Post on 29-Oct-2019
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
2
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…
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 (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.
13
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
14
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)
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
20
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
EXAMPLE 4
RB
E = 20V
RA10kΩ
5.5kΩ
AC20Vrms
A B
24
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.