Calibrating the 3ESP
(
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:
In this equation
z
n
are the roots of the numerator polynomial, giving the zeros
of the transfer function, and
p
m
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
n
and
p
m
, 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.
4.1.2 Frequency response curves
The frequency response of each component of the 3ESP 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).
20
Issue G - February 2016
