E E 1205 Measurements, Data & Accuracy Measurements • Essential to Engineering • Multitude of Sensors – – – – Electromagnetic Hall Effect Photonic Simple • Yardstick • Spring Scales • Measuring cups.
Download ReportTranscript E E 1205 Measurements, Data & Accuracy Measurements • Essential to Engineering • Multitude of Sensors – – – – Electromagnetic Hall Effect Photonic Simple • Yardstick • Spring Scales • Measuring cups.
E E 1205 Measurements, Data & Accuracy Measurements • Essential to Engineering • Multitude of Sensors – – – – Electromagnetic Hall Effect Photonic Simple • Yardstick • Spring Scales • Measuring cups Measurements • Electrical – Conductivity – Field Strength • Electric • Magnetic – – – – – Frequency/Timing Voltage Current Power/Energy Luminosity Representing Data • Significant Digits – 3.14159 – 2.73 (6 sig. digits) (3 sig. digits) • Decimal Places – 3.14159 – 0.036 (5 dec. places) (3 dec. places) Representing Data • Scientific Notation – 7.382 x 10-8 – -4.690 x 105 • Engineering Notation – 45.2 x 10-6 – -613.8 x 103 Rounding Off Numbers • 52.3691 – 52.369 – 52.37 – 52.4 • 73.85 – 73.8 • 27.55 – 27.6 Excessive Significant Digits • Do not display more significant digits than can be justified – Area calculation: l = 27.4 cm, w = 18.6 cm A = l x w = 510 cm2 , not 509.64 Voltage Divider Circuit + V1 I Vs R1 R2 + V2 - Measure V2 Vs I Vs I R1 R2 R1 R2 Vs R2 V2 I R2 R2 Vs R1 R2 R1 R2 Loaded Voltage Divider R1 Vs R2 RL Req R2 RL R2 RL Vo Vs R1 R2 RL R2 RL + R2 Vo - Vo Vs RL Req Req R1 Voltage Divider Equations R2 Vo Vs R1 R2 Unloaded: Loaded: Vo Vs If RL >> R2: R2 R2 R1 1 R2 RL R2 Vo Vs R1 R2 Current Divider Circuit (1/2) Is + vo - i1 i2 G1 G2 If there are only two paths: Is i1 i2 vo G1 G2 G1 G2 G2 i2 I s Is 1 G1 G2 1 R1 R2 1 R2 Current Divider Circuit (2/2) In general: 1 i2 I s 1 R1 R2 1 R2 R1R2 R1 Is R1 R2 R1 R2 Gn in I s G1 G2 Gn D’Arsonval Meter Movement • • • • Permanent Magnet Frame Torque on rotor proportional to coil current Restraint spring opposes electric torque Angular deflection of indicator proportional to rotor coil current S N A D’Arsonval Voltmeter D’Arsonval Voltmeter • Small voltage rating on movement (~50 mV) • Small current rating on movement (~1 mA) • Must use voltage dropping resistor, Rv Rv + Vx - Id'A + VRv - + Vd'A - Example: 1 Volt F.S. Voltmeter 950 W 1 mA + + 0.95 V 1.0 V - + 50 mV - Note: d’Arsonval movement has resistance of 50 W Scale chosen for 1.0 volt full deflection. Example: 10V F.S. Voltmeter 9950 W 1 mA + + 9.95 V 10 V - + 50 mV - Scale chosen for 10 volts full deflection. D’Arsonval Ammeter • Small voltage rating on movement (~50 mV) • Small current rating on movement (~1 mA) • Must use current bypass conductor, Ga Ix IGa Ga + Vd'A - Id'A Example: 1 Amp F.S. Ammeter 1.0 A 19.98 S 999 mA + 50 mV - 1 mA Note: d’Arsonval movement has conductance of 0.02 S Ga = 19.98 S has ~50.050 mW resistance. Scale chosen for 1.0 amp full deflection. Example: 10 Amp F.S. Ammeter 10 A 199.98 S 9.999 A + 50 mV - 1 mA Ga = 199.98 S has ~5.0005 mW resistance. Scale chosen for 10 amp full deflection. Measurement Errors • • • • Inherent Instrument Error Poor Calibration Improper Use of Instrument Application of Instrument Changes What was to be Measured – Ideal Voltmeters have Infinite Resistance – Ideal Ammeters have Zero Resistance Example: Voltage Measurement 400 W 45 V True Voltage: 100 W + Vo - 10 kW voltmeter 100 W Vo 45V 9V 500 W (If voltmeter removed) Example: Voltage Measurement Measured Voltage: 100 W Vo 45V 8.9286 100 W 400 W 1 100 W 10 k W 8.9286V % Error 1100% 0.794% 9.0V Another Voltage Measurement (1/2) 40 kW 45 V True Voltage: 10 kW + Vo - 10 kW voltmeter 10 k W Vo 45V 9V 50 k W (If voltmeter removed) Another Voltage Measurement (2/2) Measured Voltage: 10 k W Vo 45V 5.0V 10 k W 40 k W 1 10 k W 10 k W 5.0V % Error 1100% 44.44% 9.0V Example: Current Measurement (1/2) 100 W 5A 25 W True Current: Io 50 mW Ammeter 25 W Io 5 A 1.0 A 125 W (If ammeter replaced by short circuit) Example: Current Measurement (2/2) Measured Current: 25 W Io 5 A 0.9996 A 125.05 W 0.9996 A % Error 1100% .04% 1.0 A Another Current Measurement (1/2) 100 mW Io 5A 25 mW True Current: 50 mW Ammeter 25 mW Io 5 A 1.0 A 125 mW (If ammeter replaced by short circuit) Another Current Measurement (2/2) Measured Current: 25 mW Io 5 A 0.7143 A 175 mW 0.7143 A % Error 1100% 28.57% 1.0 A A Digital Voltmeter • Integrating Converter • Dependent on Vref • Dependent on Temperature • Independent of RC How the DVM Works Vout up Vin tu RC Vout down 0 Vref Vref Vin td tu RC RC RC td Vout up td Vin Vref tu DVM Example Vref 5V C 10 F If R 10k W tu 100ms td 50ms 50ms Vin 5V 2.5V 100ms Measuring Resistance • Indirect – Measure Voltage across Resistor – Measure Current through Resistor – Calculate Resistance (Inaccurate) • d’Arsonval Ohmmeter – Very Simple – Inaccurate • Wheatstone Bridge (Most Accurate) D’Arsonval Ohmmeter Rb Vb Rx Radj Need to adjust Radj and zero setting each scale change. Ohmmeter Example 45 0 10 mA Full Scale (Outer Numbers) Rb+Radj+Rd’A=150 W Inner (Nonlinear) Scale in Ohms 10 0 0 50 8 150 5 7. 2. 5 5 Vb=1.5 V Wheatstone Bridge c I1 Rg R1 R2 Vad = Vbd + Vab - a Vg I2 b Iab R3 I3 d Vab= 0 and Iab= 0 I1 = I 3 I2 = I x R1I1=R2I2 Rx Ix R3I3=RxIx Rx R2 R3 R1 Example: Wheatstone Bridge c 100 W 150 W 300 W Rq I a 1 kV 450 W b 900 W d 150 W 300 W 450 W 900 W I=2A