chap2_acdcmeter1 ver2

7/31/2019 chap2_AcDcmeter1 ver2

1/14

1

CHAPTER 2

DC AND AC METER

2

OBJECTI VES

At the end of this chapter, studentsshould be able to:

1. Explain the basic contruction and workingprinciple of DArsonval meter movement.

2. Perfom basic electronic circuit analisis forDArsonval meter family.

3. Identify the difference electronic circuitdesign for measurement meters usingDArsonval meter principle.

3

CHAPTER OUTLI NE

1. DArsonval Meter Movement

2. DC Ammeter

3. DC Voltmeter

4. Multi-range Voltmeter

5. Voltmeter Loading Effects

6. Ammeter Insertion Effects

7. Ohmmeter

8. Multi-range Ohmmeter

9. Multimeter

10. AC Voltmeter using half-

wave rectifier11. AC Voltmeter Loading

Effects

12. Wheatstone Bridge

13. Kelvin Bridge

14. Bridge-controlled Circuit

4

2 .1 : D ARSORVAL METERMOVEMENT

Also called Permanent-Magnet Moving Coil(PMMC).

Based on the moving-coil galvanometerconstructed by Jacques d Arsonval in 1881.

Can be used to indicate the value of DC andAC quantity.

Basic construction of modern PMMC can beseen in Figure 2.1.


2/14

5

2.1.1:Operation of DArsonval

Meter

When current flows through the coil, thecore will rotate.

Amount of rotation is proportional to theamount of current flows through the coil.

The meter requires low current (~50uA) fora full scale deflection, thus consumes very

low power (25-200 Uw). Its accuracy is about 2% -5% of full scale

deflection

6

Pointer

Permanent magnet

CoilCore

Figure 2.1: Modern DArsonval Movement

Air Gap

7

2 .2 : DC AMM ETER

The PMMC galvanometer constitutes thebasic movement of a dc ammeter.

The coil winding of a basic movement is

small and light, so it can carry only verysmall currents.

A low value resistor (shunt resistor) is usedin DC ammeter to measure large current.

Basic DC ammeter:

8

Rsh

+

_

_

+

Rm

DArsonvalMovement

I Ish Im

Figure 2.2: Basic DC Ammeter


3/14

9

Referring to Fig. 2.2:

Rm = internal resistance of themovement

Rsh = shunt resistance

Ish =shunt current

Im = full scale deflection current

of the movementI = full scale current of the

ammeter + shunt (i.e. total current)

10

m

mmsh

msh

mmshsh

IIRIR

III

RIRI

=

=

=

11

EXAMPLE 3.1

A 1mA meter movement with aninternal resistance of 100 is to beconverted into a 0-100 mA. Calculate

the value of shunt resistancerequired. (ans: 1.01)

12

oThe range of the dc ammeter is extended by a

number of shunts, selected by a range switch.

oThe resistors is placed in parallel to give differentcurrent ranges.

oSwitch S (multiposition switch) protects the

meter movement from being damage during range

changing. (Make before break type switch)

oIncrease cost of the meter.


4/14

13

R1 R2 R3 R4

+

_

+

_Rm

DArsonvalMovement

Figure 2.3: Multirange Ammeter

S

14

Aryton shunt eliminates the possibility of having the meter inthe circuit without a shunt.

Reduce costPosition of the switch:

Ra parallel with series combination of Rb, Rc and the metermovement. Current through the shunt is more than the currentthrough the meter movement, thereby protecting the metermovement and reducing its sensitivity.

Ra and Rb in parallel with the series combination of Rc and themeter movement. The current through the meter is more than the

current through the shunt resistance.Ra, Rb and Rc in parallel with the meter. Maximum current flowsthrough the meter movement and very little through theshunt. This will increase the sensitivity.

15

Rc

Rb

Ra

Rm

DArsonvalMeter

+

_3

1

2+

_

Figure 2.4: Aryton Shunt

16

EXAMPLE 2.2 Design an Aryton shunt to provide an ammeter with a

current range of 0-1 mA, 10 mA, 50 mA and 100 mA. A D

Arsonval movement with an internal resistance of 100

and full scale current of 50 uA is used.

1mA

R2

R1

R3

R4

_DArsonvalMovement

+

+

_

10mA

50mA

100mA


5/14

17

REQUIREMENT OF A SHUNT

1 ) M in im u m Th e r m o D ie l ec t r i c Vo l t a g eDrop

Soldering of joint should not cause a voltagedrop.

2 ) So ld er a b i l it y

- never connect an ammeter across asource of e.m.f

- observe the correct polarity

- when using the multirange meter, firstuse the highest current range.

18

To use the basic meter as a dc voltmeter,must know the amount of current (I

fsd) required

to deflect the basic meter to full scale.

The sensitivity is based on the fact that thefull scale current should results whenever acertain amount of resistance is present in themeter circuit for each voltage applied.

fsdIS

1=

19

EXAMPLE 2.3

Calculate the sensitivity of a 200 uAmeter

movement which is to be used as a dc

voltmeter.

Solution:Vk

uAIS

fsd

/5200

11===

20

A basic DArsonval movement canbe converted into a DC voltmeter byadding a series resistor (multiplier)as shown in Figure 2.3.

Im

=full scale deflection current ofthe movement (Ifsd)

Rm=internal resistance of themovement

Rs =multiplier resistance

V =full range voltage of theinstrument

Rs

Im

Rm

Multiplier

V

+

_

Figure 2.5: Basic DCVoltmeter


6/14

21

From the circuit of Figure 2.5:

Therefore,

m

m

s

m

mm

mms

msm

RIVR

RI

V

I

RIVR

RRIV

=

=

=

+= )(

22

EXAMPLE 2.4

A basic D Arsonval movement with a full-scale deflection of 50 uA and internalresistance of 500 is used as a DCvoltmeter. Determine the value of themultiplier resistance needed to measure avoltage range of 0-10V.

Solution:=== k

uA

VR

I

VR m

m

s 5.19950050

10

23

Sensitivity and voltmeter range can be used tocalculate the multiplier resistance, Rs of a DCvoltmeter.

Rs=(S x Range) - Rm

From example 2.4:Im= 50uA, Rm=500, Range=10V

Sensitivity,

So, Rs = (20k/V x 10V) 500

= 199.5 k

VkuAI

Sm

/2050

11===

24

A DC voltmeter can be converted into a multirangevoltmeter by connecting a number of resistors(multipliers) in series with the meter movement.

A practical multi-range DC voltmeter is shown inFigure 2.6.

2.5: MULTI-RANGE VOLTMETER

Figure 2.6: Multirange voltmeter

R1 R2 R3 R4

+

_

V1V2

V3

V4

Rm

Im


7/14

25

EXAMPLE 2.5

Convert a basic D Arsonval movementwith an internal resistance of 50 and afull scale deflection current of 2 mA intoa multirange dc voltmeter with voltageranges of 0-10V, 0-50V,

0-100V and 0-250V.

26

2.6: VOLTMETER LOADING EFFECTS

When a voltmeter is used to measure the

voltage across a circuit component, the

voltmeter circuit itself is in parallel with the

circuit component.

Total resistance will decrease, so the voltage

across component will also decrease. This is

called voltmeter loading. The resulting error is called a loading error.

The voltmeter loading can be reduced by

using a high sensitivity voltmeter.

27

Example 1

A series circuit of two resistors Ra=20k and

Rb=10k is supplied by a 30V voltage supply.

Two voltmeters are used to measure VRb. Thesensitivity of meter 1 is 1k/V and the sensitivity

of meter 2 is 20k/V. Both meters are used on

10V range. Examine how good is meter 2

compared to meter 1 in terms of % error.

28

Example 2

A series circuit of two resistors Ra=40k and

Rb=10k is supplied by a 30V voltage supply. A

voltmeter with a sensitivity of 20k/V and threeranges of 10V, 20V and 30V is used to measure

VRb. Examine the % error due to loading effect if

the measurement is done on each range. Discuss

your answer.


8/14

29

2.7 AMMETER INSERTION

EFFECTS

Inserting Ammeter in a circuit always increasesthe resistance of the circuit and, thus alwaysreduces the current in the circuit. The expectedcurrent:

(2-4)

Placing the meter in series with R1 causes thecurrent to reduce to a value equal to:

(2-5)

1R

EIe =

m

mRR

EI

+=

1

30

2.7 AMMETER INSERTION

EFFECTS

Dividing equation (2-5) by (2-4) yields:

(2-6)

The Ammeter insertion error is given by :

Insertion Error

(2-7)

me

m

RR

R

I

I

+=

1

1

1001

100

xI

I

XI

II

e

m

e

me

=

=

31

2.8 OHMMETER (Series Type)

Current flowing through meter movementsdepends on the magnitude of the unknownresistance.(Fig 4.28 in text book)

The meter deflection is non-linearly relatedto the value of the unknown Resistance, Rx.

A major drawback as the internal voltagedecreases, reduces the full scale current andmeter will not get zero Ohm.

R2 counteracts the voltage drop to achievezero ohm. How do you get zero Ohm?

32


R1 and R2 are determined by the value of Rx= Rh where Rh = half of full scale deflectionresistance.

(2-8)

The total current of the circuit, It=V/Rh The shunt current through R2 is I2=It-Ifsd

m

mmh

RRRRRRRRR+

+=+=2

2

121 )//(


9/14

33

2.8 OHMMETER (Series Type) The voltage across the shunt, Vsh= Vm

So, I2 R2=Ifsd RmSince I2=It-Ifsd

Then,

fsdt

mfsd

II

RIR

=

2

34


Since It=V/Rh

So,

(2-9)

From equation (2-8) and (2-9):

(2-10)V

RRIRR

hmfsd

h=

1

hfsd

hmfsd

RIV

RRIR

=

2

35

Figure 2.7: Measuring circuit resistance with an ohmmeter

36

Example :

A 100 basic movement is to be used as anohmmeter requiring a full scale deflectionof 1mA and internal battery voltage of 3V .A half scale deflection marking of 2k is

desired. Calculate:i. value of R1 and R2ii. the maximum value of R2 to compensate for a 5%

drop in battery voltage


10/14

37

2.9 MULTI-RANGE OHMMETER

Another method of achieving flexibility of ameasuring instrument is by designing it to bein multi-range.

Let us analyse the following examples. (figure4.29 of your textbook)

38

2.10 MULTIMETER

Multimeter consists of an ammeter, voltmeterand ohmmeter in one unit.

It has a function switch to connect theappropriate circuit to the DArsonvalmovement.

Fig.4.33 (in text book) shows DC miliammeter,DC voltmeter, AC voltmeter, microammeterand ohmmeter.

39

2.11 AC VOLTMETER USINGHALF-WAVE RECTIFIER

The DArsonval meter movement can beused to measure alternating current by theuse of a diode rectifier to produceunidirectional current flow.

In case of a half wave rectifier, if given inputvoltage, Ein = 10 Vrms, then:

Peak voltage,

Average voltage,

VVE rmsp 14.14414.110 ==

VEEE pdcave 99.8636.0 ===

40

2.11 AC VOLTMETER USING HALF-WAVE RECTIFIER

o Since the diode conducts only duringthe positive half cycle as shown in Fig4.18(in text book), the average

voltage is given by:Eave/ 2=4.5V


11/14

41

2.11 AC VOLTMETER USING

HALF-WAVE RECTIFIER

Therefore, the pointer will deflect for a fullscale if 10 Vdc is applied and only 4.5 Vwhen a 10 Vrms sinusoidal signal isapplied.

The DC voltmeter sensitivity is given by:

VkmAI

Sm

dc /11

11

===

42

AC VOLTMETER USING HALF-WAVE

RECTIFIER

For the circuit in Figure 4.18, the ACvoltmeter sensitivity is given by:

This means that an AC voltmeter isnot as sensitive as a DC voltmeter.

VkSS dcac /45.045.0 ==

43

2.11 AC VOLTMETER USINGHALF-WAVE RECTIFIER

To get the multiplier resistor, Rs value:

(2-11)

o The AC meter scale is usually calibrated to givethe RMS value of an alternating sine waveinput.

A more general AC voltmeter circuit is shown inFig. 4.17 (in text book)

mdc

rms

mdc

dc

s

rmsdc

RI

E

RI

E

R

EE

==

=

45.0

45.0

44

2.11 AC VOLTMETER USING HALF-WAVE RECTIFIER

A shunt resistor, Rsh is used to draw morecurrent from the diode D1 to move itsoperating point to a linear region.

Diode D2 is used to conduct the current duringthe negative half cycle.

The sensitivity of AC voltmeter can be doubledby using a full wave rectifier.


12/14

45

EXAMPLE

Calculate the value of the multiplierresistor for a 10 Vrms range on thevoltmeter shown in Fig 4.19 (in textbook)

46

2.11 AC VOLTMETER USING

FULL-WAVE RECTIFIER Consider the circuit in Fig 4.20 (in text book)

Example :

Calculate the value of the multiplier resistorfor a 10 Vrms ac range on the voltmeter inFig. 4.21

macs RrangeSR =

47

2.12 WHEATSTONE BRIDGE

Accurate method for measuring resistancebetween 1 ~ 1M.

Figure 11.1 shows the schematic diagramof a Wheatstone Bridge.

When the bridge is set to null condition,voltages at point C & D are equal.

Thus

(2-12)

(2-13)

2211RIRI =

4433 RIRI =

48

2.12 WHEATSTONE BRIDGE

Since I1 = I3 and I2 = I4, divide equation 2-12 byequation 2-13:

So, (2-14)

Usually, the resistor R3 is a variable resistor tobalance the bridge.

RX is the unknown resistor to be measured.

When bridge is balance, the value of the unknownresistor RX is equal to resistance value of R3

4

2

3

1

R

R

R

R=

1

324

R

RRRR X ==


13/14

49

2.12 WHEATSTONE BRIDGE Example :

1. Given the Wheatstone bridge with R1 = 15 k,R2 = 10 k, and R3 = 4.5 k. Find RX.

2. Calculate the current through theGalvanometer in the circuit. Given R1 = 1 k,R2 = 1.6 k, R3 = 3.5 k, R4 = 7.5 k, RG =200 and V = 6V.

Answer=116A

50

2.13 KELVIN BRIDGE Kelvin Bridge is used to measure resistance

below 1 .

In low resistance measurement, the leadsconnecting the unknown resistor to the bridgemay effect the measurement.

Kelvins Double Bridge known as Kelvin Bridgeis constructed to overcome this problem.

Figure 11.10 (in text book) shows the KelvinsBridge and Figure 11.11 shows the KelvinsDouble Bridge.

51

2.13 KELVIN BRIDGE

The resistor RY represents the lead and contactresistance present in the Wheatstone Bridge.

The resistors Ra and Rb are used tocompensate this low lead-contact resistance.

From circuit analysis, the unknown Resistor RXin a balanced Kelvin Bridge is given by:

(2-15)

See example 11.4 (textbook)

a

bX

R

R

R

R

R

R==

1

3

2

52

2.14 BRIDGE CONTROLLEDCIRCUIT

When a bridge is imbalance, a potentialdifference exists at its output terminal.

If it is used as an error detector in a controlcircuit, the potential difference at the output of

the bridge is called an error signal.

The error signal is given by:

(2-16)

+

+=

V

Vs

RR

R

RR

REE

231

3


14/14

53

2.14 BRIDGE CONTROLLED

CIRCUIT

The unknown resistor RV can be any passivecircuit elements such as strain gauge,thermistor and photo resistor.

Since RV varies by only a small amount, anamplifier often needed before being used forcontrol purposes.

Fig. 11.14 shows the Wheatstone Bridge errordetector.

54

Conclusion A half wave ac voltmeter has a sensitivity of

0.45 of the sensitivity of a dc voltmeter.

A full wave ac voltmeter has a sensitivity of 0.9of the sensitivity of a dc voltmeter.

A Wheatstone bridge can be used to measurean unknown resistance in the range of 1 -1M.

55

Conclusion

A Kelvin bridge can be used to measure a smallresistance.

A bridge controlled circuit can be used todetect error in a control circuit.

chap2_acdcmeter1 ver2

Documents