EE1032 Electrical Measurements and Instrumentation Notes

Module Outline

• Module Code: EE1032
• Module Title: Electrical Measurements and Instrumentation
• Credits: 2
• Lectures: 24
• Tutorials: 2
• Practical: 6
• Semester: 1
• Evaluation: GPA
• ES (End Semester Evaluation): 70%
• CA (Continuous Assessment): 30%
• C (Compulsory)
• Hours per Semester (Notional):
  • ES: 70
  • Independent Learning and Assessments: 68
  • Active Hours (AH) = 24 + 2/2 + 6/2 = 28

Module Objective

To provide knowledge of electrical measurement instruments and their usage in practical aspects.

Learning Outcomes

After the successful completion of this module, the learner should be able to:

• LO1: Describe the basic concepts of electrical measurements.
• LO2: Explain the principle of operation of different types of electrical and electronic measuring instruments.
• LO3: Explain the principle of operation of different types of transducers.
• LO4: Compute functionalities of different measuring instruments.
• LO5: Discuss applications and interpret measurands of data logging and recording systems.

Module Content

• General principles of measurements [LO1]
  • Basics of Measurements: Accuracy, Precision, resolution, reliability, repeatability, validity, Errors, Standards of measurement.
  • Principle of operation of direct and null deflecting measuring instruments.
  • Graphical presentation of measured data.
• Direct deflecting instruments [LO2, LO4]
  • Measurement of current, voltage, power, energy, and resistance.
  • Moving coil, moving iron, induction, and dynamometer instruments.
  • Megohmmeter, multimeter. RLC meter.
  • Wheatstone bridge, Kelvin Double bridge, Hay's, Maxwell, Wien bridges
• Electronic measuring instruments [LO2, LO4]
  • Electronic voltmeter, true-rms meter, digital multimeter, vector voltmeter.
• Transducers [LO3, LO4]
  • Active and passive transducers, loading effects, transducers for measurement of non-electrical quantities - temperature, pressure, flow, force, torque, motion and light.
  • Instrument transformers
  • Non-contact measurements (eg. Thermal, Radiation, Electromagnetic fields, Light, Electronic distance)
• Recording instruments [LO5]
  • Data logger, event recorder, Synchro-phasor measurement, Statistical analysis of data
• Waveform display and analyzers [LO5]
  • Display technology, digital oscilloscopes, probes, Lissajous patterns
  • Power analyzer, signal analyzer, frequency counters

Module Assessment / Evaluation Plan

*End semester evaluation is structured type questions.

++Other Continuous Assessment Details

• CA1 Assignment on measuring instruments
• CA2 Assignment on transducers.
• CA3 Assignment on functionalities
• CA4 Assignment on recording instruments

Practical (Laboratory / Field Work) Details

• LAB1 Power measuring instruments
• LAB2 Transducers
• LAB3 Spectrum analyzer

Basics of Measurements

The measurement process involves several stages:

1. Sensing the measured variable (measurand) using a sensor.
2. Converting the variable into a suitable form.
3. Signal processing.
4. Signal presentation or recording.
5. Output measurement.
6. Signal transmission (optional).

Accuracy

Accuracy is a measure of how close the output reading of the instrument is to the correct value. Inaccuracy or measurement uncertainty is more commonly used.

Example 1.1
A pressure gauge with a measurement range of 0 - 10 bar has a quoted inaccuracy of $± 1.0\%$ of the full-scale reading.
(a) What is the maximum measurement error expected for this instrument?
(b) 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?

Precision

Precision describes an instrument’s degree of freedom from random errors.

• High precision instrument -> Spread of readings very small
• Low precision instrument -> Readings are not consistent

"Repeatability" and "Reproducibility" are similar to "Precision".

• Repeatability - closeness of output readings when the same input is applied repetitively over a short time, with the same measurement conditions
• Reproducibility - closeness of output readings for the same input when there are changes in the measurement conditions

Example 1.2
The width of a room is measured 10 times by an ultrasonic rule and the following measurements are obtained (in meters): 5.381, 5.379, 5.378, 5.382, 5.380, 5.383, 5.379, 5.377, 5.380, and 5.381. The width of the same room is then measured by a calibrated steel tape that gives a reading of 5.374 m, which can be taken as the correct value for the width of the room.
(a) What is the measurement precision of the ultrasonic rule?
(b) What is the maximum measurement inaccuracy of the ultrasonic rule?

Tolerance

Closely related to accuracy. Describes the maximum deviation of a value from some specified value

Example 1.3
A packet of resistors bought in an electronics component shop gives the nominal resistance value as $1000 \Omega$ 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?

Range

Defines the minimum and maximum values of a quantity that the instrument is designed to measure

Span

Difference between the maximum and minimum measurements (Maximum variation of the measurement)

Example 1.4
A particular micrometer is designed to measure dimensions between 50 and 75 mm. What is its measurement range ?

Threshold

When the input to an instrument is gradually increased from zero, threshold is the minimum input that will change the measurement output. Given in either absolute value or as a percentage of the full-scale reading.

Resolution

Smallest magnitude of the change in the input that produces an observable change in the instrument output Specified as an absolute value or as a percentage of the full-scale reading

Linearity

The characteristic of output reading being linearly proportional to the measured quantity. Output characteristics of a linear instrument can be expressed in a straight line

Example 1.5
A pressure transducer have an input range of 0 to $10^4 Pa$ and an output range of 4 to 20 mA. Express the ideal characteristics of this pressure transducer.

$O_{IDEAL} = KI + a$

$K = \text{ideal straight-line slope} = \frac{O<em>{MAX} - O</em>{MIN}}{I<em>{MAX} - I</em>{MIN}}$

$a = \text{ideal straight-line intercept}$

Non-Linearity

The characteristic of output reading not being linearly proportional to the measured quantity

Example 1.6
Figure shows instrument characteristic of a pressure sensor, in which the input units are expressed in ‘bars’ (1 to 9 bars) and the output units are expressed in ‘volts’ (1 to 13 V).
(a) What is the maximum nonlinearity expressed as a percentage of the full-scale deflection?

Sensitivity of measurement

$Sensitivity = \frac{Scale\ deflection}{Value\ of\ measurrand\ producing\ deflection}$

Indicates how much the instrument output changes for a unit change in instrument input. It can be calculated as the slope of the output characteristic curve.

Example 1.7
The following resistance values of a platinum resistance thermometer were measured at a range of temperatures. Determine the measurement sensitivity of the instrument in $\Omega/^{\circ}C$

Sensitivity to disturbance

Measuring instruments accuracy is valid only under controlled conditions (eg temperature, pressure, etc)

These standard ambient conditions are usually defined in the instrument specification. Environmental changes beyond the standard conditions affect the instruments in two main ways:

• Zero drift
• Sensitivity drift

Zero Drift

Zero reading of an instrument is modified by a change in ambient conditions. Causes a constant error that exists over the full range of measurement

Example 1.8
Following data shows the output measurements of a voltmeter under two sets of conditions:
(a) Measurements made in an environment kept at $20^{\circ}C$ (Standard condition)
(b) Measurements made in an environment at $50^{\circ}C$. Determine the zero drift when it is used in the $50^{\circ}C$ environment, Also calculate the zero-drift coefficient in V/$^{\circ}C$.

Sensitivity Drift

Sensitivity of measurement varies as ambient conditions change. Sensitivity drift coefficients defines the sensitivity drift for a unit change of an environmental parameter

Example 1.9
A spring balance is calibrated in an environment at $20^{\circ}C$ and has the following deflection/load characteristic. It is then used in an environment at $30^{\circ}C$ and the following deflection/load characteristic is measured. Determine the zero drift and sensitivity drift coefficients (per degrees Celsius change in ambient temperature)

Errors

Measurement errors are impossible to avoid. We can minimize their magnitude by good measurement system design accompanied by appropriate analysis and processing of measurement data.

Errors arising during the measurement process can be divided into two groups:

• Systematic errors
• Random errors

Systematic errors

The output readings of a measurement system with systematic errors are either always higher or always lower than the correct reading. Always due to faulty sensor or utilization error

Reasons for systematic errors

• System disturbance during measurement
• The effects of environmental changes
• Use of uncalibrated instruments
• Poor cabling practices
• Errors inherent in the manufacture of an instrument

Random errors

Caused by random and unpredictable effects, such that positive errors and negative errors occur in approximately equal numbers. Random errors can never be completely avoided

Reasons for random errors

• Human observation of an analog meter
• Electrical noise

Random errors can be overcome by taking the same measurement a number of times and extracting a value by averaging or other statistical techniques

Error Calculation

The value of error can be represented in three main methods

• Absolute error
• Relative error
• Relative error percentage

$absolute\ error = measured\ value - true\ value$

$relative\ error = \frac{measured\ value - true\ value}{true\ value}$

$relative\ error\$

$relative\ accuracy = 1 - relative\ error$

Example 1.10
Resistance of a conductor is measured at $21^{\circ}C$ and found to be 333 m$\Omega$. Find the percentage relative error of the measurement if the true resistance value of the conductor is 344 m$\Omega$.

Example 1.11
Relative percentage and absolute errors in measuring a voltage are found to be $1.6\%$ and 0.4 V respectively. Calculate the actual value of the voltage.

Elements of Measuring Instruments

• PSE - Primary Sensing Element: Direct contact with the measured quantity, eg –Transducer
• DCE - Data Conversion Element: Converts data from one form to another, eg- Voltage to current, ADC
• DME - Data Manipulation Element: Changes the signal level preserving its original nature, eg- amplification
• DTE - Data Transmission Element: Transmits data from one location to another, eg- optical fiber, coaxial cables
• DPE - Data Presentation Element: Used to display or store the measured data, eg- Digital display, plotters

Types of Measurements

• Direct Measurements: Measured quantity is directly compared against a standard
• Indirect Measurements: Measuring a secondary effect of the original quantity

Direct measurements are preferred due to increased accuracy and sensitivity.

Classification of Measuring Instruments

• Active Instruments: External power source is required for the instrument to produce an output
• Passive instruments: Instrument output is entirely produced by the quantity being measured.

Null-type and Deflection-type Instruments

• Deflection-type instrument – Quantity being measured is displayed as an amount of pointer movement
• Null-type instrument – The instrument exerts an influence to oppose the effect of the measurand measurement is taken when they are equal but opposite in value (null measurement)

Comparison:

Analog and Digital Instruments

• Analog instrument - Gives an output that varies continuously as the quantity being measured changes.
• Digital instrument - Gives an output that varies in discrete steps and can have only a finite number of values.

With the use of digital processors instruments with digital outputs are advantageous. Analog instruments will require additional analog-to-digital (A/D) converter when interfacing with digital systems

Measurement Standards

A standard of measurement is a physical representation of a unit of measurement.

• International Standards
  • Defined through international agreement by the International Bureau of Weights and Measures (French: Bureau International des Poids et Mesures, BIPM)
  • Definitions of the measuring units:
    • Kilogram: It is defined as the mass of a cubic decimetre of water as its temperature of maximum density of $4^{\circ}C$, replaced by a physical artifact of a specific platinum iridium bar
    • International ohm: It is defined as the resistance offered by a column of mercury having a mass of 14.4521 grams, uniform cross-section areas length of 106.300 cm, to the flow of constant current at the melting point of ice.
    • International ampere: It is an unvarying current, which when passed through a solution of silver nitrate in water deposits silver at the rate 0.00111800 grams/sec (g/s)
• Primary Standards
  • Maintained by national standards laboratories in different parts of the world
  • The main function of the primary standards is the calibration and verification of secondary standards
  • Not available to be used outside of the national laboratories
• Secondary Standards
  • Used as a reference for the working standards
  • Sent to the international standards laboratories on a periodic basis for calibration and comparison against the primary standards
• Working Standards
  • Acts as references for measurement laboratories
  • Used to calibrate laboratory instruments

Standard Hierarchy:

International Standards -> Primary Standards -> Secondary Standards -> Working Standards

Data Representation

Graphical Presentation of Data

• Easy to detect trends or features
• Can summarize large amounts of data
• Cartesian coordinate graphs (scatter plots, x-y graphs)
  • Horizontal axis (x-axis) vertical axis (y-axis)
  • Each point identified with an x and y coordinate
  • A graph requires more informative axis labels
  • The axes have the units in which the measurements were made
  • The controlled quantity is referred as the independent variable and plotted as the x coordinate
  • The quantity responding to the independent variable is the dependent variable and plotted as y coordinate

Example:

In an experiment we were to raise the temperature of an aluminium rod, we would find that the rod’s length increases.

The temperature is the controlled quantity and the independent variable which is plotted as the x coordinate. The length of the rod increases as a consequence of the temperature increase and is the dependent variable which is plotted as the y coordinate.

Graph Elements

• A graph should have a title indicating the relationship being investigated
• The axes should be clearly labelled with the names of the quantities under study and their units of measurement.
• Scales, Symbols and Keys
  • Choose scales so that the plotted points occupy most of the available graph paper
  • It is preferable to make the symbol representing the data point bigger to make them more visible
  • A key, sometimes referred to as a legend, is included on the graph when several sets of data need to be identified
• The Origin
  • Origin point has the coordinates (0,0)
  • Graphs can either include or not include the origin
• Error Bars and Line Drawing
  • Error bars are vertical and/or horizontal lines that extend from a data point.
  • The length of each error bar is a measure of the uncertainty in the quantity
  • Uncertainty can vary from one measurement to the next, varying error bars from point to point
  • When the error bars are too small to plot clearly, it is advisable to omit them.

Example 1.12
An experiment is performed in which the time for a small metal sphere to fall a fixed distance through a liquid is recorded as the temperature of the liquid increases. The data gathered appear in the Table and are plotted on the graph in the Figure. The graph contains four mistakes or omissions.

• The title of the graph is incorrect: the graph shows time versus temperature, not temperature versus time
• The units have been omitted from the x axis
• The data point gathered at temperature $42^{\circ}C$ has not been plotted
• The last data point on the graph has been incorrectly plotted.

Linear x-y Graphs

• Slope of the line and intercept with y axis can be identified
• Non-linearity can be observed
• Outliers can be identified
• Unknown points with non-measured values can be read from graph

Determining the Best Fit Line

When fitting a line to data points, try to have an equal distribution of points above and below the line.

Equation of a Line

The equation of a line is given by:

$Y = mX + c$

where:

• $m$ is the slope
• $c$ is the y-intercept

The slope can be calculated as:

$m = \frac{rise}{run} = \frac{y<em>2 - y</em>1}{x<em>2 - x</em>1}$

Uncertainty in Slope and Intercept

1. Draw the best straight line through the data.
2. Draw a line with the maximum possible slope and another with the minimum possible slope that still fit the data reasonably well.
3. Calculate the slopes of the maximum and minimum lines.
4. The uncertainty in the slope is the average of the differences between the best fit slope and the maximum and minimum slopes.
5. Repeat a similar process to find the uncertainty in the y-intercept.