Download CHAPTER 4-A

4.5 Piezoelectric Circuits:
Fig (4-14) The Piezoelectric Sensor Circuits
1. Voltage follower circuits.
2. Charge Amplifier circuits.
3. Built - in voltage follower.
4.5.1 Voltage Follower Circuits:
Fig (4-15) The Voltage follower Circuit
Ct  Transducer sensor capacitor buffer
Cs  Standardizing section in the amplification end of the circuit.
Cb  Block capacitance to protect amplifier to pass AC signal (variation)
not do signal (constant).
Cc  Cable
C  C1  C s  CC
(86)
Fig (4-16) The Equivalent Circuit of Voltage Follower
I = I1 + I2 = q =Sq. a*
I1 =CV1 = C
(87)
dV
dt
I2 Cb (V*1 –V*o) =
(88)
Vo
R
(89)
Sub with (88) and (89) in (87)
I = S*q. a* =
c  c b Vo
.  CV * o
cb
R
(90)
sQ* .a*
Vo
Vo 

RCeq
c
*
C equ 
(91)
C b .C
Cb  C
(92)
Frequency response - H (  )
a  ao * ejwt
(93)
V  Vo ejwt
Substitute (93) in (91) and differentiate
Vo 
*
JWRCeq S q a o
*
1 JwRCeq
C
H ( w) 
(94)
JWRCeq
1  JWRCeq
CVo


*
S q a 1  JWRCeq 1  JWRCeq
- 107 -
(95)
Let  =R Ceq time constant
H ( w) 
(96)
( w ) 2
w
J
2
1  ( w )
1  ( w ) 2
(97)
Fig (4-17) The Transfer Function
- 108 -
4.5.2 Charge - Amplifier Current:
Fig (4-18) The Charge Amplifier Circuit
We use 2 op-amps its provide the required input impedance and gain:
 First amplifier (op-amp (1)) is charge amplifier which converts
the charge q into voltage(V2)using cf and Rf for feedback.
 Second amplifier (op-amp(2)) is inverting amplifier, standardizing
the system voltage sensitivity, it has a variable input resistance R 1,
(98)
R1 =bRf were o  b 1
And fixed R f
Fig (4-19) The Charge Amplifier Equivalent Circuit
C = C1 + C c + C a
I = I1 + i2 = i3 = q* = sq* .a*
I1 = V1* . C
(99)
CdVc
dt
(100)
- 109 -
I2 
V1  V2
Rf
(101)
I3 = (v1* - v2* ) cf
(102)
Voltage Relations:
V 2  G1V1  V1  
Vo  G2V2  V2 
V1 
1 Vo
G1 Gc 2
(103)
1
Vo
Gc2
(104)
1
1
1
Vo
V2   . 
Vo 
 V1
G1
G1 Gc2
G1Gc2
(105)
Sub with (103) and (104) in (100), (101)and (102)
Ic 
Cdvc
 Cvc
dt
(106)
I1  CV1* 
C *
Vo
G1
(107)
 1

1

Vo  G1

i2 

Gc2 R f 




(108)
 1

i3  Vocf 
 1
 G1Gc2 
(109)
I1  I 2  I 3  Sq* .a*
(110)
We get
Vo* 
 G Sq*  *
Vo
.a
  c2
R f Ceq  Ceq 
(111)
Considering G, very high value G1 > > > 105
Ceq 
C
 Cf
G1
(112)
For high value of G1 >>>
Ceq  C f
(113)
From are previous, we can see that the source capacitance has
little effect as GI is very high value.
- 110 -
Voltage sensitivity is controlled by:
Gc 2 Sq * 1Sq *
Sv 

Cf
bC f
(114)
Parameters that control the sensitivity are b, cf
4.5.3 Built in Voltage Follower:
Fig (4-20) The Built in Voltage Follower Circuit
The voltage follower is inside the transducer housing, leading to
the absence of Cc (cable capacitance) from the charge generation side of
the circuit. C and R are (input resistance and capacitance) not affected
by the environmental conditions.
C1  Protects (shields) the recording instrument from the power
supply voltage. The meter M, monitors the transistor connection and
monitoring the voltage supply.
Fig (4-21) The Equivalent Circuit of Built in Voltage Follower
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V1  V2  i3  0 (Voltage follower)
I = i 1 +i 2 =q * = sq * .a *
I 1 = cvi *
I2 
(115)
(116)
V1
R
(117)
(V *2 – V *o ) C 1 =
Vo
R1
(118)
V1  Sq*  *
.a  S .a*
V 
 
RC  C 
*
i
S 
(119)
Sq *
C
(120)
Frequency Response:
V =V o e iwt
a = a o e iwt
H   
(121)
(122)
CVo
JR1C1
1  JR1C1

x
s q * a o 1  JR1C1 1  JR1C1
 = RC = recording system
- 112 -
(123)