin

0

0

−+=

−+=

+=

+=

−−

−−

−−

∫

INT

os

INT

os

INT

os

INT

os

INT

os

os

INTINT

os

INT

os

INTINTINT

t

INT

t

t

INT

INT

tt

t

INT

INT

tt

INT

eRve

eC

eve

eC

eve

deC

eve

ττ

τττ

ττ

ττ

α

ατ

τα

τ

1

1

min

min

0

min

0

min

F/V Conversion – Ripples (3)

( )

( )INT

os

INT

os

INT

os

INT

os

INT

os

INT

os

ttTt

t

INT

t

tT

eRevev

eRvev

evv

τττ

ττ

τ

α

α

−−

−−

−−

−−

−+=

−+=

=

1

1minmax

maxmin

( ) ( )

( )

+−−

−

−−

−

−=−

−−

−−

−

−−−

−−

−

−

osos

INT

INT

os

INT

os

INT

os

INT

INT

os

TtTt

T

tTttT

T

t

INT

eee

e

eee

e

eRvv

τττ

τ

τττ

τ

τ

α

1

11

1minmax

( )

( )INT

os

INT

INT

os

INT

INT

os

INT

os

INT

os

INT

os

INTINTINT

tT

T

t

INT

T

t

INT

t

INT

tTt

INT

e

e

eRv

e

eRv

eReev

eRevev

τ

τ

τ

τ

τ

τττ

α

α

α

α

−−

−

−

−

−

−−

−−

−

−=

−

−=

−=

−

−+=

1

1

1

1

11

1

min

max

max

maxmax

( )

( )

−

−++−=−

+−

−++−=−

−

+−−=−

−

−

−−

−−

−

−−−

INT

INT

os

INT

os

INT

INTINTINT

INTINTINT

os

INTINT

os

INTINT

INT

INTINTINT

T

ttTT

INT

TTT

TTtTTtTT

INT

TINT

e

eeeRvv

eee

eeeeeeeRvv

e

eeeRvv

τ

τττ

τττ

τττττττ

τ

τττ

α

α

α

1

1

1

1

minmax

minmax

minmax

Ripple Simulation – Limit Cycle