1. Instrumentation (AMME2700) 1 Instrumentation Dr. Xiaofeng Wu

2. Instrumentation (AMME2700) Contents to be Tested  Circuitry Theorem: Ohm’s law, passive convention, series and parallel resistors, voltage and current divider, Thevenin’s and Norton’s equivalent circuitry, node and mesh analysis  Signal conditioning: Operational amplifier, 1 st or 2 nd order low pass and high pass filter, Laplace transfer function and Laplace transform pairs, wheatstone bridge circuit  A/D conversion: resolution  Sensor: Strain gauge, potentiometer, temperature, uncertainty 2

3. Instrumentation (AMME2700) Note  Quiz 2: Friday week 13  Assignment 3: 2pm Friday week 13  Make-up lab: 10am to 13.00pm 8 th June 3

4. Instrumentation (AMME2700) Resistance Temperature Detector γ 1, ··· γ n are temperature coefficients of resistivity R 0 is the resistance of the sensor at a reference temperature T 0.

5. Instrumentation (AMME2700) Sensor Circuit

6. Instrumentation (AMME2700) Measurement Errors and Uncertainties 6 Errors are a property of the measurement. Measurement is the process of assigning a value to a physical variable based on a sampling from the population of that variable. Uncertainty is a property of the result. The outcome of a measurement is a result, and the uncertainty quantifies the quality of that result. Errors are effects, and uncertainties are numbers. While errors are the effects that cause a measured value to differ from the true value, the uncertainty is an assigned numerical value that quantifies the probable range of these errors.

7. Instrumentation (AMME2700) Distribution of Errors

8. Instrumentation (AMME2700) Propagation of Uncertainty 8 A general relationship between some dependent variable y and a measured variable x

9. Instrumentation (AMME2700) Quantization Uncertainty and Error

10. Instrumentation (AMME2700) Design Stage Uncertainty The zero-order uncertainty, u 0, 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.

11. Instrumentation (AMME2700) Example 1 11 An accelerometer with a charge sensitivity of 100pC/g ±1pC/g (95%) and a capacitance of 200pF ± 2pF (95%) is connected to a voltage follower with an input connector capacitance of 20pF (in parallel with the cable capacitance), a 10,000pF blocking capacitor and a 100MΩ resistance. A 3m long cable with a capacitance of 280pF connects the accelerometer and the voltage follower. Determine: 1.The schematic of the instrument; 2.The instrument’s sensitivity in mv/g; 3.The uncertainty of v o if the acceleration is 1g in the high frequency band. 4.If we use a 5V 10-bit A/D to sample the voltage output, what is the uncertainty in the digital output.

12. Instrumentation (AMME2700) Example 2  An RTD forms one arm of an equal-arm Wheatstone bridge. The fixed resistances, R 2 and R 3 are equal to 25Ω±0.01 Ω (95%). The RTD has a resistance of 25Ω at a temperature of 0 o C and is used to measure a temperature that is steady in time. Suppose the coefficient of resistance for this RTD is 0.004 o C -1. A temperature measurement is made by placing the RTD in the measuring environment and balancing the bridge by adjusting R 1. The value of R1 required to balance the bridge is 37.36Ω. Determine the temperature of the RTD and its uncertainty.