OWING TO THE growing concern regarding harmonic

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1 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 4, AUGUST Integrated High-Quality Rectifier Regulators Michael T. Madigan, Member, IEEE, Robert W. Erickson, Senior Member, IEEE, and Esam Hamid Ismail, Member, IEEE Abstract A new family of ac dc converters is derived which integrate the functions of low-harmonic rectification, low-frequency energy storage, and wide-bandwidth output voltage control into a single converter containing one, two, or four active switches. These converters utilize a discontinuous conduction mode input inductor, an internal energy storage capacitor, and transformer secondary circuits which resemble the bridge, forward, flyback, or Cúk dc dc converters. A large-signal equivalent circuit model for this family is presented, which uses the loss-free resistor concept. Design strategies and experimental results are given. High-performance regulation with satisfactory line-current harmonics is demonstrated with conventional duty-ratio control. Further improvements in line current are possible by simultaneous duty-ratio and switching-frequency control. Index Terms AC DC power conversion, boost integrated with flyback rectifier/energy storage/dc-dc converter, buck rectifier/energy storage/dc-dc converter, low-harmonic rectifiers, power-factor correction. Fig. 1. Single-phase power converter using a high-quality rectifier (HQR), energy storage capacitor, and a dc dc converter. I. INTRODUCTION OWING TO THE growing concern regarding harmonic pollution of the power distribution system, and the adoption of standards such as IEC [1], there is a need for single-phase power supplies with ac line currents that are low in harmonic content and have power factor close to unity. A typical costly system which allays these concerns, shown in Fig. 1, involves the addition of a second converter for input current waveshaping at the ac line side of a conventional switching power supply. In this paper, a new family of converters is introduced which inherently draw line-current waveforms of high quality. As depicted in Fig. 2, it is possible to construct a single converter, containing a single transistor, which performs all of the functions performed by the system of Fig. 1. Integrated high-quality rectifier/dc regulator (IHQRR) topologies based on the flyback, buck, and other dc dc converters are derived here, control strategies are developed, and the resulting systems are experimentally verified. The key to development of an IHQRR is the recognition that the low-frequency components of the input voltage the energy storage capacitor voltage and the load voltage must all be independent and, hence, the converter topology must possess sufficient degrees of freedom to allow these voltages to vary arbitrarily. Manuscript received October 25, 1997; revised January 14, Abstract published April 18, M. T. Madigan is with Unitrode Corporation, Cary, NC USA. R. W. Erickson is with the Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO USA. E. H. Ismail is with the Department of Electrical Engineering, College of Technological Studies, Al-Shaa b, Kuwait Publisher Item Identifier S (99) Fig. 2. Single-phase power converter using a single converter which has the integrated functions of high-quality rectification, capacitive energy storage, and the wide-bandwidth output voltage regulation (an IHQRR). There are two ways to accomplish this. First, we could place impedances between and which block the differences in the low-frequency components of these voltages. This is an undesirable approach because it requires large low-frequency reactances. The second approach is to place switching elements (highfrequency-switching transistors and/or diodes) between and, which block the difference in the low-frequency components of these voltages. This is the preferred approach. It requires that any network loop which contains at least two of the elements and also contain at least one diode or transistor. It is possible to construct such an IHQRR network which contains a loop comprised of a diode, and high-frequency reactive elements which filter only highfrequency switching harmonics, and which contains another loop comprised of a transistor, and high-frequency reactive elements. Once the required independence of and is obtained, then it is possible to cause the input line current to be proportional to the input line voltage. Two approaches are commonly used here. First, feedback can be used to force where is the rectifier emulated input resistance. Second, certain converters are known to naturally /99$ IEEE

2 750 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 4, AUGUST 1999 (a) (b) (c) Fig. 3. (a) Integration of a DCM boost rectifier with a flyback converter results in (b) a BIFRED. (c) Schematic of a BIFRED which includes the bridge rectifier and the high-frequency EMI filter. emulate a resistor, without active feedback. An example is the flyback and boost converters operating in discontinuous conduction mode (DCM) [2] [4]. II. DERIVATION OF TOPOLOGIES A. Boost Integrated with Flyback Rectifier/Energy Storage/DC DC Converter (BIFRED) At low power levels (100 W), a conventional approach is to use a boost converter for input current waveshaping, and a flyback dc dc converter for isolation and load voltage regulation. Hence, let us consider integration of a DCM boost HQR with a flyback dc dc converter, as shown in Fig. 3. To preserve the nature of the input stage, the converters must be combined in such a way that the input inductor operates independently in the DCM. The resulting IHQRR is called a BIFRED. To understand how this can be accomplished, let us examine the operation of the two-converter system in Fig. 3(a). Each switching period contains three subintervals. Assume that switches and are synchronized and that the flyback converter operates in continuous conduction mode. During the first subinterval, only switches and conduct. During this subinterval, the DCM boost HQR inductor is energized by the rectified line voltage through switch and coupled inductor is energized by energy storage capacitor through Load receives energy only from capacitor during this subinterval. During the second subinterval, only diodes and conduct. Energy storage capacitor receives all of the energy of through Inductor is completely deenergized at the end of this interval. Coupled inductor transfers some of its energy to the load and to filter capacitor through diode The third subinterval is initiated when diode becomes reverse biased by the input current reaching zero. Diode conducts only in this interval. The energy state of capacitor remains at a constant positive level. Coupled inductor continues to transfer some of its energy to the load and to filter capacitor through diode as in the second subinterval. Now, combine the two converters in Fig. 3(a) into one converter, containing a single switch. Inductor must be in series with diode in order to permit the input inductor to operate in DCM. Also, diode cannot be eliminated because the coupled inductor does not necessarily operate in DCM. Notice in Fig. 3(a) that switch has two network functions; it controls the energy flow into the primary of and it aids in balancing the volt seconds of Switch can be replaced with a conductor by connecting the energy storage capacitor in series with it and moving switch to the other side of diode Also, the polarity of the primary of coupled inductor must be reversed to preserve the states of diode during each interval. The result of combining the two converters in Fig. 3(a) is the IHQRR in Fig. 3(b), which is called a BIFRED. The BIFRED of Fig. 3(b) bears a resemblance to a Sepic converter [5]. The most obvious difference is a diode which is in series with the input inductor Diode permits the BIFRED to operate in modes which are not possible with a Sepic. As a result, the BIFRED is capable of simultaneous natural lowharmonic rectification, energy storage, and wide-bandwidth load regulation, while the dc dc Sepic is not. When the current in falls to zero, diode stops conducting, regardless of the energy state of the coupled inductor This permits to continue conducting and allows the energy level of coupled inductor to decrease. In contrast, when a Sepic converter operates in DCM, neither the input inductor nor the coupled inductor can change their stored energy levels during the discontinuous subinterval, as seen by [6]. Hence, a BIFRED has an independence of inductive

3 MADIGAN et al.: INTEGRATED HIGH-QUALITY RECTIFIER REGULATORS 751 Fig. 4. Schematic of a BIBRED, which includes the bridge rectifier and the high-frequency EMI filter. energy transfer which is not possible in a Sepic. The resulting differences in the line-current waveforms are demonstrated in Section V. B. Boost Integrated with a Buck Rectifier/Energy Storage/DC-DC Converter (BIBRED) The integration of a DCM boost HQR with a buck dc dc converter results in a BIBRED, as shown in Fig. 4. The synthesis procedure of this IHQRR is similar to the procedure for a BIFRED. Isolation can also be obtained, in a manner similar to that used for the dc dc Cúk converter [7]. The most obvious difference is diode, which is in series with The additional diode permits the BIBRED to operate in modes which are not possible with a Cúk converter, and the BIBRED is capable of simultaneous natural lowharmonic rectification, energy storage, and wide-bandwidth load regulation, while the dc dc Cúk converter is not. The additional diode of the BIBRED permits the input inductor current to remain at zero during the discontinuous subinterval, independent of the other reactive and capacitive states. In contrast, when a Cúk converter enters DCM, neither the input inductor nor the output inductor can change their energy levels during the discontinuous subinterval, as described by Cúk [8]. The resulting differences in the line-current waveforms are demonstrated in Section V. Other isolated BIBRED bridge topologies are also possible to derive as described in [9]. (a) III. DESIGN A. Modeling and Design of the BIFRED The modeling approach for the BIFRED converter is based on [2], [4], and [10]. The class of two-port lossless power processing networks are known as loss-free resistors (LFR s) [11], and have been found to be a useful artifice for modeling and understanding low-harmonic rectifier circuits. The dynamic models contain an LFR to model the rectification process, and a dc transformer network [12] to model the output dc dc conversion process of the network. The model is used to solve for the quiescent operating point, determine DCM boundaries, and derive converter design equations. Design of the BIFRED in Fig. 3(c) begins with ensuring the correct mode of operation, throughout the complete range of instantaneous line voltage. Relevant currents and voltages of network elements and are demonstrated in Fig. 5(a). (b) Fig. 5. (a) Switching waveforms of various currents and voltages in the BIFRED of Fig. 3(c). (b) Large-signal nonlinear ac model of the BIFRED in Fig. 3(c). 1) DCM Definition: In the desired DCM, the switching cycle has three distinct intervals. During the first interval, only transistor and diode conduct. During the second interval, only diodes and conduct. During the third interval, only diode conducts. The motivation behind selecting this particular mode is to guarantee that the energy in inductor is depleted before the energy in the coupled inductor is depleted. If were depleted before in this topology, may stop conducting and will become dependent on, which prevents this converter from functioning as an IHQRR. With this choice of mode, one avoids this possibility by designing the converter such that never reaches the ground state.

4 752 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 4, AUGUST 1999 The first interval of the switching cycle starts when transistor turns on, causing the current in inductor to ramp up from zero with a slope which is proportional to the instantaneous line voltage. Diode conducts and diode is reverse biased. At the end of this interval, an amount of energy is stored in which depends only on the input line voltage and is independent of the currents and voltages of the other inductors and capacitors of the converter. The second interval is initiated when transistor turns off, which causes the current in to ramp down with a slope proportional to the instantaneous line voltage minus the energy storage capacitor voltage minus the output voltage reflected to the primary. Both diode and diode conduct. The third interval commences when the current in reaches zero. Transistor remains off, is reverse biased, and conducts. During this interval, the potential energy levels of and remain unchanged. Capacitor and the load receive energy from and passes energy to the load. 2) A Large-Signal Model: Averaging over one switching cycle [13], [14] provides an analytic perspective of the overall action of the BIFRED. The resulting large-signal equations are given in (1) (2) This equation implies that the input stage of the converter operates in the boost mode; the net voltage must be greater than the peak value of the ac line voltage. However, the energy storage capacitor voltage and the reflected load voltage may individually be less than 3) Steady-State Solution: Steady-state analysis can be performed by averaging the state equations over half of a line cycle. The nonlinear term must be averaged as a unit, since superposition does not apply to that term. Assuming that the duty cycle and the switching period are constant and neglecting the ripple of voltages and the high-frequency average state equations (2) (4) are again averaged over a line half-cycle to give the steady state equations in (8) (9) (10) Solution of the voltages and requires the average value of the nonlinear term to be solved using the large-signal description of the voltage A nonseparable transcendental equation in is formed by eliminating the current from (8) and (10) and performing the averaging integral over a line half cycle. The result is (3) where The equivalent resistance and the nonlinear ratios of voltages in (1), (2), and (4) are energy related and can be modeled using a loss-free resistor with a dependent power source [2], [4]. The power consumed by or appears at the power source such that the network is lossless. This power source is connected between the converter input port and the remainder of the converter, such that its applied voltage is Hence, the current passing through the power source is equal to the power divided by the voltage (6). Thus, the nonlinear terms which are in (1), (2), and (4) describe the current from this dependent power source with the voltage described in (6) impressed upon it. It must be stressed that the dependent power source is neither a pure voltage source nor a pure current source, and is inherently a nonlinear element. A comparison between the waveform of in Fig. 5(a) and the input stage of Fig. 5(b) reveal that, in steady state, (6) must always be positive to maintain volt-seconds balance on inductor, as shown in (4) (5) (6) (7) where and (11) Here, is the steady-state voltage conversion ratio of the effective boost input stage. The nonlinear relationship in (11) can be solved numerically for a specific case, or approximated for design by a ratio of a constant divided by a first-order polynomial as in (12) (13) (14) where Equations (12) (14) are accurate to within 10% over the range of between Accuracy can be improved with successive iterations of (11). The closedform (12) (14) approximate the steady-state solution of the capacitor voltages in a BIFRED.

5 MADIGAN et al.: INTEGRATED HIGH-QUALITY RECTIFIER REGULATORS 753 4) Mode Boundaries: Steady-state (9) and the waveforms of Fig. 5(a) can be used to formulate the inequality (15), which requires that inductor completely deenergize before the next switch cycle begins (15) Essentially, the second interval must always be less than the total switch period minus the duration of the first interval. The current waveform of in Fig. 5(a) relates the duration of the second interval with the capacitor voltages and the duration of the first interval. The length of the second interval is maximum when the instantaneous line voltage is at a maximum. The inequality in (15) describes the maximum duration for a given line-to-output transfer ratio which will allow the inductor to completely deenergize. Among the reasons to use the maximum duration is to reduce the rms currents in inductor Furthermore, the longer the first interval is relative to the second interval, the more resistive the BIFRED appears to the ac line. Equation (15) can be rearranged to the approximate form as in (16), which includes the conduction coefficient by the substitution of (14) (16) Equation (15) is used to solve for the duration of the first interval for a given turns ratio and a desired line-to-output ratio. Then, the inductance can be determined as a function of the previously given parameters, the switching period and the load resistance by use of (16) and the definition (11) of the conduction coefficient The dependence of the DCM boundaries on the value of inductor is more subtle than that of because current has large-signal variations during normal operation. These variations include a dc component and a twice-line-frequency component, the phase shift of which is 180 relative to the rectified line voltage. Since inductor and capacitor are chosen for filtering switching harmonics, and the switching frequency is much higher than twice the line frequency, and can be approximated as a short circuit and an open circuit, respectively. Solution of the resulting equivalent circuit yields (17) The current of the dependent power source in the equivalent circuit model in Fig. 5(b) can also be approximated as a function of known quantities as in (18) Since is a rectified sinusoid, varies between zero and some finite peak value. The minimum value of can now be estimated using (18) and the transfer ratio between and in (17). The transfer ratio of (17) reveals a dc gain which can be different from the high-frequency gain. When the steady-state duty ratio is less than 1/2, the high-frequency gain is lower than the dc gain. The converse is also true. Since is very large, the shift in gain and the associated phase shift of 180 occurs at frequencies which are much lower than twice the line frequency. Thus, current is essentially minus plus a dc offset current. Current must always be positive to prevent an unwanted DCM, and maintain diode in the conducting state during the second and third intervals. Hence, for operation in the correct mode, we require that the dc gain of (17) be greater than the high-frequency gain, or (19) The restriction in (19) is further limited when considering the exact minimum value of current The minimum value of is given by (20) and it can be exactly solved using techniques similar to those used to find (11) (20) Restrictions set by (19) and (20) neglect switching ripple because they are concerned with states which are averaged over a switch cycle. Equation (21) is an additional criterion which must be satisfied to prevent from completely deenergizing (21) Capacitor must not completely deenergize during normal operation. A transfer ratio can be formed between and, which leads to the lower limit for given in (22) where is the allowable proportion of ripple voltage in The limiting case for the smallest value of capacitor is when the proportion of ripple in voltage is one. Typically, capacitor will be much larger than this limit, in that the proportion of ripple in voltage may be indirectly specified in terms of a holdup time of several line cycles. Capacitor is chosen to meet a switching ripple specification which is a fraction of the dc output voltage, as in (23). Thus, capacitor cannot completely deenergize unless the low-frequency output ripple is inadvertently too large (23) where is the fraction of switching in In summary, a BIFRED can be designed for a given line voltage, turns ratio, switching frequency, energy storage ripple, output voltage ripple, and output voltage using the following steps. First, select using (15). The duty ratio must be

6 754 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 4, AUGUST 1999 less than 1/2 per (19). Select using (16). Internal voltages and are then calculated using (12) (14). The minimum current in is calculated using (20). Current must be positive for the design to be valid. Inductor is then selected using (21). Capacitors and are then selected to meet ripple specifications using (22) and (23), respectively. B. BIBRED and Other Topologies Design of a BIBRED, as well as other bridge topologies presented in [9], follows many of the steps as described in designing a BIFRED; limited space precludes a detailed description here. However, an equivalent circuit model for the BIBRED is described in [9], while a complete analysis of a full-bridge BIBRED is presented in [15]. IV. CONTROL A. Simple Duty-Ratio Control Scheme Duty-ratio variations result in variations in both the output voltage and the line current. The voltage conversion ratio between the energy storage capacitor and load and, hence, also the output voltage, is proportional to the duty ratio in (14). The line current is a function of equivalent resistance which, in turn, is a function of the duty ratio, as seen in (1) and (5). Thus, duty ratio can be used to control output voltage or line current. This family of IHQRR s inherently produces line-current waveforms of low, but nonzero harmonic content, which, in most applications, can meet the harmonic limits in [1] without additional active control. Because of the low-frequency internal energy storage built into these converters, wide-bandwidth control of the output voltage is possible, without significantly degrading the line-current waveform quality. When the controller corrects for line harmonic disturbances in the output voltage, it affects line-current harmonics. This is because the line current is a function of duty ratio. Line-current distortion due to output voltage feedback can be minimized by increasing the size of the energy storage capacitor; in practice, however, such measures may be unnecessary. Laboratory results confirm that the total harmonic distortion of the line current for the closed-loop BIBRED is slightly lower than the total harmonic distortion during open-loop operation (21% compared to 19%). Thus, in this specific case, the output voltage feedback has a minimal effect on the line-current harmonic content. Regulation of output voltage using duty-ratio adjustments is also a method for controlling DCM flyback HQR s [2]. However, the bandwidth of the IHQRR is much greater than the bandwidth of the simple HQR. This is because, in an IHQRR, the load is separated from the internal energy storage capacitor by reactive devices and semiconductor switching devices. To confirm this, output voltage regulation of a BIBRED and a DCM flyback HQR using duty-ratio control is demonstrated in Fig. 6, which shows the response of each of these converters to a sudden shift in load resistance. It is instructive to compare the response in Fig. 6 with that of a DCM flyback HQR under similar conditions [2]. The response time of the BIBRED is (a) (b) Fig. 6. Comparison of 2 : 1 load current transient response with output voltage duty ratio control. (a) BIBRED, 10-kHz crossover frequency. (b) DCM flyback HQR, 3.5-Hz crossover frequency. Fig. 7. Block diagram of a variable switching period, fixed duty ratio modulator to reduce line-current harmonics. many times faster than the DCM flyback HQR. The closedloop bandwidth of the BIBRED is approximately 10 khz, compared to a bandwidth of 3.5 Hz for the DCM flyback HQR.

7 MADIGAN et al.: INTEGRATED HIGH-QUALITY RECTIFIER REGULATORS 755 TABLE I PARAMETER VALUES OF THE EXPERIMENTAL 40-W RECTIFIERS (a) (b) Fig. 8. Measured line voltage and current waveforms for 40-W BIFRED. (a) Open loop. (b) Using the switching frequency controller of Fig. 7. B. Simultaneous Duty-Ratio and Switching-Frequency Control Returning to the nonlinear large-signal state equations in (1), consider It is rearranged in (24) to demonstrate the effects of variations in (24) Fig. 9. Experimental switching frequency waveforms of the BIFRED described in Fig. 3(c) and Table I. These waveforms verify the mode of operation. where is given in (5). Incidentally, has the same form in both the BIFRED and the BIBRED topologies. If is proportional to then the IHQRR presents a linear purely resistive load to the ac line. It can be seen that one method of eliminating harmonics in the line current is to vary such that it cancels the denominator of (24). Furthermore, the denominator of (24) is positive and less than one. Therefore, can be appropriately adjusted by variations in either duty cycle or switching period or a combination of both. A modulator which can independently vary the switching frequency and the duty cycle was constructed per the block diagram in Fig. 7, using an analog multiplier and a voltage controlled oscillator. Comparison of Fig. 8(a) and (b) reveals that line harmonics can be further reduced by use of the scheme described above. Fig. 8(a) shows the line current of a 40-W BIFRED operating open loop with a fixed switching frequency and a fixed duty cycle. The total harmonic distortion of the line current in Fig. 8(a) is approximately 20%. Fig. 8(b) is the line current of the same 40-W BIFRED, operating with a variable switching period which is adjusted to correct line harmonics. The total harmonic distortion of the line current in Fig. 8(b) is approximately 4%. It is possible to use both duty-ratio adjustments and switchperiod adjustments to simultaneously regulate the output voltage and control the line-current harmonics. Equation (14) shows that the output voltage is directly proportional to duty ratio and a function of the switching period through Under the condition of the inequality in (25), it is found that the output voltage is not sensitive to changes in the switching

8 756 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 4, AUGUST 1999 (a) (b) (c) (d) Fig. 10. Comparison of the line-current waveforms of (a) BIFRED, (b) Sepic converter, (c) BIBRED, and (d) Cúk converter. period (25) However, the line current is proportional to the switching period. Thus, it is possible to regulate the output voltage with the duty cycle and reduce line harmonics with switch frequency variations. Phase control is a third method of control which can be used by the full-bridge BIBRED. Reference [15] addresses this issue in more detail. V. EXPERIMENTAL RESULTS A 40-W BIFRED and a 40-W BIBRED were designed and implemented to operate from a 110-V line to produce 20- output voltage. The schematic for the BIFRED is given in Fig. 3(c), while the schematic for the BIBRED is given in Fig. 4. The component values are given in Table I. These values were chosen to assure that the modes of each IHQRR are the same as the modes which are described in Section III. Switching waveforms of the BIFRED are shown in Fig. 9. These waveforms depict currents and near the peak of the line voltage. At that instant, the magnetizing current of is at a minimum, nonzero value, as discussed in Section III-A-4. The experimental waveforms agree with those of Fig. 5(a). Thus, the BIFRED operates in the desired mode. Comparable waveforms are also found for the BIBRED. Inductor of the BIBRED begins and ends each switch cycle at ground state, and it is the only reactive component in the BIBRED to do so. The switching waveforms of Fig. 9 demonstrate the difference between a BIFRED and a Sepic converter; the energy level of inductor in a BIFRED returns to ground state, even though the magnetizing inductance maintains a level of energy. Fig. 10(a) and (b) demonstrates the resulting difference in the line current of a BIFRED and a Sepic converter. The maximum current level in inductor of the Sepic converter was reached at a line voltage of 50 V and an output voltage of 8.8 V Under these conditions, the Sepic converter operates in continuous conduction mode. It can be seen that

9 MADIGAN et al.: INTEGRATED HIGH-QUALITY RECTIFIER REGULATORS 757 the BIFRED emulates a resistive load, while the Sepic linecurrent waveform resembles peak detection. These waveforms are not qualitatively changed when the Sepic operates in its DCM. Fig. 10(c) and (d) shows a similar comparison between a BIBRED and a Cúk converter. For this demonstration, the Sepic and Cúk converters were constructed simply by shorting diode in the respective BIFRED and BIBRED. The slow bridge rectifier diodes do not switch in the same manner as, owing to the presence of input filter elements and and, hence, the circuit input behavior is radically different. In the Sepic and Cúk converters, peak detection occurs because inductor is small in value, and has small impedance at the line frequency. As a result, the low-frequency component of voltage across is very small. The remaining components, i.e., the energy storage capacitor and the four ac rectifier diodes, operate as a peak detection circuit. In the BIBRED and BIFRED, diode is able to support the lowfrequency components of the voltage difference between the energy capacitor voltage and the rectified line voltage, such that peak detection need not occur. Thus, it has been demonstrated that the BIFRED and BIBRED naturally yield low-harmonic line-current waveforms which are distinctly different from Sepic and Cúk converters. VI. CONCLUSION A new family of converters has beem presented in this paper which exhibit low-harmonic line currents, internal energy storage, and wide-bandwidth output voltage response. These converters are derived by the integration of a DCM boost converter, energy storage capacitor, and a cascaded dc dc converter. The function of the switches in each individual converter is examined under synchronized conditions, and redundant switch functions are integrated together. A valid integration preserves the low-frequency independence of the energy storage capacitor voltage. Steady-state and dynamic operation of this new family of IHQRR s were analyzed with large-signal LFR models [Fig. 5(b)]. This modeling technique preserves the large-signal nonlinearities which affect steady-state and ac operation. Moreover, a step-by-step design procedure example using the BIFRED topology was presented. The other topologies in this family can be designed in a similar manner, [15]. Output voltage regulation using duty-ratio variations and a fixed switching period is the simplest method of control. Experimental results demonstrate that it is possible for these converters to have fast response and low line-current harmonic content. The harmonic content of the line current is low enough to satisfy typical IEC specifications. Further reduction of line-current harmonics is possible with variable-switching-frequency control, as demonstrated in Fig. 8. The comparison of the BIBRED IHQRR with the DCM flyback HQR in Fig. 6 distinguishes this family as IHQRR s, rather than simple low-bandwidth HQR s. The comparison of the BIFRED and BIBRED line currents with the line currents of their respective dc dc Sepic and Cúk converter counterparts, in Fig. 10, distinguishes these IHQRR s from simple dc dc converters. REFERENCES [1] Electromagnetic Compatibility (EMC) Part 3: Limits Section II: Limits for Harmonic Current Emissions (Equipment Input Current 16A per Phase), IEC , 1st ed., [2] R. Erickson, M. Madigan, and S. Singer, Design of a simple highpower-factor rectifier based on the flyback converter, in Proc. IEEE APEC 90, 1990, pp [3] S. Freeland, Input current shaping for single-phase AC-DC power converters, Ph.D. dissertation, pt. II, Elect. Eng. Dep., California Inst. Technol., Pasadena, Oct [4] S. Singer and R. W. Erickson, Canonical modeling of power processing circuits based on the POPI concept, IEEE Trans. Power Electron., vol. 7, pp , Jan [5] R. P. Massey and E. C. Snyder, High voltage single-ended DC-DC converter, in Proc. IEEE PESC 77, 1977, pp [6] J. Sebastian, J. Uceda, J. A. Cobos, J. Aaru, and F. Aldana, Improving power factor correction in distributed power supply systems using PWM and ZCS-QR Sepic topologies, in Proc. IEEE PESC 91, 1991, pp [7] R. D. Middlebrook and S. Cúk, Isolation and multiple output extensions of a new optimum topology switching DC-DC converter, in Proc. IEEE PESC 78, 1978, pp [8] S. Cúk, Discontinuous inductor current mode in the optimum topology switching converter, in Proc. IEEE PESC 78, 1978, pp [9] M. Madigan, R. W. Erickson, and E. Ismail, Integrated high quality rectifier-regulators, in Proc. IEEE PESC 92, 1992, pp [10] S. Singer, Canonical approach to energy processing network synthesis, IEEE Trans. Circuits Syst., vol. CAS-33, pp , Aug [11], The application of loss-free resistors in power processing circuits, IEEE Trans. Power Electron., vol. 6, pp , Oct [12] R. D. Middlebrook and S. Cúk, A general unified approach to modeling switching-converter power stages, in Proc. IEEE PESC 76, 1976, pp [13] S. Cúk and R. D. Middlebrook, A general unified approach to modeling switching DC-DC converters in discontinuous conduction mode, in Proc. IEEE PESC 77, 1977, pp [14] R. W. Erickson, Large signals in switching converters, Part I: Distortion in switching amplifiers, Part II: Transients in switching regulators, Ph.D. dissertation, Elect. Eng. Dep., California Inst. Technol., Pasadena, Nov [15] M. A. Johnston and R. W. Erickson, Reduction of voltage stress in the full-bridge BIBRED by duty ratio and phase shift control, in Proc. IEEE APEC 94, 1994, pp Michael T. Madigan (S 75 M 77) received the B.S. degree from the University of Colorado, Denver, in 1977 and the M.S. and Ph.D. degrees from the University of Colorado, Boulder, in 1988 and 1992, respectively, all in electrical engineering. He is currently an Applications Engineer with Unitrode Corporation, Cary, NC. Between , he served as a Power Electronics Consultant to Sony, Unique Mobility, and Echostar. Between , he designed control systems and power electronics for industrial and aerospace companies, such as Martin-Marietta and Honeywell. His research interests include power processing topologies, modeling, and control.

10 758 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 46, NO. 4, AUGUST 1999 Robert W. Erickson (S 82 M 82 SM 97) received the B.S., M.S., and Ph.D. degrees from California Institute of Technology, Pasadena, in 1978, 1980, and 1983, respectively. In 1982, he joined the faculty of the University of Colorado, Boulder, where he is currently a Professor of Electrical and Computer Engineering. He is the author of Fundamentals of Power Electronics (New York: Chapman & Hall, 1997), as well as more than 50 papers in power electronics conference proceedings and journal transactions. He teaches courses in power electronics, energy conversion, circuits, and control. His current research interests include low-harmonic rectification technology, modeling of converter systems and power components, low-voltage converters, and wind energy systems. Prof. Erickson received an IEEE TRANSACTIONS ON POWER ELECTRONICS Prize Paper Award for Esam Hamid Ismail (S 84 M 85) was born in Kuwait in He received the B.S. and M.S. degrees in electrical engineering from the University of Dayton, Dayton, OH, in 1983 and 1985, respectively, and the Ph.D. degree from the University of Colorado, Boulder, in From 1985 to 1988, he was with the Electrical Engineering Department, College of Technological Studies, Al-Shaa b, Kuwait, where he is currently an Assistant Professor. His research interests include low-harmonic rectification, high-frequency power conversion, and the development of new converter topologies. Dr. Ismail is a member of Tau Beta Pi.