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Instrumentation. Dr. Xiaofeng Wu. 1. Distribution of Errors. Propagation of Uncertainty. A general relationship between some dependent variable y and a measured variable x. 3. Design Stage Uncertainty.
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Instrumentation Dr. Xiaofeng Wu 1
Propagation of Uncertainty A general relationship between some dependent variable y and a measured variable x 3
Design Stage Uncertainty The zero-order uncertainty, u0, assumes that the variation expected in the measured values will be only that amount due to instrument resolution and that all other aspects of the measurement are perfectly controlled.
Expansion Methods for Measuring Temperature • Liquid-in-Glass Thermometer • An operator is needed, so the thermometer cannot be used in a closed-loop control systems. • The time required to reach the equilibrium temperature is excessive • Bimetallic Thermometer • The bimetallic sensor is used in temperature control systems, and is the primary element in most dial thermometers and many thermostats.
Resistance Thermometers • Resistance temperature detector (RTD) • Materials like platinum, nickel and so on • Stable and provide a reproducible response to temperature over long periods of time • Thermistors • Fabricated from semiconducting materials • Very high accuracy
Resistance Temperature Detector • A RTD consists of a wire coil sensor, a sheath, a linearizing circuit, a Wheatstone bridge, and a voltage display instrument.
Resistance Temperature Detector γ1, ··· γn are temperature coefficients of resistivity R0 is the resistance of the sensor at a reference temperature T0.
Example • An RTD forms one arm of an equal-arm Wheatstone bridge. The fixed resistances, R2 and R3 are equal to 25Ω±0.01 Ω (95%). The RTD has a resistance of 25Ωat a temperature of 0oC and is used to measure a temperature that is steady in time. Suppose the coefficient of resistance for this RTD is 0.004oC-1.A temperature measurement is made by placing the RTD in the measuring environment and balancing the bridge by adjusting R1. The value of R1 required to balance the bridge is 37.36Ω. Determine the temperature of the RTD and its uncertainty.