Download Resistance measurement

Measurement and instrumentation 2011
Measurement and Instrumentation 2. .................................................................................................... 2
Resistance measurement .................................................................................................................... 2
What is a resistance? ....................................................................................................................... 3
Using Ohms law (indirect measurement)........................................................................................ 3
Direct measurement (multimeters, two wires method) ................................................................. 3
By comparison of measured voltages ............................................................................................. 4
By comparison of measured currents ............................................................................................. 4
Digital multimeter ........................................................................................................................... 4
Wheatstone bridge .......................................................................................................................... 6
Impedance measurement ................................................................................................................... 6
What is the impedance? .................................................................................................................. 7
Rotating vectors .......................................................................................................................... 7
My Sim ......................................................................................................................................... 7
Complex numbers – phasor reprezantation................................................................................ 8
Three voltmeters method ............................................................................................................... 8
Bridge methods ............................................................................................................................... 9
Maxwell – Wien Bridge.............................................................................................................. 10
Wien – Bridge ............................................................................................................................ 10
Resonance method........................................................................................................................ 11
Digital multimeters ........................................................................................................................ 11
Alternative images......................................................................................................................... 11
qualitiy factor ............................................................................................................................ 12
loss factor .................................................................................................................................. 12
Measuring impedances with vector voltmeter ............................................................................. 12
Power measurement ........................................................................................................................ 13
DC – power measurement............................................................................................................. 13
AC – power basics.......................................................................................................................... 14
Active, reactive power, power factor, instantaneous power.................................................... 14
Three voltmeters measurement ............................................................................................... 14
Wattmeters ............................................................................................................................... 14
Electronic methods.................................................................................................................... 14
Digital methods ......................................................................................................................... 15
Hall-sensor ................................................................................................................................. 15
Energy measurement ........................................................................................................................ 15
DC – meter..................................................................................................................................... 15
Using by electromagnetic induction.............................................................................................. 16
Electronic energy meters .............................................................................................................. 17
Digital meters ................................................................................................................................ 18
Calibration ..................................................................................................................................... 18
Frequency and time measurement ................................................................................................... 18
Resonance method........................................................................................................................ 19
Frequency – voltage conversion.................................................................................................... 19
Digital frequency meter................................................................................................................. 20
Digital time measurement ............................................................................................................. 21
Time interval measurement .......................................................................................................... 22
Phase shift measurement .............................................................................................................. 23
Generators......................................................................................................................................... 24
Generator basics............................................................................................................................ 24
Oscillator basics ............................................................................................................................. 24
amplitude condition phase shift condition of oscillation .......................................................... 24
Sound frequency oscillator ............................................................................................................ 24
Signal generators ........................................................................................................................... 25
Meissner oscillator .................................................................................................................... 26
Modulation ................................................................................................................................ 27
Function generators ..................................................................................................................... 29
Digital function generator ......................................................................................................... 30
Pulse - generator ........................................................................................................................... 30
Power supplies .................................................................................................................................. 32
AC – stabilized power supply......................................................................................................... 32
Swiching power supply .................................................................................................................. 34
Measurement and Instrumentation 2.
Resistance measurement
What is a resistance?
𝑈 ~ 𝐼,
𝑈
𝑅= ,
𝐼
𝑙
𝑅 =𝜌∗
𝐴
Using Ohms law (indirect measurement)
Direct measurement (multimeters, two wires method)
By comparison of measured voltages
By comparison of measured currents
Digital multimeter
Electrical resistance is the easiest electrical property to measure precisely over a wide range at
moderate cost. A simple digital multimeter costing a few tens of dollars can measure
resistances in the range 10 ohm to 10 megaohm with a precision of about 1% using a two-wire
technique (circuit 1).
Circuit 1. Two-wire resistance measurement, RX = (V/I) − RL1 − RL2.
The precision of the two-wire method is limited by uncertainties in the values of the lead
resistances RL1 and RL2.
Circuits 2 & 3. Three-wire resistance measurement methods.
Providing the leads are well-matched, three-wire techniques can be used. Circuit 2 employs
two matched current sources, I1 and I2, to eliminate the effects of lead resistance providing
RL1 = RL2. Circuit 3 is an AC-bridge that is in-balance when RX = RY providing
RL1 = RL3. If a lock-in amplifier is used as a null-detector, determination of RX with an
extremely low excitation current is possible.
The 4-Wire 'Kelvin' method (circuit 4) is used in difficult cases when lead resistances vary,
RX is very small, or when very high accuracy is required. The method is immune to the
influence of lead resistance and is limited by the quality of the constant current source and
voltage measurement. Thermo-electric voltages can be eliminated by averaging two
measurements with the polarity of the excitation current reversed.
http://www.sciencebuddies.org/science-fair-projects/project_ideas/Elec_p025.shtml
Wheatstone bridge
Impedance measurement
What is the impedance?
Rotating vectors
My Sim
2
2
Current rotating vector
Real current in time
1
Voltage rotating vector
0
-1
áramerősség, feszültség
feszültség, áram y koordináta
1
0
-1
Real voltage in time
-2
-2
-2
-1
0
feszültség, áram x koordináta
1
2
0
2
4
idő (sec)
6
8
Complex numbers – phasor reprezantation
𝑍̅ = 𝑍 ∗ (cos(𝜑) + 𝑖 ∗ sin(𝜑))
̅ = 𝑍̅ ∗ 𝐼 ̅
𝑈
𝑍̅ = 𝑍 ∗ (cos(𝜑) + 𝑖 ∗ sin(𝜑))
𝑈𝑚𝑎𝑥 = 𝐼𝑚𝑎𝑥 ∗ 𝑍, 𝜑𝑈 = 𝜑𝐼 + 𝜑
Three voltmeters method
Bridge methods
- Balanced Bridge
Maxwell – Wien Bridge
Wien – Bridge
Resonance method
Digital multimeters
Alternative images
qualitiy factor
loss factor
Alternative image for real resistor
Measuring impedances with vector voltmeter
Power measurement
DC – power measurement
AC – power basics
Active, reactive power, power factor, instantaneous power
Three voltmeters measurement
Wattmeters
Electronic methods
Digital methods
Hall-sensor
Energy measurement
DC – meter
Electrodynamic DC - meter
Dc electric engine,
without metal
Aluminium disc with
permanent magnet
Using by electromagnetic induction
Magnetic field  Torque  Turning plate  Counter
Ac induction energy meter
Electronic energy meters
Analog multipliers
Digital meters
Calibration
Frequency and time measurement
Frequency and Periodic Time
measurement
T (sec)
Resonance method
Measuring frequency
Resonance method:
-mechanical
-AC RLC circuits
measured
current
C1 1u R1 1k
f0 
1
2   L  C
L1 1m
AM1
+
+
R2 1k
A
VG1
Resonance at
f_0 frequency
frequency
Frequency – voltage conversion
Frequency conversion method
Effective U of the pulse signal proportional to frequency of the sinus signal
Digital frequency meter
Digital time measurement
Time interval measurement
Phase shift measurement
Generators
Generator basics
Oscillator basics
amplitude condition phase shift condition of oscillation
Sound frequency oscillator
Signal generators
Meissner oscillator
Modulation
Function generators
Digital function generator
Pulse - generator
Power supplies
AC – stabilized power supply
Swiching power supply