Instrumentation Dr. Xiaofeng Wu 1 1

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, 1st or 2nd 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

Signal Conditioning Circuits Introduction Power Supply Signal Conditioning Circuits Amplifier Transducer Command Recorder Data Processor Controller

Resistive Potentiometer

Strain Gage ΔR is the change in resistance caused by strain R is the resistance of the undeformed gauge ϵ = ΔL/L is strain Stress: σ=ε×Em=F/A (N/m2), where F is the force, A is the area, Em is the modulus of elasticity 5

Resistance Temperature Detector γ1, ··· γn are temperature coefficients of resistivity R0 is the resistance of the sensor at a reference temperature T0.

Piezoelectric Sensors

Wheatstone Bridge 8

Second-Order RLC Filters

Laplace Transfer Function

Laplace Transform Pairs

Amplifier An amplifier is used to increase low-level signals from a transducer to a level sufficiently high. vi vo vs

Inverting Amplifier 13

Noninverting Amplifier 14

Active Filters 15

A/D Resolution and Quantization Error

Propagation of Uncertainty A general relationship between some dependent variable y and a measured variable x

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.

Example 1 A strain gauge is mounted on a steel cantilever beam of rectangular cross section. The gauge is connected in a Wheatstone bridge; initially Rgauge=R2=R3=R4=120 Ω. A gauge resistance change of 0.1 Ω is measured for the loading condition and gauge orientation shown in the following figure. If the gauge factor is 2±0.02 (95%) estimate the strain; Suppose the uncertainty of the resistance change the strain gauge, is ±0.002 Ω (95%). Estimate the uncertainty in the measured strain due to the uncertainties in the bridge resistances and gauge factor. Assume that the bridge is balanced when there is no external force; x h b 19

Final Exam Four questions and 2 hours