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Set13

# Set13 - Bridge Circuits& Variable Bridge Circuits&...

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Unformatted text preview: Bridge Circuits & Variable Bridge Circuits & Variable Bridge Circuits & Variable Bridge Circuits & Variable Impedance Devices Impedance Devices Impedance Devices Impedance Devices • Strain Gages • Bridge Circuits • Variable Impedance Devices ME365 Bridge Circuits Slide 1 Galen King Purdue University Strain Gages Strain Gages Strain Gages 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) ME365 Bridge Circuits Slide 2 Galen King Purdue University 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? Expand resistance R into a Taylor series and ignore higher order terms: Strain Gage Strain Gage Strain Gage Strain Gage Active Axis Passive Axis R R R R R L L R A A R L L = + = + + ∆ ∆ ∆ ∆ ∆ρ ρ where ∂ ∂ ∂ ∂ ∂ ∂ρ ρ ρ ME365 Bridge Circuits Slide 3 Galen King Purdue University Define Gage Factor G f : Resistance of wire: Resistivity Length of Wire Cross Sectional Area R L A L A = ρ ρ : : : v v v v A L A A A R R L L A A =- + = =- + = + + 2 2 1 2 ∆ ∆ ∆ρ ∆ ∆ ∆ ∆ρ ∆ρ ( ) ε νε ρ ν ε ρ dD¡ G R R R R G f f = = + + ⇒ = ∆ ∆ρ ∆ ε ν ε ρ ε 1 2 1 Strain Gages Strain Gages Strain Gages Strain Gages • Metallic Strain Gages: – Gage Factor: G f = 2.0 ~ 2.2 – R = 120 Ω± 1 Ω . = .4Ω∼4.8Ω • Semiconductor Strain Gage – Silicon (Si) “doped” with phosphorus (P), arsenic (As) or boron (B). ME365 Bridge Circuits Slide 4 Galen King Purdue University – ∆ R = - 2.4Ω∼4.8Ω . – Maximum gage current: 15 mA to 100 mA . – Relatively low sensitivity to temperature variation. – Gage Factor: G f = 100 ~ 175 – R = 120 Ω± 5 Ω . – High sensitivity to temperature change. • Measure Resistance (Impedance) Variation – Use constant voltage supply and measure current variation. Strain Gages Strain Gages Strain Gages Strain Gages R + ∆ R V s i Amp eter i V R R R s = + 1 1 ∆ 1/ i ME365 Bridge Circuits Slide 5 Galen King Purdue University – Use constant current source and measure voltage variation. Meter v v i V V R s s ⇒ = + ∆ t R + ∆ R i s i s v V i R R V i R i R o s o s s = = ( ) + ⇒ + ∆ ∆ t V o V o • Measure Resistance (Impedance) Variation – Use constant voltage supply and measure voltage variation. Strain Gages Strain Gages Strain Gages Strain Gages V R R R R R V o s = ( ) ( ) 1 + + + ∆ ∆ V R 1 ME365 Bridge Circuits Slide 6 Galen King Purdue University V R R R V Vs R R R R R o s = if 1 1 ⇒ + + + << ∆ ∆ d D h ¡ h t V o R + ∆ R V s o Strain Gages Strain Gages Strain Gages Strain Gages Ex: In the previous case, let V s = 5 V , R = R 1 = 100 Ω , and | ∆ R| < 2 Ω, calculate the “nominal” output voltage and the maximum output voltage...
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