Electronic Instrumentation

ELECTRONIC INSTRUMENTATION

MODULE 1

INSTRUMENT

• It is a device or a system which is designed to maintain functional relationship b/w prescribed properties of physical variable and must include ways and means of communication to human observer.

MEASUREMENT SYSTEM

• The term “measurement system” is meant to include all components in a chain of hardware and software that leads from the measured variable to processed data.

CLASSIFICATION OF TYPES OF MEASUREMENT APPLICATION

o Three major categoris:

Monitoring of processes and operation

Control of processes and operation

Experimental engineering and analysis

BASIC MEASURING SYSTEM – BLOCK DIAGRAM

• Functional element of an instrument

• Textbook Doeblin, “Measurement Systems”, MCGraw Hill.

PERFORMANCE CHARACTERISTIC OF INSTRUMENT

• Static characteristic

• Dynamic characteristic

• Text book Morris, “Principles of Measurement & Instrumentation”

STATIC CHARACTERISTIC

• Accuracy

• Precision\Repeatability\Reproducibility

• Tolerance

• Range or span

• Bias

• Linearity

• Sensitivity of measurement

• Sensitivity of disturbance

• Hysteresis

• Dead space

• Threshold

• Resolution

STATIC CHARACTERISTIC cont…

o Accuracy – extend to which reading might be wrong. Quoted as percentage of full-scale (f.s.) reading.

• Eg:- pressure gauge – 0-10 bar - ±1.0%.

o Precision\Repeatability\Reproducibility

• Precision – instruments degree of freedom from random errors. Large no: of reading – high precision instrument – spread of reading will be small.


• Repeatability – closeness of reading when same input is applied over a short period of time.

• Reproducibility – closeness of reading for same i/p – change in method of measurement, observer, measuring instrument, location, condition of use and time of measurement.

COMPARISON OF ACCURACY AND PRECISION


o Tolerance – maximum error which is to be expected in some value.

• Eg:- resistor tolerance

o Range or span – maximum and minimum value that an instrument can measure.

o Bias – constant error which exists over full range of measurement of an instrument. Removable by calibration.


o Linearity – o/p reading linearly proportional to quantity being measured.

• Non-linearity – maximum deviation of any of the o/p reading.

• Instrument output characteristic


o Sensitivity of measurement – change in instrument o/p reading when quantity being measured changes by a given amount.

• sensitivity = 𝑆𝑐𝑎𝑙𝑒 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛

𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑚𝑒𝑎𝑠𝑢𝑟𝑎𝑛𝑑 𝑐𝑎𝑢𝑠𝑖𝑛𝑔 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛.


o Sensitivity of disturbance

• All calibration and specification of an instrument are only valid under controlled condition of temp, pressure etc.

• These standards defined by instrument specification.

• Sensitivity of disturbance – measure of magnitude of this change


• Environmental change affect two ways:

Zero drift – temp change.

• Effect where zero reading is modified by a change in ambient condition.

• Effect of disturbance zero drift

STATIC CHARACTERISTIC cont..

Sensitivity drift (scale of drift) – amount by which sensitivity of measurement varies as ambient condition change

• How much drift there is for a unit change in each environment parameters

• Effect of disturbance sensitivity drift


• Instrument suffer both zero drift and sensitivity drift at the same time, typical modified o/p characteristic

• Zero drift plus sensitivity drift

STATIC CHARACTERISTIC cont… o Hysteresis – non-

coincidence b/w loading and unloading curves.

• i/p measured quantity to the instrument is steadily increased from –ve value, curve A. If the i/p variable is then steadily decreased, curve B.

• Instrument characteristic with hysteresis.


o Dead space – range of different i/p values over which there is no change in o/p value.

• Hysteresis also dead space. Some do not suffer from hysteresis still exhibit dead space.

• Instrument characteristic with dead space.


o Threshold – minimum level of i/p. If the input to an instrument is gradually increased from zero, the input will have to reach a certain minimum level before the change in the instrument output reading is of a large enough magnitude to be detectable.

o Resolution - The smallest change in a measured variable to which an instrument will respond.

DYNAMIC CHARACTERISTIC

The dynamic behavior of an instrument is determined by subjecting its primary element (sensing element) to some unknown and predetermined variations in the measured quantity.

The three most common variations:

• Step change

• Linear change

• Sinusoidal change

DYNAMIC CHARACTERISTIC cont…

• Step change – the primary element is subjected to an instantaneous and finite change in measured variable.

• Linear change – the primary element is following a measured variable, changing linearly with time.

• Sinusoidal change – the primary element follows a measured variable, the magnitude of which changes in accordance with a sinusoidal function of constant amplitude.


• The dynamic characteristics of an instrument are:

Speed of Response – rapidity with which an instrument responds to changes in the measured quantity.

Fidelity – the degree to which an instrument indicates the changes in the measured variable without dynamic error (faithful reproduction).


Lag – the retardation or delay in the response of an instrument to changes in the measured variable.

Dynamic Error – the difference between the true values of a quantity changing with time and the value indicated by the instrument, if no static error is assumed.


• The dynamic characteristics – its behavior between the time a measured quantity changes value and the time when the instrument output attains a steady value in response.

• The static characteristics of measuring instruments are concerned only with the steady state reading that the instrument settles down to, such as the accuracy of the reading etc.


• In any linear, time-invariant measuring system, the following general relation can be written between input and output for time t > 0:

𝑎𝑛𝑑𝑛𝑞𝑜𝑑𝑡𝑛

+ 𝑎𝑛−1𝑑𝑛−1𝑞𝑜𝑑𝑡𝑛−1

+ …+ 𝑎1𝑑𝑞𝑜𝑑𝑡

+ 𝑎0 𝑞𝑜

= 𝑏𝑚𝑑𝑚𝑞𝑖𝑑𝑡𝑚

+ 𝑏𝑚−1

𝑑𝑚−1𝑞𝑖𝑑𝑡𝑚−1

+ …+ 𝑏1𝑑𝑞𝑖𝑑𝑡

+ 𝑏0 𝑞𝑖

• 𝑞𝑖 − 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦

• 𝑞𝑜 −𝑜

𝑝𝑟𝑒𝑎𝑑𝑖𝑛𝑔

• 𝑎0, … , 𝑎𝑛𝑎𝑛𝑑 𝑏0, … , 𝑏𝑚 − 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑠


• If we limit consideration to that of step changes in the measured quantity only, then

𝑎𝑛𝑑𝑛𝑞𝑜𝑑𝑡𝑛

+ 𝑎𝑛−1𝑑𝑛−1𝑞𝑜𝑑𝑡𝑛−1

+ …+ 𝑎1𝑑𝑞𝑜𝑑𝑡

+ 𝑎0 𝑞𝑜 = 𝑏0 𝑞𝑖

• Zero order instrument

• If all the coefficients 𝑎1, … , 𝑎𝑛 other than 𝑎0 are assumed zero

𝑎0𝑞𝑜 = 𝑏0𝑞𝑖 𝑜𝑟 𝑞𝑜 = 𝑏0𝑞𝑖𝑎0

= 𝐾𝑞𝑖

DYNAMIC CHARACTERISTIC cont… • First order instrument

• If all the coefficients 𝑎2, … , 𝑎𝑛 other than 𝑎0, 𝑎1are assumed zero

𝑎1𝑑𝑞𝑜𝑑𝑡

+ 𝑎0𝑞𝑜 = 𝑏0𝑞𝑖

• If 𝑑 𝑑𝑡 is replaced by D operation , then 𝑎1𝐷𝑞𝑜 + 𝑎0𝑞𝑜 = 𝑏0𝑞𝑖

• Rearranging,

𝑞𝑜 =

𝑏0𝑎0 𝑞𝑖

1 +𝑎1

𝑎0 𝐷


• Defining K = 𝑏0 𝑎0 − static sensitivity

• 𝜏 = 𝑎1 𝑎0 − time constant of the s/m

• Then, 𝑞0 = 𝐾𝑞𝑖

1+𝜏𝐷

• Fig: first

order instrument

Characteristic

(thermometer)


• The liquid-in-glass thermometer is a good example of a first order instrument.

• It is well known that, if a thermometer at room temperature is plunged into boiling water, the output e.m.f. does not rise instantaneously to a level indicating 100°C, but instead approaches a reading indicating 100°C in a manner similar to that shown in Figure.


• Second order instrument

• If all the coefficients 𝑎3, … , 𝑎𝑛 other than 𝑎0, 𝑎1&𝑎2 are assumed zero

𝑎2𝑑2𝑞𝑜𝑑𝑡

+ 𝑎1𝑑𝑞𝑜𝑑𝑡

+ 𝑎0𝑞𝑜 = 𝑏0𝑞𝑖

• Applying D operation, then 𝑎2𝐷

2𝑞𝑜 + 𝑎1𝐷𝑞𝑜 + 𝑎0𝑞𝑜 = 𝑏0𝑞𝑖


• Rearranging,

𝑞𝑜 = 𝑏0𝑞𝑖

𝑎0 + 𝑎1𝐷 + 𝑎2𝐷2

• Defining, K = 𝑏0 𝑎0 − static sensitivity,

• 𝜔 = 𝑎0𝑎2 − undamped natural freq ,

• ∈ = 𝑎1 2𝑎0𝑎2 − damping ratio.

• Then, 𝑞𝑜𝑞𝑖

= 𝐾

𝐷2

𝜔2 + 2𝜀𝐷𝜔 + 1

• This is the standard equation for a second order system and any instrument whose response can be described by it is known as a second order instrument.

• If equation is solved analytically, the shape of the step response obtained depends on the value of the damping ratio parameter ∈.

• The output responses of a second order instrument for various values of following a step change in the value of the measured quantity at time t are shown in Figure

RESPONSE CHARACTERISTIC OF SECOND ORDER INSTRUMENT

ERRORS IN MEASUREMENT – ERROR ANALYSIS

• A S S I G N M E N T – Errors in measurement – error analysis.

• T e x t b o o k

• H S Kalsi, “Electronic Instrumentation”. • D.U. S Murthy, “Transducers & Instrumentation”. • Sawhney, A.K., “A Course in Electrical and Electronic

Measurements and Instrumentation”.

• W D Cooper, “Modern Electronic Instrumentation and Measurement techniques”.

• Rangan, Sarma & Mani, “Instrumentation-devices and systems”.

UNITS

• The units of measurement fall into two distinct systems:

• the English system and

• the SI system

SI UNITS

• The SI units (centimeter-gram-second (CGS)units) – based on the metric system but it should be noted that not all of the metric units are used.

• The SI system of units is maintained by the Conférence Genérale des Poids et Measures.

• Because both systems are in common use it is necessary to understand both system of units and to understand the relationship between them.

• A large number of units (electrical) in use are common to both systems.

• Older measurement systems are calibrated in English units, where as newer systems are normally calibrated in SI units

ENGLISH SYSTEM • The English system has been the standard used in the United States, but

the SI system is slowly making inroads, so that students need to be aware of both systems of units and be able to convert units from one system to the other.

• Confusion can arise over some units such as pound mass and pound weight.

• The unit for pound mass is the slug (no longer in common use), which is the equivalent of the kilogram in the SI system of units whereas pound weight is a force similar to the newton, which is the unit of force in the SI system.

• The conversion factor of 1 lb = 0.454 kg, which is used to convert mass (weight) between the two systems, is in effect equating 1-lb force to 0.454-kg mass; this being the mass that will produce a force of 4.448 N or a force of 1 lb.

• Care must be taken not to mix units of the two systems.

• For consistency some units may have to be converted before they can be used in an equation.

UNITS

• Basic Units

• Table 2.1 gives a list of the base units used in instrumentation and measurement in the English and SI systems. Note that the angle units are supplementary geometric units.

UNITS

• Units Derived from Base Units

• All other units are derived from the base units. The derived units have been broken down into units used in both systems (e.g., electrical units), the units used in the English system, and the units used in the SI system.

UNITS

• Units Common to Both the English and SI Systems

• The units used in both systems are given in Table 2.2.

UNITS

• English Units Derived from Base Units

• Table 2.3 lists some commonly used units in the English system. The correct unit for mass is the slug, which is now not normally used. The English system uses weight to infer mass, which can lead to confusion. The units for the pound in energy and horsepower are mass, whereas the units for the pound in pressure is a force. Note that the lb force = lb mass (m) × g = lb (m) ft s^−2 [3].

UNITS

• SI Units Derived from Base Units

• The SI system of units is based on the CGS or metric system, but not all of the units in the metric system are used.

• It should be noted that many of the units have a special name.

FUNDAMENTAL UNITS

SUPPLEMENTARY FUNDAMENTAL UNITS

DERIVED UNITS

STANDARDS

A standard is physical representation of a unit of measurement.

A known accurate measure of physical quantity is termed as standard.

Types of Standards • International Standards (defined based on

international agreement ) • Primary Standards (maintained by national

standards laboratories) • Secondary Standards ( used by industrial

measurement laboratories) • Working Standards ( used in general laboratory)

CALIBRATION

o Calibration of all instruments is important since it affords the opportunity to check the instruments against a known standard and subsequently to find errors and accuracy.

o Calibration Procedure involve a comparison of the particular instrument with either

• a Primary standard • a secondary standard with a higher accuracy than

the instrument to be calibrated. • an instrument of known accuracy.

UNITS-DIMENSIONS – STANDARDS INSTRUMENT CALIBRATION

• Text books

• W D Cooper, “Modern Electronic Instrumentation and Measurement techniques”

• Morris, “Principles of Measurement & Instrumentation”

• D.U. S Murthy, “Transducers & Instrumentation”

• Rangan, Sarma & Mani, “Instrumentation-devices and systems”

THANK YOU

Electronic Instrumentation

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