Nanotechnology-Enabled Sensors

2.2 Sensor Characteristics and Terminology 17
certain percentage (for instance 95%) of its final value, in response to a
stepped change of the input. The recovery time is defined in a similar way
but conversely.
Dynamic Range or Span:
The range of input signals that will result in a meaningful output for the
sensor is the dynamic range or span. All sensors are designed to perform
over a specified range. Signals outside of this range may be unintelligible,
cause unacceptably large inaccuracies, and may even result in irreversible
damage to the sensor.
2.2.2 Dynamic Characteristics
It is advantageous to use linear and time invariant mathematical representations
for sensing systems. Such representations have been widely
studied, they are easy to extract information from and give an overall vision
about the sensing systems to the users. The relationship between the
input and output of any linear time invariant measuring system can be
written as:
a
n
n
d y(
t)
+ a n
dt
n−1
n−1
d y(
t)
dy(
t)
+ ... + a1
+ a0
y(
t)
n−1
dt
dt
,
m−1
m−1
d x(
t)
d x(
t)
dx(
t)
= bm
+ bm
1 + ... + b1
+ b0
x(
t)
m − m−1
dt
dt
dt
(2.1)
where x(t) is the measured quantity (input signal) and y(t) is the output
reading and a0,…, an, bo,…, bm are constants.
x(t) can have different forms and values. As a simple and commonly encountered
example in sensing systems, x(t) may be considered to be a step
change (step function) similar to that depicted in Fig. 2.1. However, on
many occasions this is an over simplification, as there is generally a rise
and fall time for the step input to occur.