Response Time and Drift Testing

Off-line calibration of the zero and span of measurement was
the topic of the previous section. In this section, the on-line
methods of response time determination and calibration verification
will be described for sensors that have already been
installed in operating processes. As in Section 1.8, the discussion
here will also focus on temperature and pressure sensors.
FUNDAMENTALS OF RESPONSE TIME TESTING
The response time of an instrument is measured by applying
a dynamic input to it and recording the resulting output. The
recording is then analyzed to measure the response time of
the instrument. The type of analysis is a function of both the
type of instrument under test and on the type of dynamic
input applied, which can be a step, a ramp, a sine wave, or
even just random noise.
The terminology used in connection with time response
to a step change was defined in Figure 1.3z. The time constant
(
T
) of a first-order system was defined as the time required
for the output to complete 63.2% of the total rise (or decay)
resulting from a step change in the input. Figures 1.9a and
1.9b show the responses of instruments to both step changes
and ramps in their inputs and identify the time constant (
T
)
and response times (
τ
) of these instruments.
As shown in Figure 1.9a, the time constant of an instrument
that responds as a first-order system equals its response
time and it is determined by measuring, after a step change in
the input, the time it takes for the output to reach 63.2% of its
final value. The response of a first-order system is mathematically
described by a first-order differential equation,

Although most instruments are not first-order systems, their
response time is often determined as if they were, and as if
their response time were synonymous with their time constant.
However, if the system is of higher than first order,
there is a time constant for each first-order component in the
system. In spite of this, in the field, the definition of the firstorder
time constant is often also used in connection with
higher-order systems.
The ramp response time is the time interval by which the
output lags the input when both are changing at a constant
rate. For a ramp input, the response time (
τ
) is defined as the
delay shown in Figure 1.9b. This is also referred to as
ramp
time delay
and can be measured after the initial transient,
when the output response has become parallel with the input
ramp signal. For a first-order system, the ramp time delay,
response time, and time constant are synonymous. The ramp
time delay can be mathematically described as

where
C
is the ramp rate of the input signal. The derivations
of Equations 1.9(1) through 1.9(3) and the topic of Laplace
transformation is covered in the second volume of the
Instrument
Engineers’ Handbook
and also in Reference 1.
LABORATORY TESTING
The response time of temperature sensors is measured by using
a step input, whereas the response time of pressure sensors is
usually detected by using ramp input signals. This is because
obtaining a step change in temperature is easier and more
repeatable than obtaining a step change in pressure. Ramp
inputs are also preferred for the testing of pressure sensors,
because a step input can cause oscillation of the pressure transmitter
output, which may complicate the measurement.
Testing of Temperature Sensors
Figure 1.9c illustrates the equipment used in determining the
response time of a temperature sensor. This experiment is
called the
plunge test.
At the beginning of the test, the sensor
is held by a hydraulic plunger, and its output is connected to
a recorder. The heated sensor is then plunged into a tank of
water at near-ambient temperature. This step change in temperature
determines the type of transient in its output, as was
illustrated in Figure 1.9a. To identify the response time of
the temperature sensor, the time corresponding to 63.2% of
the full response is measured.

Because the response time of a temperature sensor is a
function of the type, flow rate, and temperature of the media
in which the test is performed, the American Society for
Testing and Material (ASTM) has developed Standard E644
(Reference 2), which specifies a standard plunge test. This
document specifies that a plunge test should be performed in
water that is at near room temperature and is flowing at a
velocity of 3 ft/sec (1 m/sec). A plunge test can therefore be
performed by heating the sensor and then plunging it into a
rotating tank that contains water at room temperature. By
controlling the speed and the radial position of the sensor,
the desired water velocity can be obtained for the plunge test.
There can be other ways for performing the plunge test.
For example, the sensor can be at room temperature and
plunged into warm water. Although the actual temperatures
have an effect on response time, this effect is usually small;
therefore, the response time is not significantly different if the
water is at a few degrees above or below room temperature.
Testing of Pressure Sensors
The response time of pressure sensors is usually determined
by using hydraulic ramp generators, which produce the ramp
test input signals. A photograph of a hydraulic ramp generator
is provided in Figure 1.9d. This equipment consists of two
pressure bottles, one bottle filled with gas or air and the other

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