### V d

```Chapter 5
Diode Rectifiers
• Basic rectifier concepts
• Single-Phase diode bridge rectifiers
• Voltage-Doubler rectifiers
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-1
Diode Rectifier Block Diagram
• Uncontrolled utility interface (ac to dc)
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-2

by Jose Bastos
1
V
 vR 
V sin(x)dx 

2 0

Chapter 5 Line-Frequency Diode
Rectifiers
5-3
• Current continues to flows for a while even after the input
voltage has gone negative
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-4
di
vL  L
dt
1
vL dt  di
L
1
0 L vL dt 
i ( t 3)
t1
t3
t3
 di  i(t 3)  i(0)  0
i (0)
1
1
0 L vL dt  t1 L vL dt  0
Area A  Area B  0
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-5
A Simple Circuit (Load has a dc back-emf)
• Current begins to flow when the input voltage exceeds the dc back-emf
• Current continues to flows for a while even after the input voltage has
gone below the dc back-emf
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-6
Single-Phase Diode Rectifier Bridge
• Large capacitor at the dc output for filtering and energy
storage
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-7
Diode-Rectifier Bridge Analysis
• Two simple (idealized) cases to begin with: (a) R load (b)
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-8
Waveforms with a purely resistive load at the output
 vd 
by Jose Bastos
1

V sin(x)dx 


0
2V


2

2 VRMS  0.9 VRMS
Chapter 5 Line-Frequency Diode
Rectifiers
5-9
Diode-Rectifier Bridge Input Current
I s1 
2

2 I d  0.9 I d
0 h even
I sh  
 I s1 / h h odd
THD=48.43%
DPF=1.0
PF=DPF x Is1/Is=0.9
• Idealized case with a purely dc output current
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-10
Diode-Rectifier Analysis with AC-Side
Inductance
• Output current is assumed to be purely dc
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-11
Understanding Current Commutation
• Assuming inductance to be zero
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-12
Understanding Current Commutation #2
• Assuming inductance to be zero
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-13
Understanding Current Commutation #3
• Assuming inductance to be zero
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-14
Understanding Current Commutation #4
• Inductance is included
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-15
Current Commutation Waveforms
vd
u
vL
Id
is
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-16
Current Commutation Waveforms
di
vL  V sin(t )  L
dt
V sin(t ) d (t )  L di
Id
u
 V sin(t ) d (t )  L  di   L I
0
d
0
u
Au   V sin(t ) d (t )  V (1  cosu )
0
Au  V (1  cosu )   L I d
cosu  1 
by Jose Bastos
 L Id
V
Chapter 5 Line-Frequency Diode
Rectifiers
5-17
Average voltage <Vd>
When L=0

1
V 1
 vd 
V sin(t )d (t )  
2 VRMS  0.45 VRMS

2 0
 
With finite L

u
1
1
 vd 
V sin(t )d (t ) 
V sin(t )d (t )


2 0
2 0
L
 0.45 VRMS 
Id
2
Reduction in average output voltage
L
  vd 
Id
2
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-18
Current Commutation in Full-Bridge Rectifier
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-19
Current Commutation in Full-Bridge Rectifier
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-20
Current Commutation Waveforms
di
vL  V sin(t )  L
dt
V sin(t ) d (t )  L di
Id
u
 V sin(t ) d (t )  L  di  2 L I
0
d
Id
u
Au   V sin(t ) d (t )  V (1  cosu )
0
Au  V (1  cosu )  2 L I d
2  L Id
cosu  1 
V
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-21
Average voltage <Vd>
When L=0
 vd 
1

V sin(t )d (t ) 


0
2V


2

2 VRMS  0.9 VRMS
With finite L
 vd 
1

1
u
V sin(t )d (t )   V sin(t )d (t )



0
0
 0.9 VRMS 
2 L

Id
Reduction in average output voltage
  vd 
by Jose Bastos
2 L

Id
Chapter 5 Line-Frequency Diode
Rectifiers
5-22
Conclusions
Average output voltage drops with
1. increased current
2. increased frequency
3. Increased L
Load Regulation is a major consideration in
most rectifier systems because
• voltage changes with load (IL)
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-23
Diode-Rectifier with a Capacitor Filter
resistance
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-24
Diode-Bridge Rectifier: Waveforms
• Analysis using PSpice
by Jose Bastos
Chapter 5 Line-Frequency Diode
Rectifiers
5-25
Voltage Doubler Rectifier
input
input
• In 115-V position, one capacitor at-a-time is charged from the
input.