• This circuit has a charge. generator q defined by: where: = g Kx K = proportionality constant, C/m x = deflection Crystal Charge generator q=Kx RS 0 Cable e Amplifier о Amplifier + iAmplifier = 0 vo The circuit may be simplified by converting the charge generator to a current generator Is = Dr. Shamekhi, Sahand University of Technology dq dt dx = K dt 26 ia=0 + ✓ Displacement Meas. - Piezoelectric Sensors - p5 • Modified circuit: к • Combined elements • Assuming that the amplifier current = Zero Charge generator is = Kdx/dt ic' C R V₁ = UC = i-iR=C is = ic + iR (¹) fic dt c (dv) V₁(jw) Κ,jωτ ====== X(jw) jwr+1 R=RR(R+R) Ra C = C₁ + Cc + Ca Sensor response to a step displacement Displacement Kx/C | K, = K/C (sensitivity, V/m) dx Vo = K TRC (time constant) dt dt R T Time Time • The output decays exponentially because of the finite Increasing 7 Increasing 7

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Complete the derivative of the equations.
•
This circuit has a charge.
generator q defined by:
where:
=
g Kx
K = proportionality constant, C/m
x = deflection
Crystal
Charge
generator
q=Kx
RS
0
Cable
e Amplifier
о
Amplifier
+
iAmplifier
= 0
vo
The circuit may be simplified by converting the charge generator to a current generator
Is
=
Dr. Shamekhi, Sahand University of Technology
dq
dt
dx
=
K
dt
26
ia=0
+
✓
Displacement Meas. - Piezoelectric Sensors - p5
• Modified circuit:
к
•
Combined elements
•
Assuming that the amplifier current = Zero
Charge
generator
is = Kdx/dt
ic'
C
R
V₁ = UC =
i-iR=C
is = ic + iR
(¹) fic dt
c (dv)
V₁(jw) Κ,jωτ
======
X(jw) jwr+1
R=RR(R+R) Ra
C = C₁ + Cc + Ca
Sensor response to a step displacement
Displacement
Kx/C
| K, = K/C (sensitivity, V/m)
dx
Vo
= K
TRC (time constant)
dt
dt
R
T Time
Time
•
The output decays exponentially because of the finite
Increasing 7
Increasing 7
Transcribed Image Text:• This circuit has a charge. generator q defined by: where: = g Kx K = proportionality constant, C/m x = deflection Crystal Charge generator q=Kx RS 0 Cable e Amplifier о Amplifier + iAmplifier = 0 vo The circuit may be simplified by converting the charge generator to a current generator Is = Dr. Shamekhi, Sahand University of Technology dq dt dx = K dt 26 ia=0 + ✓ Displacement Meas. - Piezoelectric Sensors - p5 • Modified circuit: к • Combined elements • Assuming that the amplifier current = Zero Charge generator is = Kdx/dt ic' C R V₁ = UC = i-iR=C is = ic + iR (¹) fic dt c (dv) V₁(jw) Κ,jωτ ====== X(jw) jwr+1 R=RR(R+R) Ra C = C₁ + Cc + Ca Sensor response to a step displacement Displacement Kx/C | K, = K/C (sensitivity, V/m) dx Vo = K TRC (time constant) dt dt R T Time Time • The output decays exponentially because of the finite Increasing 7 Increasing 7
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