E E 1205 Measurements, Data & Accuracy Measurements • Essential to Engineering • Multitude of Sensors – – – – Electromagnetic Hall Effect Photonic Simple • Yardstick • Spring Scales • Measuring cups.
Download
Report
Transcript 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