Transcript Forecasting - Portal UniMAP

ALTERNATING CURRENT METERS
Part 2
Objectives
• Ability to know the operation & Analyzed
D’Arsonval meter movement used with half
wave rectification
• Abilty to know the operation & analyzed
D’Arsonval meter movement used withfull
wave rectification
• Types of meter movement and application
for each meter movement.
2
Alternating Current Waveform
Sinusoidal wave
Square wave
Triangle wave
3
Alternating Current Waveform
Erms= E(root mean square), Ep-p= E peak-peak, Ep= E peak
4
Vavg = 0
Vrms = 0.707Vp
Vavg = 0.318Vp
Vrms = 0.5Vp
Vavg = 0.636Vp
Vrms = 0.707Vp
5
Average and RMS Value
Vavg = 0
Vrms = 0.707Vp
Sine Wave
Vavg = 0.636Vp
Vrms = 0.707Vp
Full Wave
6
Cont..
Vavg = 0.318Vp
Vrms = 0.5Vp
Half Wave
7
Five principal meter movements used
in ac instrument
1. Electrodynamometer
2. Iron Vane
3. Electrostatic
4. Thermocouple
5. D’Arsonval with rectifier
8
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
9
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
10
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
11
Two types of PMMC meter used in
AC measurement :
1. Half wave rectification
2. Full wave rectification
12
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
 0.5Vp
Vave Vdc  0.318Vp
Vave 
Vp


2  Vrms

 0.45Vrms
13
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.
14
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
15
Cont..
Commercially produced ac voltmeters that use half wave
rectification also has an additional diode and a shunt as shown
in Figure below:
16
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.
17
Example 1-1
Compute the value of the multiplier resistor
for a 15Vrms ac range on the voltmeter
shown in Fig. 1.
R
S
Ifs = 1mA
Ein = 15Vrms
Rm = 300Ω
Fig. 1: AC voltmeter using half wave rectification
18
Solution:
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
19
Cont.
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
20
Cont.
Method 3
Rs
=
=
0.45E rms
 Rm
I fs
0.45  10
 300
1m
= 4.2k
21
Example 1-2
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.
22
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.
23
Consider the circuit shown in Fig. 1-2
Fig. 1-2: AC voltmeter using full wave rectification
24
Cont.
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.
25
Cont.
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
26
Example 1-2
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
27
Solution 1-2
The dc sensitivity is
1
1
Sdc 

 1k / V
I fs 1mA
The ac sensitivity is
Sac = 0.9Sdc = 0.9 (1k) = 900 /V
28
Cont.
Therefore the multiplier resistor is
Rs
= Sac x Range – Rm
= 900 x 10Vrms – 500
= 8.5k
29
Cont.
Note:
Voltmeters using half wave and full
wave rectification are suitable for
measuring only sinusoidal ac voltages.
30
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.
31
Electrodynamometer (Cont..)
• 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
32
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.
33
Iron-vane Meter (Cont…)
• 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.
34
Thermocouple Meter
I
Thermocouple
Source
Insulating
bead
d’ Arsonval
meter
movement
Heater
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).
35
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.
Sac = 0.45Sdc
Sac = 0.9Sdc
36
Voltage and Current
Transformer Applications
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 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.
37
SUMMARY
• The D’Arsonval Meter Movement - Current-sensitive
device capable of directly measuring only very small
currents.
• D’Ársonval Meter Movement
Used In A DC Ammeter : This done by placing a low
resistance called a shunt (Rsh) in parallel, and its
function is to provide an alternate path
• The Ayrton Shunt- The purpose of designing the shunt
circuit is to allow to measure current I that is some
number n times larger than Im.
38
SUMMARY
• D’Ársonval Meter Movement
Used In A DC Voltmeter: The basic d’Ársonval meter movement
can be converted to a dc voltmeter by connecting a multiplier Rs in
series with the meter movement
• Voltmeter Loading Effects: is used to measure the voltage across
a circuit component
• 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
39
SUMMARY

D’Arsonval meter movement used
with full wave rectification: deflection of
the pointer to be greater than with the half
wave cycle, which allows current to flow
only on every other half cycle
Loading effects of AC Voltmeter:
loading effect of an ac voltmeter is
greater than that of a dc voltmeter
40