Transcript Chapter 4 - UniMAP Portal

EKT451
CHAPTER 4
DC & AC Meters.
4.0 DC Meters.
4.1 Introduction to Meters.
4.2 Analogue Meter
4.3 Introduction to DC Meters.
4.4 D’Arsonval Meter Movement in DC Meters.
4.5 Ayrton Shunt.
4.6 Ammeter Insertion Effect.
4.7 Ohmmeter.
4.1 Introduction to Meters.

A meter is any device built to accurately detect and display an
electrical quantity in a form readable by a human being.
(i) Pointer (analogue).
(ii) Series of lights (analogue).
(iii) Numeric display (digital).
In this chapter students will familiarized with the d’Arsonval meter
movement, its limitations and some of its applications.
 Electrical meters;
(i) DC, AC average quantities:
-Voltmeter
-Ammeter
-Ohmmeter
(ii) AC measurements:
-Oscilloscope

Cont’d…

A meter is any device built to accurately
detect and display an electrical quantity in a
form readable by a human being.

In the analysis and testing of circuits, there
are meters designed to measure the basic
quantities of voltage, current, and
resistance.

Most modern meters are "digital" in design,
meaning that their readable display is in the
form of numerical digits.

Older designs of meters are mechanical in
nature, using some kind of pointer device to
show quantity of measurement.

The first meter movements built were known
as galvanometers, and were usually
designed with maximum sensitivity in mind.
Figure 4.1: Galvanometer.
Figure 4.2: Voltmeter
Cont’d…

A very simple galvanometer may be made from a magnetized needle
(such as the needle from a magnetic compass) suspended from a
string, and positioned within a coil of wire.

Current through the wire coil will produce a magnetic field which will
deflect the needle from pointing in the direction of earth's magnetic
field. An antique string galvanometer is shown in Figure 4.1.

The term "galvanometer" usually refers to any design of
electromagnetic meter movement built for exceptional sensitivity, and
not necessarily a crude device such as that shown in Figure 4.1.

Practical electromagnetic meter movements can be made now where
a pivoting wire coil is suspended in a strong magnetic field, shielded
from the majority of outside influences. Such an instrument design is
generally known as a permanent-magnet, moving coil, or PMMC
movement.
4.2 Analogue Meters.




The analogue meters are mostly based on moving coil meters. The
typical structure consists of a wire wound coil placed between two
permanent magnets, Figure 4.3.
When current flows through the coil in the presence of a magnetic
field, a force is exerted on the coil;
F = Bil
This force is directly proportional
to current flowing in the coil.
If the coil is free to rotate, the
force causes a deflection of the
coil that is proportional to the
current.
By adding an indicator (e.g. needle)
and a display, the level of current
can be measured.
Figure 4.3: Analogue Meter
Cont’d…

For a given meter, there is a maximum rated current that produces
full-scale deflection of the indicator; FSD rating.

By adding external circuit components, the same basic moving
coil meter can be used to measure different ranges of voltage or
current.

Most meters are very sensitive. That is, they give full-scale deflection
for a small fraction of an amp for example a typical FSD current
rating for a moving coil meters is 50 μA, with internal wire resistance
of 1 kΩ.

With no additional circuitry, the maximum voltage that can be
measured using this meter is
50 x 10-6x 1000V = 0.05V.

Additional circuitry is needed for most practical measurements.
4.3 Introduction DC Meters.

The meter movement will have a pair of metal connection terminals
on the back for current to enter and exit.

Most meter movements are polarity-sensitive, one direction of
current driving the needle to the right and the other driving it to the
left.

Some meter movements are polarity-insensitive, relying on the
attraction of an unmagnetized, movable iron vane toward a
stationary, current-carrying wire to deflect the needle. Such meters
are ideally suited for the measurement of alternating current (AC).

A polarity-sensitive movement would just vibrate back and forth
uselessly if connected to a source of AC.
Cont’d…

An increase in measured current will drive the needle to point further
to the right. A decrease will cause the needle to drop back down
toward its resting point on the left.

Most of the mechanical meter movements are based on
electromagnetism ; electron flow through a conductor creating a
perpendicular magnetic field,

A few are based on electrostatics; the attractive or repulsive force
generated by electric charges across space.
Cont’d…
(a) Permanent Magnet Moving Coil (PMMC).
Figure 4.4: Permanent Magnet
Moving Coil (PMMC) Meter
Movement.

In the PMMC-type instruments, Figure 4.4. Current in one direction
through the wire will produce a clockwise torque on the needle
mechanism, while current the other direction will produce a
counter-clockwise torque.
Cont’d…
(b) Electrostatic Meter Movement.

In the electrostatics, the attractive or repulsive force generated by
electric charges across space, Figure 4.5.

This is the same phenomenon exhibited by certain materials; such as
wax and wool, when rubbed together.

If a voltage is applied between two conductive surfaces across an
air gap, there will be a physical force attracting the two surfaces
together capable of moving some kind of indicating mechanism.

That physical force is directly proportional to the voltage applied
between the plates, and inversely proportional to the square of the
distance between the plates.
Figure 4.5: Electrostatic Meter
Movement.
Cont’d…

The force is also irrespective of polarity, making this a polarityinsensitive type of meter movement.

Unfortunately, the force generated by the electrostatic attraction is
very small for common voltages. It is so small that such meter
movement designs are impractical for use in general test
instruments.

Typically, electrostatic meter movements are used for measuring
very high voltages; many thousands of volts.

One great advantage of the electrostatic meter movement, however,
is the fact that it has extremely high resistance, whereas
electromagnetic movements (which depend on the flow of electrons
through wire to generate a magnetic field) are much lower in
resistance.
Cont’d…

Some D'Arsonval movements have full-scale deflection current
ratings as little as 50 µA, with an (internal) wire resistance of less
than 1000 Ω.
 This makes for a voltmeter with a full-scale rating of only 50
millivolts (50 µA X 1000 Ω).
Figure 4.6: Voltmeter.
D’Arsonval Meter Movement in DC Meter.





The basic d’Arsonval meter movement has only limited usefulness
without modification.
By modification on the circuit it will increase the range of current
that can be measured with the basic meter movement.
This is done by placing the low resistance in parallel with the meter
movement resistance Rm.
The low resistance shunt (Rsh) will provide an alternate path for the
total meter current I around the meter movement.
The Ish is much greater than Im.
Where
Rsh = resistance of the shunt
Rm = internal resistance of the meter movement
(resistance of the moving coil)
Ish = current through the shunt
Im = full-scale deflection current of the
meter movement
I = full-scale deflection current for the ammeter Figure 4.7: D’Ársonval Meter Movement
Used in Ammeter Circuit
Cont’d…

The voltage drop across the meter movement
is
Vm = ImRm

Since the shunt resistor is in parallel with the meter movement, the
voltage drop across the shunt is equal to the voltage drop across the
meter movement. That is,
Vsh = Vm
The current through the shunt is equal to the total current minus the
current through the meter movement:,
Ish = I – Im
Knowing the voltage across, and the current through, the shunt allows
us to determine the shunt resistance as
Rsh = Vsh/Ish
= ImRm/Ish = (Im/Ish)(Rm)
= Im/(I – Im)*Rm Ohm


Example 4.1: D’Arsonval Movement.
A D'Arsonval meter movement having a full-scale deflection rating of 1 mA
and a coil resistance of 500 Ω:
Solution:
Ohm's Law (E=IR), determine how much voltage will drive this meter
movement directly to full scale,
E  I *R
E  (1mA) * (500)
E  0.5V
Example 4.2: D’Arsonval Meter.
Calculate the value of the shunt resistance required to convert a 1-mA
meter movement, with a 100 Ohm internal resistance, into a 0- to 10 mA
ammeter.
Solution:
Calculate Vm.
V m  I m Rm
 1mA * 100  0.1V
Vm is in parallel with Vsh. KCL
Vsh  Vm  0.1V
I sh  I  I m
.
 10mA  1mA  9mA
V
0.1V
Rsh  sh 
11.11
I sh 9mA
4.5 Ayrton Shunt.
 The purpose of designing the shunt circuit is to allow to measure a
current I that is some number n times larger than Im, Figure 4.8.
 The number n is called a multiplying factor and relates total current
and meter current as the Ayrton Shunt.
I = nIm
Substituting for I in previous equation, yields
Rsh = RmIm/(nIm-Im) = Rm/(n-1) Ohm
 Advantage:
(i) it eliminates the possibility
of the meter movement being in the
circuit without any shunt resistance.
(ii) May be used with a wide range of meter
movements.
Figure 4.8: Aryton Shunt.
Cont’d…

The individual resistance values of the shunts are calculated by
starting with the most sensitive range and working toward the least
sensitive range.

The shunt resistance is,
Rsh = Ra + Rb + Rc

On this range the shunt resistance is equal to Rsh and can be
computed by the equation,
Rsh = Rm/(n-1)

The equation needed to compute the value of each shunt, Ra, Rb, and
Rc, can be developed from the circuit in Figure 4.8.

Since the resistance Rb + Rc is in parallel with Rm + Ra, the voltage
across each parallel branch should be equal and can be written as
VRb + Rc = VRa + Rm
Cont’d…

In current and resistance terms we can write
(Rb + Rc) (I2-Im)=Im (Ra +Rm)
or
I2(Rb + Rc) - Im(Rb + Rc)= Im[Rsh-(Rb + Rc)+Rm]
Multiplying through by Im on the right yields
I2(Rb + Rc) - Im(Rb + Rc) = ImRsh- Im(Rb + Rc)+ImRm
This can be rewritten as
Rb+ Rc = Im (Rsh+ Rm)/I2
Having already found the total shunt resistance Rsh, we can now
determine Ra as
Ra = Rsh – (Rb + Rc)
The current I is the maximum current for the range on which the
ammeter is set. The resistor Rc can be determined from
Rc = Im(Rsh+ Rm)/I3
The resistor Rb can now be computed as, Rb = (Rb + Rc) – Rc
Example 4.3: Aryton Shunt.
Compute the value of the shunt resistors for the circuit below. I3 = 1A, I2 =
100 A, I1 = 10 mA, Im = 100 uA and Rm = 1K Ohm.
Solution:
The total shunt resistance is found from
Rsh 
Rm
1K

 10.1
n  1 100  1
This is the shunt for the 10 mA range. When the meter is set on the 100mA range, the resistor Rb and Rc provide the shunt . The total shunt
resistance is found by the equation.
Rb  Rc 

I m ( Rb  Rc )
I2
(100uA) * (10.1  1K)
 1.01
100mA
Cont’d…Example
The resistor Rc , which provides the shunt resistance on the 1-A range can
be found by the same equation, however the current I will now be 1A.
Rb  Rc 

I m ( Rb  Rc )
I2
(100uA) * (10.1  1K)
 0.101
1A
The resistor Rb is found from the equation below;
Rb  ( Rb  Rc )  Rc
 1.01  0.101  0.909
The resistor Ra is found from;
Ra  Rsh  ( Rb  Rc )
 10.1  (0.909  0.101)  0.909
Verify the above result.
Rsh  Ra  Rb  Rc
 9.09  0.909  0.101  10.1
.
Cont’d…
(b) Voltmeter Design.



Consider a moving coil meter with FSD rating of 1 mA and coil
resistance, Rc, of 500 Ω.
The maximum voltage required to produce FSD is 0.5 V.
The voltage range is increased by adding a series resistor,
Figure 4.9: Voltmeter.


The voltage that can be applied to the – and + terminals before FSD
current flows is then increased to:
VFSD= IFSD(Rc+ Rm)
Rm is called a multiplier resistor because it multiplies the working
range of the meter. Alternatively, it may be thought of as dividing the
measured voltage across the moving coil meter.
Cont’d…

For a given required FSD voltage, say VFSD, the multiplier resistance,
Rm, is chosen as:
Rm= (VFSD/ IFSD) –Rc
For example, to provide a voltmeter with FSD reading of 10 V with the
given meter (IFSD = 1 mA, Ri= 500 Ω):
Rm = (10 / 1 x 10-3) –500 = 9.5kΩ.

With exactly 10 V applied, there will be exactly 1 mA of current flowing,
thereby producing full-scale deflection.

There is only the maximum allowed voltage of 0.5V dropped across
the moving coil meter.

The scale of the meter must be changed to indicate the new range of
the circuit.
4.6 Ammeter Insertion Effect.

We frequently overlook the error caused by inserting an ammeter
in a circuit to obtain a current reading.

All ammeters contain some internal resistance.

By inserting the ammeter in the circuit means increase the
resistance of the circuit and result in reducing current in the circuit.

Refer to the circuit in Figure 4.10, Ie is the current without the
ammeter.

Suppose that we connect the ammeter in the circuit (b), the current
now becomes Im due to the additional resistance introduced by the
ammeter.
Figure 4.10: (a) Expected Current Value in a Series Circuit
(b) Series Circuit with Ammeter.
Cont’d…
 From the circuit;
E
Ie 
R1
 Placing the meter in series result in;
E
Im 
R1  Rm
 Divide the above equations yields;
Im
R1

I e R1  Rm
 Insertion error,
 Im 
1   *100%
Ie 

Example 4.4: Ammeter Insertion Effects.
A current meter that has an internal resistance 78 Ohm is used to
measure the current through resistor Rc in Figure 4.10. Determine the
percentage of error of the reading due to ammeter insertion.
Solution.
The Thevenin equivalent resistance.
Rth  Rc 
Ra Rb
Ra  Rb
 1K  0.5 K  1.5
The ratio of meter current to the expected current is,
Im
R1
1.5K


 0.95
I e R1  rm 1.5K  78
Solving for Im yields,
I m  0.95I e
4.7 Ohmmeter.

The d’Arsonval meter movement can be used with the battery and
resistor to construct a simple ohmmeter.

Figure 4.11 is the basic ohmmeter circuit,
I fs

E

R z  Rm
Introduce Rx between point X and Y so that we can calculate the
value of resistance.
E
I
R z  Rm  R x
Figure 4.11: Basic Ohmmeter Circuit.
Cont’d…
E /( Rz  Rm  Rx )
( R z  Rm )
I


I fs
E /( Rz  Rm )
( R z  Rm  R x )
 P represent the ratio of the current I to the full scale
deflection
Figure 4.12: Basic Ohmmeter Circuit
with Unknown Resistor Rx
Connected Between.
( R z  Rm )
I
P

I fs ( Rz  Rm  Rx )
Example 4.5: Ohmmeter.
A 1mA full-scale deflection current meter movement is to used in an
ohmmeter circuit. The meter movement has an internal resistance, Rm,
of 100 Ohm, and a 3-V battery will be used in the circuit. Mark off the
meter face for reading resistance. e to ammeter insertion.
Solution.
 Value of Rz, which will limit current to full-scale deflection is,
Rz 
E
 Rm
I fs
Rz 
3V
 100Ohm  2.9 KOhm
1mA
 Value of Rz, with 20% full-scale deflection is,
Rx 
R z  Rm
 ( R z  Rm )
P
2 . 9 K   1. 0 K 

 ( 2. 9 K   1. 0 K  )
0 .2
 12 K
Cont’d…Example

Value of Rz, with 40% full-scale deflection is,
Rx 

Value of Rz, with 50% full-scale deflection is,
Rx 

R z  Rm
 ( R z  Rm )
P
3 K

 (3K)
0. 5
 3 K
Value of Rz, with 75% full-scale deflection is,
Rx 

R z  Rm
 ( R z  Rm )
P
3 K

 (3K)
0. 4
 4. 5 K 
R z  Rm
 ( R z  Rm )
P
3 K

 (3K)
0.75
 1K
The ohmmeter is nonlinear due to the high internal resistance of
the ohmmeter.
5.0 AC Meters.
5.1 Introduction to AC Meters.
5.2 D’Arsonval Meter Movement with Half-Wave Rectification.
5.3 D’Arsonval Meter Movement with Full-Wave Rectification.
5.1 Introduction to AC Meters.

Five principal meter movement that are commonly used in ac
instruments;
(i) Electrodynamometer.
(ii) Iron-Vane.
(iii) Electrostatic.
(iv) Thermocouple.
(v) D’Arsonval (PMMC) with rectifier.

The d’Arsonval meter is the most frequently used meter movement,
event though it cannot directly measure alternating current or voltage.

In this chapter it will discuss the instruments for measuring alternating
signal that use the d’Arsonval meter movement.
Cont’d…
(a) AC voltmeters and ammeters

AC electromechanical meter movements come in two basic
arrangements:
(1) Based on DC movement designs.
(2) Engineered specifically for AC use.

Permanent-magnet moving coil (PMMC) meter movements will not
work correctly if directly connected to alternating current, because
the direction of needle movement will change with each half-cycle of
the AC.

Permanent-magnet meter movements, like permanent-magnet
motors, are devices whose motion
depends on the polarity of the
applied voltage, Figure 5.1.
Figure 5.1: D’Arsonal Electromechanical
Meter Movement.
Cont’d…
(b) DC-style Meter Movement for AC application.

If we want to use a DC-style meter movement such as the
D'Arsonval design, the alternating current must be rectified into
DC, Figure 5.2.

This can be accomplished through the use of devices called diodes.
The diodes are arranged in a bridge, four diodes will serve to steer
AC through the meter movement in a constant direction throughout
all portions of the AC cycle:
Figure 5.2: Rectified D’Arsonal
Electromechanical Meter Movement.
Cont’d…
(c) Iron-Vane Electromechanical.

The AC meter movement without the inherent polarity sensitivity of
the DC types.

This design avoid using the permanent magnets. The simplest
design is to use a non-magnetized iron vane to move the needle
against spring tension, the vane being attracted toward a stationary
coil of wire energized by the
AC quantity to be measured, Figure 5.3.

The electrostatic meter movements
are capable of measuring very high
voltages without need for range
resistors or other, external apparatus.
Figure 5.3: Iron-Vane Electromachanical
Meter Movement.
Cont’d…
(d) AC Voltmeter with Resistive Divider.

When a sensitive meter movement needs to be re-ranged to
function as an AC voltmeter, series-connected "multiplier"
resistors and/or resistive voltage dividers may be employed just
as in DC meter design, Figure 5.4.
Figure 5.4: AC Voltmeter with Resistive
Divider.
Cont’d…
(e) AC Voltmeter with Capacitive Divider.

Capacitors may be used instead of resistors, though, to make
voltmeter divider circuits. This strategy has the advantage of being
non-dissipative; no true power consumed and no heat produced.
Refer to Figure 5.5.
Figure 5.5: AC Voltmeter with
Capacitive Divider.
5.2 D’Arsonval Meter Movement
with Half-Wave Rectification.
In order to measure the alternating current with the d’Arsonval
meter movement, we must rectify the alternating current by use of
diode rectifier .
 Figure 5.6 is the DC voltmeter circuit modified to measure AC
voltage.
 The forward diode, assume to be ideal diode, has no effect on the
operation of the circuit .
 For example if the 10 V sine-wave input is fed as the source of the
circuit, the voltage across the meter movement is just the positive
half-cycle of the sine wave due to the rectifying effect of the diode.

Figure 5.6: DC Voltmeter Circuit
Modified to Measure AC Voltage.
Cont’d…
 The peak value of 10 V rms sine wave is,
E p  10Vrms *1.414  14.14V peak
E ave  E dc  0.318 * E p
or
E ave 
Ep

 0.45 * E rms
 If the output voltage from the half-wave rectifier is 10V
only, a dc voltmeter will provide an indication of
approximately 4.5 V.
E
0.45E
Rs 
 From the above equation,
dc
I dc
 Rs 
rms
I dc
 Rm
S ac  0.45S dc
Example 4.1: D’Arsonval Meter Half-Wave Rectifier.
Compute the value of the multiplier resistor for a 10 Vrms ac range on the
voltmeter shown in Figure 5.7.
Figure 5.7: AC Voltmeter Using HalfWave Rectification.
Solution:
Find the sensitivity for a half wave rectifier.
S ac  0.45S dc  0.45 *
1
450

I fs
V
Rs  S ac * Range ac  Rm

.
450 10V
*
 300  4.2 K
V
1
Cont’d…

Commercially produced ac voltmeters that use half-wave rectification
have an additional diode and shunt as shown in Figure 5.8, which
is called instrument rectifier.
Figure 5.8: Half-Wave Rectification Using an
Instrument Rectifier and a Shunt Resistor.
5.3 D’Arsonval Meter Movement
with Full-Wave Rectification.

The full-wave rectifier provide higher sensitivity rating compare to
the half-wave rectifier.

Bridge type rectifier is the most commonly used, Figure 5.9.
Figure 5.9: Full Wave Bridge
Rectifier Used in AC Voltmeter
Circuit.
Cont’d…

Operation;
(a) During the positive half cycle (red arrow), 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.
- If the deflection remains the same, the instrument using full wave
rectification will have a greater sensitivity.
(b) Vise versa for the negative half cycle (blue arrow).
Cont’d…

From the circuit in Figure 5.9, the peak value of the 10 Vrms signal
with the half-wave rectifier is,
E p  1.414 * E rms  14.14V peak

The average dc value of the pulsating sine wave is,
E ave  0.636 E p  9V

Or can be compute as,
Eave  0.9 * Erms  0.9 *10V  9V

The AC voltmeter using full-wave rectification has a sensitivity equal
to 90% of the dc sensitivity or twice the sensitivity using half-wave
rectification.
S ac  0.9 * S dc
Example 4.2: D’Arsonval Meter Full-Wave Rectifier.
Each diode in the full-wave rectifier circuit in Figure 5.10 has an average
forward bias resistance of 50 Ohm and is assumed to have an infinite
resistance in the reverse direction. Calculate,
(a) The multiplier Rs.
(b) The AC sensitivity.
© The equivalent DC sensitivity.
Figure 5.10: AC Voltmeter Using
Full-Wave Rectification and Shunt.
Solution:
(a) Calculate the current shunt and total current,
I sh 
E m 1mA * 500

 1mA
Rsh
500
and
I T  I sh  I m  1mA  1mA  2mA
Cont’d…Example

The equivalent DC voltage is,
E dc  0.9 * 10Vrms  0.9 *10V  9.0V
RT 
E dc 9.0V

 4.5 K
IT
2mA
Rs  RT  2 Rd 
Rm Rsh
Rm  Rsh
 4500  2 * 50 
500 * 500
 4.15K
500  500
(b) The ac sensitivity,
S ac 
RT
4500

 450 / V
Range
10V
(c.) The dc sensitivity,
S dc 
S ac
1

 500 / V
IT
2mA
or
S dc 
S ac 450 / V

 500 / V
0. 9
0.9