Electrical and Electronic Instruments: Concepts of Measurement and Instrumentation Systems

Fundamental Concepts of Measurement

Definition of Measurement: Measurement is the result of a quantitative comparison between a quantity whose magnitude is unknown and a predefined standard quantity.
Essential Interaction: Measurement is an essential part of the interaction between humanity and the physical world.
Basic Requirements for Measurement:
1. Standard: The standard used for comparison purposes must be accurately defined and commonly accepted.
2. Apparatus and Method: The apparatus used and the method adopted must be provable.
True Value vs. Measured Value:
- True Value: The value that would be obtained if the quantity was measured by an "Exemplar method," which is defined as a method agreed upon by experts as being adequately accurate for the purpose of the data.
- Measured Value: The numerical value obtained by measuring a physical quantity with an instrument (e.g., an ammeter reading of $5\,A$ ).

Introduction to Instrumentation and Control Systems

Instrumentation: The science of automated measurement and control. It is the technology of using instruments to measure and control the physical and chemical properties of materials.
Purpose: The basic purpose of instrumentation in a process is to obtain requisite information pertaining to the successful completion of the process.
Process Instrumentation: The term used when instruments are applied Specifically to the measurement and control of industrial manufacturing, conversion, or treatment processes.
Control System: Formed when measuring and controlling instruments are combined such that measurements provide impulses for remote automatic action.

Functional Elements of an Instrumentation System

Primary Sensing Element: The part of the system to which the quantity to be measured is applied. For example, in an ammeter, the coil carrying the current is the primary sensing element. It is generally followed by a transducer that converts the measured value to a corresponding electrical signal.
Variable Conversion Element: Receives output from the primary sensing element (voltage, frequency, etc.). If the signal is not suitable for the system (e.g., an analog signal for a digital system), this element (such as an A/D converter) converts it while retaining the original data.
Variable Manipulation Element: Manipulates the signal level if the previous stage's output is insufficient to drive the next stage. It preserves the original nature of the signal and can be placed before the variable conversion element if necessary.
Data Transmission Element: Essential when elements are physically separated; it transmits data from one stage to another.
Data Presentation Element: Provides information to the person handling the instrument in a proper form for monitoring, controlling, or analyzing. Examples include:
- Recorders: Magnetic tape recorders, high-speed cameras (for analysis).
- Visual Display Devices: For monitoring.

Classification of Instruments

Broad Categories: Mechanical, Electrical, and Electronic Instruments.
Electrical Instruments Classification:
- Absolute (Indirect) Instruments: Give the value of the quantity in terms of the constant and its deflection. They do not require comparison with standard values. Example: Tangent Galvanometer.
- Secondary (Direct) Instruments: Give the value of the quantity directly via deflection. These must be compared with absolute instruments or standard values. These are subdivided into Deflection and Null Deflection instruments.
Classification by Nature of Operation (Secondary Instruments):
1. Indicating Instruments: Display the value only at the time of measurement. Reading returns to zero when disconnected. Examples: Ammeters, Voltmeters, Wattmeters.
2. Recording Instruments: Display and record readings over time. Common in generating stations and substations. Examples: ECG, X-Rays.
3. Integrating Instruments: Display, record, and add (totalize) numerical values over time. Examples: Energy meter, Ampere-hour meter.
4. Null Deflection Instruments: Provide readings without a deflection angle by comparing with a known quantity until the difference is zero. Example: Potentiometer.
Classification by Electrical Supply:
- AC Instruments: Categorized into Single Phase and Three Phase. Examples: Induction, Electrostatic, Dynamometer, Moving Instrument (M.I.).
- DC Instruments: Example: Permanent Magnet Moving Coil (PMMC) instruments.
Classification by Effect:
- Moving Coil Instruments (PMMC and Electrodynamic/Dynamometer).
- Moving Iron (M.I.) Instruments (Attraction type and Repulsion type).
- Induction Instruments.
- Electrostatic Instruments.
- Electrolytic Instruments.
- Hot Wire Instruments.

Popular Electrical Measuring Instruments

Ammeter
Voltmeter
Ohmmeter
Multimeter
Wattmeter
Fluxmeter
LCR meter
Oscilloscope
Vectorscope
Synchroscope
Galvanometer
Energymeter
Tachometer
Speedometer
Frequency meter
Capacitance meter
Power factor meter
Ampere-hour meter
Live leakage detector
Earth leakage detector
Phase sequence detector
Insulation fault detecting instrument
Megger

Methods of Measurement

Direct Method: Unknown quantity is compared directly with a standard. No mathematical calculations are needed. Examples: Measuring cloth with a scale, resistance with an ohmmeter, voltage with a voltmeter.
Indirect Method: Measuring a different quantity and determining the required value via mathematical relationships.
- Examples: $\text{Volume} = \frac{\text{Mass}}{\text{Density}}$ ; $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ .
- Measurement of temperature using RTD (resistance) or Thermocouple (millivolts) via conversion tables.
Comparative Method: Comparing the quantity with a known value of the same quantity. Example: Comparing a sound level meter with a reference meter.
Substitution Method: Replacing the quantity to be measured with a known quantity that produces the same effect on an indicating device. Example: Calibration of weights.
Null Method: Comparing unknown and known quantities and making the difference zero. Example: Wheatstone bridge for resistance.
Fundamental Method: Measurement based on base quantities linked directly to the definition of the quantity.
- Voltage: Josephson Junction.
- Time: Cesium atomic clock.
- Length: Iodine Stabilize Helium-Neon laser.
- Temperature: Fixed point apparatus.

Static Characteristics of Instruments

Static characteristics apply when measured quantities are slowly varying or constant.

Accuracy: Closeness of a reading to the true value. Defined as:
- Point Accuracy: Accuracy at only one specific point on the scale.
- Percentage of Scale Range: For instruments with uniform scales.
- Percentage of True Value: Accuracy expressed relative to the actual value.
Precision: Reproducibility of measurements. It measures the degree to which successive measurements differ. High precision requires:
- Conformity: Necessary but not sufficient (e.g., reading $1.7\,k\Omega$ repeatedly for a value that is actually $1792\,\Omega$ because of scale limitations).
- Significant Figures: More figures indicate higher estimated precision.
Accuracy vs. Precision Example:
- True value: $30^{\circ}C$ .
- Sample A: $32.56, 32.55, 32.48, 32.49, 32.48$ .
- Sample B: $30.01, 30.15, 30.05, 30.12, 30.33$ .
- Sample B is more accurate (closer to $30$ ).
- Sample A is more precise (Range: $32.56 - 32.48 = 0.08$ , while Sample B range is $30.33 - 30.01 = 0.32$ ).
Sensitivity: Ratio of output change to input change ( $\text{Sensitivity} = \frac{\Delta a_o}{\Delta a_i}$ ). Slope of the calibration curve.
- Inverse Sensitivity (Deflection Factor): $\frac{1}{\text{Sensitivity}} = \frac{\Delta a_i}{\Delta a_o}$ .
- Calculation Example: If $8\,\Omega$ causes $4\,mm$ deflection, $\text{Sensitivity} = 0.5\,mm/\Omega$ and $\text{Deflection Factor} = 2\,\Omega/mm$ .
Linearity: Ability to reproduce input linearly.
- $\% \text{non-linearity} = \frac{\text{Maximum deviation from ideal straight line}}{\text{Full Scale Reading}} \times 100$
Repeatability: Closeness of output for repetitive inputs over a short period with the same observer, instrument, location, and conditions.
Reproducibility: Closeness of output for the same input when methods, observers, locations, or time change.
Resolution: Smallest measurable increment in input that produces an observable change in output.
- Example: Scale with $100$ divisions, full scale $200\,V$ . One division = $2\,V$ . If resolution is $1/10$ of a division, $\text{Resolution} = 0.1 \times 2 = 0.2\,V$ .
Threshold: The minimum input value below which no output change can be detected starting from zero.
Drift: Undesired shift in output over time while input is constant. Types: Zero Drift, Span Drift, Zonal Drift.
Stability: Ability to retain performance over the operating life.
Range or Span: Minimum and maximum values for which the instrument is designed.
Bias: Constant error over the full range; removable by calibration.
Dead Zone: Largest range of input values for which the instrument does not respond.

Errors in Measurement

Error Calculation:
- $E = A_t - A_m$
- Where $A_t = \text{Measured value}$ and $A_m = \text{True value}$ .
- $\% \text{error} = \frac{A_t - A_m}{A_t} \times 100$
- $\text{Accuracy} = 1 - \text{relative error} = 1 - \left|\frac{A_t - A_m}{A_t}\right|$
- Example: True value ( $A_t$ ) = $150\,V$ , Measured value ( $A_m$ ) = $148.5\,V$ . Error = $1\%$ , Accuracy = $99\%$ .
Types of Errors:
1. Gross Errors: Human/personal errors in reading, recording, or using instruments. Cannot be treated mathematically. Minimized by taking multiple readings by different observers.
2. Systematic Errors (Fixed Errors):
  - Instrumental Errors: Due to inherent shortcomings (friction, hysteresis, backlash), misuse (improper zero adjustment), or loading effects (voltmeter in a high resistance circuit).
  - Environmental Errors: Due to external conditions like humidity, pressure, temperature, or electrostatic fields.
  - Observational Errors: Introduced by observer (e.g., parallax error, improper scale selection).
3. Random Errors: Residual errors from unknown causes that remain after gross and systematic errors are accounted for. Handled using statistical methods.

Dynamic Characteristics of Instruments

Dynamic characteristics apply when the input fluctuates rapidly with time. Performance depends on mass, thermal/electrical capacitance, and inductance.

Types of Dynamic Input: Transient and Steady State Periodic.
Standard Input Variations: Step, Ramp, Parabolic, Sinusoidal.
Key Dynamic Characteristics:
1. Speed of Response: Rapidity with which a system responds to changes in the measured quantity.
2. Fidelity: Degree to which the system faithfully responds to input changes without dynamic error.
3. Lag: Delay or retardation in response.
4. Dynamic Error (Measurement Error): Difference between the true value changing with time and the indicated value (assuming zero static error).