Transcript Instrumentation Measurement Device

1.0 Device for Current Measurement
1.1 Analog ammeter
1.2 Galvanometer
2.0 Device for Voltage Measurement
2.1 Analog voltmeter
2.2 Oscilloscope
2.3 Potentiometer
3.0 Device for Resistance Measurement
3.1 Ohmmeter
3.2 Wheatstone bridge circuit
4.0
Digital Multimeter

A voltmeter is an instrument used for measuring the
potential difference between two points in an electric
circuit.
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
A voltmeter is placed in parallel with a circuit element
to measure the voltage drop across it and must be
designed to draw very little current from the circuit so
that it does not appreciably change the circuit it is
measuring.
To accomplish this, a large resistor is placed in series
with the galvanometer.
Its value is chosen so that the design voltage placed
across the meter will cause the meter to deflect to its
full-scale reading.
A galvanometer full-scale current is very small: on the
order of milliamperes.
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The moving coil galvanometer is one example of this type of
voltmeter. It employs a small coil of fine wire suspended in
a strong magnetic field.
When an electrical current is applied, the galvanometer's
indicator rotates and compresses a small spring.
The angular rotation is proportional to the current that is
flowing through the coil.
For use as a voltmeter, a series resistance is added so that
the angular rotation becomes proportional to the applied
voltage.


The basic d’Ársonval meter
movement can be converted to
a dc voltmeter by connecting a
multiplier Rs in series with the
meter movement
The purpose of the multiplier:


is to extend the voltage range of
the meter
to limit current through the
d’Arsonval meter movement to a
maximum full-scale deflection
current.
Fig 2-1 The basic d’Arsonval meter
Movement Used In A DC Voltmeter
8

To find the value of the multiplier resistor,
first determine the sensitivity, S, of the meter
movement.
1
Sensitivit y 
(/V)
I fs
Rs  S  Range  Internal Resistance
9
Calculate the value of the multiplier
resistance on the 50V range of a dc voltmeter
that used a 500A meter movement with an
internal resistance of 1k.
10
Sensitivity,
1
1
S

 2k 
V
I fs 500
Multiplier, Rs = S X Range – internal Resistance
= (2k X 50) – 1k
= 99k
11
When a voltmeter is used to measure the voltage
across a circuit component, the voltmeter circuit
itself is in parallel with the circuit component. Since
the parallel combination of two resistors is less than
either resistor alone, the resistance seen by the
source is less with the voltmeter connected than
without. Therefore, the voltage across the component
is less whenever the voltmeter is connected. The
decrease in voltage may be negligible or it may be
appreciable, depending on the sensitivity of the
voltmeter being used. This effect is called voltmeter
loading. The resulting error is called a loading error.
12
Two different voltmeters are used to
measure the voltage across resistor RB
in the circuit of Figure 2-2. The meters
are as follows.
Meter A : S = 1k/V, Rm = 0.2k,
range = 10V
Meter B : S = 20k/V, Rm = 1.5k,
range=10V
Calculate:
(a)
Voltage across RB without any meter
connected across it.
(b) Voltage across RB when meter A is used.
(c) Voltage across RB when meter B is used
(d) Error in voltmeter readings.
Fig. 2.2
13
(a) The voltage across resistor RB without either
meter connected is found Using the voltage
divider equation:
 RB

VRB  E 



R

R
B 
 A
 5kΩ 
 30V 

25k

5k


 5V
14
(b) starting with meter A,
the total resistance it
presents to the circuit is
RTA  S  Range  1k/V 10V  10kΩ
The parallel combination
of RB and meter A is
Therefore, the voltage reading
obtained with meter A, determined
by the voltage divider equation, is
RB  RTA
Re1 
RB  RTA
5kΩ 10kΩ
5kΩ  10kΩ
 3.33kΩ

 Re1 
VRB  E 

R

R
A
 e1
3.33kΩ
 30V 
3.33kΩ  25kΩ
 3.53V
15
(c) The total resistance that meter B presents to the circuit is
RTB = S x Range = 20k/V x 10 V = 200 k
The parallel combination of RB and meter B is
Re2 = (RB x RTB)/(RB + RTB) = (5kx200k)/(5k+200k) = 4.88 k
Therefore, the voltage reading obtained with meter B,
determined by use of the voltage divider equation, is
VRB = E(Re2)/(Re2+RA) = 30 V x (4.88k)/(4.88k+25k)
= 4.9 V
16
(d)
(Expected value - Measured value)
Voltmeter A error 
100%
Expected value
Voltmeter A error = (5 V – 3.53 V)/5 V x (100%
= 29.4%
Voltmeter B error = (5 V – 4.9 V)/5 V x (100%)
=2%
17
Five principal meter movements used
in ac instrument
1. Electrodynamometer
2. Iron Vane
3. Electrostatic
4. Thermocouple
5. D’Arsonval with rectifier
18
Meter
Movement
DC Use AC Use Applications
Electrodynamometer
YES
YES
Standards meter, wattmeter, frequency
meter
“Indicator” applications such as in
automobiles
Iron Vane
YES
YES
“Indicator” applications such as in
automobiles
Electrostatic
YES
YES
Measurement of high voltage when very
little current can be supplied by the circuit
being measured
Thermocouple
YES
YES
Measurement of radio frequency ac signal
D’Arsonval
YES
YES with
rectifier
Most widely used meter movement for
measuring direct current or voltage and
resistance
19
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The PMMC instrument is polarized (terminals +ve & ve) - it must be connected correctly for positive (on
scale) deflection to occur.
When an AC with a very low frequency is passed
through a PMMC, the pointer tends to follow the
instantaneous level of the AC
As the current grows positively, the pointer deflection
increases to a maximum at the peak of the AC
As the instantaneous current level falls, the pointer
deflection decreases toward zero. When the AC goes
negative, the pointer deflected (off scale) to the left of
zero
This kind of pointer movement can occur only with
AC having a frequency of perhaps 0.1Hz or lower
20
• At 50Hz or higher supply frequencies - the damping mechanism of
the instrument and the inertia of the meter movement prevent the
pointer from following the changing instantaneous levels.
•The average value of purely sinusoidal AC is zero.
• Therefore, a PMMC instrument connected directly to measure 50Hz
AC indicates zero average value.
•It is important to note that although a PMMC instrument connected
to an ac supply may indicating zero, there can actually be very large
rms current flowing in its coils
21
Two types of PMMC meter used in
AC measurement :
1. Half wave rectification
2. Full wave rectification
22
To convert alternating current (AC) to unidirectional
current flow, which produces positive deflection when
passed through a PMMC, the diode rectifier is used.
Several types of rectifiers are selected such as a copper
oxide rectifier, a vacuum diode, or semiconductor or
“crystal diode”.
VP
Vrms 
2
 0.5Vp
Vave Vdc  0.318Vp
Vave 
Vp


2  Vrms

 0.45Vrms
23
Cont…
• For example, if the output voltage from a half wave rectifier
is 10Vrms so the dc voltmeter will provide an indication of
approximately 4.5V dc  Therefore, the pointer deflected full
scale when 10V dc signal is applied.
•When we apply a 10Vrms sinusoidal AC waveform, the
pointer will deflect to 4.5V  This means that the AC
voltmeter is not as sensitive as DC voltmeter.
•In fact, an AC voltmeter using half wave rectification is only
approximately 45% as sensitive as a dc voltmeter.
24
Cont…
•Actually, the circuit would probably be designed for fullscale deflection with a 10V rms AC applied, which means
the multiplier resistor would be only 45% of the value of
the multiplier resistor for 10V dc voltmeter. Since we have
seen that the equivalent dc voltage is equal to 45% of the
rms value of the ac voltage.
E dc
0.45E rms
Rs 
 Rm 
 Rm
I dc
I dc
Sac = 0.45Sdc
25
Cont..
Commercially produced ac voltmeters that use half wave
rectification also has an additional diode and a shunt as shown
in Figure below:
26
Cont…
•The additional diode D2 is reverse biased on the positive half
cycle and has virtually no effect on the behavior of the circuit.
•In the negative half cycle, D2 is forward biased and provides an
alternate path for reverse biased leakage current that would
normally through the meter movement and diode D1.
•The purpose of the shunt resistor Rsh is to increase the current
flow through D1 during positive half cycle so that the diode is
operating in a more linear portion of its characteristic curve.
•Although this shunt resistor improves the linearity of the meter
on its low voltage ac ranges, it also further reduces the AC
sensitivity.
27
Compute the value of the multiplier resistor
for a 15Vrms ac range on the voltmeter
shown in Fig. 1.
RS
Ifs = 1mA
Ein = 15Vrms
Rm = 300Ω
Fig. 1: AC voltmeter using half wave rectification
28
Method 1
The sensitivity of the meter movement,
1
1
Sdc 

 1k / V
I fs 1m
Rs
= Sdc × Rangedc – Rm
= 1k ×
0.45E rms
1
- Rm
= 1k × 0.45(10) – 300
= 4.2k
29
Method 2
The AC sensitivity for half wave rectifier,
Sac = 0.45Sdc = 0.45(1k) = 450/V
Rs
= Sac × Rangeac – Rm
= 450 × 10 –300
= 4.2k
30
Method 3
Rs
=
=
0.45E rms
 Rm
I fs
0.45  10
 300
1m
= 4.2k
31
Calculate the ac and dc sensitivity and the value of the multiplier
resistor required to limit the full scale deflection current in the
circuit shown in Fig above.
32
D’Arsonval meter movement used
with full wave rectification
Fig.
2:
Full
bridge
rectifier used in an ac
voltmeter circuit
During the positive half cycle, currents flows through diode D2, through
the meter movement from positive to negative, and through diode D3.
The polarities in circles on the transformer secondary are for the positive
half cycle. Since current flows through the meter movement on both half
cycles, we can expect the deflection of the pointer to be greater than
with the half wave cycle, which allows current to flow only on every
other half cycle; if the deflection remains the same, the instrument using
full wave rectification will have a greater sensitivity.
33
Fig. 1-2: AC voltmeter using full wave rectification
34
When the 10Vrms of AC signal is applied to the circuit
above, where the peak value of the AC input signal is
E p  2 xE rms  1.414x (10)  14.14V
And the average full wave output signal is
E ave  E dc  0.636xE p  0.636x14.14  9V
Therefore, we can see that a 10Vrms voltage is equivalent
to 9Vdc for full-scale deflection.
35
Or
E avg  0.636E p  0.636( 2 xE rms )  0.9E rms
This means an ac voltmeter using full wave
rectification has a sensitivity equal to 90% of
the dc sensitivity
Sac = 0.9 Sdc
36
Compute the value of the multiplier resistor for a
10Vrms ac range on the voltmeter in Figure 1-2.
Fig. 1-2: AC voltmeter circuit using full wave rectification
37
The dc sensitivity is
1
1
Sdc 

 1k / V
I fs 1mA
The ac sensitivity is
Sac = 0.9Sdc = 0.9 (1k) = 900 /V
38
Therefore the multiplier resistor is
Rs
= Sac x Range – Rm
= 900 x 10Vrms – 500
= 8.5k
39
Note:
Voltmeters using half wave and full wave
rectification are suitable for measuring
only sinusoidal ac voltages.
40


An oscilloscope is a piece of
electronic test equipment that
allows signal voltages to be
viewed, usually as a twodimensional graph of one or more
electrical potential differences
(vertical axis) plotted as a
function of time or of some other
voltage (horizontal axis
Perform some computations
using data taken from the voltage
waveform that is displayed such
as:
* Rms value
* Average Amplitude
* Peak-to-peak Amplitude
* Frequency


An oscilloscope is easily the most useful instrument
available for testing circuits because it allows you to see
the signals at different points in the circuit.
Using for signal/wave display – Winamp Music Player,
Electrocardiogram,



A potentiometer is a variable resistor that functions as
a voltage divider
It is a simple electro-mechanical transducer
It converts rotary or linear motion from the operator
into a change of resistance, and this change is (or can
be) used to control any volume.




Schematic symbol for a potentiometer. The arrow
represents the moving terminal, called the wiper.
Usually, this is a three-terminal resistor with a sliding
contact in the center (the wiper) - user-adjustable resistance
If all three terminals are used, it can act as a variable
voltage divider
If only two terminals are used (one side and the wiper), it
acts as a variable resistor
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
Any current flow through the Galvanometer, G, wpuld
be a result of an imbalance in the measured voltage, Vm
and the voltage imposed across points A to B, VAB.
If Vm is not equal to VAB, a current will flow through
the galvanometer, G.
Galvanometer detects current flow due to imbalance in
voltage Vm and VAB. When Vm = VAB, there is a balance
and no current, means no displacement in
Galvanometer.


In modern usage, a potentiometer is a potential
divider, a three terminal resistor where the position of
the sliding connection is user adjustable via a knob or
slider. For instance, when attached to a volume control,
the knob can also function as an on/off switch at the
lowest volume
Potentiometers are frequently used to adjust the level
of analog signals (e.g. volume controls on audio
equipment) and as control inputs for electronic circuits
(e.g. a typical domestic light dimmer).
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
The purpose of an ohmmeter, is to measure the
resistance placed between its leads.
This resistance reading is indicated through a
mechanical meter movement which operates on electric
current. The ohmmeter must then have an internal
source of voltage to create the necessary current to
operate the movement, and also have appropriate
ranging resistors to allow just the right amount of
current through the movement at any given resistance.
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
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The original design of an ohmmeter provided a small
battery to apply a voltage to a resistance. It used a
galvanometer to measure the electric current through the
resistance.
The scale of the galvanometer was marked in ohms, because
the fixed voltage from the battery assured that as resistance
decreased, the current through the meter would increase.
A more accurate type of ohmmeter has an electronic circuit
that passes a constant current I through the resistance, and
another circuit that measures the voltage V across the
resistance.
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

The standard way to measure resistance in ohms is to
supply a constant voltage to the resistance and measure the
current through it.
That current is of course inversely proportional to the
resistance according to Ohm's law, so that you have a nonlinear scale.
The current registered by the current sensing element is
proportional to 1/R, so that a large current implies a small
resistance.
The ohmmeter consists of battery, resistor and
PMMC.
The full-scale deflection current,
E
I fs 
R Z  Rm
Fig. 2-7 Basic ohmmeter circuit
function of Rz and Rm are to limit the current through the meter
51
Rz = variable resistor
Fig. 2-8 Basic ohmmeter circuit with unknown resistor,Rx connected
between probes.
To determine the value of unknown resistor, Rx, The
Rx is connected to terminal X and Y. Fig 2-8 shows the
basic ohmmeter circuit with unknown resistor, Rx
connected between probes.
52
The circuit current,
E
I
R Z  Rm  R x
The ratio of the current, I to the full-scale deflection
current, Ifs is


E


RZ  Rm  Rx 

RZ  Rm 
I

P


RZ  Rm  Rx 
I fs
 E 


 RZ  R m 
53
A
Wheatstone bridge is a measuring
instrument invented by Samuel Hunter
Christie (British scientist & mathematician)
in 1833 and improved and popularized
by Sir Charles Wheatstone in 1843. It is
used to measure an unknown electrical
resistance by balancing two legs of a
bridge circuit, one leg of which includes
the unknown component. Its operation is
similar to the original potentiometer
except that in potentiometer circuits the
meter used is a sensitive galvanometer.
• Accurately measures resistance and
detect small changes in resistance.
Sir Charles Wheatstone (1802 – 1875)
Definition: Basic circuit configuration consists of two parallel
resistance branches with each branch containing two series elements
(resistors). To measure instruments or control instruments
Basic dc bridge used for accurate measurement of resistance:
R1R4  R2 R3
R 2R 3
R4 
R1
Fig. 5.1: Wheatstone bridge circuit
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
The dc source, E is connected across the resistance
network to provide a source of current through the
resistance network.
The sensitive current indicating meter or null detector
usually a galvanometer is connected between the
parallel branches to detect a condition of balance.
When there is no current through the meter, the
galvanometer pointer rests at 0 (midscale).
Current in one direction causes the pointer to deflect
on one side and current in the opposite direction to
otherwise.
The bridge is balanced when there is no current
through the galvanometer or the potential across the
galvanometer is zero.
At balance condition;
voltage across R1 and R2 also equal, therefore
(1)
I1R1  I 2 R2
Voltage drop across R3 and R4 is equal
I3R3= I4R4
(2)
No current flows through galvanometer G when the
bridge is balance, therefore:
I1 = I3
and
I2=I4
(3)
Cont.
Substitute (3) in Eq (2),
I1R3 = I2R4
(4)
Eq (4) devide Eq (1)
R1/R3 = R2/R4
Then rewritten as
R1R4 = R2R3
(5)
Figure 5.2 consists of the following, R1 = 12k, R2 = 15 k,
R3 = 32 k. Find the unknown resistance Rx.
Assume a null exists(current through the galvanometer
is zero).
Fig. 5-2: Circuit For example 5-1
RxR1 = R2R3
Rx
= R2R3/R1 = (15 x 32)/12 k,
Rx
= 40 k
When the bridge is in unbalanced
condition, current flows through the
galvanometer, causing a deflection of
its pointer. The amount of deflection is
a function of the sensitivity of the
galvanometer.
Deflection may be expressed in linear or angular
units of measure, and sensitivity can be expressed:
milimeters
degrees radians
S


A
A
A
Total deflection,
D  SI
Fig. 5-3: Unbalanced Wheatstone Bridge
Vth = Eab
 R3
R4 


E ab  E

 R1  R 3 R 2  R 4 
Fig. 5-4: Thevenin’s resistance
Rth = R1//R3 + R2//R4
=
R1R3/(R1 + R3)
+ R2R4(R2+R4)
An analytical tool used to extensively analyze an unbalance bridge.
Hermann von Helmholtz (1821 – 1894)
German Physicist
Léon Charles Thévenin (1857-1926)
French Engineer
Thévenin's theorem for electrical networks states that any combination of voltage
sources and resistors with two terminals is electrically equivalent to a single voltage
source V and a single series resistor R. For single frequency AC systems the theorem
can also be applied to general impedances, not just resistors. The theorem was first
discovered by German physicist Hermann von Helmholtz in 1853, but was then
rediscovered in 1883 by French telegraph engineer Léon Charles Thévenin (1857-1926).
If a galvanometer is connected to terminal a and b,
the deflection current in the galvanometer is
Vth
Ig 
R th  R g
where Rg = the internal resistance in the galvanometer
R2 = 1.5 kΩ
R1 = 1.5 kΩ
Rg = 150 Ω
E= 6 V
G
R3 = 3 kΩ
R4 = 7.8 kΩ
Figure 5.5: Unbalance Wheatstone Bridge
Calculate the current through the galvanometer ?
Slightly Unbalanced Wheatstone Bridge
If three of the four resistors in a bridge are equal to R and
the fourth differs by 5% or less, we can developed an
approximate but accurate expression for Thevenin’s
equivalent voltage and resistance.
Eth 
E  r  r 
  E
4R
 4R 
1
 R  r
 r 
Vth  Vb  Va  
  E  
 E
 R  R  r 2 
 4 R  2r 
Cont..
To find Rth:
R R
Rth    R
2 2
An approximate Thevenin’s equivalent circuit
500 Ω
10 V
500 Ω
G
500 Ω
525 Ω
Use the approximation equation to calculate the current through the
galvanometer in Figure above. The galvanometer resistance, Rg is 125 Ω and is
a center zero 200-0-200-μA movement.
The Kelvin Bridge is a modified version
of the Wheatstone bridge. The purpose of
the modification is to eliminate the
effects of contact and lead resistance
when measuring unknown low resistances.
Used to measure values of resistance
below 1 Ω .
It can be shown that, when a null exists, the value
for Rx is the same as that for the Wheatstone bridge,
which is
R2 R3
Rx 
R1
Therefore when a Kelvin Bridge is balanced
Rx R3 Rb


R2 R1 Ra
If in Figure 5-6, the ratio of Ra and Rb is 1000, R1
is 5 and R1 =0.5R2. What is the value of Rx.
The resistance of Rx can be calculated by
using the equation,
Rx/R2=R3/5=1/1000
Since R1=0.5R2, the value of R2 is calculated as
R2=R1/0.5=5/0.5=10
So, Rx=R2(1/1000)=10 x (1/1000)=0.01


A multimeter or a
multitester is an electronic
measuring instrument
that combines several
functions in one unit.
The most basic
instruments include an
ammeter, voltmeter, and
ohmmeter
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DC Voltage Measurements
AC Voltage RMS Measurements
DC and AC Current Measurements
Resistance Measurements
Capacitance/Inductance Measurements
Frequency/Period Measurements
Diode Measurements