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lec24_handout

# lec24_handout - From last time… • Bridge circuits Vs...

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Unformatted text preview: From last time… • Bridge circuits! Vs + − VO 1 4 – One arm active, use Z1 or Z3 ⋅ – Two arms active (same sign), use Z1 and Z3 – Two arms active (push-pull), use Z1 and Z4 1 2 ⋅ ⋅ε – Four arms active ME365 Bridge Circuits 1 Bridge Circuits • Calibration 1 4 ⋅ Rc – Balance the bridge while the switch is opened. – Use a calibration resistor RC to simulate a change in resistance ΔRCAL in arm 1 due to an equivalent strain εCAL. Δ ME365 Bridge Circuits 2 Bridge Circuits ME365 Bridge Circuits 3 Bridge Circuits Ex: To calibrate a bridge circuit, what should the calibration resistance be to simulate the output of a single active arm bridge with a strain of 0.02 in/in? The gage factor is 2.2 and R0 = 100 Ω. Rc Ex: Suppose that R0 = 120 Ω and the gage factor is 2.1. What equivalent strain will be indicated if the calibration resistance RC = 100 kΩ. ME365 Bridge Circuits 4 Bridge Circuits ME365 Bridge Circuits 5 Variable Impedance Devices • Potentiometer (Displacement Sensor) Without output loading RL , the potentiometer output voltage VTH is: VS 1-x + − RP x VTH RL VOUT 1 To measure VTH , a voltmeter with input impedance RL is used. The measured output voltage VOUT is: ME365 Bridge Circuits ZOUT VTH ZL VOUT 6 Variable Impedance Devices • Potentiometer (Displacement Sensor) 1 1 1 1-x OUT VS + − RP x VTH ME365 Bridge Circuits RL VOUT 7 Variable Impedance Devices • Variable Capacitance Displacement Sensor • For a typical device: 5 mm 100 mm 5 (relative permittivity of material between plates) 8.854 10 F/m (permittivity of space) Q: How would one interface with this displacement sensor? ME365 Bridge Circuits 8 Variable Impedance Devices • Variable Capacitance Displacement Sensor + Place C1 and C2 at the 1st and 4th arms of a bridge circuit, respectively. Let the resistance in arms 2 and 3 be the same: Vs − VOUT Q: What kind of supply voltage (VS) should we use? - Constant DC voltage, i.e. 6 V (DC) - Oscillating voltage source? ME365 Bridge Circuits 9 Variable Impedance Devices The output voltage VO is: ME365 Bridge Circuits 10 Variable Impedance Devices • Variable Capacitance Displacement Sensor – DC Supply Voltage constant • Capacitance is infinite at DC • No capacitance change will be sensed – AC Supply Voltage sin ME365 Bridge Circuits 11 Variable Impedance Devices • Variable Capacitance Displacement Sensor AC excited bridge circuit with variable inductance sensor: 1 ⋅ ⋅⋅ 2 Let ME365 Bridge Circuits sin 12 Ex: 1 2 ⋅ ⋅ ⋅ Let K = 2 VS = 5 sin(2π10t) [V] Output Voltage (V) x = 4 + 2 cos(2π1t) [μm] Input Distance (um) Variable Impedance Devices 4 2 0 -2 -4 -6 0 0.5 1 Time (sec) 1.5 2 0.5 1 Time (sec) 1.5 2 40 20 0 -20 -40 -60 0 ME365 Bridge Circuits 13 Variable Impedance Devices • Variable Inductance Displacement Sensor 1 1 For a typical device: d = 0.25 in d-x 2d d +x L0 = 25 mH α = 1538.4 m-1 Q: How would one use this displacement sensor? ME365 Bridge Circuits 14 Variable Impedance Devices • Variable Inductance Displacement Sensor 1 1 + Vs Place L1 and L2 at the 1st and 4th arms of a bridge circuit, respectively. Let the resistance in arms 2 and 3 be the same: − VOUT Q: What kind of supply voltage (VS) should we use? - Constant DC voltage, i.e. 6 V (DC) - Oscillating voltage source? ME365 Bridge Circuits 15 Variable Impedance Devices The output voltage VO is: ME365 Bridge Circuits 16 Variable Impedance Devices • Variable Inductance Displacement Sensor – DC Supply Voltage constant • Inductance is zero at DC • No inductance change will be sensed sin – AC Supply Voltage ME365 Bridge Circuits 17 Variable Impedance Devices • Variable Capacitance Displacement Sensor AC excited bridge circuit with variable inductance sensor: 1 21 Let ME365 Bridge Circuits ⋅ ⋅ ⋅ sin 18 Ex: 1 2 ⋅ ⋅ Let K = 2 VS = 5 sin(2π10t) [V] Output Voltage (V) x = 4 + 2 cos(2π1t) [μm] ⋅ Input Distance (um) Variable Impedance Devices ME365 Bridge Circuits 4 2 0 -2 -4 -6 0 0.5 1 Time (sec) 1.5 2 0.5 1 Time (sec) 1.5 2 40 20 0 -20 -40 -60 0 19 ...
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