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PERFORMANCE CHARECTERISTICS OF AN INSTRUMENT / MEASURING DEVICE
Understanding what is instrument and Measurement system.
An Instrument is a device used to determine the value or magnitude of quantity or a variable
A measurement system is a combination of functional units namely primary sensing element, secondary
element for signal conditioning and final element of display to measure the value or magnitude of a
quantity or a variable
FUNCTIONAL ELEMENTS OF A MEASUREMENT SYSTEM
Secondary Sensing
Element (Signal
Conditioning)
Primary Sensing
Element (Sensor)
Final Element
(Display)
Performance Characteristics of an Instrument
We need to understand the performance characteristics of an instrument in order to obtain a measured
value which is closest to the True value of the measurement
TRUE VALUE of an Instrument may be defined as the exact error free value of the measuring variable at
an ideal state.
No Instrument can actually measure the True Value of a measuring variable as an effect of presence of
Performance characteristics of that particular instrument.
The performance characteristics of an Instrument can be classified into two types
1. Static Characteristics
2. Dynamic Characteristics
Performance Characteristics of
an Instrument
Static Charecterstics
Dynamic Characteristics
Static Characteristics of an Instrument may be defined as the characteristics of an Instrument whose
measuring variable doesn’t vary with time.
Dynamic Characteristics of an Instrument may be defined as the characteristics of an Instrument whose
measuring variable varies with time
Static Characteristics of an Instrument
Accuracy
It is the closeness with which an instrument reading approaches the true value of the quantity being
measured. Thus accuracy of a measurement means conformity of truth.
Accuracy may be specified in terms of inaccuracy or limits of error can be expressed in following ways
1. Point Accuracy: This is the accuracy of the instrument only at one point on its scale. The
specification of this accuracy doesn’t give any information about the general accuracy of the
instrument. However range of instrument can be obtained by drawing up a table which specifies
the accuracy at number of points throughout the range of the scale. * see Annexure I for
definitions of Scale Range and Scale Span
2. Accuracy as a Percentage of Scale Range: When a instrument has a uniform scale its accuracy
may be expressed in terms of scale range. For example, the accuracy of a thermometer having a
range 500₀C may be expressed as ± 0.5% of the scale range. This means that the accuracy of the
thermometer when the reading is 500₀C is ±0.5% which is negligible but when the reading is
25₀C that is 20% of scale range the error is as high as (500/25) x (±0.5) = 10% and therefore
specification of accuracy in this manner is highly misleading.
3. Accuracy as a Percentage of a True value: The best way to conceive the idea of accuracy is to
specify it in terms of the true value of the quantity being measured that is within ±0.5 percent of
true value. This statement means thus as the reading get smaller so do the errors. Thus at 5% of
Full scale the accuracy of the instrument would be 20% better than that of an Instrument which
is accurate to ±0.5 % of scale range.
Precision
It is a measure of the reproducibility of the measurements. That is, given fixed value of a quantity,
Precision is a measure of the degree or an agreement within a group of measurements.
Precision is composed of two characteristics namely conformity and the number of significant figures.
i.e. Conformity and Significant figures
Conformity is nothing but a group of measurements that lie within the range of true value. If an
instrument is precise and reproducing values close to true value, but if instrument has a zero adjustment
error or parallax error then the groups of measurements are precise but don’t confirm the accuracy of
the instrument. Thus precision is a necessary but not sufficient condition for accuracy. Perfect set
precise values indicate no drift in the instrument. *see Annexure I for definition and categories of Drift
Significant figures indicate the error created by the limitation of the scale. Suppose a resistor of
139890Ώ is being read as 1.4 M Ώ and the same reading is observed throughout the group of
measurements because the scale of the instrument is confined to that value. Thus it indicates that
conformity is a necessary but not sufficient condition for Significant figures.
Sensitivity
The static sensitivity of an Instrument or a measurement system is the ratio of the magnitude of the
output signal to that of the magnitude of the input signal or quantity being measured.
To understand the sensitivity at a point of measurement See the figures Sensitivity (a) when the curve is
linear and (b) when the curve is non linear of drawings as specified in ANNEXURE II
𝑆𝑡𝑎𝑡𝑖𝑐 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑜𝑢𝑡𝑝𝑢𝑡
∆𝑞𝑜𝑢𝑡𝑝𝑢𝑡
=
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑖𝑛𝑝𝑢𝑡
∆𝑞 𝑖𝑛𝑝𝑢𝑡
Linearity
One of the best characteristics of an instrument is considered to be linearity which is nothing but output
being linearly proportional to the input. Most of the systems require a linear behavior as it is desirable.
This is because the conversion from the scale reading to the corresponding measurement value of input
quality is the most convenient if one merely has to multiply by a fixed constant rather than consulting a
non linear calibration curve or compute from non linear calibration equations
There are many definitions of linearity that exist. However, linearity defined in terms of Independent
Linearity is most preferable in many cases. The computation of independent linearity is done with
reference to the straight line showing the relation between output and input. *See the figure of
Linearity deviation in Annexure II
The non linearity in the curve may be defined as
With respect to actual reading
𝑁𝑜𝑛 𝑙𝑖𝑛𝑒𝑎𝑟𝑖𝑡𝑦 =
𝑀𝑎𝑥 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑜𝑢𝑡𝑝𝑢𝑡 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑖𝑑𝑒𝑎𝑙𝑖𝑧𝑒𝑑 𝑠𝑡 𝑙𝑖𝑛𝑒
X 100
𝐴𝑐𝑡𝑢𝑎𝑙 𝑟𝑒𝑎𝑑𝑖𝑛𝑔
With respect to full scale deflection
𝑁𝑜𝑛 𝑙𝑖𝑛𝑒𝑎𝑟𝑖𝑡𝑦 =
𝑀𝑎𝑥 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑜𝑢𝑡𝑝𝑢𝑡 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑖𝑑𝑒𝑎𝑙𝑖𝑧𝑒𝑑 𝑠𝑡 𝑙𝑖𝑛𝑒
X 100
𝐹𝑢𝑙𝑙 𝑠𝑐𝑎𝑙𝑒 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛
Resolution
The smallest increment in the input (quantity being measured) which can be detected with certainty by
an instrument is its Resolution or Discrimination. So Resolution is the smallest input change while the
Threshold is defined as smallest measurable input
Hysteresis
Hysteresis is a phenomenon which depicts different output effects when loading and unloading whether
it is a mechanical system or a electrical system and for that matter any system. Hysteresis is a non
coincidence of loading and unloading curves. Hysteresis in a system arises due to the fact that all the
energy put into the stressed parts when loading is not recoverable upon unloading. *See Annexure I for
Second law of thermodynamics and Annexure II for the drawing on Hysteresis curve.
Dead Zone
It is defined as the largest change of input quantity for which there is no output of the instrument. For
Example the input applied to the instrument may not be sufficient to overcome the friction and will, in
that case, not move at all. It will only move when the input is such that it produces a driving force which
can overcome friction forces. Other factors which produce dead zone are backlash and high hysteresis in
the instrument.
The term Dead zone is sometimes used interchangeably with terms of Hysteresis. However it may
defined as a total range of input values possible for a given output and may thus be numerically twice
the Hysteresis.
Loading Effect
The incapability of the system to faithfully measure, record or control the input signals (measurand) in
an undistorted form is called Loading Effect
Input Impedance
**The figure Input Impedance circuit in Annexure II shows a voltage signal resource and input device
connected across it. The magnitude of the impedance of element connected across the signal source is
called Input Impedance
The magnitude of the input impedance is given by
Zi = ei /ii
The instantaneous power extracted by the input device from the signal source is given by
P = ei ii = ei2 / zi
Thus it is clear from the above equations a low input impedance device connected across the voltage
signal resource draws more current and drains more power from signal resource than a high input
impedance device. In other words a low input impedance device connected across a voltage signal
resource loads the source more heavily than a high input impedance device
Output Impedance
The output impedance of a device is defined as its equivalent impedance as seen by the load. The
definition of output device is only meaningful for an active device at a pair of terminals considered as
source. ** See the figure output impedance circuit (a) and (b) in Annexure II The term equivalent
impedance implies the device can be represented by a Thevenin’s Equivalent circuit. As in Fig (b)
Let eo = voltage appearing across the output terminals of the device when the load is not connected,
and eL = voltage appearing across the across the output terminals of the device when the load is
connected
The output impedance of an active device is defined as
zo = eo – eL / iL
The above equation conveys the idea that the drop in the output voltage (eo – eL) = il . zo is determined
by the output impedance as system is loaded. It is clear from the expression derived the lower the
output impedance the lesser is the effect of load on the output voltage.
Power loss in voltage source
P = (eo – eL) iL = il2 zo
Thus, for voltage sources, the lower the output impedance the lower is voltage drop and also lower is
the power consumption. Ideally there should not be any loading effect and this requires the output
impedance zo of the voltage source be equal to Zero.
ANNEXURE I
SCALE RANGE AND SCALE SPAN
The Scale range of an Instrument is defined as the difference between the largest and smallest reading
of the instrument supposing that the highest point of calibration as Xmax while the lowest is Xmin now we
can say the range of the instrument is between Xmin and Xmax
The scale span of the instrument is given by Xmax – Xmin
REPRODUCIBILITY AND DRIFT
Reproducibility is the degree of closeness with which a given value may be repeatedly measured. It may
be specified in terms of units for a given period of time. Perfect Reproducibility means that the
instrument has no drift. No drift means that with given input the measured values don’t vary with time.
Drift may be classified into three categories
1. Zero Drift: if the whole calibration gradually shifts due to slippage, permanent set, or due to
undue warming up of electronic tube circuits, zero drift sets in. This can be prevented by zero
setting. The input output characteristics with zero drift are shown in Fig (a)
2. Span Drift: If there is proportional change in the indication all along the upward scale, the drift is
called span drift or sensitivity drift. The characteristics with span drift is shown in fig (b) and the
characteristics with both span drift and zero drift are shown in fig (c)
3. Zonal Drift: in case the drift occurs only over a portion of span of an instrument, it is called as
zonal drift.
See Figures in attached sheet
Second Law of Thermo dyanamics: