Electrical Measurements and Instrumentations

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This section covers the classification of measurement errors and three classical AC bridge circuits — Maxwell, Schering, and Wien bridges — used for precision measurement of inductance, capacitance, and frequency.

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Static & Dynamic Errors Error Type Description Static error The error remaining when the measured quantity is constant (not changing with time); arises from instrument imperfections (e.g. calibration, friction, gravity effects), environmental factors, and observational errors Gross error Large errors typically due to human mistakes (misreading, incorrect recording, wrong instrument use) Systematic error Consistent, repeatable error due to known/predictable causes (instrumental, environmental, or observational); can often be corrected via calibration Random (accidental) error Small, unpredictable variations from unknown causes; cannot be eliminated but can be reduced/estimated statistically (e.g. by averaging repeated readings) Dynamic error The error that occurs when the measured quantity is changing with time, due to the instrument's inability to respond instantaneously (finite response time/bandwidth) to rapidly varying inputs Maxwell Bridge A Maxwell (Maxwell-Wien) bridge measures an unknown inductance by balancing it against a known capacitance (and resistances) in an AC bridge configuration; particularly suited to measuring medium-Q inductors, since the balance equations are independent of frequency (a notable practical advantage).

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Schering Bridge A Schering bridge measures an unknown capacitance (and its dissipation factor/loss angle) by balancing it against a known standard capacitor and resistances; widely used for testing insulation and high-voltage capacitors, and for measuring small capacitances with high accuracy.

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Wien Bridge A Wien bridge is primarily used to measure an unknown frequency (given known R and C values) or, conversely, is used as the frequency-determining feedback network in a Wien-bridge oscillator; at balance, both a magnitude and a frequency condition must be satisfied simultaneously.

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This section covers the principles of moving coil and moving iron instruments, the major analog measuring instruments built on them, and methods for measuring resistance.

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Moving Coil & Moving Iron Instruments Instrument Type Principle Permanent Magnet Moving Coil (PMMC) A current-carrying coil in a permanent magnet's field experiences a torque (F=BIl); deflection is proportional to current; responds only to DC (average value is zero for pure AC) unless used with a rectifier; highly accurate, uniform scale Moving Iron (MI) A piece of soft iron is attracted/repelled by the magnetic field of a current-carrying coil; deflection is proportional to the square of the current, so it responds to both AC and DC (reads true rms on AC); scale is non-uniform (cramped at the low end), less accurate than PMMC but robust and cheaper Key Measuring Instruments Instrument Function Galvanometer Detects/measures very small currents; highly sensitive, used mainly as a null detector in bridge circuits Ammeter Measures current; connected in series with the circuit; ideally has very low (near-zero) resistance Voltmeter Measures voltage/potential difference; connected in parallel (across the element); ideally has very high (near-infinite) resistance Wattmeter Measures power; typically an electrodynamometer-type instrument with a current coil (in series with load) and a pressure/voltage coil (in parallel), deflection ∝ VIcosφ Watt-hour meter (energy meter) Measures energy (integrates power over time); the common household induction-disc type uses eddy currents in a rotating aluminium disc, with rotation count/speed proportional to energy consumed Maximum demand meter Records the highest average power demand over a specified interval (e.g.

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15/30 minutes) within a billing period, used for demand-based tariffs Frequency meter Measures supply frequency; common types include the vibrating-reed type (mechanical resonance) and electrical resonance/ratiometer types Power factor meter Measures the power factor (cosφ) of a circuit directly, typically using crossed-coil electrodynamometer movement Measurement of Resistance Method Application Wheatstone bridge For medium resistances (~1Ω to 1MΩ); balances an unknown resistance against three known resistances Kelvin double bridge For low resistances (<1Ω); eliminates the effect of lead/contact resistance using an additional ratio arm Megger (insulation resistance tester) For very high resistances (insulation resistance, MΩ to GΩ range); applies a high DC test voltage

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This section covers electrical, mechanical, and thermal transducers/sensors used to convert physical quantities into measurable electrical signals.

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Displacement/Position Transducers Transducer Principle Potentiometer A resistive element with a sliding contact (wiper); output voltage varies linearly with the wiper's linear/angular displacement LVDT (Linear Variable Differential Transformer) A transformer with a movable core; core displacement changes the differential output voltage between two secondary windings, giving a linear, high-resolution measurement of linear displacement Force/Strain Sensors Sensor Principle Strain gauge A resistive element (e.g. thin metal foil) whose resistance changes proportionally with mechanical strain (deformation) applied to it, R=R₀(1+Gε) where G is the gauge factor and ε is strain Load cell A force-measuring transducer, typically using strain gauges bonded to an elastic structural element, converting applied force/weight into a proportional electrical signal Other Electrical & Mechanical Sensors Sensor Principle Hall Effect sensor Based on the Hall effect: a voltage is generated across a current-carrying conductor/semiconductor placed in a magnetic field, perpendicular to both current and field; used for magnetic field, current, and position sensing Piezoelectric sensor Certain crystals (e.g. quartz) generate an electrical charge/voltage proportional to applied mechanical stress/pressure (the piezoelectric effect); used for dynamic force, pressure, and vibration sensing Capacitive sensor Senses changes in capacitance caused by changes in plate distance, overlap area, or dielectric — used for proximity, displacement, level, and humidity sensing Thermal Sensors Sensor Principle Thermistor A semiconductor resistor whose resistance changes significantly (usually decreasing, for NTC types) with temperature; highly sensitive but non-linear response, limited temperature range Thermocouple Two dissimilar metal wires joined at a junction generate a small voltage (Seebeck effect) proportional to the temperature difference between the measuring junction and a reference junction; wide temperature range, self-generating (no external excitation needed) Optical/Light Sensors Sensor Principle Photoconductive cell (LDR) A semiconductor whose resistance decreases as incident light intensity increases (photoconductivity) Photodiode A semiconductor PN junction that generates/modulates a current in proportion to incident light, operated in reverse bias (photoconductive mode) or generating its own voltage (photovoltaic mode)

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This section covers digital-to-analog (D/A) converter architectures — weighted resistor and R-2R ladder types — and analog-to-digital (A/D) converter architectures — dual-ramp (integrating) and successive approximation types.

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Digital-to-Analog (D/A) Converters Type Principle Weighted resistor D/A converter Uses a set of binary-weighted resistors (R, 2R, 4R, 8R, ...), one per input bit, summed via an operational amplifier summing circuit; simple concept but requires a wide range of precise resistor values (impractical for many bits, since the resistor spread grows exponentially) R-2R ladder D/A converter Uses a repeating ladder network of only two resistor values (R and 2R); avoids the wide resistor value spread of the weighted-resistor type, making it far more practical to fabricate accurately for higher bit counts Analog-to-Digital (A/D) Converters Type Principle Dual-ramp (dual- slope integrating) A/D converter Integrates the unknown input voltage for a fixed time, then integrates a known reference voltage (of opposite polarity) until the integrator output returns to zero; the time taken for the second (de-integration) phase is proportional to the input voltage; highly accurate and noise- immune (errors in the integrator/clock tend to cancel), but relatively slow — used in precision instruments like digital multimeters Successive approximation A/D converter Uses a successive-approximation register (SAR) and an internal D/A converter to perform a binary search: testing each bit from most-significant to least-significant, comparing the D/A output to the input at each step; offers a good balance of speed and accuracy (moderate speed, conversion time independent of input magnitude), widely used in general-purpose data acquisition

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This section covers the fundamental principles of digital instrumentation, how instruments interface to computers, and microprocessor-based instrumentation.

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Fundamental Principles Digital instrumentation converts a measured analog quantity to a digital representation (via an A/D converter) for processing, display, storage, and transmission, offering advantages over analog instruments such as higher accuracy/resolution, noise immunity, ease of data logging/processing, and remote monitoring capability.

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A typical digital instrumentation system comprises: sensor/transducer → signal conditioning (amplification, filtering) → A/D converter → digital processing (microprocessor/microcontroller) → display/storage/communication.

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Interfacing to Computers Interface Standard Application RS-232 Serial communication standard for connecting instruments to computers over relatively short distances; simple, widely supported legacy standard GPIB (IEEE-488) Parallel bus interface standard specifically designed for connecting programmable test/measurement instruments to a controller computer USB Modern, high-speed serial interface, now widely used for connecting instruments to computers, often with plug-and-play capability Ethernet/LAN Network-based interface allowing remote instrument access/control and data transfer over local or wide-area networks Microprocessor-Based Instrumentation A microprocessor-based instrument uses an embedded microprocessor/microcontroller to control measurement sequencing, perform calculations/corrections (e.g. linearization, temperature compensation), store/display results, and communicate with external systems — offering greater flexibility, accuracy, and functionality (e.g. self-calibration, multiple measurement ranges/functions) than purely analog or hard-wired digital designs.

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This final section of the chapter covers the construction and operating principles of Current Transformers (CTs) — both measuring and protection types — and Potential (Voltage) Transformers, used to scale high currents/voltages down to standard, safe levels for instruments and protection relays.

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Current Transformers (CTs) A Current Transformer (CT) has a primary winding (few turns, often just the line conductor itself, carrying the full line current) connected in series with the circuit, and a secondary winding (many turns) that supplies a proportionally scaled-down current (commonly standardized to 1A or 5A) to connected meters/relays.

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Important safety rule: a CT's secondary must never be left open-circuited while the primary is energized — with an open secondary, the full primary current becomes magnetizing current, driving the core into deep saturation and inducing a dangerously high voltage across the open secondary terminals (a safety hazard and potential insulation failure).

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Measuring vs Protection CTs CT Type Design Characteristic Measuring (metering) CT Designed for accuracy over the normal operating current range; deliberately designed to saturate at currents somewhat above rated (e.g. during a fault), protecting connected metering instruments from damaging high currents/voltages Protection CT Designed to remain accurate (largely unsaturated) up to many times rated current (high fault currents), so connected protection relays receive an accurate current signal to correctly detect and respond to faults Potential Transformers (PTs) A Potential (Voltage) Transformer (PT/VT) has a primary winding connected in parallel (across the line) and a secondary winding that supplies a proportionally scaled-down voltage (commonly standardized to 110V or 120V) to connected meters/relays; constructed essentially like a small power transformer, but designed for high accuracy at very light (essentially voltmeter-only) secondary loading.

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Safety consideration: unlike a CT, a PT's secondary should never be short-circuited while energized, since (being a near-constant-voltage source) a short would drive excessive current through the windings, risking damage.