Transcript AC Meters - UniMAP Portal

EMT 462
ELECTRICAL
SYSTEM
TECHNOLOGY
Chapter 4:
AC Meters
By:
En. Muhammad Mahyiddin Ramli
Alternating Current Waveform
Sinusoidal wave
Square wave
Triangle wave
Chap 4: AC Meters
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Alternating Current Waveform
Chap 4: AC Meters
3
Chap 4: AC Meters
4
Average and RMS Value
Vavg = 0
Vrms = 0.707Vp
Sine Wave
Vavg = 0.636Vp
Vrms = 0.707Vp
Full Wave
Chap 4: AC Meters
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Con’t
Vavg = 0.318Vp
Vrms = 0.5Vp
Half Wave
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Five Principal Meter Movements Used
In AC Instrument

1. Electrodynamometer

2. Iron Vane

3. Electrostatic

4. Thermocouple

5. D’Arsonval with rectifier
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Application of Meter Movements
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
Chap 4: AC Meters
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PMMC Instrument on AC

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
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PMMC Instrument on AC
 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
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Two Types of PMMC Meter Used In AC
Measurement

1. Half wave rectification

2. Full wave rectification
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D’Arsonval meter movement used with half
wave rectification
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
Vave Vdc  0.318Vp
Vave 
Chap 4: AC Meters
Vp


2  Vrms

 0.45Vrms
12
Con’t
 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.
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Con’t
 Actually, the circuit would probably be designed for full-scale
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
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Con’t
 Commercially produced ac voltmeters that use half wave
rectification also has an additional diode and a shunt as
shown in Figure below:
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Con’t
 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.
Chap 4: AC Meters
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Example 3.1

Compute the value of the multiplier resistor for
a 10Vrms ac range on the voltmeter shown
below:
RS
Ifs = 1mA
Ein = 15Vrms
Rm = 300Ω
AC voltmeter using half wave rectification
Chap 4: AC Meters
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Solution

Method 1

The sensitivity of 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
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Con’t

Method 2

The AC sensitivity for half way rectifier
Sac = 0.45Sdc = 0.45(1k) = 450/V
Rs
= Sac × Rangeac – Rm
= 450 × 10 –300
= 4.2k
Chap 4: AC Meters
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


D’Arsonval meter movement used with full wave
rectification
Electrodynamometer, Iron-vane meter, thermocouple
meter
Loading effects of AC Voltmeter
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D’Arsonval Meter Movement Used With Full
Wave Rectification
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.
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Consider the following circuit:
AC voltmeter using full wave rectification
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Con’t
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.
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Con’t
Or
E avg  0.636E p  0.636( 2xE 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
Chap 4: AC Meters
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Example 3.2
Compute the value of the multiplier resistor for a
10Vrms ac range on the voltmeter in Figure 1-2.
AC voltmeter circuit using full wave rectification
Chap 4: AC Meters
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Solution
The dc sensitivity is:
1
1
Sdc 

 1k / V
I fs 1mA
The ac sensitivity is:
Sac = 0.9Sdc = 0.9 (1k) = 900 /V
Chap 4: AC Meters
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Con’t
Therefore the multiplier resistor is:
Rs
= Sac x Range – Rm
= 900 x 10Vrms – 500
= 8.5k
Chap 4: AC Meters
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Assignment AC Meters
RS
Ein = 10Vrms
Ifs = 1mA
Rsh = 0.5kΩ

Rm = 0.5kΩ
Each diode in full-wave rectifier circuit above has an
average forward resistance of 50Ω and is assumed to
have an infinite resistance in the reverse direction.
Calculate:
a) Multiplier resistance, RS
b) AC sensitivity
c) The equivalent dc sensitivity.
Chap 4: AC Meters
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Notice
Note:
 Voltmeters using half wave and full wave
rectification are suitable for measuring
sinusoidal ac voltages only.
Chap 4: AC Meters
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Electrodynamometer Movement
Source
Fixed Coil
Moving
Coil
Fixed Coil
 Most fundamental and versatile meter use today.
 Is a current-sensitive device – the pointer deflects up scale because of
current flow through moving coil.
 Most important applications: voltmeter and ammeter standard.
Chap 4: AC Meters
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Electrodynamometer Movement



The single-coil electrodynamometer movement consists of a fixed coil divided into
two equal halves.
Both halves of the split fixed coil and the moving coil are connected in series –
current from the circuit being measured passed through all the coils causing
magnetic field around the fixed coils. The moving coil rotates in this magnetic
field.
The electrodynamometer – handle much more current than d’ Arsonval
movement. It can handle ~ 100mA.

The electrodynamometer – have a very low sensitivity rating of ~ 20 to 100 Ω/V.

Most extensive application: Wattmeter.

The magnetic torque that cause pointer deflect up scale:
 m  K m El cos 
Θm – angular deflection of the pointer
Km – instrument constant (degrees/watt)
cos θ – power factor
E – rms value of source voltage
l – rms value of source current
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Iron-Vane Meter Movement
• The iron-vane meter movement
consists of a fixed coil of many turns
and two iron vanes placed inside the
fixed coil.
• it is widely used in industry.
I
• the current can be measured passes
through the winding of the fixed coil
setting up a magnetic field that
magnetized the two iron vanes with
the same polarity.
Chap 4: AC Meters
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Iron-Vane Meter Movement

If one iron vanes is attached to the frame of a fixed coil – the other
iron vane will then be repelled by amount related to the square of
current.

Although it is responsive to direct current (the hysteresis) – the iron
vanes causes appreciable error. (used only for a very inexpensive
indicators, i.e charge-discharge indicators on automobiles).

It is used extensively in industry for measuring ac when errors on
the order of 5% to 10% are acceptable.

Iron-vane movement very sensitive to frequency change (25 – 125
Hz) - it is because the magnetization of the iron vane is nonlinear.
Chap 4: AC Meters
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Thermocouple Meter
Basic thermocouple meter
 Usually consists a heater element – fine wire, a thermocouple, and
d’Arsonval meter movement.
 To measure a very high-frequency ac (very accurate well > 50Hz).
Chap 4: AC Meters
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Loading Effect of AC Voltmeter
The sensitivity of ac voltmeters, using either
half wave or full wave rectification, is less than
the sensitivity of dc voltmeters. Therefore,
loading effect of an ac voltmeter is greater
than that of a dc voltmeter.
Sac = 0.45Sdc
Sac = 0.9Sdc
Chap 4: AC Meters
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Voltage and Current
Transformer Applications
 Calibrating AC voltmeters and ammeters for different fullscale ranges of operation is much the same as with DC
instruments: series "multiplier" resistors are used to give
voltmeter movement a higher range, and parallel "shunt"
resistors are used to allow ammeter movements to measure
currents beyond their natural range.
 However, we are not limited to these techniques as we were
with DC: because we can use transformers with AC too.
Chap 4: AC Meters
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Summary

For general purposes, the d’Arsonval movement – either half-wave
or full-wave rectifier, is widely used.
Meter Movement
App. Voltage & Freq.
Reading Obtained
D’Arsonval
10Vrms, 60 Hz
0V
Iron vane
10Vrms, 60 Hz
10V
Electrodynamometer
10Vrms, 60 Hz
10V
Thermocouple
10Vrms, 60 Hz
10V
D’Arsonval with halfwave rectifier
10Vrms, 60 Hz
4.5V
D’Arsonval with fullwave rectifier
10Vrms, 60 Hz
9.0V
Iron vane
10VDC
10V
Electrodynamometer
10VDC
10V
Thermocouple
10VDC
10V
Chap 4: AC Meters
37
Success is the ability to go from
one failure to another with no
loss of enthusiasm.
- Sir Winston Churchill
Chap 4: AC Meters
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