D
OCUMENT
301900,
R
EVISION
D
38
E
PI
S
ENSOR
U
SER
G
UIDE
Pole Zero Representation
of the EpiSensor
EpiSensor accelerometers are closed-loop, force-feedback sensors
measuring the relative displacement of a moving mass (plates) with respect
to the sensor case. The sensor’s transfer function (TF) depends almost
entirely on the electronic components rather than on the mechanical
components of the sensors. The influence on the transfer function of the
mechanical damping, spring elements and internal RC low-pass filter in the
trans-conductance amplifier stage within the closed-loop path of the sensor
are negligible for most applications.
We have determined a good empirical model of the system, which uses two
pairs of conjugate poles to represent the transfer function of the instrument.
If this transfer function is corrected for the DC sensitivity of the sensor, the
amplitude agreement is within
"
.0.5 dB over the bandwidth of the sensor.
The phase agreement is within
"
2.5
$
in the 0-100 Hz band and within
"
5
$
over the full bandwidth of the instrument. This model can be represented as:
)
)(
)(
)(
(
2
*
1
)
(
)
(
4
3
2
1
p
s
p
s
p
s
p
s
k
k
s
A
s
V
&
&
&
&
'
where
k1 = 2.46 x 10
13
k2 = Sensitivity of sensor in V/g (from Table 3-1)
s is the Laplace transform variable
p
1
= -981 + 1009i (Pole 1)
p
2
= -981 - 1009i (Pole 2)
p
3
= -3290 + 1263i (Pole 3)
p
4
= -3290 - 1263i (Pole 4)
V (s) is the Laplace transform of the output voltage
A (s) is the Laplace transform of the input acceleration
Figure 19 on the next page show the amplitude, phase and step response of
this pole zero representation. Additional references to pole zero responses
and damping are available on the Kinemetrics website. Application Note 39
gives the response of the FIR filters used in the Altus Recorders. The FIR
filter response dominates the overall system response at sample rates up to
250 samples per second.