This document discusses half-wave rectifiers. It begins by stating the learning outcomes which include evaluating the performance of various power electronic converters. It then defines half-wave rectifiers as converting AC to DC by only allowing current flow during one half of the AC cycle. The document analyzes half-wave rectifiers with resistive and resistive-inductive loads. It also discusses freewheeling of the inductor current and controlled half-wave rectifiers using thyristors. Equations for various voltages and currents are provided.
2. Course Learning Outcome (CLO)
CLO1
• Ability to analyse operation and applications of power electronic
devices and addressing the needs of EMC requirements.
CLO2
• Ability to evaluate the performance of AC-DC converters.
CLO3
• Ability to evaluate the performance of AC-AC converters.
CLO4
• Ability to evaluate the performance of DC-DC converters.
CLO5
• Ability to evaluate the performance of DC-AC converters.
2
3. Introduction
Converts ac to dc.
To produce an output that is:
-pure dc
-waveform that has a specific dc component
pure dc waveform that has a dc component
3
4. Resistive Load
Diode allows current in positive direction and blocks
current in negative direction.
4
5. Resistive Load
m
o avg m
0
V
1
V V V sin( t)d( t)
2
o m
o
V V
I
R R
2 m
rms m
0
V
1
V V sin( t) d( t)
2 2
rms m
rms
V V
I
R 2R
2
2
rms
rms
V
P I R
R
5
7. Resistive-Inductive Load
Inductor current cannot change
instantaneously. It does not stop
instantly at π but continue to flow
until all magnetic energy stored in
inductor is released at β.
7
8. Resistive-Inductive Load
/
m
V
i( ) sin sin e 0
Z
t/
m
2
2 1
V
sin t sin e for 0 t
i t Z
0 for t 2
L L
where Z R L , tan , and
R R
m
o
V sin t for 0 t
v t
0 for t 2
8
10. Freewheeling of Inductor Current
Freewheeling diode is connected across RL load.
During negative half cycle of ac source, freewheeling diode
is forward biased and inductor current freewheels.
D1 on, D2 off
when source
voltage is
positive (vs>0)
Freewheeling- D1
off, D2 on when
source voltage is
negative
(vs<0)
10
11. Freewheeling of Inductor Current
The inductor charge up and reaches periodic steady-state
after a few periods (depending on then L/R time constant).
11
12. Freewheeling of Inductor Current
The load voltage is a half wave rectified sine wave which
can be expressed as
The half-wave rectified sine wave can be expresses as a
Fourier Series
m
o
V sin t for 0 t
v t
0 for t 2
Load voltage and
current waveforms
at steady-state.
m m m
o 0 0
2
n 2,4,6...
V V 2V
v (t) sin t cos n t
2 n 1
12
13. Freewheeling of Inductor Current
If the inductance is infinitely large, the impedance of the
load to ac terms in the Fourier Series is infinite and
therefore the load current is purely dc.
The load current is then
The ripple in load current
can be estimated as
o m
o o
V V L
i t I
R R R
o 1
1
I 2I
where I is amplitude of first
ac term in the Fourier Series
Voltage and
current
waveforms
at infinite L
13
16. Controlled Half-Wave Rectifier
The conduction of diodes are uncontrolled and therefore
the half-wave rectifiers analyzed previously are classified
as uncontrolled rectifiers.
In uncontrolled rectifiers, the dc level of the output and
power transferred to the load are fixed once the source
and load parameters are established.
To control the output of a half-wave rectifier, controllable
semiconductor switches can be used.
e.g. SCR: Conducts when,
1. SCR must be forward biased
2. current must be applied to the gate of SCR
16
17. Controlled Half-Wave Rectifier
Resistive load
Load current starts
flowing at ωt=α and
stops at ωt=π.
m
o
V sin t for t
v t
0 for t 2
m
o
V
V 1 cos
2
m
rms
V sin(2 )
V 1
2 2
17
20. Controlled Half-Wave Rectifier
RL load
Load current can be expressed as
The extinction angle, β can be obtained by solving
Output voltage can be expressed as
( t)/
m
V
sin t sin e for t
i t Z
0 otherwise
( )/
m
V
i 0 sin sin e
Z
m
o
V sin t for t
v t
0 for t 2
m
o
V
V cos cos
2
20
