A Singlestage Isolated Bridgeless PFC Converter (patents pending) has a single isolation transformer, three switches, and 98% efficiency compared to four magnetic pieces, 14 switches, and 89% efficiency of the conventional Threestage approach.
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Another Isolated Bridgeless PFC converter (patents pending) with pulsating input current and based on a novel Hybridswitching method eliminates the frontend fullbridge rectifier, yet provides isolation in a Singlestage power processing, resulting in performance, size, and cost advantages over conventional Three stage, bridgetype PFC converters.
The singlestage isolated bridgeless PFC Converter with pulsating input current attains improved efficiency of over 98% (achievable with appropriate switching devices) compared to 89% of the Threestage approach, offering simultaneously significant size and cost reductions, while maintaining the near unity power factor of 0.999 and 1.7% total harmonic distortion. The singlestage converter uses just a single magnetic part (the isolation transformer) and three switches, compared with compared to four magnetic pieces and 14switches of the conventional Threestage approach. This pulsating version requires only a single resonant capacitor and no input inductor, when compared to the Isolated Bridgeless Converter presented in October 2010 issue of Power Electronics Technology.
The new nonisolated Bridgeless PFC converter with pulsating input current of Fig. 1a operates directly of the ac line and without the need for a FullBridge rectifier in front. Despite the use of a resonant inductor and a resonant capacitor, thanks to the novel hybridswitching method, the DC voltage gain depends on the duty ratio only and NOT on resonant component values or the load current. Furthermore, the converter's DC voltage gain is the same for either positive input voltage or negative input voltage. Hence, it provides automatic ac line rectification, without the need for a bridge rectifier.
Although the converter topology resembles that of conventional flyback converter, its voltage gain characteristics in the operating stepup region is entirely different and not the flyback converter type with DC voltage gain of D/ (1D), but instead of the boost converter type with DC voltage gain 1/(1D).
The isolated version of the converter is obtained simply by replacing replacing a single inductance L in converter of Fig. 1a with a twowinding isolation transformer with NP:NS turns ratio, as illustrated in the SingleStage Isolated Bridgeless PFC converter Fig. 1b. The duty ratio control of the power stage with the help of Bridgeless PFC IC Controller and high frequency input filter shown in Fig. 1b results in clean sinusoidal input current drawn in phase with sinusoidal input line voltage and proportional to it, resulting in unity power factor. The measured power factor on experimental 400W prototype was 0.999 for 110V ac, 60Hz line.
BRIDGELESS PFC CONVERTER OPERATION
A very clear objective to increase the efficiency is to devise a converter, which can eliminate a frontend fullbridge rectifier. Past attempts failed to eliminate diodebridge rectifiers, leading to the belief that the solution to such a goal may be “impossible” and that such converter topology could not exist. This is shown to be no longer the case as the July and August issues of Power Electronics Technology demonstrated a nonisolated True Bridgeless PFC converter and the October issue introduced an Isolated Bridgeless PFC converter based on it. Here, another True Bridgeless PFC converter topology (nonisolated and isolated ones ) is introduced which is even simpler, such as the pulsating input current converter topology of Fig. 1a.
This converter topology comprises only three switches: one controllable switch S and two passive current rectifier switches CR1 and CR2 as seen in Fig. 1a, which turnON and turnOFF in response to the state of the main controlling switch S for either positive or negative polarity of the input ac voltage.
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Thus, switch S alone controls both diode switches, whose states are changed automatically according to the polarity of the ac input voltage. For example, for the positive polarity of the ac input voltage, current rectifier CR1 conducts during the ONtime interval of switch S. Then, for negative polarity of ac input voltage, the same current rectifier CR1 conducts during the OFFtime interval of switch S. The current rectifier CR2 also responds automatically to the state of the switch S and polarity of the input ac voltage. For the positive polarity it conducts during the OFFtime interval of switch S and for negative polarity, it conducts during the ONtime interval of switch S.
Thus, the three switches operate at all times, for both positive and negative halfcycles of the input ac line voltage. Hence, this true Bridgeless PFC converter^{™} operates without the fullbridge rectifier, since the converter topology itself performs an implied ac line rectification to result in DC output voltage for either polarity of input ac line voltage. Eliminating the fullbridge rectifier directly eliminates large losses, especially for the low line of 85V.
As seen in Fig. 1a, this topology also consists of the floating energy transferring capacitor Cr, which acts as a resonant capacitor for the part of the switching cycle, and a resonant inductor Lr and an isolation transformer.
VOLTAGE STRESSES OF THE SWITCHES
The ACDC converter shown in Fig. 1a when operated from a positive halfcycle of sinusoidal ac line voltage is well represented with a DCDC converter shown in Fig. 2a. The corresponding converter models for ONtime interval (Fig. 2b) and for OFFtime interval (Fig. 2c) directly result in the voltage stresses of three switches as:
V_{CR1} = V_{CR2} = V_{S} = V (1)
where V is the output DC voltage, since from Fig. 2c:
V_{g} + V_{Cr} = V (2)
The relationship (1) is graphically shown on Fig. 2d as a straight line with relative gain of 1, to illustrate the important advantage of this topology that all three switches have for any operating duty ratio the same voltage stress equal to the output voltage V. This should be, for example, compared with the voltage stresses for the flyback converter. Although the flyback converter has two switches only, each of the switches has at 50% duty ratio the voltage stress equal to twice the output DC voltage.
Therefore, if the flyback converter were used for an ACDC converter with V=400V output, it would need switches rated at 1200V, as opposed to 600V rated switches in the converter of Fig. 1a. However, the 1200V rated switch (in this case, IXYS' IXTH12N1200 switch in a TO247 package), exhibits 1.4Ω ONresistance and 280pF draintosource capacitance. By comparison, the bestinclass 600V rated device in the same TO247 package, the IPW66R037C6 from Infineon, exhibits a 37mΩ ONresistance and 130pF draintosource capacitance.
Note that this configuration achieves almost a 40 times a reduction in ONresistance and corresponding reduced conduction losses, and more than 2 times reduced draintosource capacitance for reduced switching losses as well. This clearly makes the flyback converter much less efficient than the new converter topology of Fig. 1a. When it is also recognized that the conventional flyback converter cannot be used without frontend bridge rectifier for ACDC conversion, the efficiency gap becomes even much bigger.
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DETAILED ANALYSIS
Operation from Positive Input Voltage
First, we analyze the operation of the converter in Fig. 3a in which the input voltage source is positive dc voltage and having the switch states as in Fig. 3b. The linear switched network for ONtime interval is shown in Fig. 3c and linear switched network for OFFtime interval is shown in Fig. 3d. To simplify the analysis, we will assume that the inductor L is very large, resulting in a constant input dc current I with negligible ac ripple current.
Flux Balance of Two Inductors and DC Voltage Gain
The Voltsecond (flux balance) on inductor L requires that for the steadystate, the positive and negative areas of the voltage waveform in Fig. 4a must be equal so that:
V_{g}DT_{S} = V_{Cr} (1D)T_{S} (3)
where:
V_{g} = input voltage
D = Duty ratio
T_{s} = Switching period in seconds
V_{Cr}= DC voltage on the resonant capacitor
Unlike the PWM inductor, L, which was flux balanced over the entire switching period Ts, the resonant inductor Lr must be fully flux balanced during the ONtime interval only as seen in Fig. 4b. Thus applying the steadystate criteria for the resonant inductor Lr in the loop consisting of Vg, Cr, Lr and V results in:
Vg + V_{Cr} V = 0 (4)
as the resonant inductor must be fluxbalanced and cannot support any net DC voltage.
Solving (3) and (4) results in;
V_{Cr} = V_{g} D / (1D) (5)
V = V_{g} 1/ (1D) (6)
Note that the dc conversion ratio given by Equation (6) is the same as for wellknown boost converter. Furthermore, despite the resonant circuit consisting of resonant capacitor Cr and resonant inductor Lr, and corresponding sinusoidal and cosinusoidal time domain waveforms of resonant current and resonant capacitor voltage, the dc conversion ratio does not depend on either one of them and their values or the switching period T_{s}, but only depends on the operating duty ratio, D, as in conventional PWM dcdc converters. Hence, the regular duty ratio control can be employed to use this converter as a basis for PFC control as in boost and other conventional converters.
The resonant inductor current ir during entire switching period is shown in Fig. 5a, while the resonant capacitor voltage shown in Fig. 5b displays the linear charging of the resonant capacitor Cr during the OFFtime interval. Note also the continuity of the capacitor voltage at the transition between two switching intervals.
Operation from Negative Input Voltage
Next, we analyze the operation of the converter in Fig. 6a, in which the input voltage source is negative polarity dc voltage and having the switch states as in Fig. 6b. Fig. 6cshows the linear switched networks for ONtime interval, while Fig. 6d shows the linear switched network for the OFFtime interval.
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Flux (Voltsecond) Balance of Two Inductors and DC voltage Gain
We now use the two linear switched networks in Fig. 6c and Fig. 6d to construct the time domain of the current in the PWM inductor L and in the resonant inductor Lr. The voltage waveform on inductor L is shown in Fig. 7a to be just as in conventional PWM squarewave switching converters, while the resonant capacitor V_{cr} voltage is illustrated in Fig. 7b only for ONtime resonant interval and its complete time domain waveform in Fig. 8b.
The Voltsecond (flux) balance on inductor L requires that for the steadystate, the positive and negative areas of the voltage waveforms in Fig. 7a must be equal so that:
V_{g}DT_{S} = (V  V_{Cr} ) (1D)T_{S} (7)
Unlike the PWM inductor, which was flux balanced over the entire period T_{s}, the resonant inductor must be fully fluxbalanced during the ONtime interval only as per converter model of Fig. 6c, in which the loop consisting of Vg, Cr, and Lr forms the resonant circuit model. From which:
Vg  V_{Cr} = 0 (8)
Solving (7) and (8) results in:
V_{Cr} = Vg (9)
V = Vg 1/ (1D) (10)
Therefore, despite different DC voltages on the resonant capacitor Cr for positive input voltage (D/ (1D)) and for negative input voltage (input DC voltage Vg), the DC conversion ratios are identical for positive and negative polarity input voltages as shown by (6) and (10).
As before, the resonant current ir charging capacitor Cr is limited to only a positive cycle of resonant current as current rectifier CR2 now permits conduction in only one direction as in Fig. 8a. As the resonant current starts at zero level, this effectively restricts the resonant charge interval once again to exactly onehalf of the resonant period, the same as for positive input voltage.
The waveforms over the complete period for resonant inductor current ir(t) and resonant capacitor voltage vCr(t) are illustrated in Fig. 8a and Fig. 8b. Note how the continuity of the voltage on resonant capacitor results in the same ac ripple voltage Δvr at the transition between two intervals. Once again, the resonant capacitor dc voltage is now different and equal to dc input voltage Vg. Thus, the same dc voltage gain is obtained despite drastically different steadystate values of dc voltage on capacitor Cr The final resonant circuit model for both positive input voltage and for negative input voltage are identical and illustrated in Fig. 9.
RESONANT CIRCUIT ANALYSIS
As seen above, operation of the converter from positive input voltage and negative input voltage results in the same resonant circuit model, which results in the following solution:
i_{r}(t) = I_{P} sin(ω_{r}t) (11)
v_{Cr} (t) = Δv_{r} cos(ω_{r}t) (12)
Δv_{r} = I_{P} R_{N} (13)
R_{N} = √ L_{r} /C_{r} (14)
Ω_{r} = 1/√L_{r}C_{r} (15)
f_{r} = ω_{r} /(2 π) (16)
where RN is the natural resistance, fr is the resonant frequency and ωr radial frequency.
The Bridgeless PFC converter of Fig. 1a has one controlling switch S. From the description of the converter operation for positive and negative output voltages, it is clear that this switch S must have a twoquadrant switching characteristic operating in the first and third quadrant as illustrated in Fig. 10a. In other words, switch S must for positive input voltage operate in first quadrant, but should also be able to sustain a full reverse voltage (third quadrant operation). Clearly, neither bipolar nor MOSFET transistors can do that as they are not designed to sustain voltage in the third quadrant (MOSFET due to presence of the body diode). However, the Reverse Blocking Isolated Gate Bipolar Transistor (RBIGBT) can sustain the full reverse voltage as it is designed to do so and can sustain the full voltage of opposing polarity. Therefore, the switch S implementation of Fig. 10b uses two such RBIGBT devices in parallel.
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Yet, in many practical applications the MOSFET implementation is desired due to high switching frequency capability and low conduction losses. At present, a single MOSFET implementation is not possible due to builtin bodydiode, so that switch S must be implemented by use of the two MOSFET devices connected backtoback in series as shown in Fig. 11a by using two nchannel MOSFET devices, S1 and S2, connected at their sources and driven by a common floating gate drive circuit. Such an implementation results in full fourquadrant switch capability as shown in Fig. 11b, which is not required for converter operation as the twoquadrant of Fig. 10a is sufficient.
It is expected that a single firstthird quadrant switch having the characteristics of Fig. 10a will be produced as a planar nchannel MOSFET in which twoquadrant operation comes naturally from the semiconductor device construction. This will dramatically reduce the conduction losses of the switch S by a factor of four times or more, since such two nchannel devices could be connected in parallel and not in series. As conduction losses are the converter's biggest losses by far, such a switch implementation could push the converter's efficiency over 98% in the near future.
The current direction in the resonant inductor is changing from one direction in OFFtime interval to another in ONtime interval. This shortduration change could cause the voltage spikes on the switch S  the faster the change, the larger the voltage spike. But due to small energy stored in this small inductor, this spike can be effectively suppressed by use of a Zener diode. Since the converter operates for both polarities of the input voltage, a bidirectional Zener diode, called Transorber, is used to dissipate all of the spike energy and limit the spike voltage. This, once again would dissipate all of the spike energy and limit the spike voltage. However, several nondissipative ways also can be employed to recover most of the energy contained and deliver it to the load, thus increasing the efficiency and reducing switch stresses during the transition.
DCDC CONVERTER CONTROL
Duty ratio control with constant switching frequency
We now describe one of the possible control methods of the dcdc converter in Fig. 3a using the constant switching frequency and variable duty ratio control. The converter prototype was built to verify operation and record the characteristic waveforms for three operating duty ratios: D=0.5 (Fig. 12a), D= 0.66 (Fig. 12b) and D= 0.8 (Fig. 12c) resulting in output voltages of 18.1V, 28.6V, and 56V respectively, for the 10V input. The measurements were made at a constant 0.5A load current. The four traces show, from top to bottom: draintosource voltage of the controlling switch S, input source current, output load current and inductor L current.
Note how the input current (second trace) consists of the sum of resonant inductor Lr current (third trace) and inductor L current (fourth trace) thus confirming the fundamental relationships of the converter in Fig. 3a:
i_{g} = i_{r} + i_{L} (17)
i_{0} = i_{r} (18)
Note also from (18) that the output current is identical to the resonant inductor current and therefore it has both the same shape and duration for all three operating cases and is therefore not changing, but has the same shape and magnitude as for 50% duty ratio. Therefore, the input current shape and magnitude are changing so that the DC current conversion ratio is changed, which ultimately results in corresponding change in the DC voltage conversion ratios. This is qualitatively different from the conventional boost converter operation, in which the high duty ratios result in shorter duration of the pulse delivery of the load current (at 0.9 duty ratio it would be 10% of the period). In this example, the delivery of the load current is always at 50% of the constant switching period.
In this case, the resonant interval is designed to coincide with the 50% duty ratio so that the time variation of the inductor L current at that operating point is hidden and not explicitly seen (Fig. 12a) as it is in the waveforms of Fig. 12b and Fig. 12c for duty ratios higher than 50%.
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Constant ONtimeinterval and variable OFFtime interval control
The converter prototype is then operated with constant ONtime and variable OFFtime control and the characteristic waveforms for three effective operating duty ratios are recorded: D=0.5 (Fig. 13a), D= 0.66 (Fig. 13b) and D= 0.8 (Fig. 13c) resulting in output voltages of 19.3V, 28.8V and 45V, respectively for the 10V input voltage. The measurements were made at a constant 0.5A load current. The four traces show from top to bottom: draintosource voltage of the controlling switch S, input source current, output load current and inductor L current.
Note how for higher duty ratios, both input current and output current are conducting for almost the entire interval, resulting in quasicontinuous input and output currents. The output current also has reduced peak values of the resonant currents and will require minimum output capacitance to filter this nearly continuous output current.
TWO DCDC CONVERTERS IN ONE
Voltage gains (6) and (10) derived so far are really representing dc voltage gain only for the converter in Fig. 3a for the duty ratios D higher than the resonant duty ratio DR
that is:
V/Vg = 1/ (1D) for D > D_{R} (19)
D_{R} = T_{R} / 2T_{S} (20)
T_{R} = 1/fr (21)
and (20 and (21) are definitions of the two quantities DR and T_{R}. The voltage conversion ratio for duty ratios lower than D_{R} can be evaluated using the extension of the StateSpace Averaging Method (1,2) introduced in (3) is outside of the scope of this article. Nevertheless, the following analytical results is obtained:
V/Vg = D/ (1D) D_{R} for D < D_{R} (22)
Note how the DC voltage gain (22) for D=DR changes into formula for DC conversion given by (19). As DR is simply a design constant, the overall dc voltage gain of the converter in Fig. 3a changes form the stepdown/stepup conversion given by (22) for low duty ratios to stepup only voltage gain given by (19) for higher duty ratios with a continuous smooth transition at duty ratio DR. This results in two converters in one, as shown in the composite voltage gain in Fig. 14.
Therefore the dcdc converter of Fig. 3a solves two problems which were plaguing conventional boost and buckboost converters:

boost converter due to its boost voltage gain 1/(1D) in its nonisolated version did not have a soft start, and just the opposite had a high inrush input current so that additional circuit needed to be employed to reduce inrush currents. In the isolated case, separate circuitry is needed to charge the capacitor on the output to the input voltage so that the converter could be started.

buckboost (flyback) converter has a stepdown/stepup dc voltage gain so that a soft start is provided without any additional circuitry for both nonisolated and isolated versions. On the other hand, as shown earlier, the buckboost converter causes very high voltage stresses on its two switching devices several times that of the output DC voltage.
The dc converter of Fig. 3a, however, combines the best features of both boost and flyback converters and simultaneously eliminates their bad properties such that:

voltage stresses of all switches are equal to output dc voltage under all operating conditions

softstart is provided with voltage dc gain having characteristic of stepdown/stepup dc voltage gain in the low duty ration region.
It is easy to verify that the above properties are also present in the dcdc converter with the negative dc input voltage, so that the above advantages will be also present if the bridgeless acdc converters of Fig. 1a and Fig. 1b. These converters also allow operation directly of the ac line and eliminate the bridge rectifier, unlike conventional boost and flyback converters.
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PFC Conversion Function
The equality of the dc conversion gains as a function of duty ratio D of the controlling switch S proven above is one important prerequisite for a converter to operate as a SingleStage acdc (Bridgeless) converter with PFC function.
Another factor is that both DC conversion gains are having a stepup dc gain characteristic which is another prerequisite needed for the converter topology to qualify as SingleStage acdc (Bridgeless) converter topology. This therefore establishes that the converter of Fig. 1b is able to operate as a singlestage (bridgeless) acdc PFC converter.
In a departure from previous attempts at bridgeless PFC conversion, all three switches, inductor L, resonant inductor Lr, and resonant capacitor Cr are 100% utilized as they take part in PFC operation for both positive as well as negative part of input line ac voltage.
The Power Factor Correction is based on controlling the average input current of the converters in Fig. 1b to become proportional and in phase to the input ac line voltage by use of the Bridgeless PFC IC controller. Thus, the duty ratio modulation is used to control average input current of the acdc switching converter of Fig. 1b, since it was demonstrated that such a duty ratio control is effective in controlling the converter for either positive or negative parts of the ac line voltage. The PFC control operates in two modes:

Duty ratio modulation with constant switching frequency.

Constant ONtime and variable OFF time and therefore, variable switching frequency.
LOOKING AHEAD
The fourth in a series of “impossible” converter solutions, The Bidirectional Isolated Stepup Converter, will be introduced in the January 2011 issue of Power Electronics Technology. This converter, shown in Fig. 15, comprisesthree MOSFET switches and two magnetic components. It has a bidirectional power flow capability to convert input low battery voltage VL (14V32V) to high output battery voltage VH (270V) and vice versa.
Editorial Note: For questions regarding this article and for contact information to the author the readers are directed to TESLAcoís Web site www.teslaco.com.
Footnote: Isolated Bridgeless PFC Converter^{™} and SingleStage Isolated PFC Converter^{™} are trademarks of TESLAco.
REFERENCES

Slobodan Cuk, “Modelling, Analysis and Design of Switching Converters”, PhD thesis, November 1976, California Institute of Technology, Pasadena, California, USA.

Slobodan Cuk, R.D. Middlebrook, “Advances in SwitchedMode Power Conversion”, Vol. 1, II, and III, TESLAco 1981 and 1983.

Slobodan Cuk, “StateSpace Averaging: Past, Present and Future”. Invited paper, APEC Power Electronics Conference, Fort Worth, Texas, March 6, 2011.
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