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 10 5 • Engineering Notation – 45.2 x 10 -6 – -613.8 x 10 3
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 cm 2 , not 509.64
Measurement
Accuracy and Precision
Voltage Divider Circuit
+ V 1 V s I R 1 R 2 + V 2 Measure V 2
V s
1
V
2 2
R
2
R
1
V s
R
2
R
2
I
R
1
V s
R
2
R
1
R
2
R
2
V s
Loaded Voltage Divider
R 1 V s
R eq
R R R
2
L
2
R L V o
V s
1 2
R R
2
L R L
R R
2
L
R 2 + V o R L
V o
V s R eq R eq
R
1
Voltage Divider Equations
Unloaded: Loaded:
V o V o
V s V s R
1
R
1
R
2
R
2
R
2
R
2
R L
If R L >> R 2 :
V o
V s R
1
R
2
R
2
R
2
Current Divider Circuit (1/2)
I s + v o i 1 G 1 i 2 G 2 If there are only two paths:
v o
i
1
G
1
i
2
G
2
G
1
I
s G
2
i
2
I s G
1
G
2
G
2
I s
1
R
1 1
R
2 1
R
2
Current Divider Circuit (2/2)
i
2
I s
1
R
1 1
R
2 1
R
2
R R
1 2
R R
1 2
I s R
1
R
1
R
2
In general:
i n
I s G
1
G
2
G n
G n
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, R v
+ V x R v I + V Rv d'A + V d'A -
Example: 1 Volt F.S. Voltmeter 950
W
1 mA + 1.0 V + 0.95 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 + 10 V + 9.95 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, G a
I x G a I Ga + V d'A I d'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 G a = 19.98 S has ~50.050 m
W
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 G a = 199.98 S has ~5.0005 m
W
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 100
W
+ V o 10 k
W
volt meter True Voltage:
V o
45
V
100 W 500 W 9
V
(If voltmeter removed)
Example: Voltage Measurement Measured Voltage:
V o
45
V
400 100 W 100 W 10
k
W 100 W 8.9286
%
Error
8.9286
V
9.0
V
0.794%
Another Voltage Measurement (1/2) 40 k
W
45 V 10 k
W
+ V o 10 k
W
volt meter True Voltage:
V o
45
V
10
k
W 50
k
W 9
V
(If voltmeter removed)
Another Voltage Measurement (2/2) Measured Voltage:
V o
45
V
40
k
10
k
W 10
k
W 10
k
W 10
k
W 5.0
V
%
Error
5.0
V
9.0
V
44.44%
Example: Current Measurement (1/2) 100
W
5A 25
W
I o 50 m
W
Ammeter True Current:
I o
5 25
A
125 W W 1.0
A
(If ammeter replaced by short circuit)
Example: Current Measurement (2/2) Measured Current:
I o
5 25 W
A
125.05
W 0.9996
A
%
Error
0.9996
A
1.0
A
.04%
Another Current Measurement (1/2) 100 m
W
5A 25 m
W
I o 50 m
W
Ammeter True Current:
I o
5 25
A
125
m
W
m
W 1.0
A
(If ammeter replaced by short circuit)
Another Current Measurement (2/2) Measured Current:
I o
5 25
A
175
m
W
m
W 0.7143
A
%
Error
0.7143
A
1.0
A
28.57%
A Digital Voltmeter • Integrating Converter • Dependent on V ref • Dependent on Temperature • Independent of RC
How the DVM Works
V V
V in RC t u V ref RC t d
V V ref RC t d
V in RC t u V in
V ref t d t u
DVM Example
V ref
5
V R
10
k
W
C
If 10
t d
F t u
50
ms
100
ms V in
5
V
50
ms
100
ms
2.5
V
Hall Effect Transducer • Use as Gaussmeter • Use as Wattmeter
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
R
b V b
R
x
R
adj Need to adjust R adj change.
and zero setting each scale
Ohmmeter Example 5 2.
5 45 0 150 50 7.5
8 10 mA Full Scale (Outer Numbers) R b +R adj +R d’A =150
W
Inner (Nonlinear) Scale in Ohms V b =1.5 V
Wheatstone Bridge
R g V g R 1 a c I 1 R 2 + Vab I ab R 3 R x I 3 d b I 2 I x V ab = 0 and I ab = 0 V ad = V bd I 1 = I 3 R R
R x
1 3 I I 1 3 =R =R I
2 3
R
1
2 x 2 I I 2 x = I x
100
W
I 1 kV
Example: Wheatstone Bridge
c 150
W
a 450
W
R q 300
W
b 900
W
d
150 W 450 W 300 W 900 W
I = 2 A