NIELIT Aurangabad B.Tech : Electronics Engineering (Electronic ...
Power Electronics Electronic Science
Transcript of Power Electronics Electronic Science
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Electronic Science Power Electronics
8. Diode Rectifiers
Module 8: Diode Rectifiers
1. Introduction
2. Performance parameters
2.1. Single phase half-wave rectifier (HWR)
2.2. Center tapped full wave rectifier (FWR)
2.3. Bridge rectifier
3. Half-Wave Rectifiers
3.1. HWR to RL load without freewheeling diode
3.2. HWR to RL load with freewheeling
3.3. HWR for Battery Charging
4. Bridge rectifier with RLE load
5. Rectifier Filter Design
5.1. DC filters (load or output side filters)
5.2. AC filters (input side filters)
6. Summary
Learning objectives
1 To know types of Rectifiers
2 To understand Working of Single phase Rectifiers
3 To define and Determine Performance Parameters
4 To study Rectifiers with different Types of Loads
5 To study Rectifier Filters
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Electronic Science Power Electronics
8. Diode Rectifiers
1. Introduction
Diodes are also called as rectifiers and are extensively used as rectifiers in most of the applications.
Rectifier converts bidirectional input voltage in unidirectional voltage. This process is called as
rectification. In short, rectifier circuit is ac to dc converter. The rectifiers can also be categorized
according to type of input or source voltage, for example, single phase rectifier and multiphase rectifier.
Practically, most of the multiphase rectifiers are three phase rectifiers. Rectifiers can be categorized
according to rectifier circuits, for example, half wave and full wave rectifiers. Rectifiers are widely used
in DC Power Supply, SMPS, DC Motor Drives etc. In the subsequent sections various single phase
rectifier circuits are discussed.
2. Performance Parameters
There are different types of rectifiers. The rectifier circuit is selected according to the requirements of a
application. It is necessary to evaluate quality of rectifier quantitatively. Such quantitative evaluation of
rectifier performance is generally on the basis of rectifier parameters as listed below.
a) Average value of the output voltage, Vdc.
b) Average value of the output current, Idc.
c) Output DC Power, Pdc = Vdc Idc,
d) Rms value of the of the output voltage, Vrms,
e) Output ac power, Pac = VrmsIrms.
f) Efficiency, η = Pdc/Pac.
g) Form factor, FF = Vrms/Vdc.
h) Ripple Factor, RF = Vac/Vdc.
i) Transformer Utilization Factor TUF = Pdc/VsIs.
j) Displacement Factor, DF = cos().
k) Harmonic Factor, HF = ((Is2-Is1
2)/Is1
2)
1/2 = [(Is/Is1)
2-1]
1/2.
l) Power Factor, PF = (VsIs1/VsIs) cos = (Is1/Is) cos .
m) Crest Factor, CF = (Is(peak)/Is).
n) Peak inverse voltage (PIV) of a diode.
o) Pulse Number: The ratio of the fundamental frequency of the DC ripple (fripple) to the AC supply
frequency (fs).
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8. Diode Rectifiers
The simplifying assumptions for the analysis of idealized circuits are as follows.
a) The voltage drop across switching devices is neglected while they are conducting, and the leakage
current is neglected while they are blocking.
b) The turn-on and turn-off times of the switching devices are negligible.
c) The AC line voltage is sinusoidal and there is no stray impedance; for example line impedance,
transformer reactance.
d) DC current constant over each cycle at its average value.
2.1 Single Phase Half-Wave Rectifier (HWR)
A single phase half wave rectifier (HWR) is shown in Figure 1(a). It consists of a transformer, a
diode with resistive load R. During the positive half cycle diode is forward biased and current
flow through diode D and resistor R. Thus the input appears at load resistor. During negative half
cycle, diode is reverse biased and hence it turns off. Therefore no current flows through load and
the load voltage is zero. The output voltage across the resistor is half wave rectified. Hence it is
called as half wave rectifier. Input and output voltages as well as currents are graphically
represented in Figure 1(b).
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8. Diode Rectifiers
Figure 1 Single phase half wave rectifier with purely resistive load (a) circuit and (b) input and output
waveforms.
The rms and dc values of input and output can be determined from waveforms as follows.
VV
dtwtVT
dttvT
V m
T
m
T
rms 5.02
))sin((1
)(1
2
1
2
0
22
1
0
2
0
R
V
R
VI mrms
rms
5.0
mm
T
m
T
dc VV
dttVT
dttvT
V 318.0)sin(1
)(1 2
000
ωt
vo
Vm
π 2π 0
0 ωt
vo Vm
0 ωt
Vm/R
i0
0 ωt
vD
-Vm
+
-
+ - is
R
vD
vp vs vo
+
- -
+ i0
(a)
D
(b)
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Electronic Science Power Electronics
8. Diode Rectifiers
fT
f 2,1
R
V
R
VI mdc
dc
318.0
R
VPand
R
VP m
acm
dc
225.0318.0
The remaining parameters can be easily calculated as follows.
%45.40ac
dc
P
P
%12121.1157.11 22 FFRF
mm
T
ms VV
dttVV 707.02
sin2
1 2
1
0
2
R
VII m
loads
5.0
286.0
)5.0
)(707.0(
318.02
R
VV
R
V
IV
PTUF
mm
m
ss
dc
It is evident from the output voltage the pulse number is 1. The maximum reverse voltage across diode is
–Vm. hence the diode PIV = Vm.
2.2 Center Tapped Full Wave Rectifier (FWR)
A single phase center tapped full wave rectifier (FWR) is shown in Figure 2(a). It consists of a
transformer, two diodes D1 and D2 with resistive load R. During the positive half cycle diode D1
is forward biased and D2 is reverse biased hence it turns off. The current flows through diode D1
and resistor R. Thus the input positive half cycle appears at load resistor. During negative half
cycle, diode D1 is reverse biased hence it turns off and D2 is forward biased. The current flows
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8. Diode Rectifiers
through diode D1 and resistor R. Thus the input positive half cycle appears at load resistor. Thus
during both half cycles the positive output voltage appears across the resistor. Hence it is called
as full wave rectifier. Input and output voltages as well as currents are graphically represented in
Figure 2(b).
Figure 2 Single phase center tapped full wave rectifier with purely resistive load (a) circuit, (b) input and
output waveforms and (c) waveforms of secondary current.
The rms and dc values of input and output can be determined from waveforms as follows.
VV
dtwtVT
dttvT
V m
T
m
T
Lrms 5.02
))sin((1
)(1
2
1
2
0
22
1
0
2
vD1 is1
R D1
vp
vs1 vo
+
-
+
-
vs2
is2
D2
+
-
+
-
vD2
+ -
+ -
i0
vs = vs1 = vs2
(a)
0
Vm/R
is1
0
Vm/R
is2
π 2π
(c)
0
vo Vm
ωt
vo
Vm
π 2π 0
0
Vm/R i0
0
vD1
-2Vm
(b)
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8. Diode Rectifiers
R
V
R
VI mrms
rms
5.0
)12
(cos)sin(1
)(1 2
00
T
T
VdttV
Tdttv
TV m
T
m
T
Ldc
fT
f 2,1
R
V
R
VIV
VV mdc
dcmm
dc
318.0318.0
R
VPand
R
VP m
acm
dc
225.0318.0
%45.40ac
dc
P
P
%12121.1157.11 22 FFRF
mm
T
ms VV
dttVV 707.02
sin2
1 2
1
0
2
R
VII m
loads
5.0
286.0
)5.0
)(707.0(
318.02
R
VV
R
V
IV
PTUF
mm
m
ss
dc
It is evident from the output voltage the pulse number is 2. The maximum reverse voltage across diode is
–2Vm. hence the diode PIV = 2Vm.
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8. Diode Rectifiers
2.3 Bridge rectifier
A single phase bridge type full wave rectifier (FWR) is shown in Figure 3(a). It consists of a
transformer, four diodes D1, D2, D3, and D4 with resistive load R. During the positive half cycle
diode D1 and D2 is forward biased hence turns on and D3 and D4 are reverse biased hence it turns
off. The current flows through diode D1, resistor R and diode D2.. Thus the input positive half
cycle appears at load resistor R. During negative half cycle diode D3 and D4 is forward biased
hence turns on and D1 and D2 are reverse biased hence it turns off. The current flows through
diode D3, resistor R and diode D4.. Thus the input positive half cycle appears at load resistor R.
Thus during both half cycles the positive output voltage appears across the resistor. Hence it is
called as full wave rectifier. Timing waveforms of input and output voltages as well as currents
are shown in Figure 3(b).
Figure 3 Single Phase Bridge Rectifier with purely resistive load (a) circuit, (b) input and output
waveforms and (c) secondary current waveform.
R
D1 D3
D4 D2
i0
iD1
is
v
0
+
-
vs
+
-
vp
+
-
(a) (b)
ωt
vs
Vm
π 2π 0
π 2π 0
io
Vm/R
π
vo
Vm
2π 0
vD1 π 2π
0
-
Vm
(c) is
Vm/R
π 2
π
0
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Electronic Science Power Electronics
8. Diode Rectifiers
It is evident from the output voltage the pulse number is 2. The maximum reverse voltage across diode is
–2Vm. hence the diode PIV = 2Vm.
3. Half-Wave Rectifiers
Let us consider the circuit of half wave rectifier with RL load as shown in Figure 4(a). Due to inductive
load the conduction period diode D1 will extend beyond 1800, until current returns to zero at ωt=π+.
The waveforms of current and voltage are as shown in Figure 4(b). The average voltage across the
inductor vL is zero.
3.1 Half-Wave Rectifier to RL load without freewheeling diode
R D1
L
i0 iS
vp
+
- vS
+
-
v0
+
-
vD1 + - (a) (b)
vS
ωt π 2π
Vm
0
i0
Im = Vm/R
0
vR
0
v0
σ
0
vD
0
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8. Diode Rectifiers
Figure 4 Single phase half wave rectifier with RL load without freewheeling diode, Dm (a) circuit and (b)
input and output waveforms.
The average output voltage is given as
cos1mdc
VV and
the average load current is given as RVI dcdc .
From these equations it can be seen that the average output voltage and hence current are dependent on
value of σ. It clearly shows Vdc is decreased significantly and dependent on the inductor value.
When diode turns off, the inductor back emf creates high voltage transient. It may lead to the destructive
breakdown of a diode if power dissipation is high during turn off.
3.2 Half-Wave Rectifier to RL load with freewheeling diode
From the equations of average output voltage and current, it can be seen that the average output voltage
and hence current can be increased and reach to maximum by adjusting σ = 0. The drawback of the above
circuit of half wave rectifier can be removed with the use of freewheeling diode Dm. this diode is to be
connected across the RL load as shown in the Figure 5(a). This diode is used in reverse bias as shown in
the Figure 5(a) to avoid the negative voltage appearing across the load. This increases the stored magnetic
energy. At time t = t1 = π/ω, the current from D1, is transferred to Dm. This process is called as
commutation of diodes and the corresponding input and output waveforms are as shown in the Figure
5(b) and 5(c). Depending on the load time constant, the load current may be discontinuous. The load
current i0 is discontinuous with resistive load and continuous with very high inductive load. The
continuity of the load current depends on its time constant
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8. Diode Rectifiers
Figure 5 Single phase half wave rectifier with RL load with freewheeling diode, Dm (a) circuit and (b)
input and output waveforms.
3.3 Half Wave Rectifier for Battery Charging
Figure 6 Single phase half wave rectifier for battery charging (a) circuit and (b) input and output
waveforms.
n:1
R D
E
i0
vs
+
-
vp +
-
(a) vs
ωt
E
0
Vm
π 2π
i0
(Vm-E)/R Im
0
(b)
(b)
R D1
L
i0 iS
vp
+
-
vS
+
-
v0
+
-
vD1 + - (a)
Dm
iD m
vS
ωt π 2π
Vm
0
vR
0
vD
0
v0
0
(c)
iDm
0
i0
0
Im
R
iS
Im
R 0 π 2π
ωt
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8. Diode Rectifiers
If the output of the diode circuit is connected to a battery, the diode rectifier can be used as a
battery charger. This is shown in the Figure 6.
For vs > E, diode D conducts. The angle when the diode starts conducting can be found from
the condition Vm sin = E.
The diode turns off when vs < E at β = π - . The charging current can be found from the
equation:
tforR
EtV
R
Evi ms sin0 .
4. Bridge rectifier with RLE load
Vm (c)
v0
vS
ωt π 2π
0
Vm E
0
i0
0
is
β 0
0
(b)
vS
ωt π 2π
Vm
v0
0
i0
0
I
is
π+θ θ π/2 0
(a) i0
vp
+
-
vS
+
-
iS R
D1 D3
D4 D2 L
E
v0
+
‒
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8. Diode Rectifiers
Figure 7 Single Phase Bridge Rectifier with purely resistive load (a) circuit, (b) input and output
waveforms when E=0 and (c) input and output waveforms when E is positive.
5. Rectifier Filter Design
5.1 DC filters (load or output side filters)
It is seen that, the output of a rectifier circuit contains ripple voltage Vr in addition to dc voltage
VDC. It is necessary to include a filter between the rectifier and the load in order to reduce ripple
components. Filter should reduce the ac component. Passive filters are used because it does not
require additional power sources. Mainly the following passive filters are used at the output of
rectifiers.
1. Shunt capacitor filter
2. Series inductor filter
3. Chock input (LC) filter
4. π section filter or CLC filter or capacitor input filter
In the consequent discussion resistive load R is considered for discussion.
Shunt Capacitor filter
It consists of a large value of capacitor, C connected across the load resistor RL as shown in
Figure 8 (a). This capacitor offers a low reactance to the ac components. The reactance of a
capacitor is XC = 1/2πfC. XC should be smaller than load resistance R. The capacitor C gets
charged when the diode/s of the rectifiers conducting and gets discharged when diode/s in the
rectifier are off. When the input voltage, 𝑣 = 𝑉𝑚 sin (𝜔𝑡), is greater than the capacitor voltage, C
gets charged. When the input voltage is less than that of the capacitor voltage, C will discharge
through R. The stored energy in the capacitor maintains the load voltage at a high value for a
long period. The diode conducts only for a short interval of high current. The waveforms are as
shown in Figure 8 (b). Capacitor opposes sudden fluctuations in voltage across it. So the ripple
voltage is minimized.
0
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8. Diode Rectifiers
Figure 8 FWR with shunt capacitor filter.
The discharging of the capacitor depends upon the time constant τ = RC. As the value of C
increases, the ripple voltage decreases increasing the smoothness of the output. But, as value of
the capacitor increases Crest factor of rectifier increases. This filter is used in circuits with small
load current like transistor radio receivers, calculators, etc.
Series inductor filter
The working of series inductor filter depends on the inherent property of the inductor to oppose
any variation in current intend to take place. Figure 9 (a) shows a series inductor filter connected
at the output of a Full wave rectifier. Here the reactance of the inductor is more for ac
components and it offers more opposition to them. At the same time it provides no impedance
for dc component. Therefore the inductor blocks ac components in the output of the rectifier and
allows only dc component to flow through RL. The action of an inductor depends upon the
current through it and it requires current to flow at all time. Therefore filter circuits consisting
inductors can only be used together with full wave rectifiers. In inductor filter an increase in load
current will improve the filtering action and results in reduced ripple. Series inductor filters are
used in equipments of high load currents. Series inductor filters are used in resistive welding
machines.
+
-
RL C
FW
R
(a) vo
0 t1
t2
T/2
π 2π
vr(PP)
ωt
(b)
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8. Diode Rectifiers
Figure 9 FWR with series inductor filter
LC filter
It is a combination of inductor and capacitor filter. Here an inductor is connected in series and a
capacitor is connected in parallel to the load as shown in Figure 10 (a). As discussed earlier, a
series inductor filter will reduce the ripple, when increasing the load current. But in case of a
capacitor filter it is reverse that when increasing current the ripple also increases. So a
combination of these two filters would make ripple independent of load current. Since the dc
resistance of the inductor is very low it allows dc current to flow easily through it. The capacitor
appears open for dc and so all dc component passes through it. The capacitor appears open for dc
and so all dc components passes through the load resistor RL.
Figure 10 FWR with LC filter
π – Filter (Capacitor input filter) or CLC filter
This filter is basically a capacitor filter followed by an LC filter as shown in Figure 11 (a). Since
its shape (C-L-C) is like the letter π it is called π – filter. It is also called capacitor input filter
because the rectifier feeds directly into the capacitor C1. Here the first capacitor C1 offers a low
FW
R
(a)
+
-
RL
L
vo C
(b)
vo
0 π 2π
ωt
vr(PP)
FW
R
(a)
+
-
RL
L
vo
(b)
vo
0 π 2π
vr(PP)
ωt
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Electronic Science Power Electronics
8. Diode Rectifiers
reactance to ac component of rectifier output but provide more reactance to dc components.
Therefore most of the ac components will bypass through C1 and the dc component flows
through chock L. The chock offers very high reactance to the ac component. Thus it blocks ac
components while pass the dc The capacitor C2 bypasses any other ac component appears across
the load and we get study dc output as shown below.
Figure 11 Rectifier with CLC filter and waveforms.
Bleeder resistor
For proper operation of a rectifier, the inductor requires a minimum current to flow through, at
all time. When the current falls below the minimum current, the output voltage will increase
sharply. It may generate voltage transient and hence leads to the poor voltage regulation. To keep
up the circuit current above this minimum value, a shunt resistor is permanently connected
across the filtering capacitor. This resistor is called bleeder resistor. Bleeder resistor always
draws a minimum current even if the external load is removed and avoids overcharging of
capacitor. It provides a path for the capacitor to discharge when power supply is turned off.
FW
R
(b) vo
0 π 2π
ωt
RL
L
C1 C2
(a)
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Electronic Science Power Electronics
8. Diode Rectifiers
Comparison of DC Filters
Filter
Type
Shunt C Series L Series LC π section (CLC)
Cost Low high high high
Size and
weight
Small Bulky
due to choke
Bulky
due to choke
Bulky
due to choke
DC output
Voltage
Improved DC
output
Lower DC output Lower DC output More output
voltage
Ripple
voltage
Reduced ripples
output
Higher ripple
output
Reduced ripple
output
Ripple less output
Suitability Can be connected
for both Half wave
and Full wave
rectifiers
Can be connected
for HWR with
additional
freewheeling
diode
Can be connected
for HWR with
additional
freewheeling
diode
Suitable to be used
with both HWR
and FWR
In-rush
current
Very high
during power on
Lowest - Limited
due to choke
Lesser than shunt
C filter
Lesser than shunt
C filter
Load
current
Low load current
applications
high load currents
applications
Action is
independent of
load current
high load currents
applications
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8. Diode Rectifiers
5.2 AC filters (input side filters)
Due to rectification of the input voltage, input current of rectifier contain harmonics. For bridge
rectifier circuit with resistive load, harmonic content is lowest. Due to dc output filters, the input
current largely deviates from sinusoidal nature increasing harmonic content in input current. To
reduce the harmonic content, filters are necessary at input side or ac side. Harmonic contents also
reduce the power factor. Electric utility or electricity supply distribution companies/ boards
restricts the power drawn by the consumers, so as to reduce the harmonic content in the input
current, or make it sinusoidal.
Two methods are used to design the input filter, (a) passive filters and (b) Active filters
(switching type) to make of input line current close to sinusoidal. Here we are presenting passive
filters only. The active filter will be discussed in subsequent sections.
Low pass (L-C) filter circuit on ac side:
Let us consider single phase bridge rectifier with LC filter at output side as shown in Figure 12
(a). Assume the average (dc) load current is without any ripple. In this case, the ac input (source)
current is square wave in nature as shown in Figure 12 (b).
Figure 12 Rectifier with LC filter and waveforms.
Rectifier
+
LC Filter
(a)
+
–
vs
is +
-
v0
i0
RL
(c)
is
Ia
-Ia
0 2 t
(b)
t
i0
Ia
0
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Electronic Science Power Electronics
8. Diode Rectifiers
Figure 13 Rectifier with LC filter and waveforms.
A low pass filter is needed on the input (source) side to reduce the harmonic components in the
input current. Generally LC or T filter is used at the input side as shown in Figure 13 (a) and (b).
The inductors used tend both to improve the power factor and also reduce harmonics. The overall
energy efficiency remains the same, though additional losses occur in the inductors, but
conduction losses in the diodes are reduced.
6. Summary
Rectifiers are used for ac to dc applications with fixed output voltage. The p erformance
parameters are used for the quantitative analysis, Single phase half-wave rectifiers are not used
in high power applications. Center tapped full wave rectifier and bridge rectifier are widely used
on power electronics due to better performance parameters. -Wave Rectifiers In order to increase
the dc contents DC filters (load or output side filters) are must for single phase applications. AC
filters (input side filters) are required for reducing switching noise in the input.
Rec
tifi
er
+
Fil
ter
(a)
+
-
L
C
+
-
vs
is
v0
i0
RL
Recti
fier
+
Fil
ter
(b)
L1 L2
C
+
-
v0
i0
RL
+
-
vs
is