SHAIFUL NIZAM MOHYAR
UNIVERSITI MALAYSIA PERLIS
SCHOOL OF MICROELECTRONIC ENGINEERING
2007/2008
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).
4.1 Introduction to Meters.
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.
Figure 4.1: Galvanometer.
 Most modern meters are "digital" in design, meaning
that their readable display is in the form of numerical
digits.
Cont’d…
 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 4.2: 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.
Cont’d…
 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 permanentmagnet, 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
Figure 4.3: Analogue Meter
Cont’d…
 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.
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.
Cont’d…
 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.
Cont’d…
 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.
(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.
(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
polarity-insensitive 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
Figure 4.7: D’Ársonval Meter Movement
I = full-scale deflection current for the ammeter
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. Vm  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
Vsh 0.1V
Rsh 

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) = ImRshIm(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
Rm
1K
Rsh 

 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.
I m ( Rb  Rc )
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.
I m ( Rb  Rc )
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
(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…

E
From the circuit; I e 
R1
 Placing the meter in series result in;
 Divide the above equations yields;
 Insertion error,
 Im 
1   *100%
Ie 

E
Im 
R1  Rm
Im
R1

I e R1  Rm
Ex 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.
Ra Rb
Rth  Rc 
Ra  Rb
 1K  0.5K  1.5
The ratio of meter current to the expected current is,
Solving for Im yields,
I m  0.95I e
Im
R1
1.5K


 0.95
I e R1  rm 1.5K  78
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,
E
I fs 
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…
( R z  Rm )
I E /( Rz  Rm  Rx )


I fs
E /( Rz  Rm )
( R z  Rm  R x )
 P represent the ratio of the current I to the full scale
deflection
( R z  Rm )
I
P

I fs ( Rz  Rm  Rx )
Figure 4.12: Basic Ohmmeter Circuit with Unknown Resistor Rx Connected Between.
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
3V
 100Ohm  2.9 KOhm
1mA
 Value of Rz, with 20% full-scale deflection is,
Rz 
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,
Value of Rz, with 50% full-scale deflection is,
Rx 
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. 5
 3 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.
 Value of Rz, with 75% full-scale deflection is, R x 
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.
(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.
(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.
(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.
(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 halfcycle 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.
Edc
0.45Erms
Rs 
 Rs 
 Rm
I dc
I dc
 From the above equation,
S ac  0.45S dc
Ex 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 Half-Wave
Rectification.
Solution:
Find the sensitivity for a half wave
rectifier.
S ac  0.45S dc
1
450
 0.45 *

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
Ex 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 FullWave 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
(a) The equivalent DC voltage is,
E dc  0.9 * 10Vrms  0.9 *10V  9.0V
RT 
Rs  RT  2 Rd 
E dc 9.0V

 4.5 K
IT
2mA
Rm Rsh
Rm  Rsh
 4500  2 * 50 
(b) The ac sensitivity,
(c.) The dc sensitivity,
S ac 
500 * 500
 4.15K
500  500
RT
4500

 450 / V
Range
10V
S dc 
S ac
1

 500 / V
IT
2mA
or
S dc
S ac 450 / V


 500 / V
0. 9
0.9