1. Power Electronics
& Drives
College of Engineering and Technology
Adigrat University
Electrical & Computer Engineering Department
ECEg4222/4312: Power Electronics
G/Tsadik Teklay (M.Sc. Electrical Power Engineering)
Chapter 2
Uncontrolled Rectifiers
2. Contents
Basic rectifier concepts and AC to DC Converters
Types of Uncontrolled Rectifiers
• Single-Phase Half-Wave Rectifiers
• Single-Phase Full-Wave Rectifiers
• Three-Phase Rectifiers (Half-Wave and Full-Wave)
Effect of source inductance on rectifier operation
3. Objectives
Understand operation of half-wave and full-wave rectifier circuits
Determination of dc output voltages and currents for single phase and three phase
rectifiers.
Analyze the performance of a single phase and three phase uncontrolled rectifiers.
Analyze the operation of rectifier circuit with capacitor filter
Calculation of peak inverse voltage for rectifier circuits
Define the problem occurs when connecting inductive load to single phase half
wave rectifier and how to solve it using freewheeling diode.
Analyze the effect of source inductance on rectification process.
4. Introduction to Rectifiers (AC to DC Converters)
For nearly a century, rectifier circuits have been the most common
power electronic circuits used to convert a c to dc.
The word rectification is used not because these circuits produce dc,
but rather because the current flows in one direction; only the
average output signal (voltage or current) has a dc component.
Moreover, since these circuits allow power to flow only from the
source to load, the are often termed unidirectional converters.
As will be seen shortly, when rectifier circuits are used solely, their
outputs consist of dc along with high-ripple ac components.
To significantly reduce or eliminate the output ripple, additional
filtering circuitry is added at the output.
5. Basic rectifier concepts
• Several types of rectifier circuits
are available: single-phase and
three-phase half-wave and full-
wave, controlled and uncontrolled,
etc. For a given application, the
type used is determined by the
requirements of that application.
• In general the types of rectifiers are:
1. Uncontrolled Rectifier
• Provide a fixed d.c. output
voltage for a given a.c. supply
where diodes are used only.
2. Controlled Rectifier
• Provide an adjustable d.c. output
voltage by controlling the phase
at which the devices are turned
on, where thyristors and diodes
are used.
6. Cont’d
Controlled Rectifiers
A. Half-controlled
• allows electrical power flow from a.c. to d.c. (i.e. rectification only )
B. Fully-controlled
• allow power flow in both directions (i.e. rectification and inversion )
7. Uncontrolled Rectifiers
The diode rectifiers are referred to as uncontrolled rectifiers, which make use of
power semiconductor diodes to carry the load current.
The diode rectifiers give a fixed dc output voltage (fixed average output voltage)
and each diode rectifying element conducts for one half cycle duration (T/2
seconds), that is the diode conduction angle = 1800 or π radians.
• We cannot control (we cannot vary) the dc output voltage or the average dc load current
in a diode rectifier circuit.
Controlled SCR rectifiers are line-commutated ac to dc power converters that are
used to convert a fixed voltage, fixed frequency ac power supply into variable dc
output voltage.
8. Cont’d
Applications of Rectifier Circuits:
• DC welder
• DC motor drive (Variable speed DC drives)
• Battery charger
• DC power supply
• HVDC
Power rating of a single-phase rectifier tends to be lower than 10 kW.
Three-phase bridge rectifiers are used for delivering higher power
output, up to 500 kW at 500 V dc or even more.
10. Single-phase Half-Wave Uncontrolled Rectifier with resistive load
A single-phase half-wave rectifier consists of a
single diode connected
This is the simplest of the rectifier circuits. It
produces an output waveform that is half of the
incoming AC voltage waveform.
19. Analysis of Single-phase Half-Wave Uncontrolled Rectifier with resistive load
Average (dc) value of output voltage:
#
287
.
0
2
2
)
2
(
*
)
2
(
. 2
2
2
R
V
V
R
V
I
V
P
TUF
m
m
m
S
S
dc
20. With R-L Load
An increase in the conduction period of the load current can be achieved
by adding inductor in series with the load resistance.
Due to the inductive load, the conduction period of the diode will extend
beyond 180o until the current becomes zero,
This means the load current flows not only during
Vs <0, but also for a portion of Vs<0. the diode is
kept in the on state by inductor’s voltage, which
offsets the negative voltage of Vs(t). The load
current is present between T/2 and T, but never
for the entire period, regardless of the inductor
size. This can be easily explained by assuming that
the diode conducts for the entire period.
Consequently, the output voltage V0 must equal
Vs, since the diode voltage is zero. This can occur
only when the load current is alternating. This is
clearly a contradiction, and there must be a time
in which the diode stops conducting.
21. A Simple Circuit (R-L Load)
• Current continues to flows for a while even after the input
voltage has gone negative
22. A Simple Circuit (R-L Load)
0
Area
Area
0
1
1
0
)
0
(
)
3
(
1
1
3
1
1
0
3
0
)
3
(
)
0
(
B
A
dt
v
L
dt
v
L
i
t
i
di
dt
v
L
di
dt
v
L
dt
di
L
v
t
t
L
t
L
t t
i
i
L
L
L
24. Cont’d
t
V
R
i
dt
di
L m
sin
R
L
L
R
Z
t
e
Sin
t
Sin
Z
V
i
t
m
tan
;
0
];
)
(
2
2
2
tan
0
,
i
t
tan
sin
)
(
0
e
Sin
During diode conduction,
The solution of this differential equation is :
At
This is a transcendental equation and can be
solved by iterative techniques. The
extinction angle can be determined for a
given load impedance angle .
25. Cont’d
Equation of the current:
• The equation for the current through R-L load can be found from the solution of the
differential equation (3.16) which can be re-written as:
• This is a first order differential equation. The solution of this equation has two parts:
Force response
or particular
response (has
the same form
as the input)
Natural response or
homogeneous response
(due to the behavior the
circuit itself)
28. Cont’d
The average output voltage is
The average output current is
)
cos
1
(
2
sin
2 0
m
m
dc
V
t
d
t
V
V
)
cos
1
(
2
R
V
I m
dc
29. Peak Inverse Voltage
The maximum amount of reverse bias that a diode will be exposed
to is called the peak inverse voltage or PIV.
For the half wave rectifier, the value of PIV is:
The reasoning for the above equation is that when the diode is
reverse biased, there is no voltage across the load.
Therefore, all of the secondary voltage (Vm) appears across the
diode. The PIV is important because it determines the minimum
allowable value of reverse voltage for any diode used in the circuit.
30. With free-wheeling Diode
Without free-wheeling, as the previous diode, the
circuit is characterized by discontinuous and high
ripple current.
Continuous load current can result when a diode Dm ,
called free-wheeling diode, is added across the load. Dm
prevents the voltage across the load (output voltage) from
reversing during the -ve half-cycle of the supply voltage.
When diode D1 ceases to conduct at zero volts, Dm
provides an alternative free-wheeling path. That means
when D1 is off, Dm allows energy in the circuit to maintain
continuity by providing a path through which the inductor
current can “free wheel”.
32. Half-wave Rectifier with Capacitor Filter
The capacitor is the most basic filter type and is
the most commonly used. The half-wave rectifier
for power supply application is shown below.
A capacitor filter is connected in parallel with the
load. The rectifier circuit is supplied from a
transformer.
Circuit operation
The operation of this circuit during positive half
cycle of the source voltage is shown in figure 8.
During the positive half cycle, diode D1 will
conduct, and the capacitor charges rapidly. As the
input starts to go negative, D1 turns off, and the
capacitor will slowly discharge through the load
(figure 9).
Figure 8: Half wave rectifier with
capacitor filter – positive half
cycle
Figure 9: Half wave rectifier with
capacitor filter – negative half cycle
33. Using the previous half wave rectifier
as an example, figure 10 examines
what is happening with our filter.
(a) Unfiltered output from the
half wave rectifier
(b) When the next pulse does arrive,
it charges the capacitor back to full
charge as shown on the right. The
thick line shows the charge –
discharge waveform at the capacitor.
(c) The load sees a reasonably
constant DC voltage now, with a
ripple voltage on top of it.
34. 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
35. Effect of source inductance on rectifier operation
Ideal VS real rectifier with source inductance
The output DC voltages of the rectifier circuits discussed so far
have been found by assuming that diode currents transfer
(commutate) from one diode to another instantaneously
(rectification in previous reciter was insensitive to the location
of L). However this can not happen when the AC source has
some inductance Ls. (Change of current through any
inductance must take some time!).
The presence of inductance on the ac side as well as on the dc
side creates a third topological state of network: both diodes
are on simultaneously. This state is known as commutation
state because the load current is transferred, or commutated,
from one diode to the other during this state.
This source inductance is associated with the leakage
inductance of the supply transformer and the inductance of the
AC supply network to the input transformer.
The commutation process (or the overlap process) forces
more than one diode or a pair of diodes (in a bridge rectifier)
to conduct simultaneously, resulting in a drop voltage from the
output terminals which is proportional to the load current.
36. Commutation Process
In the following analysis, we will assume that L/R
>>T/2 so that the load current io is constant. This
assumption is valid since in many applications the load
inductance is very much larger than the ac-side
inductance.
The behavior of the circuit can easily be analyzed by
assuming that one of the diodes, D1, is conducting for
some time during the positive half cycle of the source
Vs(t), while D2 is off.
Since the current in D1 is constant, then the voltage
across Ls is zero and the voltage across D2 or Vo is
positive and is forced to equal the source voltage.
During this mode, we have the following current and
voltage values:
37. Cont’d
At t=T/2, Vs(t) starts to become negative, causing D1 to stop
conducting. However, since the current in D1 is the same as
the inductance current, which is not allowed to change
instantaneously, D2 turns on in order to maintain the inductor
current’s continuity.
During this overlapping time, when both diodes are
conducting, is(t) changes from +I0 to zero, while iD2(t)
changes from zero to +I0. the time during which both D1 and
D2 are is known as the commutation period, and has a
duration 𝜇 in electrical degrees. This is why the ac-side
inductance, Ls, is know as the commutation inductance.
This circuit mode of operation is referred to as commutation
mode.
During mode, the following equations hod:
38. Cont’d
The initial condition for for is(t) at t=T/2 is I0. using the above VLs
equation with the given initial condition, we obtain the following
input current integration:
Substituting for VLs(t)=Vssin 𝜔𝑡 in the integral and solving for is(t),
we obtain
39. Cont’d
At the end of the commutation period, 𝑡 = 𝑡1 + 𝑇/2;
is(t) becomes zero, forcing D1 to turn off at zero
current; and D2 remains forward biased, carrying
the load current as shown in the circuit mode 3:
In this mode we have the following current and
voltage equations”
40.
41. Cont’d
Let us assume that the load current Id is smooth and ripple-free
(i.e., of constant, due to the highly inductive load).Assume also
that for ωt > 0, the load current flows through the rectifier diode
and that for ωt > π, it commutates to the free-wheeling diode
Df. This transfer of the load current between the rectifier and the
freewheeling diodes can not however be instantaneous, because
of the source inductance Ls. This transfer takes place over a small
commutation or overlap angle µ, during which time, the current
gradually falls to zero in one circuit and it rises to Id in the other
circuit at the same rate. Clearly, the two diodes simultaneously
conduct during the commutation process (µ).
44. Full-Wave Rectifiers with R load
Center-tapped
D1
is
+
vs
_
vo +
iD1
iD2
io
+
vs1
_
+
vs2
_
D
2
+ vD1
+ vD2
• Center-tapped (CT) rectifier requires center-tap
transformer. Full Bridge (FB) does not.
• CT: 2 diodes
• FB: 4 diodes. Hence, CT experienced only one diode
volt-drop per half-cycle
• Conduction losses for CT is half.
• Diodes ratings for CT is twice than FB
m
m
m
o
m
m
o
V
V
t
d
t
V
V
t
t
V
t
t
V
v
637
.
0
2
sin
1
:
voltage
(DC)
Average
2
sin
0
sin
circuits,
both
For
0
+
vs
_
is
i
D1
+
vo
_
i
o
Full Bridge
D1
D2
D4
D
3
49. Full wave bridge, R-L load
+
vs
_
is
i
D1
+
vo
_
io
+
vR
_
+
vL
_
vo
vs
io
iD1 , iD2
iD3 ,iD4
is
t
2
50. 50
Approximation with large L
,
for
,
2
:
i.e.
terms,
harmonic
the
all
drop
to
possible
is
it
enough,
large
is
If
.
increasing
ry
rapidly ve
decreases
Thus
decreases.
harmonic
increases,
As
:
currents
harmonic
The
curent
DC
The
1
1
1
1
2
terms
harmonics
the
and
2
term
DC
the
where
)
cos(
)
(
Series,
Fourier
Using
...
4
,
2
R
L
R
V
R
V
I
t
i
L
n
I
V
n
L
jn
R
V
Z
V
I
R
V
I
n
n
V
V
V
V
t
n
V
V
t
v
m
o
o
n
n
n
n
n
n
o
o
m
n
m
o
n
n
o
o
51. 51
R-L load approximation
vo
vs
io
iD1 , iD2
iD3 ,iD4
is
t
2
R
I
P
I
I
I
I
R
V
R
V
I
RMS
o
o
RMS
n
o
RMS
m
o
o
2
2
,
2
:
load
the
to
delivered
Power
,
2
current
e
Approximat
with a large L (i.e. L → ∞) is used in the
filter, io becomes a constant DC current
52. Cont’d
Average output rectified voltage is:
Input power factor calculations
• The input real power is defined by:
• Vs is the RMS value of the input voltage (vs); Is1 is the RMS current of the
fundamental component of is ; θ represents the phase difference between
vs and is1
• Since the input current (is) is now a square waveform, using Fourier series,
is can be expressed as:
55. Cont’d
Full Bridge Rectifier – Simple Constant Load Current (Idealized case with a purely dc output current
odd
h
/
even
h
0
9
.
0
2
2
1
1
h
I
I
I
I
I
s
sh
d
d
s
THD=48.43%
56. Three-phase rectifiers
Many industrial applications require high power that a single-phase system is
unable to provide.
Three-phase diode rectifier circuits are used widely in high-power applications with
low output ripple.
In this section, we will cover both half- and full-wave rectifier circuits under
resistive and high inductive loads.
57. Cont’d
Figure below shows the general configuration for
an m-phase half-wave rectifier connected to a
single load.
The explanation of the circuit is quite simple
since all diode cathodes are connected to the
same point, creating diode-OR arrangement.
At any given time, the highest anode voltage
will cause its corresponding diode to conduct,
with all other diodes in the reverse-bias state.
In other words, the output voltage will ride on
the peak voltage at all times.
Fig 2 shows four random sine functions and the
output voltage.
58. Cont’d
The half-wave three-phase resistive-load rectifier circuit is
shown.
We assume that the three-phase voltage source is ∆
configuration with the three balanced voltages given by
𝑣1 = 𝑉
𝑠 sin 𝜔𝑡
𝑣2 = 𝑉
𝑠 sin(𝜔𝑡 − 120)
𝑣3 = 𝑉
𝑠 sin(𝜔𝑡 − 240)
Figure (b) shows the output waveform. This circuit is also known
as a three-pulse rectifier circuit. Here, the number of pulses
refers to the number of voltage peaks in a given cycle.
59. • A diode will turn-on when its voltage is higher
than the other two diodes, i.e., the diode
connected to the highest of the three voltages
will conduct. The resulting output is shown in
Fig. 2.30b; notice that the diode conduction
starts and ends when two of the three voltages
are equal.
• Also, each diode conducts for an angle of 120 ,
and the output voltage has 3 pulses, during
one cycle of the input.
• Therefore, the fundamental frequency of the
output voltage is three times the frequency of
the input voltage. The DC component of the
output of each of them can be calculated by
the average over its period as:
The DC voltage is higher than the output voltage of a single-phase full-
wave rectifier. Of course, the drawback is the need of a three-phase
source, which is most common for industrial applications.
60. Cont’d
Fig (a) and (b) show the equivalent circuit for a half-
wave circuit under a highly inductive load and
waveforms, respectively.
61. Three-phase Full-Wave rectifiers
Two groups with three diodes each
• The full-bridge rectifier is more common since it provides a high output voltage and less ripple.
• If two 3-pulse rectifiers are connected the resulting topology is shown in Fig.. This circuit is known
as a 6-pulse rectifier, and it is the building block for all high power multiple-pulse rectifier
circuits.
63. Three-phase rectifiers
63
D1
vo =vp vn
+
vo
_
vpn
vnn
io
D3
D2
D6
+ vcn -
n
+ vbn -
+ van -
D5
D4
2
0 4
Vm
Vm
van vbn vcn
vn
vp
vo =vp - vn
3
64. Cont’d
Top group: diode with its anode at the highest potential will
conduct. The other two will be reversed.
Bottom group: diode with the its cathode at the lowest potential will
conduct. The other two will be reversed.
For example, if D1 (of the top group) conducts, vp is connected to
van.. If D6 (of the bottom group) conducts, vn connects to vbn . All
other diodes are off.
The resulting output waveform is given as: vo=vp-vn
For peak of the output voltage is equal to the peak of the line to
line voltage vab.
66. Cont’d
The 6-pulse rectifier is the building block for all high power multiple-pulse rectifier circuits.
Two 6-pulse rectifier circuits can be connected through the use of Y-Y and Δ Y transformers for
building 12-pulse rectifiers.
If the two rectifiers are connected in series, the resulting circuit is shown in Fig. 2.32a and is
suitable for high voltage, whereas the converter is connected in parallel as shown in Fig. 2.32b, the
circuit is suitable for high current.
The natural response of a circuit refers to the behavior (in terms of voltages and currents) of the circuit itself, with no external sources of excitation. The natural response or transient response is the circuit’s temporary response that will die out with time. The forced response or steady-state response is the behavior of the circuit
a long time after an external excitation is applied.
