Drawing Number: 21067
Revision: A
PIEZOELECTRIC CHARGE MODE PRESSURE SENSOR GENERAL OPERATION MANUAL
8
Figure 6.2 illustrates a block diagram of the piezo-
electric system where:
C
t
= Shunt capacitor
C
s
= Series blocking capacitor
With the series blocking capacitor C
s
in place as shown,
the dynamic charge (Q) generated by the sensor element
is distributed across the two capacitors, C
t
and C
s
, in
proportion to the size (capacitance) of each. If C
s
, for
example, is equal to 100 times C
t
, 99% of the charge
appears at the input of the charge amplifier, while 1% is
across the shunt capacitor C
t
. This results in a 1%
decrease in apparent sensitivity of the system.
This therefore demonstrates the importance of selecting
the series blocking capacitor at least two orders of
magnitude higher than the total shunt capacitance C
t
across the input of the charge amplifier.
It is also important that this capacitor be of high quality,
with a leakage resistance of greater that 10
12
ohms, to
avoid the DC offset discussed previously in 6.1,
Introduction.
6.4
Low-Frequency Response
Limitations
In a normal charge amplifier, the low-frequency
response is set by the RC time constant, as established
by the product of C
f
and R
f
. The system acts like a high-
pass first order RC filter with a -3 dB frequency
established by the relationship:
Equation 2
f
f
o
C
R
.16
f
=
where:
f
o
=
-3 dB Frequency (Hz)
R
f
=
Feedback resistor (ohms)
C
t
=
Feedback capacitor (farads)
However, after the addition of the series blocking
capacitor C
s
, the system becomes the equivalent of two
high-pass filters in series, one as previously mentioned
and one comprised of series capacitor C
s
and total
equivalent shunt resistance R
i
. This new cutoff
frequency is:
Equation 3
s
i
o
C
R
.16
f
=
To avoid compromise of the low-frequency response
established by the charge amplifier parameters and
illustrated by Equation 2, the product of R
i
C
s
should be
several orders of magnitude higher than R
f
C
f
.
The approximate final system discharge time constant
becomes:
Equation 4a
seconds
C
R
1
C
R
1
1
TC
f
f
s
i
+
=
If the input coupling time constant (R
i
C
s
) is very much
greater than the discharge time constant of the charge
amplifier (R
f
C
f
), Equation 4a then becomes:
Equation 4b
Seconds
0
C
R
1
s
i
⇒
Equation 5
TC =
R
f
C
f