1 emt 113: v-2008 school of computer and communication engineering, unimap prepared by: prepared by:...

1EMT 113: V-2008EMT 113: V-2008

School of Computer and Communication School of Computer and Communication Engineering, UniMAPEngineering, UniMAP

Prepared By: Prepared By: Amir Razif b. Jamil AbdullahAmir Razif b. Jamil Abdullah

DC Meter.DC Meter.

CHAPTER CHAPTER 44

2

4.1 Introduction to Meters.4.1 Introduction to Meters.

4.2 Analogue Meter4.2 Analogue Meter

4.3 Introduction to DC Meters.4.3 Introduction to DC Meters.

4.4 D’Arsonval Meter Movement in DC 4.4 D’Arsonval Meter Movement in DC Meters.Meters.

4.5 Ayrton Shunt.4.5 Ayrton Shunt.

4.6 Voltmeter Loading Effect.4.6 Voltmeter Loading Effect.

4.7 Ammeter Insertion Effect.4.7 Ammeter Insertion Effect.

4.8 Ohmmeter.4.8 Ohmmeter.

4.0 DC Meters.4.0 DC Meters.

3

4.1 Introduction to Meters.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

4

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 4.2: Voltmeter

Figure 4.1: Galvanometer.

Cont’d…Cont’d…

5

GalvanometerGalvanometer 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.


6

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.

4.2 Analogue Meters.4.2 Analogue Meters.

Figure 4.3: Analogue Meter

7

For a given meter, there is a maximum rated current that produces full-scale deflection of the indicator; FSD rating.

By adding external circuit componentsadding 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 (A) 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 1000 = 0.05V.

Additional circuitry is needed for most practical measurements.


8

The meter movement will have a pair of metal connection terminals on the back for current to enter and exit.

Meter; (i) Polarity sensitive.(i) Polarity sensitive.(ii) Polarity-insensitive.(ii) Polarity-insensitive.

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-ininsensitive, relying on the attraction of an un-magnetized, 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.

4.3 Introduction DC 4.3 Introduction DC Meters.Meters.

9

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.


10

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.

(a) (a) Permanent Magnet Moving Coil (PMMC).Permanent Magnet Moving Coil (PMMC).

Figure 4.4: Permanent Magnet Moving Coil (PMMC) Meter Movement.


11

(b) (b) Electrostatic Meter Movement.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 physical force attracting the two surfacesattracting 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 Figure 4.5: Electrostatic Meter Movement.Movement.


12

The force is also irrespective of polarity, making this a polarity-ininsensitive 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.


13

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.Figure 4.6: Voltmeter.


14

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 shuntRm = internal resistance of the meter movement (resistance of the moving coil)Ish = current through the shunt Im = full-scale deflection current of the

meter movementI = full-scale deflection current for the ammeter

Figure 4.7: D’Ársonval Meter Figure 4.7: D’Ársonval Meter Movement Used in Ammeter Movement Used in Ammeter

CircuitCircuit

4.4 D’Arsonval Meter 4.4 D’Arsonval Meter Movement in DC Meter.Movement in DC Meter.

15

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 asRsh = Vsh/Ish

= ImRm/Ish = (Im/Ish)(Rm) = Im/(I – Im)*Rm


16

Example 4.1:Example 4.1: D’Arsonval Movement. D’Arsonval Movement.A D'Arsonval meter movement having a full-scale deflection rating of 1 mA A D'Arsonval meter movement having a full-scale deflection rating of 1 mA and a coil resistance of 500 Ω: and a coil resistance of 500 Ω:

Ohm's Law (E=IR), determine how much voltage will drive this meter movement directly to full scale,

Solution:Solution:

.VE

mAE

RIE

5.0

)500(*)1(

*

17

Example 4.2:Example 4.2: D’Arsonval Meter. D’Arsonval Meter. Calculate the value of the shunt resistance required to convert a 1-mA meter Calculate the value of the shunt resistance required to convert a 1-mA meter movement, with a 100 movement, with a 100 internal resistance, into a 0 - to 10 mA ammeter. internal resistance, into a 0 - to 10 mA ammeter.

Solution:Solution:Calculate Vm.

Vm is in parallel with Vsh.KCL

. VmA

RIV mmm

1.0100*1

11.119

1.0

9110

1.0

mA

V

I

VR

mAmAmA

III

VVV

sh

shsh

msh

msh

18

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.

Substituting for I in previous equation, yields

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.

4.5 Ayrton Shunt.4.5 Ayrton Shunt.

Figure 4.8: Aryton Shunt.

mnII

)1()(

n

R

InI

IRR m

m

mmsh

19

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 resistanceshunt resistance is,

On this range the shunt resistance is equal to Rsh and can be computed by the equation,

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

cbash RRRR


)1(

n

RR m

sh

RmRaRcRb VVVV

20

In current and resistance terms we can write

orI2(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


)())(( 2 mammcb RRIIIRR

21

Example 4.3:Example 4.3: Aryton Shunt.Aryton Shunt. Compute the value of the shunt resistors for the circuit below. ICompute the value of the shunt resistors for the circuit below. I33 = 1A, I= 1A, I22 = 100 mA, I = 100 mA, I11 = 10 mA, I = 10 mA, Imm = 100 uA and R = 100 uA and Rmm = 1K Ohm. = 1K Ohm.

Solution:Solution:

The total shunt resistance is found from

This is the shunt for the 10 mA range. When the meter is set on the 100-mA range, the resistor Rb and Rc provide the shunt . The total shunt resistance is found by the equation.

1.101100

1

1

K

n

RR m

sh

01.1100

)11.10(*)100(

)(

2

mA

KuA

I

RRIRR mshm

cb

22

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.

The resistor Rb is found from the equation below;

The resistor Ra is found from;

Verify the above result.

.

101.01

)11.10(*)100(

)(

3

A

KuA

I

RRIR mshm

c

909.0101.001.1

)( ccbb RRRR

909.0)101.0909.0(1.10

)( cbsha RRRR

1.10101.0909.009.9cbash RRRR


23

Example 4.4 (T2-2005):Example 4.4 (T2-2005): Aryton Shunt.Aryton Shunt. Figure below is an Aryton Shunt circuit. Given that RFigure below is an Aryton Shunt circuit. Given that R11 = 0.5 = 0.5 , R, R22 = 6.5 = 6.5 , R, R33 = = 55.5 55.5 RRmm = 1 k = 1 kIImm=100 =100 and n = 16. Calculate the value of, and n = 16. Calculate the value of, II11, , II22, , II33 and and II44..

Solution:Solution:

Find RshFind Rsh

II3 3

Can be easily derived

mAI

KA

RRR

RRII

I

RRIRRR

K

n

RR

mshm

mshm

msh

707.15.555.65.0

)167.66(100

)(

)(

67.66116

1

1

3

3213

3321

24

II22

II33

II44

....

mAI

KAI

R

RRII

I

RRIR

mshm

mshm

33.3135.0

)167.66(100

)(

)(

1

1

11

11

mAI

KAI

RR

RRII

I

RRIRR

mshm

mshm

238.155.65.0

)167.66(100

)(

)(

2

2

212

221

mAI

KA

RRRR

RRII

I

RRIRRRR

mshm

mshm

60.117.4555.65.0

)167.66(100

)(

)(

4

43214

44321

67.664321 RRRRRsh

25

(a) (a) D’Arsonval Meter Movement Used in a DC D’Arsonval Meter Movement Used in a DC Voltmeter.Voltmeter.

The basic d’Arsonval meter movement can be converted to a dc voltmeter by connecting a multiplier Rs in series with the meter movement, as in Figure 4.10 below.

The multiplier will extend the voltage range of the meter to limit current through the d’Arsonval meter movement to a full scale deflrction current.

The value of the multiplier resistor can be found by determine the sensitivity.

4.6 Voltmeter Loading 4.6 Voltmeter Loading Effect.Effect.

Figure 4.10: The d’Arsonval meter movement used in the Figure 4.10: The d’Arsonval meter movement used in the DC voltmeter.DC voltmeter.

)/(1

VI

ySensitivitfs

26

Voltmeter Design.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,

The voltage that can be applied to the – and + terminals before FSD current flows, is then increased to:

Rm is called a multiplier resistor because it multiplies the working range of the meter.

Figure 4.11: Voltmeter.


)( mcFSDFSD RRIV

27

For a given required FSD voltage, say VFSD, the multiplier resistance, Rm, is chosen as:

For example, to provide a voltmeter with FSD reading of 10 V with the given meter (IFSD = 1 mA, Rc= 500 Ω):

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.

cFSD

FSDm R

I

VR


k

mA

VR

I

VR c

FSD

FSDm 5.9500

1

10

28

Example 4.5:Example 4.5: Voltmeter Sensitivity. Voltmeter Sensitivity. Calculate the sensitivity of 100 uA meter movement Calculate the sensitivity of 100 uA meter movement

which is to be used as dc voltmeter.which is to be used as dc voltmeter.Solution.Solution.The sensitivity is compute as

.

The unit of sensitivity is expressed as the value of multiple resistance for 1-V range.

To calculate the value of the multiplier for voltage range greater than 1V, multiply the sensitivity by the range and subtract the internal resistance of the meter movement.

VkAI

SySensitivitfs

/10100

11,

cesisInternalRangeSRs tanRe*

29

Example 4.6:Example 4.6: Sensitivity Voltmeter Range. Sensitivity Voltmeter Range. Calculate the value of multiplier resistance on the 50-V range of a dc voltmeter Calculate the value of multiplier resistance on the 50-V range of a dc voltmeter that used a 500-uA meter movement with an internal resistance of 1kthat used a 500-uA meter movement with an internal resistance of 1k..

Solution.Solution.

The sensitivity of 500uA movement is,

The value of the multiplier Rs is calculated as,

.

kkVV

kR

cesisInternalRangeSR

s

s

99150*2

tanRe*

V

k

AISySensitivit

fs

2

500

11,

Figure 4.12: The Volmeter.Figure 4.12: The Volmeter.

30

(b) (b) Voltmeter Loading Effect.Voltmeter Loading Effect. When the voltmeter is used to measure the voltage

across a circuit component the voltmeter circuit itself is in parallel with the circuit component.

The parallel combination of two resistor is less than either resistor alone.

The resistance seen by the source is less with the voltmeter connected than without.

The voltage across the source is less when the voltmeter is connected. This effect is called voltmeter loading. The resulting error is called loading error.


31

Example 4.7:Example 4.7: Voltmeter Loading Effect. Voltmeter Loading Effect. In the voltmeter loading effect experiment, the two In the voltmeter loading effect experiment, the two different voltmeters are used to measure the voltage different voltmeters are used to measure the voltage across resistor Racross resistor RBB in the circuit in the circuit Figure 4.13 Figure 4.13 below, The below, The meters are as follow,meters are as follow,

Meter A: S = 1 kMeter A: S = 1 k /V, R /V, Rmm = 0.2 k = 0.2 k , range = 10V , range = 10V

Meter B: S = 20 kMeter B: S = 20 k /V, R /V, Rmm = 1.5 k = 1.5 k , range = 10V , range = 10VCalculate,Calculate,

(i) Voltage across R(i) Voltage across RBB without any meter connected across without any meter connected across it.it.

(ii) Voltage across R(ii) Voltage across RBB when meter A is used. when meter A is used.

(iii) Voltage across R(iii) Voltage across RBB when meter B is used. when meter B is used.(iv) Error in voltmeter readings.(iv) Error in voltmeter readings.

Solution.Solution. Figure 4.13: The Voltmeter Figure 4.13: The Voltmeter Loading Effect.Loading Effect.

32

(i) Voltage across RB without any meter connected across it.

(ii) Voltage across RB when meter A is used.

The parallel combination of RB and meter A,

Therefore the voltage reading obtained with meter A, determine by the voltage divider equation is

Vkk

kV

RR

REV

BA

BRB 5

525

5)30(

kkVV

kRRangeSR mS 91)10(

1*

kkk

kk

RR

RRR

TAB

TABe 33.3

105

)10)(5())((1

Vkk

kV

RR

REV

Ae

eRB 53.3

2533.3

33.3)30(

1

1

33

(iii) Voltage across RB when meter B is used. The total resistance that meter B presents to the

circuit is

The parallel combination of RB and meter B is

the voltage reading obtain with meter B, determine by use of the voltage divider equation

(iv) Error in voltmeter readings. Voltmeter A error ` Voltmeter B error .

kVV

kRangeSRTB 200)10(

20*

kkk

kk

RR

RRR

TBB

TBBe 88.4

2005

)200)(5(2

Vkk

kV

RR

REV

Ae

eRB 9.4

2588.4

88.4)30(

2

2

%4.29%100*5

53.35

V

VV

%2%100*5

9.45

V

VV

34

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 4.14, 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.

4.6 Ammeter Insertion 4.6 Ammeter Insertion Effect.Effect.

Figure 4.14: (a) Expected Current Value in a Series Circuit(b) Series Circuit with Ammeter.

35

From the circuit;

Placing the meter in series result in;

Divide the above equations yields;

Insertion error,

1R

EI e

mm RR

EI

1

me

m

RR

R

I

I

1

1

%100*1

e

m

I

I


36

Example 4.8:Example 4.8: Ammeter Insertion Effects. Ammeter Insertion Effects. A current meter that has an internal resistance 78 Ohm is used to A current meter that has an internal resistance 78 Ohm is used to measure the current through resistor Rmeasure the current through resistor Rcc in in Figure 4.14Figure 4.14. Determine the . Determine the percentage of errorpercentage of error of the reading due to ammeter insertion. of the reading due to ammeter insertion.

Solution.Solution.

Look back into the circuit from terminal X and Y.Look back into the circuit from terminal X and Y.

37

Solution.Solution.The Thevenin equivalent resistance.

The ratio of meter current to the expected current is,

Solving for Im yields,

.

KKK

RR

RRRR

ba

bacth

5.15.01

95.0785.1

5.1

1

1

K

K

rR

R

I

I

me

m

em II 95.0

%0.5%100*1

e

m

I

IerrorInsertion

38

The d’Arsonval meter movement can be used with the battery and resistor to construct a simple ohmmeter.

Figure 4.15 is the basic ohmmeter circuit,

Introduce Rx between point X and Y so that we can calculate the value of resistance.

mzfs RR

EI

4.7 Ohmmeter.4.7 Ohmmeter.

Figure 4.15: Basic Ohmmeter Figure 4.15: Basic Ohmmeter Circuit.Circuit.

xmz RRR

EI

39

P represent the ratio of the current I to the full scale deflection

)(

)(

)/(

)/(

xmz

mz

mz

xmz

fs RRR

RR

RRE

RRRE

I

I

)(

)(

xmz

mz

fs RRR

RR

I

IP

Figure 4.16: Basic Ohmmeter Circuit Figure 4.16: Basic Ohmmeter Circuit with Unknown Resistor Rwith Unknown Resistor Rxx Connected Connected

Between.Between.


40

Example 4.9:Example 4.9: Ohmmeter. Ohmmeter.A 1mA full-scale deflection current meter movement is to A 1mA full-scale deflection current meter movement is to used in an ohmmeter circuit. The meter movement has an used in an ohmmeter circuit. The meter movement has an internal resistance, Rinternal resistance, Rmm, of 100 Ohm, and a 3-V battery will be , of 100 Ohm, and a 3-V battery will be used in the circuit. Mark off the meter face for reading used in the circuit. Mark off the meter face for reading resistance.resistance.Solution.Solution.Value of Rz, which will limit current to full-scale deflection is,

Value of Rz, with 20% full-scale deflection is,

KOhmOhmmA

VR

RI

ER

z

mfs

z

9.21001

3

K

KKKK

RRP

RRR mz

mzx

12

)0.19.2(2.0

0.19.2

)(

41




The ohmmeter is nonlinear due to the high internal resistance of the ohmmeter.

K

KK

RRP

RRR mz

mzx

1

)3(75.0

3

)(

K

KK

RRP

RRR mz

mzx

5.4

)3(4.0

3

)(

K

KK

RRP

RRR mz

mzx

3

)3(5.0

3

)(


1 emt 113: v-2008 school of computer and communication engineering, unimap prepared by: prepared by:...

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