CHAPTER 2

DC and AC Meters

(part2)

1

STRUCTURE FOR CHAPTER 2

PART 1 (DC)

PART 2 (AC)

Introduction to DC

meters

D’ Arsonval meter

movement

DC ammeter

DC voltmeter

DC ohmmeter

• Introduction to AC meters

• D’ Arsonval meter movement (half-wave rectification)

• D’ Arsonval meter movement (full-wave rectification)

• Loading effects of AC meter

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PART 2 – AC METERS (INTRO..)

Several types of meter movements maybe used to

measure AC current or voltage.

The five principle meter movements used in ac

instruments are listed in Table below:

3

No Meter Movement DC Use AC Use Applications

1 Electro-dynamometer YES YES Standard meter,Wattmeter,

etc..

2 Iron-Vane YES YES Indicator applications, etc…

3 Electro-static YES YES High voltage measurement.

4 Thermocouple YES YES Radio freq measurement

5 D’Arsonval YES YES-w/

rectifiers

Voltage, currents, resistance,

etc…

SINE WAVEFORM

4

peak peak-peak

IF THE DMM IS CONNECTED TO AC

SOURCE?

5

HOW TO MODIFY THE DMM TO BE AS AC

METERS?

Needs for rectification

Convert AC source to DC source

Most common rectification device is

diode (a nonlinear device)

Two types of rectifier circuits:

Half-Wave rectifier circuit

Full-Wave rectifier circuit

6

D’ ARSONVAL METER MOVEMENT

(HALF-WAVE RECTIFICATION)

7

Rm

Rs Im

+

AC

DC suppose we replace the 10-Vdc

with 10Vrms…

DMM (HALF-WAVE RECTIFICATION)

CONT’D

8

Peak Value,

Average value, or DC value

rmsrmsp ExEE 414.12

rmsp

p

dcave EEE

EE 45.0 318.0

DMM (HALF-WAVE RECTIFICATION)

CONT’D

Diode = Produces half sine wave across load resistor

* DC/Ave. Voltage The dc meter will only respond to the average value of

ac sine wave.

Simple example:

If we were to measure 10V DC, the meter will deflect which indicate 10V

However, if we were to measure 10 V rms, the meter will deflect which

indicate only 4.5V

DC voltmeter = 4.5V ( Meter read dc/average voltage only)

• Ac voltmeter is not sensitive as a dc voltmeter

• Approximately 45% as sensitive as a dc voltmeter

9

DMM (HALF-WAVE RECTIFICATION)

CONT’D

10

dcac SS 45.0

DC

DCmsT

I

ERRR

m

fsdc

rmsm

fsDC

DCs R

I

ER

I

ER

//

45.0

Therefore,

Rs = S x 0.45 Erms – Rm

In general, multiplier resistor (Rs)

where S = 1/Idc (Ω/V)

Rs = (Sdc x Rangedc) - Rm

Rs = (Sac x Rangeac) - Rm

for DC

for AC

Rs = (S x Range) - Rm

EXAMPLE 1

Compute the value of Rs for a 10-Vrms AC range on the voltmeter shown in Figure 1.

Given that Ein= 10Vrms, Ifs= 1mA, Rm=300Ω.

11

RS

Rm Im

+

_

Ein

COMMERCIAL AC VOLTMETERS

12

Instrument rectifier

COMMERCIAL AC VOLTMETERS (CONT’D)

Rsh :

increase current flow through D1 during the +ve ½ cycle

diode will be operating in linear region

improve linearity of AC meter during measurement of low voltage, but

further reduces the ac sensitivity

D2 :

+ve ½ cycle = no effect (Reverse-bias)

-ve ½ cycle = provides an alternate path for reverse biased leakage

current that would normally flow through meter movement and D1.

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Instrument rectifier

EXAMPLE 2

In the ½ wave rectifier shown below, D1 and D2 have an average forward resistance of 50Ω and are assumed to have an infinite resistance in reverse biased. Calculate the following:

(a) Rs value

(b) Sdc

(c) Sac

Given that Ein = 10-Vrms, Rsh = 200Ω, Ifs = 100µA, Rm = 200Ω

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Rs

Rm

D2

D1

RshEin

IT

Ish

Im

D’ ARSONVAL METER MOVEMENT

(FULL-WAVE RECTIFICATION)

15

Full-wave has higher sensitivity rating

Change the input waveform from +ve & -ve to

only +ve

DMM FULL-WAVE RECTIFICATION (CONT’D)

16

DMM FULL-WAVE RECTIFICATION (CONT’D)

POSITIVE CYCLE NEGATIVE CYCLE

17

(Diode Ideal, R=0)

Ein = VRs + VRm

VRm = Ein - VRs

(Diode Ideal, R=0)

Ein = VRs + VRm

VRm = Ein - VRs

DMM FULL-WAVE RECTIFICATION (CONT’D)

18

Peak Value,

Average value, or DC value,

2rmsp EE

rms

rmsp

avg xEEE

E 9.0.222

dcac SS 9.0AC Sensitivity,

DC Sensitivity,

Tdc

Tdc

IRange

RS

1

Total Resistance of AC voltmeter,

ac x RangeSI

ER ac

T

dcT

EXAMPLE 3

19

Compute the value of the multiplier resistor

for a 10-V rms range on the voltmeter

shown above. Let Ein = 10Vrms, Ifs=1mA,

Rm=500Ω

LOADING EFFECTS OF AC METER

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Sensitivity AC < Sensitivity DC

Therefore

Loading Effects AC > Loading Effect DC ----Rangedc=10 V, Rangeac=10

Vrms

AC

R1= 10 kΩ

R2= 10 kΩ

Rs

Ifs= 100μA

Eac = 20 Vrms

Edc = 20 V

A B

REFRESH LOADING EFFECT

(DC VOLTMETER)

V

k

AIS

fs

dc

10

100

11

21

VERR

RE dcR actual 10)(,

21

22

Actual value of E2,

DC voltmeter,

kVxV

kxRangeSR dcdcT 1001010

VV

RRR

RRE

T

T

R erDCvoltemet 52.9)20(,12

2

2

LOADING EFFECTS OF AC METER

(CONT’D)

HALF-WAVE FULL-WAVE

22

V

kSS dchw

5.445.0

kVxV

kxRangeSR dchwT 45105.4

VE

RRR

RRE dc

T

T

R HalfWave 0.9)(,12

2

2

V

kSS dcfw

0.99.0

kVxV

kxRangeSR dcwT 45105.4

VE

RRR

RRE dc

T

T

R FullWave 47.9)(,12

2

2

SENSITIVITY AC < SENSITIVITY DC

23

V

kSS dchw

5.445.0

V

kSS dcfw

0.99.0

V

k

AIS

fs

dc

10

100

11

EXAMPLE 4

RB

E = 20V

RA10kΩ

5.5kΩ

AC20Vrms

A B

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a) Determine the reading obtained with

a

DC voltmeter at RB when the switch

is set at point B.

b) Determine the reading at the

same RB using ½ wave and

Full wave rectifier AC meter

respectively when the switch

is set at point A.

Given that Ifs = 100-µA and

set at 10-V dc or rms range.

END OF PART 2

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