Keynote paper, First International Conference on Energy, Power, and Motion Control
May 5-6, 1997, Tel Aviv, Israel
Some Topologies of High Quality Rectifiers
Robert W. Erickson
Department of Electrical and Computer Engineering
University of Colorado, Boulder 80309-0425
Abstract— Several basic classes of three-phase
high-quality rectifiers are described. Both single-switch
and six-switch three-phase rectifier topologies can be
derived from parent dc-dc converters. Single-switch
rectifiers are compared with the basic six-switch PWM
rectifiers performing similar power conversion functions,
using the measures of total semiconductor stress and
active semiconductor utilization. The single-switch
approach is shown to utilize the semiconductor devices
more effectively. Zero current switching and multiresonant approaches are found to exhibit low switch
stress over a wide range of operating points, with low
THD.
3øac
input
øa
øb
øc
dc output
ia
ib
Re
Re
ptot =
pa + pb + pc
ic
+
R
v
–
Re
Fig. 1. Functional equivalent circuit of a three-phase
high-quality rectifier: input resistor emulation and
dc output power source characteristic.
1. Introduction
modeled by a power source equal to the total threephase instantaneous input power as shown in Fig. 1
[1-3].
The various active approaches to high-quality
three-phase rectification fall into two classes. The first
comprises PWM converters operating in the
continuous conduction mode (CCM), with the three ac
line currents independently and actively regulated.
These converters usually contain six or more active
devices, and are capable of bidirectional power flow.
The second class may contain as little as one active
device, and input resistor emulation is obtained via the
natural response of the converter reactive elements to
the high-frequency switching of the active device. In
this paper, both approaches are discussed, and the
utilizations of their active semiconductor devices are
compared.
High-quality low-harmonic rectification is
becoming increasingly required, to meet regulations
which limit ac line current harmonic content, such as
IEC-555 and IEEE-519. The application requirements
of three-phase high-quality rectifiers are varied. In
some simple cases, it may be necessary only to
produce a dc output voltage nearly equal the peak input
line-to-line voltage. In other cases, an output voltage
of variable and controlled magnitude, substantially
smaller or larger than the input line-to-line voltage,
may be required. Isolation of the dc load from the ac
line is also a requirement in applications such as
battery charging in the telecommunications or electric
vehicle areas. High-frequency EMI and common-mode
currents, generated by non-isolated low-harmonic
rectifiers, is also a major concern.
Figure 1 illustrates the desired properties of an
ideal three-phase rectifier, which presents a balanced
resistive load to the utility system. A three-phase
converter system is controlled such that resistor
emulation is obtained in each input phase. The rectifier
three-phase input port can then be modeled by perphase effective resistances R e , as illustrated in Fig. 1.
The harmonic content of the ac input currents therefore
match the harmonic content of the applied ac input
voltages, and hence are correspondingly low. The
instantaneous powers apparently consumed by these
effective resistors are transferred to the rectifier dc
output port. The rectifier output port can therefore be
2. Three-phase PWM rectifiers
operating in CCM
A variety of 3øac-dc PWM rectifiers are known; a
few of the many references on this subject are listed
here [4-10]. The most well-known topology is the
three-phase ac-to-dc boost rectifier, illustrated in Fig.
2. This converter requires six SPST currentbidirectional two-quadrant switches. The inductors and
capacitor filter the high-frequency switching
harmonics, and have little influence on the lowfrequency ac components of the waveforms. The
switches of each phase are controlled to obtain input
resistor emulation, either with a multiplying controller
1
i1(t)
ia (t)
L
ib (t)
L
ic(t)
L
øa
øb
øc
output voltage V that is less than the peak line-line ac
input voltage. This converter resembles what is
known as the current-source inverter, except that the
converter is operated as a rectifier, and the converter is
controlled via high-frequency pulse-width modulation.
Two-quadrant voltage-bidirectional switches are
required in this converter. A disadvantage of the 3ø
buck rectifier is the higher conduction losses induced
by the series connection of devices. Also, the rms
transistor currents are greater than in the 3ø boost
rectifier; this further increases the conduction loss.
The converter is capable of operation in inverter mode
by reversal of the polarity of the output voltage v(t). A
substantial input filter is usually required to smooth
the pulsating ac line currents.
PWM 3øac-dc rectifiers which resemble most
other dc-dc converter topologies are also possible. Two
examples are the 3øac-dc rectifier circuits of Figs. 3(b)
and 3(c), based on the dc-dc buck-boost [9] and Cuk
converters. These converters can be viewed as being
derived from parent dc-dc converters via a
transformation in which the dc input and switch
network are replaced by a three-phase input and six-
dc output
3øac
input
Q1
D1
i2(t)
Q2
D2
i3(t)
Q3
+
D3
C
Q4
D4
Q5
D5
Q6
load v(t)
D6
–
Fig. 2.
Boost-type 3øac-dc rectifier.
scheme employing average current control, or with
some other approach. To obtain undistorted line
current waveforms, the dc output voltage V must be
greater than or equal to the peak line-to-line ac input
voltage V L,pk. In a typical realization, V is somewhat
greater than V L,pk. This converter resembles the wellknown voltage-source inverter, except that the
converter is operated as a rectifier, and the converter is
controlled via high-frequency pulse-width modulation.
The three-phase boost rectifier of Fig. 2 has
several attributes which make it the leading candidate
for most 3øac-dc rectifier applications. The ac input
currents are nonpulsating, and hence
very little additional input EMI
a)
filtering is required. As in the case of
L
dc output
3øac
the single-phase boost rectifier, the
input
iL(t)
Q
Q
Q
+
rms transistor currents and also the
ia(t)
øa
conduction losses of the three-phase
D
D
D
ib(t)
boost rectifier are low relative to other
C
øb
load v(t)
3øac-dc topologies such as those of
ic(t)
Q
Q
Q
Fig. 3. The converter is capable of
øc
–
bidirectional
power
flow.
A
input filter
D
D
D
disadvantage is the requirement for six
active devices: when compared with a
b)
dc-dc converter of similar ratings, the
dc output
active semiconductor utilization is 3øac
input
Q
Q
Q
D
+
low. Also, since the rectifier has a
i (t)
Q
ø
i (t)
boost characteristic, it is not suitable
D
D
D
i (t)
for direct replacement of traditional
C
ø
L
load v(t)
buck-type phase-controlled rectifiers.
Q
Q
Q
i (t)
ø
Three-phase ac-to-dc rectifiers
–
input filter
having buck, buck-boost, or other
D
D
D
characteristics, are possible, but find
c)
much less use than the boost
dc output
topology. An example is the 3øac-dc 3øac
buck rectifier illustrated in Fig. 3(a). input
L2
L 1 ia(t)
+
Q
Q
Q
C1
D
D
D
Unlike the single-phase case, in threeøa
phase applications the buck topology
L 1 ib(t)
D
load
øb
C2
can supply constant power to a dc
v(t)
Q
load, with negligible distortion of the
L 1 ic(t)
Q
Q
Q
øc
D
D
D
ac line current waveforms. When the
–
voltage of one phase is zero, the other
two phases have nonzero voltage and
Fig. 3.
Several other non-isolated three-phase ac-dc rectifiers: (a) based
can supply the dc load power. This
on the buck dc-dc converter, (b) based on the buck-boost dc-dc
converter can produce a controlled dc
converter, (c) based on the Cuk dc-dc converter.
1
2
1
2
4
3
5
4
1
3
6
5
2
6
3
7
a
7
a
L
2
1
3
b
b
c
4
5
6
c
4
1
5
1
2
6
2
3
3
7
7
4
2
4
5
6
5
6
a)
switch bridge network. High-frequency isolation
transformers can be incorporated into most of these
converters, in a manner similar to that used to obtain
isolation in the parent dc-dc converters.
van(t)
VM
t
3. Some other approaches to threephase high-quality rectification
The CCM three-phase rectifier approaches
described in section 2 require six or more active
devices. Compared with conventional low-power-factor
passive rectifier approaches, the increased active silicon
area and reduced semiconductor utilization of the sixswitch approach can be expensive. In view of this, one
might ask what is the minimum active silicon area
required to perform the desired functions of the ideal
rectification application. It is well known that lowharmonic 3øac-dc rectification can be performed using
a conventional passive six-diode rectifier and a
harmonic trap filter. Hence fundamentally, no
semiconductor devices other than diodes are required.
When control of the output voltage is requisite, at
least one active device is needed. If it is desired to
avoid the use of low-frequency filter elements, then a
source of high-frequency switching harmonics is
needed, again necessitating inclusion of at least one
active device. So a single active device is the
minimum needed to synthesize low-harmonic 3ø
rectifiers containing no low-frequency reactive
elements, having control of the output voltage, and
having unidirectional power flow. Several singleswitch approaches to three-phase rectification are
known. Depending on the application, some of these
approaches may exhibit better active switch utilization
and reduced semiconductor area than six-switch
approaches. On the other hand, these single-switch
approaches generally require additional high-frequency
reactive elements.
A single-switch 3øac-dc rectifier based on the
DCM boost converter [11,12] is illustrated in Fig. 4.
The input current waveform ia(t) is illustrated in Fig.
5(b). Transistor Q1 is controlled in the same manner as
a dc-dc boost converter. Inductors L 1, L 2, and L 3 are of
equal small value, such that they operate in the
discontinuous conduction mode in conjunction with
diodes D1 - D6. At the end of the transistor Q1
conduction subinterval, the inductor currents reach
peak values which are also proportional to the applied
three-phase line-to-neutral voltages. When transistor
Q1 turns off, then diode D7 becomes forward-biased and
the inductors release their stored energies to the dc
output. Since the peak input currents are proportional
to the applied input line-to-neutral voltages, then the
average values of the input currents are also
approximately proportional to the input line-to-neutral
voltages. Approximate three-phase input resistor
b)
DCM boost
ia(t)
t
c)
DCM flyback
i a(t)
t
d)
ZCS buck
i a(t)
t
e)
Multiresonant ZCS buck
vcra(t)
t
Fig. 5.
Input current waveforms of various singleswitch three-phase rectifier circuits: (a) input lineto-neutral voltage v an(t); (b) 3ø DCM boost; (c) 3ø
DCM flyback; (d) zero-current-switching quasiresonant buck; (e) phase a tank capacitor voltage,
multi-resonant zero-current-switching buck.
emulation is obtained. The three-phase DCM boost
rectifier does generate a modest amount of lowfrequency input current harmonics; the THD can be
reduced by increasing the dc output voltage.
The three-phase DCM boost rectifier has the
advantage of very simple control. The transistor can
operate at constant switching frequency. Variation of
the duty cycle allows control of the dc output power.
Only a single active device such as a MOSFET or
3
dc output
3øac
input
øa
øb
øc
L1
ia (t)
L2
ib (t)
L3
ic (t)
D1
Fig. 4.
D5
D6
+
D7
D3
Q1
D4
input filter
D2
C
v(t)
–
Single-switch three-phase DCM boost rectifier.
are therefore approximately proportional to the
respective applied line-to-neutral voltages. At full load,
a THD of approximately 13-14% is observed; nearly
all of the THD can be attributed to the fifth harmonic.
The THD can be reduced to less than 10%, by use of
any control scheme that leads to constant
instantaneous power flow.
Transistor Q1 operates with zero current
switching. An IGBT, inverter-grade SCR, or other
device can be used. The peak voltage stress on Q1 is
equal to the applied peak input line-to-line voltage,
while the peak current is approximately twice the dc
output current.
Transistor Q1 operates with an approximately
constant on-time, equal to the length of the resonant
current pulse. The output power is controlled by
variation of the transistor off-time, and hence the
converter operates with a variable switching frequency.
The rectifier requires an input filter, to remove the
high-frequency components of the pulsating input
current waveforms.
Another buck-type single-switch 3øac-dc rectifier
[16,17] is illustrated in Fig. 8. This is a multiresonant
rectifier, in which diodes D1 - D7 operate with zero
voltage switching, while transistor Q1 operates with
zero current switching. Input capacitors C r1 and dc-side
IGBT is needed. A disadvantage is the need for an input
filter to remove the high-frequency components of the
pulsating input currents. As in all single-switch threephase rectifiers, bidirectional power is not possible.
A similar scheme, based on the DCM flyback
converter [13,14], is illustrated in Fig. 6. A typical
input current waveform is given in Fig. 5(c). This
converter is effectively three independent single-phase
DCM flyback rectifiers, which share a single transistor
switch. The peak transformer magnetizing currents
directly follow the applied ac phase voltages. This
causes the average input currents to directly follow the
applied line-to-neutral voltages, without generation of
low-frequency current harmonics. The rectifier can both
increase and decrease the voltage magnitude, and is
inherently capable of inrush current limiting. In lowpower applications, this is a simple way to obtain
low-harmonic three-phase rectifier which incorporates
high-frequency isolation transformers. It has the
disadvantage of requiring an
3øac
dc output
input filter for removal of the input
T
T
i
(t)
1
high-frequency components of ø
1
a
D
D
D
D
D
D
+
a
the pulsating input current
T2
T2
ib(t)
Q
waveforms.
øb
C
v(t)
A buck-derived singleT3
T3
ic(t)
switch rectifier [15] is øc
D
D
D
D
D
D
–
illustrated in Fig. 7. This
input filter
converter is based on the zeroFig. 6.
Single-switch three-phase DCM flyback rectifier.
current-switching
(ZCS)
quasi-resonant dc-dc buck
3øac
L
dc output
Q
input
converter. A resonant inductor
+
Lr
ia (t)
D
D
D
L r is placed in each input
øa
phase. As illustrated in Fig.
Lr
ib (t)
v(t)
øb
C
D
Cr
5(d), when transistor Q1
Lr
ic (t)
conducts,
the
resonant
øc
D
D
D
–
inductors
Lr
ring
in
input filter
conjunction with resonant
Fig. 7. Single-switch three-phase zero-current-switching quasi-resonant buck rectifier.
capacitor C r. Input currents
3øac
Ld
dc output
Q
input
ia(t), ib(t), and ic (t) are
+
ia(t) L a
approximately
sinusoidal
D
D
D
øa
+
Lr
C r1
vcra (t)
pulses, having peak amplitude
–
ib(t) L a
proportional to the applied
øb
v(t)
C
C r1
line-to-neutral voltages v an(t),
ic(t) L a
C r2
D
øc
D
D
D
v bn(t),
and
v cn (t),
C r1
–
respectively. The average
values of ia(t), ib(t), and ic (t) Fig. 8. Single-switch three-phase multiresonant zero-current-switching buck rectifier.
1
2
3
7
8
9
10
11
12
1
4
5
6
1
1
2
3
7
4
5
6
1
1
2
3
4
5
6
7
4
capacitor C r2 form a resonant network, in conjunction
with inductor L r. Inductors L a and L d operate in the
continuous conduction mode, with small switching
ripple. This converter exhibits nonpulsating input and
output currents, and requires minimal additional
filtering of the input current waveforms. This
converter exhibits low EMI and low switching loss.
The phase a resonant capacitor voltage waveform
v cra(t) is illustrated in Fig. 5(e). This voltage is
approximately sinusoidal, with peak amplitude
proportional to the input current ia(t). Approximate
input resistor emulation is therefore obtained. The
input current THD is a function of the value of L a;
THD less than 4% can be obtained at full load.
Transistor Q1 can be realized using an IGBT, SCR, or
other device. The peak transistor voltage is typically
twice the input line-to-line peak voltage. The dc load
power is controlled by variation of the switching
frequency.
A variety of other three-phase rectifier schemes
having a reduced number of switches are known. In
[18], a CCM PWM approach is described which
requires only three active devices. An approach
requiring two active devices which operate with zerocurrent switching is described in [19].
respectively. The total switch stress is also listed; this
is defined as the product of the switch blocking
voltages and peak currents, summed over all active
switches in the converter. The switch stress is a
measure of the total active silicon area required for
realization of the converter. Also shown is the silicon
utilization, defined as the converter output power
divided by the total switch stress.
In the dc-dc case, the quasi-resonant switch
approach is commonly thought of as restricted to low
power applications, because of the increased peak
switch stresses, poor switch utilization, and increased
conduction losses. However, these arguments do not
apply to the single-switch ZCS rectifier of Fig. 7,
because the 2:1 increase in peak current due to resonant
switching is more than offset by the 1:6 reduction in
total active semiconductor area arising from the singleswitch approach. The six-switch bridge network leads
to poor silicon utilization, since the semiconductor
devices are effectively utilized only near the peaks of
the applied ac phase current waveforms. For example,
if the six IGBT devices of a three-phase bridge module
were reconnected in parallel (forming a single device)
and then operated in an equivalent single-switch ZCS
rectifier, then the peak current density in each silicon
device would be reduced by a factor of one-third.
4. Comparison of six-switch vs.
single-switch approaches
Table 3. Comparison of per-switch stresses, singleswitch multiresonant vs. six-switch PWM approaches
Voltage
Peak current
multiresonant
685V
77.4A
6-switch PWM
340V
40.8A
Consider an application in which it is desired to
replace a phase-controlled rectifier system with a highquality rectifier. It is therefore required that the output
voltage be of variable and controllable magnitude, less
than the peak input line-to-line voltage. Any of the
approaches of Fig. 3 could be employed in this
application; the buck topology of Fig. 3(a) is the
simplest. The single-switch converters of Figs. 6-8
could also be employed. Let us compare the buckderived single-switch rectifiers of Figs. 7 and 8 with
the six-switch buck rectifier of Fig. 3(a).
The active switch blocking voltages and peak
currents of the single-switch ZCS quasi-resonant buck
rectifier (Fig. 7) and six-switch CCM buck rectifier
(Fig. 3(a)) are compared in Tables 1 and 2, for a 25kW
application [15]. The input voltage is 440Vac, and the
load voltage and current are 370V and 67.5A,
Table 4. Comparison of total active switch stress
Total stress
Silicon utilization
multiresonant
53kVA
0.113
6-switch PWM
83kVA
0.072
The single-switch multiresonant rectifier of Fig. 8
is compared with the six-switch buck rectifier of Fig.
3(a) in Tables 3 and 4. The ac input voltage is 240V,
and the load is 147V at 6kW - 0.6kW. The
multiresonant approach has the disadvantage of
increased peak switch voltage stress (by a factor of
approximately two); nonetheless, the total stress and
silicon utilization are superior to the six-switch
approach. The multiresonant rectifier exhibits the
advantages of (1) non-pulsating input currents, (2) very
low input current THD (less than 4% has been
demonstrated [17]), and zero voltage switching of all
diodes.
Table 1. Comparison of per-switch stresses, singleswitch ZCS vs. six-switch PWM approaches
Voltage
Peak current
ZCS rectifier
622V
100A
6-switch PWM
622V
46A
5. Conclusions
Three-phase high-quality rectifiers can be derived
from known dc-dc converter topologies. As a result,
rectifiers sharing the properties of their parent dc-dc
converters can be derived, including buck, boost, and
Table 2. Comparison of total active switch stress
Total stress
Silicon utilization
ZCS rectifier
62.2kVA
0.4
6-switch PWM
171.7kVA
0.14
5
Electronics Specialists Conference, 1989 Record,
pp. 58-66.
buck-boost conversion ratios, as well as highfrequency transformer isolation. Both single-switch and
six-switch 3ø inputs can be obtained. The singleswitch approach utilizes the active semiconductor
devices more effectively. Zero current switching of the
active semiconductor devices, and zero voltage
switching of diodes, can be obtained.
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Robert W. Erickson received the B.S., M.S., and
Ph.D. degrees from the California Institute of
Technology, Pasadena, CA, U.S.A., in 1978, 1980,
and 1982, respectively. He then joined the Department
of Electrical and Computer Engineering at the
University of Colorado, Boulder, U.S.A., where he
currently holds the rank of Associate Professor. He is
the author of numerous conference and journal papers,
as well as the soon-to-be-published textbook
Fundamentals of Power Electronics.
6