Instrumentations and Measurements Static Characteristics of Measuring Instruments
Lecture-3
Static Characteristics of Measuring
Instruments
3.1 Introduction
The performance of measuring system is strongly governed by the
characteristics of the instruments and the transducers used within these
instruments. The instrument is a device used for determining the value or
magnitude of a quantity or variable. The knowledge of the characteristic is
essential in designing and using of instruments to ensure that the measurement
requirements are met.
The characteristics of any instrument or transducer are normally given in the
data sheet supplied by the manufacturer.
Static characteristics are those that describe the instrument parameters in
steady-state, i.e, when the instrument output is settled to a steady readings. The
static characteristics have a fundamental effect on the quality of measurements
obtained from the instrument.
3.2 Static Characteristics
The various static characteristics are given as follows:
(1- Lecture-3) Assist. Prof. Dr. Haider K. Latif
Instrumentations and Measurements Static Characteristics of Measuring Instruments
1. Accuracy
Accuracy is the degree of correctness of measurement. It is the closeness
with which the measured value approaches the true value.
The measurement accuracy is given as:
| − |
= − × %
Where,
A= Accuracy
Xm= the measured value
XT= the true value.
Inaccuracy or measurement uncertainty is the extent to which a reading might be
wrong and is often quoted as a percentage of the full-scale reading of an
instrument. Inaccuracy is given as:
| − |
= × %
2. Precision
Precision is the closeness of the measured values to each other. It’s a
numerical value refers to the closeness of the measured values to the mean value.
The precision is given as:
| − |
= − × %
(2- Lecture-3) Assist. Prof. Dr. Haider K. Latif
Instrumentations and Measurements Static Characteristics of Measuring Instruments
Where,
Pi= the precision of the ith measured value.
Xi= the ith measured value.
= the mean of the measured values.
3. Repeatability
Is the closeness of the output readings of an instrument when the same
input is applied repetitively over a short period of time, with the same instrument,
observer, location, condition and method of measurement.
4. Reproducibility
Is the closeness of the output readings of an instrument when the same
input is applied repetitively, but for different instrument, observer, location,
condition, method and time of measurement.
5. Sensitivity
Sensitivity is the ratio of the change in the instrument output to the change
in the measured quantity. i.e,
∆ ∆
= =
∆ ∆
The sensitivity of measurement is therefore the slope of the straight line drawn to
represent the relationship between the measured quantity and output reading.
(3- Lecture-3) Assist. Prof. Dr. Haider K. Latif
Instrumentations and Measurements Static Characteristics of Measuring Instruments
output (Instrument Reading)
Nominal Characteristic
0 Input (measured quantity)
Fig. (3.1) The graph of sensitivity
The amount by which the instrument's sensitivity varies as ambient conditions
change is called the sensitivity drift.
The effect of sensitivity drift on the output reading of instrument is shown in
Fig.(3.2).
Characteristic with sensitivity drift
output (Instrument Reading)
Nominal Characteristic
0 Input (measured quantity)
(4- Lecture-3) Assist. Prof. Dr. Haider K. Latif
Instrumentations and Measurements Static Characteristics of Measuring Instruments
The effect when the zero reading of the instrument is modified by the change in
the ambient conditions is called the zero drift. The description of the zero drift is
illustrated in Fig.(3.3).
output (Instrument Reading)
Characteristic with Zero drift
Nominal Characteristic
Zero drift
0 Input (measured quantity)
If the instrument suffers both the sensitivity drift and zero drift at the same time,
output (Instrument Reading)
Characteristic with sensitivity and drift
Nominal Characteristic
Zero drift
Input (measured quantity)
(5- Lecture-3) Assist. Prof. Dr. Haider K. Latif
Instrumentations and Measurements Static Characteristics of Measuring Instruments
6. Resolution
Resolution is the ability of instrument to sense the smallest change in the
measured quantity.
The resolution is generally specified as a percentage of the full scale
deflection (FSD) as follows:
=
.
7. Tolerance
Tolerance is the maximum deviation of a manufactured component from a
specified value.
8. Range and Span
Are the maximum and minimum values of the quantity that the instrument
is designed to measure.
To describe the principles of range and span, consider the instrument
(thermometer) shown in Fig.(3.5).
-20 oC 0V
Thermometer
60 oC 50 V
Fig. (3.5) The input and output range and span
(6- Lecture-3) Assist. Prof. Dr. Haider K. Latif
Instrumentations and Measurements Static Characteristics of Measuring Instruments
For this thermometer:
The input range is from -20 oC to 60 oC
The input span is (60- (-20)) = 80 oC
The output range is from 0 V to 50 V
The input span is (50- 0) = 50 V
9. Significant Figure
The significant figure conveys the actual information regarding the
magnitude and the measurement precision of the measured quantity.
10. Backlash
Backlash is the maximum distance or angle through which any part of the
mechanical system of instrument may be moved in one direction without applying
appreciable force or motion to the next part in the mechanical sequence.
11. Threshold
Is the minimum input which is necessary to cause a detectable change from
zero output. The threshold may be caused by backlash or internal noise.
12. Dead band
It is the largest change of the measured quantity or variable to which the
measuring instrument does not respond. It is some time known as "dead zone" or
"dead space". It may be produced by the backlash, hysteresis and friction.
(7- Lecture-3) Assist. Prof. Dr. Haider K. Latif
Instrumentations and Measurements Static Characteristics of Measuring Instruments
A description of the instrument characteristic with threshold and dead band is
shown in Fig.(3.7).
output (Instrument Reading)
Threshold Point
Input (measured quantity)
Dead band
threshold and dead band
13. Hysteresis
Is the non-coincidence between the loading and the unloading curves of the
output characteristics of the measuring instrument.
Therefore, to minimize the values of the threshold and the dead band, it is
important should be minimized the effect of hysteresis. The hysteresis effect can
be minimized by making the iron parts of instruments small so that they
demagnetize themselves quickly. Also, the hysteresis effect may be minimized by
using an iron parts with low flux density such as the nickel-iron alloys.
Illustration of the
(8- Lecture-3) Assist. Prof. Dr. Haider K. Latif
Instrumentations and Measurements Static Characteristics of Measuring Instruments
Fig. (3.6) The instrument characteristic with hysteresis
14. Zero Stability
It is the ability of instrument to restore to zero reading after the measured
quantity is return to zero and other variations have been removed. These
variations may include pressure, temperature, humidity, vibration, frequencies,
…….etc.
(9- Lecture-3) Assist. Prof. Dr. Haider K. Latif
Instrumentations and Measurements Static Characteristics of Measuring Instruments
Examples – L3
Ex3.1 By using a mass scale, five readings were taken to measure a mass of 50 Kg
as follows: (50.8, 50.9, 50.7, 50.6 and 51) Kg
For this measuring instrument and according to the fifth reading,
determine (i) The accuracy (ii) The precision.
Sol.
(i)
| − |
= − × %
Or
| − |
= − × %
Thus, A = 98 %
(ii)
| − |
= − × %
The mean value for the measured values is given as follows:
+ + + +
= =
Or
. + . + . + . +
=
Or
= .
| − . |
= − × %
.
Or
= 99.61 %
Ex3.2 A pressure gauge with a measurement range of 0-10 bar has a quoted
inaccuracy of 1% of the full-scale reading.
(i) What is the maximum measurement error expected for this
instrument?
(ii) What is the likely measurement error expressed as a percentage of the
output reading if this pressure gauge is measuring a pressure of 1 bar?
Sol.
(i)
= × = .
(10- Lecture-3) Assist. Prof. Dr. Haider K. Latif
Instrumentations and Measurements Static Characteristics of Measuring Instruments
(ii)
= . × = .
This example carries a very important message. Because the maximum measurement
error in an instrument is usually related to the full-scale reading of the instrument,
measuring quantities that are substantially less than the full-scale reading means that
the possible measurement error is amplified. For this reason, it is an important that
instruments are chosen such that their range is appropriate to the values being
measured, so that the best possible accuracy is maintained in instrument readings.
Clearly, if we are measuring pressures with expected values between 0 and 1 bar, we
would not use an instrument with a measurement range of 0-10 bar.
o
Ex3.3 An electrical mass measuring instrument is calibrated at 20 C and has the
following mass/voltage characteristics:
Mass (Kg) 0 20 40 60 80 100
Voltage (mV) 0 100 200 300 400 500
This instrument is then used at environment of 60 oC and the following
measurements are taken:
Mass (Kg) 0 20 40 60 80 100
Voltage (mV) 25 165 305 455 585 725
For this instrument, determine:
(i) The zero drift per oC change in ambient temperature.
(ii) The sensitivity drift per oC change in ambient temperature.
Sol.
Temperature change is given by:
60 – 20 = 40 oC
(i)
= − =
Therefore,
/ = = . /
(ii)
=
At 20 oC
−
= = =
−
At 60 oC
−
= = =
−
(11- Lecture-3) Assist. Prof. Dr. Haider K. Latif
Instrumentations and Measurements Static Characteristics of Measuring Instruments
Therefore,
= − =
And the sensitivity drift per oC change is given as:
= = . . /
Ex3.4 Two resistors, R1 and R2 are connected in series. The individual resistance
measurements, using digital ohmmeter, give R1=20.35 Ω and R2= 15.735 Ω.
Calculate the total resistance to the appropriate number of significant
figure.
Sol.
R1 = 20.35 Ω (four significant figures).
R2 = 15.735 Ω (five significant figures).
Now,
= + = . + . = . Ω
Thus the total resistance to the appropriate number of significant figure is given as:
= . Ω (four significant figures).
Ex3.4 A packet of resistors bought in an electronics component shop gives the
nominal resistance value as 1000 Ω and the manufacturing tolerance as
5%. If one resistor is chosen at random from the packet, what is the
minimum and maximum resistance value that this particular resistor is
likely to have?
Sol.
= × = Ω
= − = Ω
= + = Ω
Ex3.5 A moving coil ammeter has a uniform scale with 50 divisions and a full
Sol.
= = = .
.
(12- Lecture-3) Assist. Prof. Dr. Haider K. Latif
