Calibrating the 40T
This relationship, given in terms of the Laplace variable
s
, takes the form
(
V
x
)
(
s
)=
G
×
A
×
H
(
s
)
In this equation
•
G
is the acceleration output sensitivity (gain constant) of the instrument.
This relates the actual output to the desired input over the flat portion of the
frequency response.
•
A
is a constant which is evaluated so that
A × H (s)
is dimensionless and has
a value of 1 over the flat portion of the frequency response. In practice, it is
possible to design a system transfer function with a very wide-range flat
frequency response.
The normalising constant
A
is calculated at a normalising frequency value
f
m
= 1 Hz, with
s = j f
m
, where
j = √–1.
•
H (s)
is the transfer function of the sensor, which can be expressed in
factored form:
H
(
s
)=
N
∏
i
=
1
,n
s
−
Z
i
∏
j
=
1
,n
s
−
P
j
In this equation
Z
i
are the roots of the numerator polynomial, giving the zeros
of the transfer function, and
P
j
are the roots of the denominator polynomial
giving the poles of the transfer function.
In the calibration pack,
G
is the sensitivity given for each component on the first
page, whilst the roots
Z
i
and
P
j
, together with the normalising factor
A
, are given in
the
Poles and Zeros
table. The poles and zeros given are measured directly at Güralp
Systems' factory using a spectrum analyser. Transfer functions for the vertical and
horizontal sensors may be provided separately.
5.1.2
Frequency response curves
The frequency response of each component of the 40T is described in the normalised
amplitude and phase plots provided. The response is measured at low and high
frequencies in two separate experiments. Each plot marks the low-frequency and
high-frequency cut-off values (also known as –3 dB or half-power points).
26
Issue F - June 2019
