Highlights of the Chapter 4
1. The current-doubler rectifier can be used to double the load capability of isolated dc – dc converters with bipolar secondaryside voltage. Some industry-generated papers recommend its use for applications of over 25 A load if natural cooling is used,
or over 100 A load if additional cooling units, as discussed in Section 1.3, are used. The center-tapped secondary is replaced by
a winding in a single-ended configuration, rendering the structure of the transformer simpler. Two filter inductors are used ,
leading to a better distribution of the heat dissipation, what it is beneficial in densely packed power supplies. The secondary
winding , as well as each one of the two inductors carry only half of the load current, leading to less copper loss in the
secondary. The diodes carry all the load current, similar to the case of full-wave center-tapped or diode bridge rectifiers. A
current-mode control , for example of peak-current type , has to be used for keeping equal the average values of the two output
inductors currents. Due to the interleaving operation of the two output inductors, a ripple cancellation appears in the output
current, what causes a reduced ripple in the output voltage, allowing for the choice of a smaller value for the output capacitor.
The designed value of the transformer turns ratio influences the designed value of the duty-cycle, and thus the ripple
cancellation effect. A higher turns ratio Np : Ns will produce a greater degree of ripple cancellation. Less ripple in the output
current also results in lower noise, and thus in lower emission of radiation at the converter output. Synchronous MOSFETs are
often used as rectifiers because the CDR is suited for low-voltage high load current applications. The synchronous rectifiers
can be driven from the PWM controller which commands the operation of the primary-side switches ,through a signal
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transformer . Or, each gate is driven by the voltage across the output inductor that is in the charging phase . A transformer is
used between the inductor and gate to limit the gate signal to maximum ± 20 V . in addition to the need for two output
inductors, the CDR comes with one more penalty, either in a much higher current stress the primary-side switches are
subjected to, or , for keeping the same primary-side current stress as in full-wave rectifiers, output inductors of much larger
value have to be used. The idea can be extended to a current-tripler, and even to a current-multiplier rectifier, suitable for very
high load currents, low output voltage applications, by using a n-winding configuration high-frequency transformer, n
inductors , each one carrying 1 ∕ n of the load, and n synchronous MOSFETs. This structure presents the best thermal
distribution, it can deliver more current under a same thermal limitation.
2. The voltage multiplier/ divider rectifier is a circuit formed by capacitors and diodes or synchronous MOSFETs. Its purpose is
to step-up / step-down many times the input voltage .It can be used as a secondary stage of an isolation transformer in which
the secondary voltage is a bipolar waveform. Or, it can be used as an independent circuit in a non-isolated structure. The
voltage multiplier (also called charge-pump) and divider have many applications in electronics as open-loop (unregulated)
circuits. We are here interested only in their application in power supplies. The voltage multiplier can be inserted as the
rectifier in a dc-dc converter in which the primary switches are controlled by a PWM chip, or an equivalent control. Or , the
voltage multiplier/ divider can be inserted in the structure of a non-isolated converter of boost, respectively buck type, to get a
large dc gain. Or, switched-capacitor dc power supplies have been developed. In all these output-loaded , line and load
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regulated converters, the actual output voltage is lower than the voltage the multiplier could provide in a no-load, nonregulated structure. The actual value of the output voltage depends on its ripple. The conduction losses due to the parasitic
resistances of the capacitors ( which are not charged at saturation ) and forward voltages of the diodes further reduce the value
of the dc load voltage. The number of stages of a voltage multiplier/divider can not be made as large as we’d like, because
each subsequent capacitor-diode cell adds less to the output voltage than the preceding one. Voltage doublers , triplers and
quadruplers are quite used. To get a large dc conversion ratio, it is preferred to use such a simple electronic circuit than a
transformer with a very large winding turns ratio, that would have a very low efficiency. Different arrangements of the
capacitors and diodes have been proposed : full-wave voltage doublers, Greinacher structures, Cockcroft-Walton multipliers,
etc. Their characteristics are quite similar. Following the energy conservation principle, at a given input power, a
multiplication of the load voltage implies a corresponding reduction in the load current. From all the possible capacitor-switch
configurations , the Fibonacci converter presents the highest dc conversion ratio for a given number of components. For a
given number of capacitors, n , the output capacitor excluded, the maximum attainable ideal dc gain is given by the nth
Fibonacci number of the series 1, 2 , 3, 5, 8, …, Nn , where Nn is given by the formula N n  N n2  N n1 ( n = 0,1,2,3,4….).
However, its components are submitted to unequal voltage and current stresses.
3. Quadratic converters can be obtained by cascading two basic converters , applying simple manipulations on the elements, and
replacing the transistor of one of the converters by a passive switch, such that to be able to obtain the same voltage conversion
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ratio for the new power supply as that of the cascaded converters. The advantage of quadratic converters is that they offer the
same large step-down or step-up of the input voltage as that realized in a converters cascade, but by using a single active
switch, rendering thus unnecessary the driving and control circuit of the second transistor. Even if the diodes are replaced by
synchronous MOSFETs , it is still more economic to have a single externally controlled switch in a quadratic converter than
two in a cascade of two converters. A buck quadratic converter can be seen as a cascade of a “passive buck structure” and a
regular (active) buck one. A dependence of the dc voltage gain on the square of the duty-cycle is obtained. A dependence on a
higher power of the duty-cycle can be realized in a power supply containing more cascaded passive buck structures and a
regular (active) buck converter. Or, in another structure, the passive buck structure can be followed by a buck-boost converter.
A quadratic buck-boost converter operating with a duty-cycle of less than 0.5 can also be seen as formed by a “passive buckboost structure” and a regular buck-boost converter.
4. For the applications requiring a load voltage within the range of the input voltage, we can use converters like buck-boost, Ćuk ,
SEPIC or Zeta , with a dc gain
D
that can be smaller or larger than 1, depending on the value of D. However, all these
1 D
converters present no direct path of line-to-load energy transfer. Thus, there is a penalty in the components stress and
inductor energy storage requirement compared to the buck and boost converters that feature a direct line-to-load energy
transfer in one of their switching topologies. By interleaving a boost switching stage with a buck one, in any desired order,
two-switch buck-boost converters are obtained . A controller can be designed in such a way as to assure the operation of the
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converter in either the boost or in buck mode, according to the requirements imposed by the actual line voltage and the
imposed output voltage. In the boost operation mode, one of the transistors is maintained in conduction in all the switching
stages. In the buck operation mode, one of the transistors is turned off in all the switching stages. Due to the increased count of
elements, the two-switch converter is more expensive than the classical boost converter. However, in both operation modes of
the two-switch converter, there is one switching stage featuring a direct line to load path, thus minimizing the amount of
indirect transferred energy and , consequently, the inductor storage energy requirement. Another two-switch buck-boost
converter can be obtained by inserting a Z-source network, formed by two inductors and two capacitors in a double Z form
connection, in a switching structure. A circuit of similar complexity with the precedent one is obtained, however featuring a
very pulsating input current. According to the values of the duty-cycle of the two transistors ,determined by the controller, the
Z-source converter acts like a buck or like a boost converter. It presents a switching stage where direct line-to-load energy
transfer takes place. The input source and load have a common ground. The output voltage has the same polarity as the input
voltage, i.e. different from the basic buck-boost converter, the Z-source buck-boost converter has a non-inverting character. All
the switches carry large currents, due to the additional charging and discharging of the passive elements in the Z-source
network. In order to compare the voltage stresses the switches are submitted to with those in their counterparts in a buck-boost
converter, the formulas in Table 4.1 have to be calculated for the actual values of the input and output voltages in the given
application.
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5. An other class of non-isolated converters with large dc gain can be obtained by integrating any one of the classical converters
(buck ,boost, buck-boost, Ćuk ,Sepic ,Zeta) with some new defined switched-capacitor and switched-inductor cells. Such cells
, formed by two capacitors and two or three diodes, or two inductors and two or three diodes, can be used either for steppingdown or for stepping-up the voltage. For each category, three possible cells have been identified. There is duality between the
two categories of cells. For the step-down cells, their capacitors/inductors have to be charged in series in one of the two
switching stages from the source, or generally from the left-side part of the converter, and discharged in parallel to the load, or
generally to the right side part of the converter in the other switching stage. For the step-up cells, their capacitors/inductors
have to be charged in parallel in one of the two switching stages, and discharged in series in the other switching stage .Table
4.2 shows the possibilities of integrating the switched cells with the classical converters. The new converters contain a single
active switch. The integration of the cell is possible only for those converters in which the on-off operation of the controlled
switch can determine a switched operation of the cell that gives the desired dc gain, i.e. either step-down or step-up of the
voltage. This family of converters can be compared with the quadratic converters from the point of view of their purpose,
complexity, switches stresses, and dc gain.
The KY converters allow to obtain a step-up voltage gain typical for a boost converter with a circuit of buck-like input and
output. These converters feature two important advantages over the boost converter or any other boost-type converter: a) their
control transfer function contains no right-half plane zero ; b) in both switching stages , there is a direct line-to-load energy
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transfer path, i.e. a part of the energy is never processed two times. There are first-order KY converters, containing a single cell
formed by two switches , a diode and an energy-transferring capacitor, and second-order KY converters, containing two such
cells. The transistors operate in anti-phase. The first-order KY structure can be seen as a two-switch converter, or as a buck
converter integrated with a simple switched-capacitor cell. The second-order KY converters can be operated with two different
PWM control strategies, yielding in a little different voltage gains and a little different voltage stresses on switches. The
disadvantages of the KY converter come from its higher elements count and its less dc voltage gain : the first-order KY circuit
has more elements than a classical boost converter, and the second-order KY structure has more elements than a cascade of
two boost converters.
The Watkins-Johnson converter, with a small elements count, offers a bipolar output voltage by controlling the duty-cycle in
either a range larger than 0.5 for positive load voltage, or less than 0.5 for negative load voltage. It presents a bidirectional
input current, so it suits only applications whose input source accepts a bidirectional flow of energy. By operating the
converter with a steady-state duty-cycle just a little larger than 0.5, an extremely low output voltage is obtained from a given
input voltage, what compares very favorably with a buck converter that would require in the same purpose an extreme low
duty-cycle.
6. The Sheppard-Taylor converter provides non-pulsating input and output currents, similar to the Ćuk converter. Compared to
the last one, the former presents a larger elements count : one more active switch and three more diodes. However, the
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Sheppard-Taylor converter has its additional benefits. When operated in CCM, its dc voltage conversion ratio is more sensible
to the variation of the duty-cycle. In the regulation process, a large variation in the input voltage requires only small changes in
the duty-cycle for keeping constant the output voltage. In universal line applications, this is a considerable benefit. In its
isolated version, the Sheppard-Taylor converter is more suitable for low-output voltage high-output current applications than
the isolated Ćuk converter : a) The capacitor in the secondary side of the Ćuk converter determines important conduction
losses in its ESR at high current ; b) The primary winding voltage in the Ćuk converter changes between a very high value in
the on-switching topology to a very low one in the off-switching topology for low load voltage. Consequently, the time for
core demagnetization becomes longer, decreasing the possible duration of the on-topology, i.e. limiting the maximum possible
value of the duty-cycle. The result is a limitation in the regulation capability. The Sheppard-Taylor converter contains no
secondary side capacitor ( however, it contains an additional secondary side diode, that is in conduction in the on-switching
topology) and its magnetizing circuit is independent from the output circuit. The magnetizing inductance is submitted only to
± the voltage across the energy-transferring capacitor. The Sheppard-Taylor converter can operate in CCM or in a few
discontinuous conduction modes : DICM with either discontinuous input inductor current or discontinuous output inductor
current, and DCVM. In all these cases, in both the isolated and non-isolated version, it is very suitable for PFC ac-dc
applications.
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7. There are many applications, for example in railway traction or power factor correction ac-dc rectifiers, where the supply
voltage can be at kilo-volts level, under several kilo-watts power. The four primary-side switches of a full-bridge converter
usually used in such cases must sustain the input voltage when they are turned off. So, transistors with a very high breakdown
voltage, and consequently a very large nominal on-resistance will be necessary, inducing important conduction losses. At
very large voltages, it is likely that we can not find on the market the necessary rated transistors, at the desired high switching
frequency. For reducing the rated voltage of the chosen transistors, it is possible to implement each switch by two series
transistors . However, such a solution will not only double the active switches ‘ count, but will necessitate a voltage-balancing
circuit to avoid dynamic imbalances due to the practical impossibility of finding 100% identical transistors. By rotating one leg
formed by two series switches of the full-bridge converter and connecting it in series with the other leg formed by two
switches , a new full-bridge-derived converter is obtained. Each leg is connected across a large input capacitor, the two series
input capacitors being connected across the input source. The mid-points of the two switch legs are connected to the highfrequency transformer primary winding. In the new structure, each primary-side switch has to sustain only half of the input
voltage when in off-state, so transistors with half breakdown voltage can be used. As the nominal dc resistance is proportional
to VBV
2.5 2.7
,even if the rms value of primary current is increased , this solution brings an important saving in conduction
losses, justifying the use of additional capacitors. An equivalent solution is offered by the three-level converters, where a
combination of capacitors and clamping diodes assures that the voltage across the switches in off-state is limited to half of the
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input voltage. The structure can be generalized to converters with Vin /3 voltage stress on the primary-side switches, by using
three legs of switches pairs , each one connected across an input capacitor, a transformer in Delta connection, and a current
tripler for the rectifier side. And it can be further generalized to a Vin /n voltage stress converter. As these converters operate
with soft-switching, they will be studied in detail in Vol. III.
The three-level boost converter is used in applications like single-phase PFC rectifiers where the output voltage is around 400
V or higher , and the power level can be multi-kilo watts. It contains three additional components compared with the basic
boost converter : one active switch, one diode, and one output capacitor. The increased elements’ count is economical viable in
such applications, because : a) the switches in off-state are submitted to a voltage equal to half of the required output voltage,
i.e. to a voltage stress that is half of that the switches are submitted to in a basic boost converter. This permits the choice of
switches with half voltage rating. b) for assuring the same input current ripple, the input inductor of the three-level boost
converter needs an inductance value four times smaller than that of its counterpart in the classical boost converter.
8.
By replacing the inductor in a basic converter with a tapped-inductor , new converters
with steep dc conversion ratio are obtained. The turns ratio of the magnetic element
introduces an extra degree of freedom in the design, as the dc gain of a tapped-inductor
converter depends on both duty cycle and turns ratio. By choosing the turns ratio at a
convenient value, it is possible to obtain the desired dc voltage gain without using
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extreme low or extreme large values for the duty-cycle. The tapped-inductor buck and
boost converters keep the simplicity and low components’ count of the basic buck and
boost converters, adding the advantage of steep dc gain. Also, they keep the presence of
one switching stage of direct line-to-load energy transfer. Depending on the component
which is connected to the tap of the inductor, there are three possible configurations :
diode-to-tap , active switch-to-tap and rail-to-tap . Any one of these three configurations
used in a buck converter allows for the realization of a very low output voltage with a
duty-cycle designed at a steady-state value that does not affect the efficiency and the
operation of the switch drive and controller. In particular, the rail-to-tap buck converter,
which is a Watkins-Johnson structure, found its way in automotive applications for
stepping the 48 V of the battery to 3 V required by the many electronic loads of the
modern vehicle . This was due to its low components’ count and good efficiency at kilowatts power level. The Watkins-Johnson structure makes use of a center-tapped inductor
( i.e. a tapped inductor with equal outer legs). However, the tapped-inductor solutions
have the disadvantage of ringing between the leakage inductance of the inductor and
parasitic capacitance of the switch at turn-off, what causes voltage overstress that could
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destroy the switch if not over-designed for the voltage peak. Clamping ( ZVS) solutions
can solve the problem. The tapped-inductor boost converter presents a right-half plane
zero in the small-signal control transfer function.
The voltage regulator modules are step-down dc-dc converters used as power supplies of
microprocessors. They have to feature a very steep dc voltage ratio, in order to provide
the low voltage required in this application. Their design is challenging, due to the
additional requirements, tougher with each year : very high output current, very small
steady-state output voltage ripple, very tight regulation during transients, quick transient
response at very large load changes. The VRMs operate with switching frequencies of
several MHz . Tapped-inductor synchronous buck converters are a solution at hand.
Soft-switching in non-isolated and isolated solutions improves the efficiency. Multiphase converters formed by parallel units operating with interleaving can provide better
performances. After learning more about the control of such systems in Vol. IV, we will
discuss the modern VRMs.
9.
Different more complex isolated converters have been developed for overcoming the
disadvantages of the classical topologies. However, in addition with more complexity,
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other limitations appear. The current-driven dual-bridge converter ,with six primary-side
switches and two large primary-side capacitors, alternates in each half-switching cycle
the operation between a full-bridge and a half-bridge converter. The input inductor is
center-tapped. Line to-load energy takes place in each switching stage, the input inductor
being alternatively charged and discharged according to the duty-cycle. The input
inductor is in the same circuit with the primary-reflected load in all the switching stages.
The converter presents a proportional dependence of the dc voltage gain on the dutycycle. The duty-cycle to load voltage ac small-signal transfer function exhibits no righthalf plane zero . A smaller input inductor than that required in a current-driven fullbridge converter is needed in order to assure the same input current ripple. This
characteristic provides a faster transient response. These advantages are mitigated by the
limited line regulation capability of the dual-bridge converter : the input voltage range
has to be limited to 2:1.
Several other solutions of more efficient isolated converters, with resonant voltage
clamping circuits and soft-switching, have been made available in the last years, as we
shall learn in Vol. III.
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