E1C09 09/14/2010
15:4:54 Page 391
to the absolute capacitance. Oscillator and bridge circuits are commonly used to operate the circuit
and to measure the small capacitance change providing an output voltage E 0 .
Example 9.5
Estimate the theoretical capacitance of a sensor similar to that of Figure 9.13 if the plate area is
1 mm
2 and the instantaneous plate separation is 1 mm. What is the sensor sensitivity? Assume the
plates are separated by air.
SOLUTION With A ¼ 1 mm
2 , t ¼ 1 mm, e ¼ 8.85 Â 10
À15 F/mm, c ¼ 1:
C ¼ ceA=t ¼ ð1Þð8:85 Â 10
15 F=mmÞð1 mm
2
Þ=ð1 mmÞ ¼ 8:85 Â 10
À15 F
or C ¼ 8.85 Â 10
À3 pF (picofarads). For small pressure changes, the diaphragm curvature has a
negligible effect on the area-averaged plate gap so that pressure can be treated as linear with the
area-average gap value.
The sensor sensitivity is K s ¼ qC=qt ¼ À8:85 Â 10
À3
 ðcA=t
2
Þ pF=mm.
The capacitance pressure transducer has the attractive features of other diaphragm transducers,
including small size and a wide operating range. Many common and inexpensive pressure
transducers use this measuring principle and are suitable for many engineering measurement
demands, including a niche as the on-board car tire pressure sensor of choice. However, the principle
is sensitive to temperature changes and has a relatively high impedance output. If attention is paid to
these shortcomings, an accurate and stable transducer can be made.
Piezoelectric Crystal Elements
Piezoelectric crystals form effective secondary elements for dynamic (transient) pressure measurements. Under the action of compression, tension, or shear, a piezoelectric crystal deforms and
develops a surface charge q, which is proportional to the force acting to bring about the deformation.
In a piezoelectric pressure transducer, a preloaded crystal is mounted to the diaphragm sensor, as
p measured
To
circuit
t
To
circuit
Fixed
plate
Deflected
diaphragm
Thin
metallic
diaphragm
∋
p ref
Figure 9.13 Capacitance pressure transducer. In
this schematic, the diaphragm is conductive and
its deflection exaggerated.
9.4 Pressure Transducers 391
15:4:54 Page 391
to the absolute capacitance. Oscillator and bridge circuits are commonly used to operate the circuit
and to measure the small capacitance change providing an output voltage E 0 .
Example 9.5
Estimate the theoretical capacitance of a sensor similar to that of Figure 9.13 if the plate area is
1 mm
2 and the instantaneous plate separation is 1 mm. What is the sensor sensitivity? Assume the
plates are separated by air.
SOLUTION With A ¼ 1 mm
2 , t ¼ 1 mm, e ¼ 8.85 Â 10
À15 F/mm, c ¼ 1:
C ¼ ceA=t ¼ ð1Þð8:85 Â 10
15 F=mmÞð1 mm
2
Þ=ð1 mmÞ ¼ 8:85 Â 10
À15 F
or C ¼ 8.85 Â 10
À3 pF (picofarads). For small pressure changes, the diaphragm curvature has a
negligible effect on the area-averaged plate gap so that pressure can be treated as linear with the
area-average gap value.
The sensor sensitivity is K s ¼ qC=qt ¼ À8:85 Â 10
À3
 ðcA=t
2
Þ pF=mm.
The capacitance pressure transducer has the attractive features of other diaphragm transducers,
including small size and a wide operating range. Many common and inexpensive pressure
transducers use this measuring principle and are suitable for many engineering measurement
demands, including a niche as the on-board car tire pressure sensor of choice. However, the principle
is sensitive to temperature changes and has a relatively high impedance output. If attention is paid to
these shortcomings, an accurate and stable transducer can be made.
Piezoelectric Crystal Elements
Piezoelectric crystals form effective secondary elements for dynamic (transient) pressure measurements. Under the action of compression, tension, or shear, a piezoelectric crystal deforms and
develops a surface charge q, which is proportional to the force acting to bring about the deformation.
In a piezoelectric pressure transducer, a preloaded crystal is mounted to the diaphragm sensor, as
p measured
To
circuit
t
To
circuit
Fixed
plate
Deflected
diaphragm
Thin
metallic
diaphragm
∋
p ref
Figure 9.13 Capacitance pressure transducer. In
this schematic, the diaphragm is conductive and
its deflection exaggerated.
9.4 Pressure Transducers 391