Output Current Ripple Factor Performance of Half-Wave
Half-Wave Rectifier
Rectifier
With and Without Freewheeling Diode
Diode
Taufik
Ali O.
0.Shaban
Shaban
Ahmad Nafisi
Department
Engineering
Department of Electrical
Electrical Engineering
Engineering
California
University
University
California Polytechnic
Polytechnic State University
Obispo, CA 93407
San Luis Obispo,
93407
-
Abstract - The objective
objective of this work is to investigate
investigate ripple
ripple
factor of half-wave
circuits. The ripple
factor is one of
half-wave rectifier
rectifier circuits.
ripple factor
important characteristic
necessary when designing
characteristic necessary
designing a power
electronic converter.
converter. The ripple factor
factor measures how much
much
deviation
output parameter
deviation the converter
converter output
parameter has, such as the
current, from
from its nominal designed
output current,
designed value. In this paper
output current of half-wave
the ripple factor
factor of the output
half-wave rectifiers
rectifiers will
investigated. More specifically,
ripple factor
factor of output
be investigated.
specifically, the ripple
output
current from more practical
half-wave rectifiers
include
current
practical half-wave
rectifiers that include
inductive load with or without
freewheeling diode will be
without a freewheeling
analyzed and then compared to that of the basic half-wave
half-wave
rectifier consisting
consisting only of a resistive
rectifier
resistive load. Derivation
Derivation of the
equations for
for the ripple
factor for
for the three half-wave
equations
ripple factor
half-wave rectifier
rectifier
circuits will first
first be presented.
From these results,
circuits
presented. From
results, plots will be
generated using Pspice that will allow us to conveniently
conveniently
compare
performance of each of the rectifiers.
rectifiers.
compare the ripple
ripple factor
factor performance
INTRODUCTION
I. INTRODUCTION
In power conversion
conversion circuits, the actual
actual output waveform
of any converter constructed
constructed from the input sources will in
from the input. This tells us that the
general be different
different from
output must contain unwanted components along with the
wanted components.
components. These unwanted components are
unfortunately unavoidable
unavoidable and they can be described
unfortunately
described as the
Fourier components.
components. The complete collection of unwanted
unwanted
components
defines distortion. The terms harmonic distortion
distortion
components defines
simply harmonics
or simply
harmonics refer to this unwanted
unwanted behavior.
behavior.
Particularly in dc application
Particularly
application such as that of rectifier circuits,
the collected
collected unwanted
unwanted· components are typically referred to
by the term ripple. A more specific definition is ripple factor
measure how much deviation
which is a tool to measure
deviation the converter
output parameter
nominal designed value.
parameter has from its nominal
value.
distortion of
Due to the fact that ripple is closely related to distortion
waveform, it is therefore crucial to consider
consider
the output waveform,
addressing
distortions in the initial steps
addressing the questions
questions about distortions
of converter
converter design.
design. How much the load can tolerate, whether
or not there
there are specific
specific frequencies
frequencies that are especially
especially bad
avoided, the necessity for filtering,
and should be avoided,
filtering, and
ripple-related
specifying
distortion limits are some of the ripple-related
specifying distortion
issues that might be brought up prior to designing
designing the
converter. Moreover, prior knowledge
converter.
knowledge of the ripple factor is
also
also very significant since it can be used as an indicator of the
quality
waveform. From practical point of view,
view,
quality of the output waveform.
knowledge
knowledge of the ripple factor before hand will aid us in
designing
designing a cost-effective
cost-effective converter sircuit,
circuit, such determining
determining
the need of having an extra freewheeling
freewheeling diode used in a halfhalf­
half­
waveform.
wave rectifier to improve the quality of output waveform.
In most dc applications,
applications, the output ripple represents
represents both a
variation
around the desired dc level and a possible
variation around
possible energy
effect at undesired
undesired frequencies
frequencies [1].
[l]. In a standard
standard dc supply,
supply, it
specify the maximum peak to peak ripple, and
is common to specify
often the ripple rms magnitude
magnitude as well.
well. For example,
example, typical
50-100 mv range
numbers
numbers for peak to peak ripple fall in the 50-100
for low dc voltages.
voltages. A good rule of thumb is that the ripple
fo.r
ripple
output.
will
WIll be about 11%
% of the nominal output.
II. THE
THE BASIC HAW-WAVE
HALF-WAVE RECTIFIER
Rectification is the process of converting ac power to dc
Rectification
power.
uncontrolled rectifier uses only diodes
diodes as
power. An uncontrolled
rectifying
elements. The dc output voltage
rectifying elements.
voltage is fixed in
magnitude by the amplitude
amplitude of the ac supply voltage.
voltage.
magnitude
However,
contains
However, the dc output is not pure, that is, it contains
significant
components or ripple. To suppress
significant ac components
suppress this ripple, a
typically inserted
inserted after the rectifier. The simplest
simplest
filter is typically
configuration of rectifier is the half-wave
circuit configuration
half-wave rectifier and
1. Here, the half-wave
is shown in figure
figure 1.
half-wave rectifier circuit
whose
source voltage
supplying a purely
wh?s~ source
volta~e is a sine wave is supplying
resistive
load. During
cycle, when the
reSIstive load.
Durmg the positive half cycle,
voltage at the anode is positive with respect to the cathode,
cathode,
the diode turns on.
on. This allows current through
through the load
positive half sine
resistor. Thus, the load voltage follows
follows the positive
sine
wave.
half-cycle, the voltage
anode
wave. During the negative
negative half-cycle,
voltage at the anode
becomes negative
diode
negative with respect to the cathode and the diode
turns off. There is no current flows
flows through
R. Figure 2
through R.
shows
half-wave rectifier
shows the output voltage
voltage waveform of the half-wave
rectifier
using an input waveform
sinm
frequency of
waveform of i,sin
0Jt and with frequency
v,
60Hz.
60Hz.
Fig. 1. Half-wave rectifier with resistive load
Fig.
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0-7803-6401-5/00/$10.00
Q 2000
2000 IEEE
EEE
1186
1186
12 .. .,.......,~--~----::----."..---~-----;:----,
to"
( 5 ) into equation
equation (4)
(4) yields:
yields:
Substitutions of equations (1) and (5)
K
r = 1.21
IS,=
1.21
::
t
(6)
(4)
which tells us that the ripple factor for a half-wave
rectifier
half-wave rectifier
with resistive
resistive load is constant.
constant.
0'"
1111r.i
2D11S
311M
_IRS
SIllS
611lts
7-.s
8116
9111tS
IV.
Iv. THE HALF-WAVE RECTIFIER
RECTIFIER WITH INDUCTIVE
INDUCTIVE LOAD
Ti_
rill
Fig. 2.
2. Load voltage
half-wave rectifier with resistive
resistive load
Fig.
voltage waveform
wavefonn of half-wave
The load current,
current, IIR,
R, which is equal to the diode current will
be periodic
periodic since
since the input signal is periodic. However,
similar to the output voltage,
voltage, the load current is also a very
poor de
dc with its value equal to its average:
average:
A
I
I R =2,.
t
V
f iR(t)drot = 2,. R f sin rotdrot = -1CR'
_--L
a
P+---l
A
1 V "
21t+a
An improved
improved version of the basic half-wave
half-wave rectifier circuit
figure 3, whereby an inductive
inductive load is
is depicted in figure
connected rather than just a simple resistive load.
load.
(1)
0
Half-wave rectifier with inductive load
Fig. 3. Half-wave
Equation (1) shows that with this type of rectifier the average
1/3 of its peak value.
load current is less than 1/3
III.
111.THE
THE RIPPLE
RIPPLE FACTOR
example, we can easily see that the ioad
Using the previous example,
current will have ripple, and if we define this ripple to be:
In steady
periodic
steady state, the output current IR(t)
IR(t) must be periodic
sinusoidal input waveform is a periodic
since the sinusoidal
periodic waveform.
waveform.
By applying KVL:
KVL:
diR(t)
R.
V,.
di,
(t) R
vs
OX
--+-1
+ -i,R (t)=-smwt
(1) = -sin
L
dt
L
L
(7)
It can be shown that the solution for the this differential
differential
equation is:
is:
(2)
where:
where:
(8)
2lt+a
11RI= 2~ fi;(t)drot
(3)
a
where:
where:
current, then we can define
define the
is the rms value of the load current,
normalized ripple or ripple factor which is given by;
(4)
(4)
</l = tan
_[WL]
Ii
(9)
(9)
I
Using the same method as was done in equation
equation (1),
( l ) , the
average value of the current described by equation (8) with
conduction angle a
c1 is found to be:
dimensionless and is useful in measuring
The ripple factor is dimensionless
from its
how much deviation the output parameter has from
nominal designed
designed value,
value, and therefore plays an important role
nominal
in designing
designing a converter circuit.
circuit.
To determine
determine the ripple factor of our previous example,
example, the
calculated:
rms value of the load current needs to be calculated:
(10)
The rms of equation
equation (8) can be derived by using the same
definition in equation (5)
( 5 ) which yields to:
definition
(1 I)
(5)
1187
1187
.
where:
+
~
4Lsm 2 t/l
able to investigate which scheme yields the smallest rippie
ripple
factor. Recall that for the case where the half-wave rectifier
has resistive load only, the ripple factor is found to be
constant as shown in (6).
[(a-t/l)-t sin 2(a-t/l)] (12)
of the purely resistive load,
As previously done in the case of
once the expressions for the average value and the rms are
obtained, the ripple factor may then be derived using (4).
half wave rectifier is illustrated in figure
A more practical half
of an extra diode allows the load current
4. Here the insertion of
freewheel the
to continue to flow, or in other words to freewheel
current. Henceforth, this additional diode is called the
current.
freewheeling diode. For continuous conduction, that is the
freewheeling
of
current never decays to zero, it can be shown that the ratio of
1t!ro.
the inductor and the load resistor has to be greater than Ida.
The load current for this particular circuit can be described
as::
as
-~I]
V [ sin(rot-(/»+--:z;-e
sin(/>
iR(t)=-!...
L
Z
when
And,
l-e
The three different circuit configurations for the half-wave
I, 3, and 4 are then simulated
rectifier, as shown in figures 1,
and the results are recorded and compiled to produce several
plots from which we can conveniently check to see which
configuration gives us the best performance in terms of
of the
ripple factor. Overall, five different cases are provided using
different values of
of either the resistor load or the inductor.
inductor. The
first three cases, the value of
of the resistor
re::istor is kept constant at
R=O.10,10, and l0Q
100 for cases 1,2,
1, 2, and 3 respectively.
respectively. In the
R=O.lQ,lQ,
last two cases, the inductor values are fixed at kL=30mH
3 0 m H and
300mH for cases 4 and 5 respectively. The results of
of the
computer simulations for all five cases are shown in figures
55,6,7,8
, 6 , 7 , 8 and 9.
Normalized ~
Ripple
with R-0.10
R=O.10 Ohm
Normalbul
ipple
Factor wlth
(13)
1L
t
0 << rot
O
o t < 1t
x
V[
iR(t)=--.!..
Z
sin (/>
(/>
R
_.!1.(Lt)]
eL'
y---------------...,
0.8
~
~
Without FD
0.7 I\".
----------------1
0.6
jO.5
(14)
wim Fb
J lVr
l-e -u '
0.4
0.3
< orott e
< 2n
21t
21t
where 1t
xc
with:
with:
Z
Z=
=~r-R-;:-2
& q+-:(wL---:-:;-Y
z y
0.2 -I---.._
-I---.._ _
0.24
,
.
0.0 0.1
0.0
0.1
0.29 0.3
0.3
0.0
0
--l
~ I
'
I
,
0.6
0.4 0.5 0
.6 0.7
Indust.llca
Inductence V.lw.8
Valuea fhl
[HI
(15)
(15)
The same procedure can again be conducted to yield the
average and rms values of the currents in (13) and (14), as
were done in the previous two cases using the same
definitions as shown in (3) and ((5)
respectively. Once these
definitions
5 ) respectively.
values
obtained, then the ripple factor equation for these
values are obtained,
currents
currents can be derived using equation (4).
,
0.8
0.8
0.9
1.0
1.0
(FD)
Fig. 5. Ripple factor with and without Freewheeling Diode (FD)
when Rd.lOf2
R=O.lOO -Case
- Case 11
I
NormaliZed Ripple Factor with R-1
R=1 Ohm
Normailzed
1
1.0,. 0 . . - - - - - . , . . . _ - - - - - - - - - - - ,
I
0.9
0.9
,Q :::1'-...
1 --------------j
V. COMPUTER SIMULATIONS
v.
SIMULATIONS
~
~
To aid the analysis
analysis of the ripple factors
factors of the three cases,
namely,
namely, the half-wave rectifier with resistive load, with
inductive
inductive load,
load, and with freewheeling diode, a computer
simulation
used. Using this tool, we will be
simulation using Pspice is used.
0.8
ii!
ii!
3 0.5
I
0.4
)0.4
I
without FD
Without
FD
0.7
.66
00.
IP ~::",I
0.1
0.0
O
V
~_-
0.0 0.1
0.1
0.0
O.O
With
FD
wim FD
_ __-
0.2
0.2
'
0.3
0.3
_ __0.4
0.4
0.5
0.5
_ __l
0.6
0.6
0.7
0.7
__
0.6 0.9
0.8
~
I
1.0
1.0
Inductance Value.lHl
Values M
Fig.
Fig.6.
6. Ripple Factor with and
and without Freewheeling
Freewheeling Diode (FD)
(FD)
when
when R=10·
R=lQ Case
Case 22
-
Fig.
Fig. 4.
4. Half-wave
Half-waverectifier
rectifier with inductive
inductive load
load
1188
1188
~~
I
Normalized Ripple Factor
Factor with R=10
R=10 Ohm
Ohm
t-----------------...,
1.o
1.0
.0
8
0.9
~ 0.8
0.8
2 0.7
:.
WlthoutFD
%..
0.6
~ 0.6
.-
~
a o0.5s
...4.~ 0.4
$~ 0.3
0.3
e~ 02
0.2 1
With FD
0.1
OO.o.J---_-_-.,..-_-_-_-..--_---!
0.0
.'
0.2
0.7
0.8
0.2 0.3
0.3 0.4 0.5 0.6
0.6 0.7
0.8 0.9 1.0
0.0 0.1
0.0
0.1
Inductance
Values [H]
Inductance Values
[HI
~
Fig.
Freewheeling Diode (FD)
(FD)
Fig. 7. Ripple
Ripple Factor with and without Freewheeling
when R=lOQ -- Case 3
Normalized
with L..
30 mH
NormallzedRipple
Ripple Factor
Factor wlth
L-30
mH
,
I
The
The results show that in general the half-wave rectifier
with freewheeling diode performs the best in terms of the
ripple factor
factor of its output current.
current. In the case of half-wave
rectifier with resistive
load, the value of the ripple factor is
resistive load,
constant at 1.21
1.21 and is independent of the load resistor and
the amplitude of the input voltage source.
source. However, as the
further show, this is not true for the other two
results further
rectifiers with inductive
inductive load where the ripple factor is
dependent upon both the load impedance and the input
source.
diode, if
source. In the half-wave rectifier with freewheeling diode,
the load resistor is kept constant
constant while inductance value is
varied, the ripple factor of half-wave rectifier with
freewheeling diode is always lower than those of the other
freewheeling
two rectifiers. Moreover, its minimum ripple factor is found
to be about 0.25. Another interesting observation is that the
higher the value of the load resistor, the higher the value of
the inductance needed to reach its minimum ripple factor
point. In another case where the inductance is fixed but the
load resistor is varied, the ripple factor for both half-wave
rectifiers with inductive
inductive load will reach its lowest value and
then converges to the ripple factor of the half-wave rectifier
with resistive load.
1
1.2 . 2 . , - - - - - - - - - - - - - - - - - - - ,I /
~
t
1.0 1.0
EL.a0.8
I-ii:Ba 0.6
Ij1
VI. CONCLUSIONS
CONCLUSIONS
WllhoulFO
Without
FD
I
0.6 -
r·6
4 0.4
z
0.2
0.0 I----_---_---.,..------.---~
10
20
30
40
10
o0
50
Resistance Vaiuea
[Ohms]
Resistance
Values [Ohms]
Fig. 8.
8. Ripple
Fig.
Ripple Factor
Factor with and without Freewheeling Diode (FD)
(FD)
when kL=30mH
3 O m H - Case 4
Normalized
with L=300
NormalizedRipple
RIpple Faclor
Factor wlth
L-300 mH
mH
I
1.2 r--------------------,
In this paper, the ripple factor
factor characteristics of three
different circuit configurations
configurations of the half-wave rectifiers
different
were investigated. Several examples on how to derive
derive the
equations for the average and rms values were presented from
which the expression for the ripple factor can further be
obtained.
obtained. Results from
from computer simulations were provided
and several plots were included from five
five different cases.
From these results, it is clear that the smallest
smallest and therefore
the best ripple factor
factor can be obtained when inductive load
with the extra freewheeling
freewheeling diode is used. Further work for
this project will include,
include, but not limited to,
to, lab
implementations
implementations and measurements
measurements of these circuits to
supply us with empirical results which can then be compared
with those results that are obtained from the computer
simulations.
simulations.
REFERENCES
REFERENCES
Withoul
FD
WllhoUIFO
~
1.0
J5-
0.8
0.8
.!!
n
st
[ l ] P.T. Krein, Elements of
of Power Electronics,
ed.,
[I]
Electronics, 1lst
ed.,
Oxford, New York, 1998.
1998.
!l:
E 0.6
ii:
0.6
I5j 0.4
o6
=z 0.2
~ 0.4
0.2
0
. 0 . J - - - _ - - _ - - _ - - _ - - _ - - - lI
0.0 1
500
300
100
100
200
300
400
500
600
o0
Resistance
ResistanCBValues [Ohms]
[Ohms]
Fig. 9.
Ripple Factor with and
Fig.
9. Ripple
and without Freewheeling Diode (FD)
(FD)
L300mH -- Case 5
when L=300mH
1189
1189