Download - 1 Phase Rectifier
![Page 1: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/1.jpg)
Single-Phase Half-Wave Rectifier
![Page 2: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/2.jpg)
Waveforms
![Page 3: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/3.jpg)
Single-Phase Half-Wave Rectifier
![Page 4: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/4.jpg)
Performance Parameters
• Average value of the output voltage, Vdc
• Average value of the output current, Idc
• Output dc power, Pdc
– Pdc = VdcIdc
• rms value of the output voltage, Vrms
• Output ac power, Pac
– Pac = VrmsIrms
![Page 5: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/5.jpg)
Performance Parameters (continued)
• Efficiency, η– η = Pdc/Pac
• Effective (rms) value of the ac component of the output voltage, Vac
– Vac = Vrms2 – Vdc
2
• Form factor, FF– FF = Vrms/Vdc
• Ripple factor, RF– RF = Vac/Vdc
![Page 6: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/6.jpg)
Performance Parameters (continued)
• Alternate form for ripple factor
• Transformer utilization factor, TUF– TUF = Pdc/VsIs
– Vs, Is are rms voltage and current of the transformer secondary
2 2( ) 1 1rms
dc
VRF FF
V
![Page 7: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/7.jpg)
Input Voltage and Current
![Page 8: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/8.jpg)
Performance Parameters (continued)
• Displacement angle, Φ
• Displacement Factor, DF– DF = cos(Φ)
• Harmonic Factor, HF
122 2
1221
2
1 1
( ) ( ) 1s s s
s s
I I IHF
I I
![Page 9: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/9.jpg)
Performance Parameters (continued)
• Power Factor, PF
1 1cos coss s s
s s s
V I IPF
V I I
![Page 10: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/10.jpg)
Performance Parameters (continued)
• Crest Factor, CF
( )s peak
s
ICF
I
![Page 11: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/11.jpg)
Example 3.1
• Determine η, FF, RF, TUF, PIV of the diode, CF of the input current, input PF.
![Page 12: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/12.jpg)
Determine the Average Voltage, Vdc
0
2
0
1( )
1sin
(cos 1)2
T
dc L
T
dc m
m
dc
V v t dtT
V V tdtTV T
VT
![Page 13: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/13.jpg)
1
2
0.318
0.318
m
dc m
dc m
dc
fT
f
VV V
V VI
R R
![Page 14: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/14.jpg)
Determine the rms Voltage, Vrms 12
2
0
12
22
0
1( )
1( sin )
0.52
0.5
T
rms L
T
rms m
m
rms m
rms m
rms
V v t dtT
V V t dtTV
V V
V VI
R R
![Page 15: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/15.jpg)
Determine Pdc, Pac, and η
2
2
2
2
(0.318 )
(0.5 )
(0.318 )40.5%
(0.5 )
m
dc
m
ac
m
m
VP
RV
PRVV
![Page 16: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/16.jpg)
Determine FF and RF
2
2
0.50.318
1.57 157%
1
1.57 1 1.21 121%
rms m
dc m
V VFF
V V
FF
RF FF
RF
![Page 17: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/17.jpg)
Determine the TUF
12
2
0
2
1( sin ) 0.707
20.5
(0.318 )
0.5(0.707 )( )
0.286
Tm
s m m
m
s load
m
dc
ms s
m
VV V t dt V
TV
I IR
VP RTUF VV I V
RTUF
![Page 18: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/18.jpg)
Determine the PIV
• PIV is the maximum (peak) voltage that appears across the diode when reverse biased. Here, PIV = Vm.
-
+
+- PIV
![Page 19: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/19.jpg)
Determine CF
( )
( )
0.5
20.5
s peak
s
ms peak
ms
m
m
ICF
I
VI
RV
IRV
RCFV
R
![Page 20: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/20.jpg)
Determine PF
2
cos
(0.5 )
0.7070.5
(0.707 )( )
ac
m
mm
PPF
VA
V
RPFV
VR
![Page 21: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/21.jpg)
Summary – Half-Wave Rectifier
• RF=121% High
• Efficiency = 40.5 Low
• TUF = 0.286 Low– 1/TUF = 3.496– transformer must be 3.496 times larger than
when using a pure ac voltage source
![Page 22: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/22.jpg)
Half-Wave Rectifier with R-L Load
![Page 23: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/23.jpg)
Waveforms of Current and Voltage
Conduction period of D1 extends beyond ωt = π
![Page 24: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/24.jpg)
Average Output Voltage
0
0
sin ( )2
cos2
1 cos( )2
mdc
mdc
mdc
dcdc
VV td t
VV t
VV
VI
R
Increase average voltage and current by making σ = 0
![Page 25: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/25.jpg)
Waveforms with Dm installed
![Page 26: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/26.jpg)
Application as a Battery Charger
Diode conducts for vs > E, starting when Vmsinα = E
![Page 27: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/27.jpg)
Waveforms for the Battery Charger
Diode turns off when vs < E (at β = π – α)
Charging current io = (vs – E)/R
io = (Vmsinωt – E)/R for α < ωt < β
![Page 28: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/28.jpg)
Single-Phase Full-Wave Rectifier
Center-Tapped Transformer
![Page 29: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/29.jpg)
Waveforms for the Full-Wave Rectifier
2
0
2sin
2
0.636
T
dc m
mdc
dc m
V V tT
VV
V V
![Page 30: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/30.jpg)
Single-Phase Full-Wave Rectifier
PIV = 2Vm
![Page 31: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/31.jpg)
Full-Wave Bridge Rectifier
![Page 32: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/32.jpg)
Waveforms for the Full-Wave Bridge
![Page 33: 1 Phase Rectifier](https://reader035.vdocuments.net/reader035/viewer/2022062300/55cf9152550346f57b8c8a8f/html5/thumbnails/33.jpg)
Full-Wave Bridge with Waveforms
Conduction pattern
D1 – D2 D3 – D4
PIV = Vm