Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Question
Phase (deg)
Magnitude (dB)
20
20
40
180
135
90
45
10'
0
ġ(t)
하
R
www
Mechanical
Deformation
Piezo
Charge
Amplifer
10
10
Frequency (rad's)
v(t)
Figure 2: Frequency response function
of a microphone
Figure 3: A simple model for
piezoelectric sensor
3. Figure 3 is a simple circuit modeling a piezoelectric sensor. Mechanical deformation of the
sensor induces charge q(t), which is first modeled as a current source. The capacitance C
models the piezoelectric material, and the resistance R represents impedance of a charge
amplifier with output voltage v(t). Usually, C is fixed for a sensor, but R is adjustable from
the amplifier. The frequency response function from q(t) to v(t) is
Answer the following questions.
G(w)=
=
jRw
1+jRCw
(6)
(a) Consider the case when C = 1 Farad and R = 0.5 Ohm. (The numbers are chosen to
ease calculations. In practical applications, C is much smaller and R is much bigger.) If
the input deformation induces electric charge
=
q(t) cost+2 sin 3t
(7)
predict the voltage output v(t) in time domain.
(b) For the output voltage v(t) in part (a), calculate and plot its frequency spectrum.
(c) For the same sensor with C = 1 Farad, what should be the resistance R to ensure that
the output voltage v(t) is proportional to the induced charge q(t) in (7)?
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Transcribed Image Text:Phase (deg) Magnitude (dB) 20 20 40 180 135 90 45 10' 0 ġ(t) 하 R www Mechanical Deformation Piezo Charge Amplifer 10 10 Frequency (rad's) v(t) Figure 2: Frequency response function of a microphone Figure 3: A simple model for piezoelectric sensor 3. Figure 3 is a simple circuit modeling a piezoelectric sensor. Mechanical deformation of the sensor induces charge q(t), which is first modeled as a current source. The capacitance C models the piezoelectric material, and the resistance R represents impedance of a charge amplifier with output voltage v(t). Usually, C is fixed for a sensor, but R is adjustable from the amplifier. The frequency response function from q(t) to v(t) is Answer the following questions. G(w)= = jRw 1+jRCw (6) (a) Consider the case when C = 1 Farad and R = 0.5 Ohm. (The numbers are chosen to ease calculations. In practical applications, C is much smaller and R is much bigger.) If the input deformation induces electric charge = q(t) cost+2 sin 3t (7) predict the voltage output v(t) in time domain. (b) For the output voltage v(t) in part (a), calculate and plot its frequency spectrum. (c) For the same sensor with C = 1 Farad, what should be the resistance R to ensure that the output voltage v(t) is proportional to the induced charge q(t) in (7)?
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