Half wave, full wave rectifiers

1. AEI 302.4 1
Half Wave Rectifier
• The Half wave rectifier is a circuit, which converts an ac
voltage to dc voltage.

2. AEI 302.4 2
The Half-wave Rectifier Circuit (without filter)
switch
230v Ac
50 Hz
230v

3. AEI 302.4 3
Transformer secondary voltage
Vin = Vm sin ωt
V out Calculation









Tt
T
for
T
tfortV
tv
m
2
0
2
sin
)(


4. AEI 302.4 4
rmsrms
m
mm
mm
m
T
dc
VV
V
VV
V
t
V
dtdttV
dttv
T
V
45.0)2(318.0
318.0)]1()1([
2
)]0cos()cos([
2
]cos[
2
]0sin[
2
1
)(
1
0
0
2
0





 









 

Vdc = Vavg
Compute the average voltage (dc voltage) Vavg or Vdc
for one complete cycle

5. AEI 302.4 5









Tt
T
for
T
tfortV
tv
m
2
0
2
sin
)(

2
)]000(
4
[
)]0(2sin
2
1
0)2sin(
2
1
(
4
[
]|)2sin
2
1
(
4
[
])2cos1(
4
[
,2),2cos1(
2
1
sin
)](sin
2
[
])(0)(sin[
2
1
[
)(
1
2/1
2
2/1
2
2/1
0
2
0
2/1
2
2
2/
0
2/12
2
2/
0
2/1
2/
22
0
2
m
m
m
m
m
rms
T
m
T T
T
m
T
rms
V
V
V
t
V
d
V
V
tTtt
tdt
V
tdtdtV
dttv
T
V











 
















Vrms at the Load Resistance

6. AEI 302.4 6
Ripple Factor = RMS value of the AC component/DC
value of the component
2114.1
1
2
1
/
2/
1
2
2
2
22
























m
m
dc
rms
dc
dcrms
dc
rms
V
V
V
V
V
VV
V
V r
R ipple

7. AEI 302.4 7
%6.40
406.0
4
)2/(
)/(
/
/
22
2
2
2






or
V
V
RV
RV
m
m
Lrms
Ldc
η = (dc output power/ac input power) x 100%
Efficiency
η = pdc/ pac
Where pdc = v dc /RL and pac = v rms / RL
2 2

8. AEI 302.4 8
Form Factor
Form Factor = rms value / average value
= (Vm/2)/(Vm/π)= π/2 = 1.11
Peak Factor
Peak factor = Peak value / rms value = Vm/(Vm/2) = 2

9. AEI302.5 9
1. What is Rectifier ?
Rectifier is a circuit which converts AC to DC
4. What is ripple ?
2. What is Half wave Rectifier ?
Half wave Rectifier is a circuit which converts either
positive half cycle or negative half cycle of AC to DC
3. Shall we call this output as perfect DC ?
No, this out put called pulsating DC
The presence of AC component in output is called Ripple

10. AEI302.5 10
5. What is the need for FW rectifier ?
• To get more dc output
• Low Ripple factor ( low ac ripple)
• More efficiency
• To get continuity output current

11. AEI302.5 11
Circuit diagram of centre tapped full wave rectifier
D2
D1
Fig.1

12. AEI302.5 12
Working of centre tapped rectifier
During positive half cycle
• Diode D1 conducts and D2 is
open circuited
• The current direction is as shown
in the fig.2
• During positive half cycle, current
flows through D1 ,load resistor RL and
half of the Secondary winding:
D1
B
C
Fig.2

13. AEI302.5 13
• The voltages at points A and B on
the transformer are changing in
opposite directions
• When A is increasing in a positive
direction, B is increasing negatively
• During the first half cycle, A is positive and B is
negative
• D1 has positive on its anode and negative on its
cathode. Hence D1 is forward biased
D1
B
C

14. AEI302.5 14
• Current flows around the circuit
formed by D1 diode, the load and the
transformer winding, as shown in the
second diagram
Fig.3

15. AEI302.5 15
Output waveform when D1 is in conduction
Fig.4
• The current flowing down through the load produces a
pulse of voltage across the load as shown in the fig.4

16. AEI302.5 16
During negative half cycle
C
A
B
D2
• Diode D2 conducts and D1 is
open circuited
• The current direction is as shown
in the fig.5
• During negative half cycle, current
flows through D2,load resistor RL and
half of the Secondary winding
Fig.5
Fig.6

17. AEI302.5 17
• During the next half cycle, B is
negative and C is positive.
• D2 has positive on its anode and
negative on its cathode. D2
forward biased
• Current flows around the circuit
as shown in the fig.6
•C
•A
•B
Fig.6
C

18. AEI302.5 18
Output waveform when D2 is in conduction
Fig.7

19. AEI302.5 19
Input and output wave forms of Centre-tapped
FWR
• It can be observed that
current flows in the same
direction in both the cases
and the output is
unidirectional.
• The output in RL is
additive and appears as
shown in fig.8 Fig.8

20. AEI302.5 20
• Since there are two pulses for each cycle of input,
there are 100 pulses per second in the output
• In both cases the current flows in the same
direction through the load and produce another
pulse of voltage
• Since the full cycle is used in this circuit the
circuit is called a FULL-WAVE rectifier

21. AEI302.5 21
Advantages
• More dc output
• Low Ripple factor ( low AC ripple)
• More efficiency
• Continuity output current

22. AEI302.5 22
Disadvantages
• Centre tapped transformer is required
• PIV is double that of HWR
• Bulky and more cost

23. AEI302.5 23
Comparison with H.W.R
Centre tapped FWR
• No. of diodes are two
• PIV is 2Vm
• Bigger secondary of
transformer is required
• Ripple frequency is
Twice that of line
frequency
HWR
• One diode only
• PIV is Vm
• Secondary of transformer
requires half windings for
the same voltage
• Ripple frequency is equal
to that of line frequency

24. AEI 302.6 24
What is Bridge Rectifier ?
Bridge Rectifier is
• A full wave rectifier constructed in the
form of a bridge .

25. AEI 302.6 25
What is the need for a bridge rectifier ?
• No centre tapped transformer is required.
• Transformer is optional.
• Smaller in size
• Low Cost
• Low PIV

26. AEI 302.6 26
Circuit diagram of Bridge rectifier
D1
D2
D3
D4
Fig 1. Bridge rectifier

27. AEI 302.6 27
Working of bridge rectifier
During positive half cycle
Fig.2

28. AEI 302.6 28
• The voltages at points A and B on the transformer
are changing in opposite directions.
• When A is increasing in a positive direction, B is
increasing negatively.
• During the first half cycle, A is positive and B is
negative.
• D1 has positive on its anode, D2 has negative on
its cathode. Both are forward biased. (fig. 2)
Working of bridge rectifier (Contd)

29. AEI 302.6 29
• Current flows around
the circuit formed by
these diodes, the load and
the transformer winding.
• The current flowing up
through the load produces
a pulse of voltage across
the load as shown in the
waveform.
Fig. 3
Working of bridge rectifier (Contd)

30. AEI 302.6 30
Output waveform when D1 and D2 are in
conduction
Fig.4

31. AEI 302.6 31
During negative half cycle
Fig. 5

32. AEI 302.6 32
• During the next half cycle, A is negative
and B is positive.
• D4 has positive on its anode, D3 has negative
on its cathode. Both are forward biased.
• Current flows around the circuit as shown in the
diagram.

33. AEI 302.6 33
Output waveform when D3 and D4 are in conduction

34. AEI 302.6 34
Input and output wave forms of Bridge FWR
Fig. 6

35. AEI 302.6 35
• Since there are two pulses for each cycle of
input, there are 100 pulses per second out.
• In both cases the current flows in the same
direction through the load and produce another
pulse of voltage.
• Since the full cycle is used this circuit is called
a FULL-WAVE rectifier.

36. AEI 302.6 36
Advantages
• No centre tap is required
• PIV is one half that of centre tap FWR
• OUTPUT is double to that of centre tap FWR

37. AEI 302.6 37
Disadvantages
• Four diodes are required
• Rectification efficiency is less due to two diodes
are in conduction at a time at lower voltages
• Output is double to that of centre tap FWR

38. AEI 302.6 38
Comparison with centre tapped F.W.R
Centre tapped FWR
• No. of diodes are two
• PIV is 2Vm
• Bigger secondary of
transformer is required
• Preferred for low
voltage and high current
circuits
Bridge FWR
• No. of diodes are four
• PIV is Vm
• Secondary of
transformer
requires half windings
for
the same voltage
• Preferred for low
voltage and high current
circuits

39. AEI302.7 39
1. What is the difference between AC and DC?
2. Give the relation between RMS and maximum
value of a sine wave.
Introduction
In AC amplitude and phase will change with time
In DC amplitude and phase will not change with time
max
2
imumValueRMS Value 

40. AEI302.7 40
3. Give the average (dc) value of sine wave. ZERO
4. What is the relation between average value and
maximum value in a half wave rectifier?
maximum value
Average value



41. AEI302.7 41
5. What is ripple factor?
Ripple factor is a measure of purity of the DC output
of a rectifier
6. Define ripple factor of a rectifier?
RMS value of wave
Ripple factor
average value
 

42. AEI302.7 42
7. What is meant by conversion efficiency η of a
rectifier circuit ?
It represents what percentage of ac input power is
converted in to useful dc output power.
8. Define efficiency of a rectifier?
dc power delivered to the load
Efficiency
ac input power
 

43. AEI302.7 43
RMS Value of FWR
RMS value of the voltage at
the load resistance is
L mi I Sin t
   
 
1 1
1 2
2
2
2 4
.
2 2
2 2 2
0 0
2
0
2
0
2
I i d t I Sin td t
I COS t d t
I t Sin t
I I
rms mL
m
m
m m
  
 
 

 



 


 
  
  
     
 
 
 
 
  
 
 

 
 
 


44. AEI302.7 44
Average Value of FWR
0
1
Ldc
I i d t


 
  
 
 
 
0
1
mI Sin td t

 

 
0
mI
Cos t



 
 1 1mI

  
2 mI



45. AEI302.7 45
Ripple factor of FWR
2
1rms
dc
I
I
 
  
 
2
2 1
2
m
m
I
I

 
 
  
 
 
 
2
1
2 2
 
  
 
0.482

46. AEI302.7 46
Efficiency of FWR
Efficiency of the rectifier
dc output power
ac input power
 
2
dc dc L
The dc output power of FWR
P I R
2
2 m
L
I
R

 
 
 
 2
ac rms d L
The ac input power of FWR
P I r R 
 
2
2
m
d L
I
r R
 
  
 

47. AEI302.7 47
Efficiency of the FWR
dc output power
ac input power
 
 
2
2
2
2
m
L
m
d L
I
R
I
r R


 
 
 
 
 
 
2
8 1
1 d
L
r
R


 
 
 
0.812
1 d
L
r
R

 
 
 
81.2
%
1 d
L
r
R
 
 
 
 
0
, 81.2
dFor ideal diode r
then efficiency 



48. AEI302.8 48
1. Can you name some filters that are used in rectifiers
2. What is their purpose?
Introduction
Capacitor filter,
Inductor filter,
RC,LC,CLC,CRC filters
To remove the ripple

49. AEI302.8 49
Pulsating DC
4. The variations in the out put of the rectifier are
called
Ripples
3. Is The output of a rectifier circuit called pure DC or
pulsating DC?

50. AEI302.8 50
7. Why is it called pulsating DC?
Its amplitude is varying even though the polarity is
constant
5. What is a rectifier?
A circuit which converts AC to DC
6. What is the term we use to refer the
output of a rectifier?
Pulsating DC

51. AEI302.8 51
8. To remove /reduce the AC component from
the output of a rectifier ------are used
Between the rectifier and the load
Filters
9. Where do you connect Filters?

52. AEI302.8 52
10. What are the useful properties of Capacitor
to act as filter
• Very high impedance for DC
• Very low Impedance for AC
• Capacitors store the energy in the electrostatic form
• When voltage decreases it tries to keep the voltage
constant. If no voltage is there, it discharges slowly providing
some voltage across the load.
• Capacitor filter should be connected always in shunt to the
load.

53. AEI302.8 53
Working of HWR
• For positive half cycles
• diode conducts
• current flows in the circuit
• For negative half cycles
• diode does not conduct
• No current flows
Input Wave Form
Output Wave Form

54. AEI302.8 54
Circuit diagram of HWR:
Working of HWR
• Conducts for positive cycle
only
• The conduction takes place
when secondary ac voltage
appears between A&B
• The diode conducts 1800 per
cycle
• The output appears as shown
in the figure

55. AEI302.8 55
Working of capacitor filter
• The capacitor filter is connected
in shunt to the load
• During the conduction of the diode
• The capacitor charges to its maximum
value of the input voltage
• Keeps the voltage at the maximum.

56. AEI302.8 56
• The voltage across the capacitor is more
positive
• It keeps the diode in reverse bias, i.e.,
even the i/p voltage during the remaining
positive half cycle input
• The output appears as shown in the figure
• When I/P at AB is less than its max or
peak value (after point E)
E
F
Working of capacitor filter

57. AEI302.8 57
• The diode state in reverse bias condition, continues till the
anode voltage is more positive than cathode (after point F )
• Capacitor discharges through the load until the diode comes
into conduction depending on its time constant
• If load is not connected, the capacitor holds the charge
for a long time
• In general, a high value of resistance is connected across the
output terminals to provide a path for discharge
• This resistance is also called BLEEDER RESISTANCE
E
F

58. AEI302.8 58
Important features of capacitor filter
Fixed value filter capacitance:
• Larger the load resistance, larger will be the
discharge time constant, lower ripple and
more output voltage.
• Lower the load resistance, lower be the time
constant, more ripple and lower output voltage.
Larger the capacitance value
Holds more charge
Discharges less
• Average value increases

59. AEI302.8 59
Smaller the capacitance
• Less charge it can hold
• Ripple is more
• DC level decreases
• Larger capacitance value requires larger current and
this current is limited by max. forward current of diode

60. AEI302.8 60
In HWR
• Without Capacitor filter, current flows only for half cycle
through the load
• Using capacitor filter, current flows through the load
continuously, when proper time constant is chosen for
discharging
For HWR using capacitor filter :
• Ripple factor
• PIV = 2Vm
1
2 3 LfCR

61. AEI302.8 61
Full wave rectifier
• FWR using two diodes requires
a centre tapped transformer where
as Bridge rectifier requires four diodes
• FWR, using two diodes and
a centre tapped transformer or
Bridge rectifier, output waveforms
are same
• The input and output waveforms
are shown in the figures
• Though diodes are conducting
alternatively current flows in a
unidirectional way through the load

62. AEI302.8 62
• When capacitor is connected across
the load the output waveform is different
• The output waveform appears as shown
• The amount of variation is reduced and the
average value is increased
• Compared to HWR with filter circuit
FWR
Full wave rectifier(contd)

63. AEI302.8 63
• Capacitor discharges twice during one
• cycle and Ripple frequency is twice
• Non conducting period has reduced
• Ripple voltage has been reduced to
half
• V dc has been increased
FWR
Full wave rectifier (contd)

64. AEI302.8 64
• Ripple factor using capacitor filter for
full wave rectifier is
• The expressions for ripple factor of HWR and FWR
using capacitor filter reveals that capacitor filter is
more useful at smaller load currents
L
1
4 3 f CR
Full wave rectifier(contd)

65. AEI302.9to10 65
Pulsating DC
2. The variations in the out put of the rectifier are called
Ripples
1. Is The output of a rectifier circuit called pure DC or
pulsating DC?
Filters

66. AEI302.9to10 66
5. Why is it called pulsating DC?
Its amplitude is varying even though the polarity is
constant
3. What is a rectifier?
A circuit which converts AC to DC
4. What is the term we use to refer the output of a
rectifier?
Pulsating DC

67. AEI302.9to10 67
6. To remove /reduce the ac component from
the output of a rectifier ------are used.
Between the rectifier and the load
Filters
7. Where do you connect Filters?

68. AEI302.9to10 68
8. Can you name some filters that are used in rectifiers.
• Capacitor filter,
• Inductor filter,
• RC,LC,CLC,CRC filters
9. What is their purpose?
• To remove the ripple
• To improve regulation

69. AEI302.9to10 69
10. What are the useful properties of Capacitor
to act as filter
• Very high impedance for DC
• Very low Impedance for AC
• Capacitors store the energy in the electrostatic form
• When voltage decreases it tries to keep the voltage
constant. If no voltage is there, it discharges slowly providing
some voltage across the load.
• Capacitor filter should be connected always in shunt to the
• load.

70. AEI302.9to10 70
11. What are the main features of Capacitor Filters ?
• Capacitor charges to the peak value of the applied
voltage
• Acts as good filter for smaller load currents
• Continuous output voltage
• reduced ripple
• Improved regulation

71. AEI302.9to10 71
12 . What are the main features of Inductors ?
Inductors offers
• Zero resistance for DC
• Very high impedance to AC
• Inductor charges to the average value and
• Stores the energy in the form of the magnetic field,
• Opposes any change in current due to induced voltage
or back emf
• Acts as good filter for larger load currents
• Connected always in series to the Load

72. AEI302.9to10 72
• reduced ripple
• Improved regulation
• It requires certain minimum current ALWAYS.
13. Inductor filters are not preferred in HWR. Why?
As the minimum current is not
flowing through the inductor in
HWR, output falls as shown in
figure

73. AEI302.9to10 73
• The output voltage approximates the average
value of the rectified input to the filter
• The reactance of the inductor (XL) reduces the
amplitude of applied ripple voltage
• Ripple factor using Inductor filter:
• The rectified output of the FWR appears as
input to the Inductor filter.
• And gives the dc output voltage without reducing
by an appreciable amount.
Inductor Filter
LR
3 2 L

74. AEI302.9to10 74
Working of LC filter:
• Practical filter circuits are derived by combining the
voltage stabilizing action of shunt capacitor with the current
smoothing action of series choke coil
LC Choke-Input Filter
The LC choke-input filter is used primarily in power supplies
where the voltage regulation is important the output
current is relatively high
LC OR L-Section Filter

75. AEI302.9to10 75
Inductor L is placed at the input to the filter
and is in series with the output of the
rectifier circuit.
Since the action of an inductor is to oppose
any change in current flow, the inductor
tends to keep a constant current flowing
to the load throughout the complete cycle
of the applied voltage.
As a result, the output voltage never
reaches the peak value of the applied
voltage.
This filter consists of an input inductor (L), or filter choke,
and an output filter capacitor (C).

76. AEI302.9to10 76
• Instead, the output voltage
approximates the average value of
the rectified input to the filter,
as shown in the figure.
• The reactance of the inductor (XL)
reduces the amplitude of ripple
voltage without reducing the dc
output voltage by an appreciable
amount.
• The shunt capacitor (C) charges and
discharges at the ripple frequency
rate, but the amplitude of the ripple
voltage (Er) is relatively small
because the inductor (L) tends to
keep a constant current flowing from
the rectifier circuit to the load.

77. AEI302.9to10 77
• In addition, the reactance of the shunt
capacitor (XC) presents
• A low impedance to the ripple component
existing at the output of the filter, and shunts
the ripple component around the load
• The capacitor attempts to hold the output
voltage relatively constant at the average
value of the voltage.
• The value of the filter capacitor C must be
relatively large to present a low opposition (X)
to the pulsating current and to store a
substantial charge.

78. AEI302.9to10 78
The rate of the charge for the capacitor is limited by
• The low impedance of the ac source (the transformer),
• The small resistance of the diode, and
• The counter electromotive force (CEMF) developed by
the coil.
• Therefore, the RC charge time constant is short compared to
its discharge time.
• Consequently, when the pulsating voltage is first applied to
the LC choke –input filter
• The inductor (L) produces a EMF which opposes the
constantly increasing input voltage

79. AEI302.9to10 79
• After the input voltage reaches
its peak and decreases sufficiently,
the capacitor C1 attempts to
discharge through the load
resistance RL.
• C1 will only partially discharge
relatively long discharge time
constant. The larger the value of
the filter capacitor, the better the
filtering action.
• The net result is to effectively
prevent the rapid charging of the filter
capacitor (C)
• Ripple factor using LC filter = 2
1
6 2 CL

80. AEI302.9to10 80
Characteristics of LC filter
• Better voltage regulation
• Less value of inductor can be used
• Ripple factor becomes independent of Load
• Needs bleeder resistance
Disadvantages
• Larger cost, more weight, larger size
• Larger RMS current

81. AEI302.9to10 81
• At the same time, C2 offers a very low reactance to ac ripple
• C1 reduces the ripple to a
relatively low level
• L and C2 form the LC filter, which
reduces the ripple even further.
• L has a high value of inductance
therefore, a high value of XL which
offers a high reactance to the ripple
frequency.
Working OF CLC OR ∏ Filter

82. AEI302.9to10 82
• Only a slight trace of ripple
appears across C2 and the load
• While the L -C2 network greatly
reduces ac ripple it has little effect
on DC
• L and C2 for an ac voltage divider
and, because the reactance of L much
higher than that of C2, most of the
ripple voltage is dropped across L.
• Ripple factor using CLC filter = 3
1 2
2
8 LLC C R

83. AEI302.9to10 83
Summary
• Filters are used to remove ripple.
• Capacitors and inductors are used individually or in
combination as filter elements.
• Capacitor filters are connected in shunt with the load
.
Capacitor filter
• Improves average current
• Reduces ripple
• PIV in HWR is Doubled
• Improves the regulation

84. AEI302.9to10 84
• Bleeder resistor provides discharging path
when load is not connected.
• Ripple factor using
• Inductor filter:
• LC filter:
• CLC filter:
• The LC filter provides good filtering action
over a wide range of current.
• The capacitor filters best when the load is
drawing little current
LR
3 2 L
2
1
6 2 CL
3
1 2
2
8 LLC C R