3.1
Introduction
CHAPTER 3
AC METER
Figure 3.1: Alternating current waveform
3.2 Calculation rms and average value a) Sine wave b) Full wave
Figure 3.2: Sine wave
V avg
= 0
V rms
= 0.707V
m
V avg
= 0.636V
m
V rms
= 0.707V
m
Figure 3.3: Full wave
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c) Half wave
Output
V max
Figure 3.4: Half wave
1
V avg
=
T t
0
∫
+
T
V t
0
( t ) dt
=
1
2
π
π
∫
0
V m sin(
ω t ) d (
ω t ) + 0 rms average time
V avg
= 0.318V
m
V rms
= 0.5V
m
=
V m
2
π
(
− cos(
ω t )
)
|
0
π
=
V m
2
π
( 1
+
1 )
V avg
=
V m
π
V avg
=
V m
π
1
V rms
=
T t
0
∫
+
T t
0 v
2
( t ) dt
=
1
2
π
0
π
∫
[ V m sin(
ω t )]
2 d (
ω t ) + 0
=
V
2 m
2
π
π
∫
0 sin
2
(
ω t ) d (
ω t )
= V m
1
2
π
π
∫
0 sin
2
(
ω t ) d (
ω t )
Sin
2 x
=
1
− cos 2 x
2
35

= V m
1
2
π t
∫
0
1
− cos 2
ω t
2
=
V p
2
Five principal meter movements used in ac instrument:
1.
Electrodynamometer
2.
Iron Vane
3.
Electrostatic
4.
Thermocouple
5.
D’Arsonval with rectifier
Application of meter movements:
Meter Movement DC Use AC Use Applications
Electrodynamometer YES YES Standards meter, wattmeter, frequency meter
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 ac signal rectifier movement for measuring direct current or voltage and resistance
Table 3.1
36

3.3 PMMC Instrument on AC
The PMMC instrument is polarized, that is, its terminals are identified as + and -, and it must be connected correctly for positive (on scale) deflection to occur. When an alternating current with a very low frequency is passed through a PMMC instrument, 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. Then 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. With the normal frequency 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. Instead the instrument pointer settles at the average value of the current following through the moving coil. The average value of purely sinusoidal ac is zero. Therefore, a PMMC instrument connected directly to measure 50Hz ac indicates zero. 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.
Two types of PMMC meter used in AC measurement:
1.
Half wave rectification
2.
Full wave rectification
3.4 D’Arsonval meter movement used with half wave rectification
To convert alternating current 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”.
37

Figure 3.5: DC voltmeter circuit modified to measure ac voltage
V rms
=
V
2
P
(Half wave)
V ave
=
V dc
=
0 .
318 V p
V ave
=
V p
π
=
2 xV rms
π
=
0 .
45 V rms
Sine wave
For example, if the output voltage from a half wave rectifier is 10V rms
so the dc voltmeter will provide an indication of approximately 4.5V
dc
. Therefore, we can see that the pointer that deflected full scale when 10V dc signal was applied. When we apply a 10V rms 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 .
Actually, the circuit would probably be designed for full-scale deflection with a 10V rms alternating current 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.
38

R s
=
E dc
I dc
−
R m
=
0 .
45 E rms
I dc
−
R m or
S ac
= 0.45S
dc
Commercially to produce ac voltmeters that use half wave rectification also has an additional diode and a shunt as shown in Figure 3.6.
Figure 3.6: Half wave rectification using an instrument rectifier and a shunt resistor to
improve linearity.
The additional diode D
2
is reversed biased on the positive half cycle and has virtually no effect on the behaviour of the circuit. In the negative half cycle, D
2
is forward biased and provides an alternate path for reverse biased leakage current that would normally through the meter movement and diode D
1
. The purpose of the shunt resistor R sh
is to increase the current flow through D
1
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.
39

Example:
Compute the value of the multiplier resistor for a 10V rms
ac range on the voltmeter shown in Figure 3.7.
R s
E in
=
10 V rms
I
R fs m
=
1 mA
=
300
Ω
Figure 3.7: AC voltmeter using half wave rectification
Solution:
Method 1
The sensitivity of the meter movement , S dc
=
1
I fs
=
1
1 m
=
1 k
Ω
/ V
R s
= S dc
X Range dc
– R m
0 .
45 E
X
1 rms
- R m
= 1k X 0.45(10) – 300
=
Method 2
The ac sensitivity for half wave rectifier, S ac
= 0.45S
dc
= 0.45(1k) = 450
Ω
/V
R s
= S ac
X Range ac
– R m
= 450 X 10 –300
=
40

Solution:
Method 3
0 .
45 E
R s
=
I fs rms −
R m
=
0 .
45 X 10
1 m
−
300
=
Example:
In the half wave rectifier shown in Figure 3.8, diodes D1 and D2 have an average forward resistance of 50
Ω
and assumed to have infinite resistance in the reverse direction.
Calculate the following: a) The value of the multiplier R s b) The ac sensitivity c) The equivalent dc sensitivity
R s
D
1 I m
I
T
I sh
E in
=
10 V rms
D
2
R sh
=
200
Ω I fs
R m
=
1
µ
A
=
200
Ω
Figure 3.8: Half wave rectifier with shunt resistor
41

Example:
Using the E-I curve, you can determine the diode in the circuit in Figure 3.9 to have 1k
Ω static resistance with full-scale deflection current of 100
µ
A through it. Compute the value of the multiplier resistor using the value Rd at full-scale deflection. Compute the diode resistance with 20
µ
A current and the value of input voltage that would cause 20
µ
A to flow.
Solution:
Figure 3.9: Circuit and E-I curve
42

3.5 D’Arsonval meter movement used with full wave rectification
It is more desirable to use a full wave rather than a half wave rectifier in ac voltmeters because higher sensitivity rating. Figure 3.10 shows the full wave rectifier using bridge type rectifier.
Figure 3.10: Full bridge rectifier used in an ac voltmeter circuit
During the positive half cycle, currents flows through diode D
2
, through the meter movement from positive to negative, and through diode D
3
. 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.
43

Consider the circuit shown in Figure 3.11.
Figure 3.11: AC voltmeter using full wave rectification
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 .
414 x ( 10 )
=
14 .
14 V and the average full wave output signal is
E ave
=
E dc
=
0 .
636 xE p
=
0 .
636 x 14 .
14
=
9 V
Therefore, we can see that a 10V rms voltage is equivalent to 9V dc for full-scale deflection.
We can conclude, when full wave rectification is used, the pointer will deflect to 90% of full scale. This means an ac voltmeter using full wave rectification has sensitivity equal to 90% of the dc sensitivity. As with the half wave rectifier, the circuit would be designed for full-scale deflection, which means the value of the multiplier resistor would be only
90% of the value for a 10V dc voltmeter. We may write this for a full wave rectifier as
S ac
= 0.9S
dc
44

Example:
Compute the value of the multiplier resistor for a 10Vrms ac range on the voltmeter in
Figure 3.12
Figure 3.12: AC voltmeter circuit using full wave rectification
Solution:
The dc sensitivity is
S dc
=
1
I fs
=
1
1 mA
=
1 k
Ω
/ V
The ac sensitivity is
S ac
= 0.9S
dc
= 0.9 (1k) = 1k
Ω
/V
Therefore the multiplier resistor is
R s
= S ac
x Range – R m
= 900 x 10Vrms – 500
45

** Voltmeters using half wave and full wave rectification are suitable for measuring only sinusoidal ac voltages.
Example:
Each diode in the full rectifier circuit shown in Figure 3.13 has an average forward resistance of 50
Ω
and assumed to have an infinite resistance in the reverse direction.
Calculate the following: a.
The value of the multiplier R s b.
The ac sensitivity c.
The equivalent dc sensitivity
Figure 3.13: AC voltmeter using full wave rectification and shunt
46

3.6 Loading effects 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.
3.7 Electrodynamometer Movement
The electrodynamometer movement (Figure 3.14) has the same basic operating principle as the D’Arsonval meter movement, except that the permanent magnet is replaced by fixed coils. The moving coil and pointer, which are attached to the coil, are suspended between and connected in series with the two field coils. The two fixed coils and moving coil are connected in series such that the same current flows through each coil.
Figure 3.14: Electrodynamometer Movement
Current flow through the three coils in either direction causes a magnetic field to be produced between the fixed coils. The same current flow through the moving coil causes it to act as a magnet exerting a force against the spring. If the current is reversed, the field polarity and the polarity of the moving coil reverse, and the force continues in the same direction. Due to this characteristic of the electrodynamometer movement, it can
47

be used in both AC and DC systems to measure current. Some voltmeters and ammeters use the electrodynamometer. However, its most important use is in the wattmeter.
3.8 Moving Iron Vane Movement
The moving iron vane movement (Figure 3.15) can be used to measure both AC current and voltage. By changing the meter scale calibration, the movement can be used to measure DC current and voltage. The moving iron vane meter operates on the principle of magnetic repulsion between like poles. The measured current flows through a fixed coil, which produces a magnetic field proportional to the magnitude of current.
Suspended in this field are two iron vanes attached to a pointer. The two iron vanes consist of one fixed and one moveable vane. The magnetic field produced by the current flow magnetizes the two iron vanes with the same polarity regardless of the direction of current through the coil. Since like poles repel one another, the moving iron vane pulls away from the fixed vane and moves the meter pointer. This motion exerts a force against a spring. The distance the moving iron vane will travel against the spring depends on the strength of the magnetic field. The strength of the magnetic field depends on the magnitude of current flow.
Figure 3.15: Moving Iron Vane Meter Movement
48

As stated previously, this type of meter movement may also be used to measure voltage.
When this type of movement is used to measure voltage, the field coil consists of many turns of fine wire used to generate a strong magnetic field with only a small current flow.
3.9 Voltage and current transformers application
Calibrating AC voltmeters and ammeters for different full-scale ranges of operation is much the same as with DC instruments: series "multiplier" resistors are used to give voltmeter movements’ 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 to use transformers with AC, meter ranges can be electro-magnetically rather than resistively "stepped up" or
"stepped down," sometimes far beyond what resistors would have practically allowed for.
Voltage Transformers (PT's) and Current Transformers (CT's) are precision instrument devices manufactured to produce very precise ratios of transformation between primary and secondary windings. They can allow small, simple AC meter movements to indicate extremely high voltages and currents in power systems with accuracy and complete electrical isolation (something multiplier and shunt resistors could never do):
Two wiring connection for ac voltmeter/ammeter (refer to Figure 3.16 and 3.17):
1.
Direct connected
2.
With instrument transformer (voltage transformer (VT or PT) / with current transformer (CT))
49

Figure 3.16: Wiring connection for ac voltmeter
Figure 3.17: Wiring connection for ac ammeter
3.10 Voltage transformers (VTs)
These may be classified as follows:
1.
Instrument transformers i) Conventional two winding, electromagnetic voltage transformer ii) Residual voltage transformers (RVTs) and iii) Capacitor voltage transformers (CVTs). These may be used for metering or protection, with very little difference between two as noted later
50

2.
Control transformer
Figure 3.18 (a): Transformers with HT fuse a) 33kV single-phase outdoor b) 11kV three-phase indoor
Figure 3.18 (b): Typical HT instrument voltage transformers
51

3.11.1 VT burden
The burden of a VT is defined in terms of the volt-amperes at the rated secondary voltage, but often on site, as with the CT, it is incorrectly referred to as the impedance of the secondary circuit expressed in ohms.
Table 3.2: Typical values of VA burden
** These VA burdens are for moving iron instruments. For electronic meters these values would be of the order of 0.1 to 0.5VA
3.11.2 VT accuracy classes
The accuracy classes are defined in BS 3941 as shown in Table 2. The accuracy class defines, in the main, the voltage ratio error, for example class 0.1 has a voltage ration error of
±
0.1% and class 3P has a voltage ratio error of
±
3%. The accuracy class also specifies a phase displacement between primary and secondary.
Measurement VTs are required to maintain accuracy between 80% and 120% of rated
HV voltage over a specific range of burdens.
52

Table 3.3: Recommended class of accuracy for different types of meters
Note: To choose a higher class of accuracy than necessary is not desirable
These may be one of the following types:
1.
Ring
2.
Bar primary
3.
Wound primary
53

Figure 3.19 : Type of Current Transformer
3.12.1 CT Burden
The burden on a CT is a measurement of the load expressed in volt-amperes (VA) at the rated secondary current. For example if the rated secondary current was 5A and the impedance was 2
Ω
, the burden would be
(5 x 2) x 5 = 50VA
(V) x (A)
Measurement CTs are required to maintain specified accuracy up to 120% of rated current, when the burden connected is equal to the rated output of the CT.
54

Table 3.4: CT burden
3.12.2
Accuracy class
This defines the maximum permissible current error at the rated current for particular accuracy class. The standard accuracy classes for the measuring CTs may be one of 0.1,
0.2, 0.5, 1, 3 and 5. This limits of error in magnitude of the secondary current and the phase error. Phase error is the phase displacement between the primary and the secondary current phasors.
Table 3.5: Class of accuracy
55