Guralp Systems CMG-40T - Manual (Page 24)

CMG-40T
Poles and zeroes
Most users of seismometers find it convenient to consider the sensor as a “black
box”, which produces an output signal V from a measured input x. So long as
the relationship between V and x is known, the details of the internal mechanics
and electronics can be disregarded. 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 fm = 1 Hz, with s = j fm, 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.
24 Issue A