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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
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