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ME365chap9_bdgci

# ME365chap9_bdgci - Bridge Circuits Variable Impedance...

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KARTIK B. ARIYUR PURDUE UNIVERSITY Bridge Circuits & Variable Impedance Devices Strain Gages Bridge Circuits Variable Impedance Devices 1

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KARTIK B. ARIYUR PURDUE UNIVERSITY Strain Gages Strain Gage The change in resistance of the device is a reasonably linear function of its deformation. The elastic element to which the strain gage is attached deforms in response to the physical phenomenon (input) that is of interest, for example, force, torque, pressure, displacement, acceleration, …etc. Elastic Element Strain Gage Input Force; Torque; Pressure; ... Deformation Variable Resistance Q: How does one measure resistance variation? 2
KARTIK B. ARIYUR PURDUE UNIVERSITY Expand resistance R into a Taylor series and ignore higher order terms: Define Gage Factor G f : Strain Gage Active Axis Passive Axis Resistance of wire: Resistivity Length of Wire Cross Sectional Area R L A L A : : : R R G R R R R G f f    1 2 1 R R R R R L L R A A R A L L A A L A 0 2   where  3

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KARTIK B. ARIYUR PURDUE UNIVERSITY Strain Gages Metallic Strain Gages: Gage Factor: G f = 2.0 ~ 2.2 R 0 = 120 W  1 W . R =  2.4 W ~ 4.8 W . Maximum gage current: 15 mA to 100 mA . Relatively low sensitivity to temperature variation. Semiconductor Strain Gage Silicon (Si) “doped” with phosphorus (P), arsenic (As) or boron (B). Gage Factor: G f = 100 ~ 175 R 0 = 120 W  5 W . High sensitivity to temperature change. 4
KARTIK B. ARIYUR PURDUE UNIVERSITY Measure Resistance (Impedance) Variation Use constant voltage supply and measure current variation. Use constant current source and measure voltage variation. Strain Gages R 0 + R V s i Amp Meter i V R R i R V V R s s s 0 0 1 1 R 1/ i R 0 + R i s i s V i R R V i R i R o s o s s = = ( ) 0 0 R V o V o 5

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KARTIK B. ARIYUR PURDUE UNIVERSITY Measure Resistance (Impedance) Variation Use constant voltage supply and measure voltage variation. Strain Gages V R R R R R V V R R R V Vs R R R R R o s o s = ( ) ( ) = if 0 1 0 0 1 0 1 0 0  R V o R 0 + R V s V o R 1 6
KARTIK B. ARIYUR PURDUE UNIVERSITY Strain Gages Ex: In the previous case, let V s = 5 V , R 0 = R 1 = 100 W , and | R| < 2 W, calculate the “nominal” output voltage and the maximum output voltage variation. If a 10-bit ADC with an input range from 0 to 5 V is used to digitize the output voltage, how many effective bits of resolution are available to measure the variation in resistance? 2.5 2 5 0.05 200 nom V V V V 7

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