The performance of a process instrument such as a temperature
or pressure sensor normally depends on its accuracy
and response time.
Accuracy
is a qualitative term that describes
how well the instrument may measure the process
parameter (see Section 1.4 for an in-depth discussion), and
response time
specifies the speed by which the instrument
can detect any significant change in the value of a process
parameter. Accuracy and response time are largely independent
and are therefore identified through separate procedures.
The accuracy of a process instrument is established
through its calibration, and the response time is determined by
exposing the instrument to a dynamic input and measuring its
response time from the transient output. Response time is
discussed in more detail in Section 1.9. Calibration is done by
providing the instrument with a number of known and stable
inputs to ensure that the output accurately represents the input.
Two terms are important in instrument calibration. These
terms are
zero
and
span
, as illustrated in Figure 1.8a. In this
figure, the calibration of a linear transmitter is approximated
with a straight line, represented by the equation
y
=
mx
+
b
,
where
y
is the output,
x
is the input,
m
is the slope of the
line, and
b
is the intercept. The calibration of an instrument
may change due to a change in zero, a change in span, or a
change in both zero and span. A change in zero is also
referred to as a
bias error,
DC offset
, or
zero shift.
A zero
shift results in a change in instrument reading (either positive
or negative) at all points along its range (Figure 1.8b). A zero
shift can result from several causes, such as a change in
ambient temperature affecting the calibration. For example,
if an instrument is calibrated at room temperature and used
at a different temperature, its output may include a bias error
(or zero shift) due to the temperature difference.
The change in span is also referred to as a
gain
error
or
span shift. A span shift means an increase or a decrease in the
slope of the instrument output line for the same input (see
Figure 1.8c). Typically, calibration errors involving span shift
alone are less common than calibration errors due to both zero
and span shifts. In Figure 1.8c, both cases are shown: span shift
without zero shift and span shift with zero shift. In pressure
transmitters, about 40% of the calibration changes are caused
by zero shift, about 30% by span shift, and only about 20% by
span shift alone.
1
As for the remaining 10%, the calibration
changes are due to other effects, such as nonlinearity.

Calibration of Pressure Sensors
Calibration of pressure sensors (including both absolute and
differential-pressure sensors) involves using a constant pressure
source such as a deadweight tester (see Figure 1.8d).
With a deadweight tester, constant pressure is produced for
the sensor while the sensor output is monitored and adjusted

a pressure that corresponds to 100% of the span is applied
by the deadweight tester, and the sensor output is adjusted
to 20 mA. These adjustments to the output are made by
setting two potentiometers provided in the pressure sensor.
These adjustment devices are referred to as the
zero
and
span
potentiometers. The next step in the calibration of a pressure
transmitter is to apply known pressures between 0 and 100%
of span to verify the linearity of the transmitter and to make
any necessary adjustments to obtain accurate mA outputs for
all inputs.
The zero and span adjustments of a pressure sensor interact,
meaning that changing one will cause the other to change,
and vice versa. Thus, in calibrating a pressure sensor, the
zero and span are often both adjusted to produce the most
accurate output that can be achieved for each input pressure.
Because of the nonlinearities in some pressure sensors, the
input/output relationships cannot be exactly matched, no
matter how well the span and zero adjustments are tuned
together. For that reason, in most pressure sensors, a linearity
adjustment is also provided (in addition to the zero and span
potentiometers) to help achieve the best agreement between
the input pressure and the output current.
In lieu of a deadweight tester, one can also use a stable
pressure source and a precision pressure gauge as the input.
Precision pressure gauges are available in a variety of ranges
from a number of manufacturers (see Section 5.11). Highly
accurate digital pressure indicators can also be used for calibration.
As will be seen later, automated pressure sensor
calibration equipment is also available that uses digital technology
to offer both accuracy and convenience.
As-Found and As-Left Data
The calibration of an instrument can change with time. Therefore,
instruments are recalibrated periodically. The periodic
calibration procedure typically involves two steps: (1) determine
if calibration is needed, and (2) calibrate if needed.
In the first step, known input signals (e.g., 0, 25, 50, 75, and
100% of span) are applied to the instrument, and its output
is recorded on a data sheet. The data thus generated is referred
to as the
as-found
calibration data (see Table 1.8e). If the asfound
data show that the instrument’s calibration is still acceptable,
no calibration is needed. Otherwise, the instrument is

to make the electrical output proportional to the applied pressure.
For example, a pressure sensor may be calibrated to
produce an output in the range of 4 to 20 mA for pressure
inputs covering the whole span of the sensor (0 to 100%).
For most pressure sensors, with no pressure applied, the
transmitter output is adjusted to produce a 4-mA signal. Next,

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