Title: Analysis and design of isolated flyback voltage‐multiplier converter for low‐voltage input and high‐voltage output applications
Abstract: IET Power ElectronicsVolume 6, Issue 6 p. 1100-1110 ArticleFree Access Analysis and design of isolated flyback voltage-multiplier converter for low-voltage input and high-voltage output applications Zhang Zhiguo, Corresponding Author Zhang Zhiguo [email protected] State Key Laboratory of Transmission & Distribution Equipment and Power System Safety and New Technology, Chongqing, 400030 People's Republic of ChinaSearch for more papers by this authorZhou Lin, Zhou Lin State Key Laboratory of Transmission & Distribution Equipment and Power System Safety and New Technology, Chongqing, 400030 People's Republic of ChinaSearch for more papers by this author Zhang Zhiguo, Corresponding Author Zhang Zhiguo [email protected] State Key Laboratory of Transmission & Distribution Equipment and Power System Safety and New Technology, Chongqing, 400030 People's Republic of ChinaSearch for more papers by this authorZhou Lin, Zhou Lin State Key Laboratory of Transmission & Distribution Equipment and Power System Safety and New Technology, Chongqing, 400030 People's Republic of ChinaSearch for more papers by this author First published: 01 July 2013 https://doi.org/10.1049/iet-pel.2012.0552Citations: 19AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract An isolated flyback voltage-multiplier (VM) converter is presented in this study in light of the basic line frequency voltage-multiplying rectifier. The proposed circuit with a high conversion ratio operates in discontinuous conduction mode and combines the merits of the VM with flyback converters. It is very suitable to be used in low-voltage input and high-voltage output applications where compact size and a high conversion ratio are needed. The operations and prominent characteristics of the circuit are described, and the dynamic and steady-state transfer function of the output-voltage/input-voltage is also derived. A laboratory prototype has been built based on the analysis. The validity of analysis for this circuit is verified by experimental results. 1 Introduction High-voltage dc power supplies are widely used in many fields [1] such as industry, military and medical applications. There are several challenging issues related to the design of such a power supply where a set-up transformer is needed, because the large turn ratio of the transformer exacerbates transformer non-idealities [2]. Firstly, the leakage inductance of the transformer causes undesired voltage spikes that may damage circuit components. Secondly, the stray capacitance may result in current spikes and long rise time. These non-idealities can lead to greatly increased switching, snubber losses, low efficiency and reliabilities. Therefore stray capacitance and leakage inductance of the transformer are crucial to the design of high-voltage power supply because of larger parasitic elements that may degrade its performance. The converter with high step-up voltage gain is generally demanded in some applications, where the input voltage and output voltage are, respectively, several ten volts input and multi-kilovolts. The characteristics of this converter are shown as follows: (a) ultra high-voltage conversion ratio (100–200); (b) low power and compact size; (c) wide input voltage range; and (d) simple implementation and isolation. Among the existing methods of producing high-output voltage, the use of voltage multipliers in low frequency rectifiers, especially the half-wave Cockcroft-Walton voltage multipliers (H-W C-W VM) is a classical solution. The first design of a VM was introduced by H. Greinacher in 1919. Since then, many more have been presented based on a great variant of choices interconnecting capacitors and diodes [3-9]. As is known, these structures can produce an output voltage higher than the input voltage without the use of magnetic elements. Certainly, this technique also can be used in high-frequency isolated dc–dc converters, mainly for high output voltage (kV) applications, reducing the problems presented by the high frequency and high-voltage power transformers [7]. Each one of them provides different ideal voltage gain. However, there is a voltage drop and a peak-to-peak voltage ripple when the circuit is loaded [8]. It is very difficult to keep the output voltage constant when the input voltage and load vary widely. Some researchers developed VM topologies to improve their performance by high frequency switches [10-12]. For example, the voltage gain of the circuit proposed in [10] may be arbitrarily large in proportion to the number of capacitors, and Prudente et al.[11] had introduced the use of the voltage multiplier applied to non-isolated dc–dc converter in order to reduce the maximum switch voltage stress. However, these circuits are not suitable to the applications which require electrical isolation between input ports and output ports. Another example is that high set-up ratio converters are able to interface low-voltage high-current energy sources with the utility grid, and the flyback converter with an active clamp at the transformer primary side and a voltage multiplier at the transformer secondary side was presented in [12] to reduce the circulating current during the active clamp operation and thus increase the overall efficiency for this converter. Another attractive alternative for high-voltage dc applications is the use of a series or parallel resonant converter (PRC) in which the transformer non-idealities are incorporated into the basic operation of the circuits. The series resonant converter (SRC) becomes uncontrollable while operating at light load. Moreover, the stray capacitance is not integrated into the resonant tank in the SRC [13, 14]. The PRC is difficult to control when load and input voltage vary widely [15, 16]. To resolve these problems, the hybrid series-PRC (SPRC) with three or more resonant elements has been proposed [17-20] where it combines the advantages of SRC and PRC. Meanwhile, parasitic parameters of the transformer are fully utilised in this converter. Although resonant converters have many virtues, they are usually controlled by variation of the switching frequency where optimisation of the filter components in such wide frequency range is difficult. Besides they generally are used in high power high-voltage applications. The voltage lift technique [21-23] is another method to design high-voltage gain converter and its output voltage increases stage by stage. Multi-inductors are needed in these circuits in order to attain high-voltage gain. As we know, the presence of an inductor is a serious drawback because the output filter inductor can become a large and expensive component in high-voltage applications. Another possible means of high-voltage low power supply application is flyback converter for its simplicity of topology. However, higher output voltage is seldom directly generated by the flyback topology as it needs the larger turn ratio of the transformer which may lead to larger leakage energy and high-voltage stress etc. Therefore the multi-resonant flyback converter topology [24] is used to reduce power losses in the power supplies for space instruments which require high-voltage but very little power. As is typical of resonant circuits, the voltage levels and hence power losses, are very sensitive to circuit parameters. Small changes in the resonant frequency can cause large voltage variations. In this paper, an alternative for implementation of high step-up structures is proposed with the use of the voltage multiplier cells integrated with classical flyback converters operated in the PWM method. The use of voltage multipliers in flyback converters adds some new operation characteristics, becoming the resultant structure well suited to produce low-voltage input and high-voltage output power supply in embedded applications. In particular, it is preferable to operate in discontinued conduction modes where it can be applied to the compact-size high-voltage output power supply when its load is small. The rest of the paper is arranged as follows: Section 2 presents the proposed flyback voltage-multiplier converter and its work principle of operation. The characteristics of steady state and dynamic state for this circuit are investigated, respectively, in Sections 3 and 4. Section 5 contains the experimental results and analysis. Finally, Section 6 provides a brief conclusion. 2 Flyback voltage-multiplier converters 2.1 Conventional voltage-multiplier circuit The voltage-multiplier circuit initially proposed by Greinacher, Cockcroft and Walton is used widely in high-voltage power supply applications. An m-order voltage-multiplier is sketched in Fig. 1. Fig. 1Open in figure viewerPowerPoint Conventional voltage-multiplier rectifier It is excited with a line frequency ac power of source voltage vi(t) = Um sin(ωt). This circuit without any load ideally does not show any ripple or voltage drop in the output voltage waveforms. In this condition, the output dc voltage is defined by (1)With heavy load, however, the output dc voltage is distorted and shows a voltage drop ΔV0 and ripple 2δV. Assume that every stage capacitance is equal: , the voltage drop ΔV0 and the ripple 2δV are defined as follows [8] (2) (3)It's obviously impossible to keep the output voltage constant for this circuit with the change for the input voltage or the load resistance R. 2.2 Flyback voltage-multiplier converters It is natural to think that the flyback converter can be applied in the voltage-multiplying rectifier after the above discussions. The topology of the flyback voltage-multiplier converter for m-order is illustrated in Fig. 2. This converter employs the PWM control method. The transformer T is virtually a coupled inductor with two windings, which was also called flyback transformer. The m-order voltage-multiplier sub-circuit is constructed by the capacitors C2i+2(i = 0, 1, …, m) and the diodes D2i+2(i = 0, 1, …, m). Fig. 2Open in figure viewerPowerPoint Isolated flyback voltage-multiplier converters for m-order The operation principle of the flyback voltage-multiplier will be described as follows: the switch Q conducts, the input voltage source VI is applied to the transformer primary winding, which causes an increase of the transformer magnetising current. The voltage value of the secondary winding is equal to VI, multiplied by the turn ratio n:1. Meanwhile diodes D2i+1 (i = 0, 1, …, m) become forward-biased and capacitors C2i+1 (i = 0, 1, …, m) are charged, whereas diodes D2i+2 (i = 0, 1, …, m) are reverse-biased. When the switch Q is in the off-state, the magnetising current must flow out of the secondary winding, diodes D2i+1 (i = 0, 1, …, m) are reverse-biased, diodes D2i+2 (i = 0, 1, …, m) are conducted and capacitors C2i+2 (i = 0, 1, …, m) are charged. In a switching period, the energy stored in the transformer is transmitted to the secondary side in turn-off state for switch Q, which is similar to the flyback converter. Combining both the virtues of voltage-multiplier and flyback converter, this converter is therefore named flyback voltage-multiplier converters. Although this topology is somewhat similar to the conventional voltage-multiplier circuit, the essences of the flyback voltage-multiplier converter are much different. The differences are The flyback voltage-multiplier converter is able to keep the output voltage constant when the load resistance and input voltage vary, since a switching transistor is introduced and it provides a new degree of freedom for control. This transformer operating in the high frequency state is different from the line frequency transformer, and it practically functions as an inductor with two windings. During the off-state for Q, the capacitors C2i+2 (i = 0, 1, …, m) are charged by the transformer secondary winding virtually as a current source. The value of output voltage is due to the energy stored in the transformer, not the turn ratio of the transformer. 3 Steady-state analysis of the flyback voltage-mutiplier converter 3.1 Discontinuous conduction mode Fig. 3 shows the operation waveforms of flyback voltage-multiplier converters. vds, iLp and iLs represent, respectively, the drain–source voltage of Q, the primary side current and secondary side current of the transformer T. To simplify the analysis for the steady-state operation, it is assumed that all the components and devices are ideal and the capacitance for C2i+1 (i = 0, 1, …, m) is large enough. Therefore the voltages across these capacitors are constant when the converter remains in the steady-state operation. A detailed description for this converter in DCM is followed in Fig. 4. Fig. 3Open in figure viewerPowerPoint Waveforms of voltage-multiplier forward-flyback converters operating in dcm Fig. 4Open in figure viewerPowerPoint Equivalent circuits of each operation stages a Mode I b Mode II c Mode III Mode I: The switch Q conducts, for t0 ≤ t < t1, Let d1T = t1 − t0, the primary-side current of the transformer increases linearly. The diodes D2i+1 (i = 0, 1, …, m) become conducted and the diodes D2m are reverse-biased. The capacitors are discharged to the load resistor. This converter reduces to the network of Fig. 4a. The primary side voltage of the transformer and the voltage of the capacitor C2i+1 (i = 0, 1, …, m) are given by (4)Consider the capacitors C2, C4, …, and C2m as a virtual capacitor C and its charging current iC is shown as Fig. 5. The charging current iC can be expressed in the following form in this interval (5) Fig. 5Open in figure viewerPowerPoint Virtual capacitor C for capacitors C2i (i = 1, 2, …, m) The current for this subinterval is given by (6)In the steady state for this circuit, the currents through the diodes D1, 1D3, …, D2m+1 are all zero (7)Substituting (7) into (6), we can obtain the following equation (8)Mode II: The switch Q begins to turn off, the diodes D2i+1 (i = 0, 1, …, m) become reverse-biased and the diodes C2i+2 (i = 0, 1, …, m) conduct during the second subinterval, t1 ≤ t < t2, d2T = t2 − t1. The energy stored in the transformer is discharged to the capacitors C2i+2 (i = 0, 1, …, m) and the load resistor through the diodes D2i+2 (i = 0, 1, …, m). The primary side voltage of the transformer and the voltage of these capacitors are given by (9)The currents of the virtual capacitors C for this subinterval are given by (10)From Fig. 4b, we can obtain (11)Hence, we can obtain (12)Mode III: During the third subinterval, t2 ≤ t < T, all the power semiconductor devices in this converter are in the off state, and Fig. 4c is obtained. The equations are (13) (14)Therefore in steady state the integral of the applied primary winding voltage of transformer T must be zero (15)A similar argument can be applied to the capacitors C2i+2 (i = 0, 1, …, m), or the virtual capacitor C. Therefore in equilibrium the integral of the virtual capacitor current over one switching period should be zero (Fig. 5). (16)By consolidating and simplifying (15) and (16), we can reach the conclusions as follows (17) (18) (19) (20)where (21)The condition for this converter operating in DCM must be satisfied (22)With (23)If the load power is very small, the load resistance R is rather large. Furthermore, the switching frequency fs = 1/Ts and the value of transformer parameters are finite or constant whereas the converter has been constructed completely. Hence, parameter K is much less than 1 in the DCM. That is to say (24)Simplifying (19) with the condition for (24), we can obtain (25). (25)It can be inferred from (25) that the output-to-input transfer function for steady state includes two parts. The first term ‘(mn/2)’ shows a similar characteristic to the conventional voltage-multiplier rectifier; the second one ‘’ is similar to that of the flyback converter in DCM. When the load power is small, this converter is capable of producing high voltage with lower number of winding turns. It is contributed to reduce leakage inductance, cost and size of the transformer. 3.2 Continuous conduction mode (CCM) If (22) is not satisfied, this circuit operates in CCM, only including two intervals, t0 − t1 and t1 − T. Fig. 6 shows the waveforms of flyback voltage-multiplier converters in CCM. During the first interval t0 − t1, this circuit resembles Fig. 4a. During the second interval t1 − T, it resembles Fig. 4b. Similar arguments can be applied in the two intervals. Fig. 6Open in figure viewerPowerPoint Waveforms of flyback voltage-multiplier converters operating in CCM Application of the principle of voltage-second balance to the primary-side magnetising inductances yields (26)Application of the principle of charge balance to the output capacitors C2i+2 (i = 0, 1, …, m) (27)From (26), we can obtain (28)Equation (28) also includes two parts. The first term shows the virtues of VMs, and the second term indicates the features of flyback converters. 4 Dynamic modelling and control design 4.1 Small-signal model derivation in DCM In order to understand the advantage of the voltage-multiplier converter and design control loop, precise small signal model is indispensable. The remove averaging analysis has been investigated on many different types of PWM converters. In this section, we extend this approach to the flyback voltage-multiplier converter. To simplify the analysis, it is assumed that the output capacitor Ci (i = 1, 2, …, 2m + 2) is large enough that the output voltage vo can be approximated to be constant. A second assumption is that the circuit losses are negligible. Under these conditions, the flyback voltage-multiplier converter can be viewed as a piecewise linear system. Since the merits of the flyback voltage-multiplier in DCM are very attractive, its small signal ac models are needed. We employ average switch modelling [25] to derive its equivalent circuit model. The current of transformer T1 in Fig. 4 is equal to zero at the beginning of each switching period. During the first subinterval (t0 ≤ t < t1), the primary side current iLp increases with a slope of vI/Lp. At the end of the first subinterval, the current iLp reaches the peak value given by (29)During the second subinterval (t1 ≤ t < t2), while the diodes (D2i+2, i = 0, 1, …, m) conduct, the secondary side current iLs decreases with a slope equal to (vo/nm–vI). The second subinterval ends when the diodes become reverse-biased, at time t = (d1 + d2)Ts. The current of transformer T1 then remains zero for the balance of the switching period, and still is zero in the third subinterval (t2 ≤ t < Ts). The average primary side winding voltage 〈vLp〉Ts is founded by (30)A similar analysis leads to the following expression for the current of the virtual capacitor C discussed above (31)One approach to finding the subinterval length d2 is by solving the current waveforms of transformer T1. There is no net change in the current of transformer T1 over one complete switching period, and no net volt-seconds are applied to transformer T1 over any complete switching period. Therefore the average voltage 〈vLp〉Ts computed over this period is zero (32)Then the second subinterval length d2 is derived as (33)By substitution of (29) and (33) into (31), we can obtain a simple expression for the average current 〈ic(t)〉Ts of virtual capacitor C. (34) Equation (34) can be expressed in the following form (35)Expansion of function (35) in a three-dimensional Taylor series about the quiescent operating point leads to (36)By equating the dc terms on both sides of (36), we obtain (37)The high-order non-linear terms are discarded, leaving the following first-order linear ac terms (38)where (39)Hence, the line-to-output transfer function Gvi(s) is obtained by letting d(s) = 0 in (38). Solution for vo then leads to (40)with (41)This line-to-output transfer function describes how variation and disturbance in the applied input voltage leads to the output voltage vo(t). The control-to-output transfer function Gvd(s) is found by setting the input voltage variations vi(s) to zero, and then solving (38) for vo(s) as a function of d(s) (42)This transfer function describes how control variation d(s) influences the output voltage vo(s). 4.2 Control loop considerations In order to achieve proper stability margins and dynamic closed-loop performances, the design flow of an analogue controller for dc–dc power converters usually requires knowledge of its control-to-output transfer function. In design approaches for a digital controller, many scholars have conducted a lot of research work and discovered some research results [26-28]. In consideration of complexity and cost in the experiment, an analogue controller is employed in this paper. The influence of the voltage multiplier in converter dynamic is analysed with the small-signal frequency response. The analysis is useful for the controller design in order to attain transient and steady-state control specifications. To understand the control scheme applied in the voltage-multiplier regulation system well, its control block is proposed as shown in Fig. 7, where an analogue voltage-mode controller is depicted. The output voltage vo(t) is measured, using a sensor with gain H(s). The sensor is composed of two resistors (R1 and R2) in series. The sensor output signal is compared with a reference voltage vref(s). Our objective is to make H(s) × vo(s) equal to vref(s), so that vo(s) can accurately follow vref(s) regardless of disturbance or component variations in the compensator, pulse width modulator, gate driver or converter power stage. If the feedback system works perfectly, then the error signal ve(s) is zero. In practice, the error signal is usually non-zero but nonetheless small. Obtaining a small error is one of the objectives in adding a compensator network Gc(s) as shown in Fig. 7b. Fig. 7Open in figure viewerPowerPoint Control loop for flyback voltage-multiplier converter a Feedback loop block diagram b Functional block diagram From Fig. 7b, we can find the output voltage variation vo(s) (43)Let us define the loop gain T(s) as the small signal open-loop gain in the forward and feedback paths of feedback loop. Equation (43) can be written in the form (44)where (45)It is found that this transfer function from a disturbance to the output is multiplied by the factor 1/(1 + T(s)). Hence, when the loop gain T(s) is large in magnitude, then the influence of disturbances on the output voltage is small. A large loop gain also causes the output voltage vo(s) to be equal to vref(s)/H(s). Hence, the loop gain magnitude ||T(s)|| is a measure of how well the feedback system works. All these gains can be easily constructed using the algebra-on-the-graph method. The parameters of the control loop design are listed in Table 1. The loop gains and phases of the transfer function T(s) for both before and after the compensation are plotted in Fig. 8, where the PI compensator transfer function Gc(s) is given by (46) Table 1. Parameters for control loop T(s) VI 15 V Kcrt 0.5 VO 3500 V Vm 4 m 2 Lp 20 μH n 11 Ts 25 μs D 0.2 R 1.75 MΩ R1:R2 1400: 1 M Vo/VI C 0.047/m A 100 Fig. 8Open in figure viewerPowerPoint Bode plots of the loop gain transfer function T(s) without compensator and with PI compensator The PI compensator network is designed to attain adequate phase margin and increase the low-frequency open-loop gain. This leads to better rejection of low-frequency disturbances and very small steady-state error. From Fig. 8, we can find that the phase margin of the loop gain T(s) is approximately equal to 75° at the crossover frequency fc = 2 kHz. 5 Experiment verification A prototype for two-order flyback voltage-multiplier converters example illustrated in Fig. 9 was built in order to validate the above analysis. The design goal is followed as: the normal input voltage is at about 15 V, the output voltage is at the range of 3500 V ± 100 V, the load current is not higher than 2 mA. Fig. 10 is the prototype of two-order flyback voltage-multiplier converters. The main devices of this circuit are listed in Table 2. Table 2. Parameters of two-order flyback voltage-multiplier converters Name Denomination Value MOSFET Q 600 V/11 A (SPI11N60C3) diodes D1 3 kV/1 A (three US1M in series) D2 D3 D4 capacitor C1 ceramic multilayer capacitor, 3 kV/1 A C2 C3 C4 switching frequency — 40 kHz transformer T core PC40P18/11 airgap 0.2 mm primary inductance 20 μH primary leakage inductance 0.6 μH turn ratio 9:99 load R 1.75 MΩ/5 kV Fig. 9Open in figure viewerPowerPoint Two-order flyback voltage-multiplier converters Fig. 10Open in figure viewerPowerPoint Prototype of two-order flyback voltage-multiplier converters Fig. 11 shows the gate drive voltage waveform Qg and primary winding current waveform iLp. The primary current waveform iLp indicates that the converter operates in discontinuous conduction mode. Fig. 12 shows the waveforms for the input voltage and the output voltage when the converter is in steady state and load current is 2 mA. It can be seen from Fig. 12a that the ratio of output-to-input voltage is as high as 233 V, with the input voltage 15 V and the output voltage 3470 V. The output voltage ripple is shown in Fig. 12b. Fig. 11Open in figure viewerPowerPoint Driving waveforms of the switch and primary current Fig. 12Open in figure viewerPowerPoint Input and output voltages waveforms a DC waveforms of input and output voltages b Output voltage ripple The voltage waveforms for C1–C4 are illustrated, respectively, in Figs. 13a–d. The voltage value across capacitor C1 is about 210 V when the converter is in steady state, whereas the theoretical value calculated by (12) is 165 V. The difference between the experiment result and theory analysis value is induced by neglecting the leakage inductance of the transformer. The voltage values for C2, C3 and C4 are approximately 1.740 kV in steady state. The experimental results for C2, C3 and C4 coincide with the theory analysis. Fig. 13Open in figure viewerPowerPoint Voltages waveforms of the capacitors a Voltage across capacitor C1 b Voltage across capacitor C2 c Voltage across capacitor C3 d Voltage across capacitor C4 The dynamic waveforms of output voltage are shown in Figs. 14 and 15. Fig. 14 presents the output voltage waveform when the load current varies from 2 mA (full load) to zero (no load), and Fig. 15 presents the output voltage waveform when the load current varies from zero to 2 mA. The load current is indicated by the voltage of a high-precision resistance (1 kΩ) which is in series with load resistance, as Figs. 14 and 15, respectively, show. Fig. 14Open in figure viewerPowerPoint Output voltage waveforms for the load current step from full load to no load Fig. 15Open in figure viewerPowerPoint Output voltage waveforms for the load current step from no load to full load 6 Conclusion The flyback voltage-multiplier converter proposed in this paper combines the merits of the voltage-multiplier with the flyback converter. The critical condition at the boundary between the discontinued conduction mode and the continued mode was deduced. The converter that operates in DCM has advantages as follow: The winding turn number of the transformer was so small that the leakage inductance and winding capacitance were negligible. This converter can be used in high-voltage power supply applications with compact size. The voltage stress of the primary-side main transistor is rather lower than in the flyback converter. It is capable of keeping the output voltage constant when the input voltage and load resistance greatly vary. The prototype validates the characteristic of this converter which is suitable to be used for constructing high output voltage power supply with low load power and wide range of input voltage. 7 References 1Iannello C., Luo S.G., and Batarseh I.: ‘Full bridge ZCS PWM converter for high-voltage high-power applications’, IEEE Trans. Aerosp. Electron. Syst., 2002, 38, (2), pp. 515– 526 (doi: http://doi.org/10.1109/TAES.2002.1008983) 2Johnson S.D., Witulski A.F., and Erickson R.W.: ‘Comparison of resonant topologies in high-voltage DC applications’, IEEE Trans. Aerosp. Electron. Syst., 1988, 24, (3), pp. 263– 274 (doi: http://doi.org/10.1109/7.192094) 3Bellar M.D., Watanabe H., and Mesquita A.C.: ‘Analysis of the dynamic and steady-state performance of Cockcroft–Walton cascade rectifiers’, IEEE Trans. Power Electron., 1992, 7, (3), pp. 526– 534 (doi: http://doi.org/10.1109/63.145140) 4Lamantia A., Maranesi P.G., and Radrizzani L.: ‘Small-signal model of the Cockcroft–Walton voltage multiplier’, IEEE Trans. Power Electron., 1994, 9, (1), pp. 18– 25 (doi: http://doi.org/10.1109/63.285489) 5Malesani L., and Piovan R.: ‘Theoretical performance of the capacitor diode voltage multiplier fed by a current source’, IEEE Trans. Power Electron., 1993, 8, (2), pp. 147– 155 (doi: http://doi.org/10.1109/63.223966) 6Franko L.C., Pfitscher L.L., and Gules R.: ‘ A new high static gain non-isolated DC-DC converter’. Proc. IEEE 34th Annual Power Electronics Specialist Conf., Sao Leopoldo, Brazil, June 2003, pp. 1367– 1372 7Gules R., and Barbi I.: ‘Isolated dc–dc converters with high-output voltage for TWTA telecommunication satellite applications’, IEEE Trans. Power Electron., 2003, 18, (4), pp. 975– 984 (doi: http://doi.org/10.1109/TPEL.2003.813762) 8Hwang F., Shen Y., and Jayaram S.H.: ‘Low-ripple compact high-voltage DC power supply’, IEEE Trans. Ind. Appl., 2006, 42, (5), pp. 1139– 1145 (doi: http://doi.org/10.1109/TIA.2006.880845) 9Kobougias I.C., and Tatakis E.C.: ‘Optimal design of a half-wave Cockcroft–Walton voltage multiplier with minimum total capacitance’, IEEE Trans. Power Electron., 2010, 25, (9), pp. 2460– 2468 (doi: http://doi.org/10.1109/TPEL.2010.2049380) 10Shenkman A., Berkovich Y., and Axelrod B.: ‘Novel AC-DC and DC/DC converters with a diode-capacitor multiplier’, IEEE Trans. Aerosp. Electron. Syst., 2004, 40, (4), pp. 1286– 1293 (doi: http://doi.org/10.1109/TAES.2004.1386881) 11Prudente M., Pfitscher L.L., Emmendoerfer G., Romaneli E.F., and Gules R.: ‘Voltage multiplier cells applied to non-isolated DC-DC converters’, IEEE Trans. Power Electron., 2008, 23, (2), pp. 871– 887 (doi: http://doi.org/10.1109/TPEL.2007.915762) 12Spiazzi G., Mattavelli P., and Costabeber A.: ‘High step-up ratio flyback converter with active clamp and voltage multiplier’, IEEE Trans. Power Electron., 2011, 26, (11), pp. 3205– 3214 (doi: http://doi.org/10.1109/TPEL.2011.2134871) 13Yang E.X., Lee F., and Jovanovic M.M.: ‘ Small-signal modelling of LCC resonant converter’. Proc. PESC, Blacksburg, VA, June 1992, pp. 941– 948 14Sun J., Ding X., Nakaoka M., and Takano H.: ‘Series resonant ZCS-PFM DGDC converter with multistage rectified voltage multiplier and dual-mode PFM control scheme for medical-use high-voltage X-ray power generator’, IEE Pinc. Elecli. Power Appl., 2000, 147, (6), pp. 527– 534 (doi: http://doi.org/10.1049/ip-epa:20000711) 15Steigerwald R.L.: ‘A comparison of half-bridge resonant converter topologies’, IEEE Trans. Ind. Electon., 1988, 3, (2), pp. 174– 182 16Johnson S.D., and Erikson R.D.: ‘Steady-state analysis and design of the parallel resonant converter’, IEEE Trans. Power Electron., 1988, 3, (1), pp. 93– 104 (doi: http://doi.org/10.1109/63.4335) 17Bhat A.K.S.: ‘Analysis and design of a series–parallel resonant converter with capacitive output filter’, IEEE Trans. Ind. Appl., 1991, 27, (3), pp. 523– 530 (doi: http://doi.org/10.1109/28.81837) 18Ramos J.M., Diaz J., Pernía A.M., Nuño F., and Lopera J.M.: ‘Dynamic and steady-state models for the PRC-LCC resonant topology with a capacitor as output filter’, IEEE Trans. Ind. Electron., 2007, 54, (4), pp. 2262– 2275 (doi: http://doi.org/10.1109/TIE.2007.894763) 19Martin-Ramos J.A., Pernia A.M., Diaz J., Nuno F., and Martinez J.A.: ‘Power supply for a high-voltage application’, IEEE Trans. Power Electron., 2008, 23, (4), pp. 1608– 1619 (doi: http://doi.org/10.1109/TPEL.2008.925153) 20Garciá V., Rico M., Sebastián J., Hernando M., and Uceda J.: ‘ An optimized dc–dc converter topology for high voltage pulse loads applications’. IEEE PESC 94, Oviedo, Spain, June 1994, pp. 1413– 1421 21Luo F.L., and Ye H.: ‘Positive output super-lift converters’, IEEE Trans. Power Electron., 2003, 18, (1), pp. 105– 113 (doi: http://doi.org/10.1109/TPEL.2002.807198) 22Luo F.L., and Ye H.: ‘Negative output super-lift converters’, IEEE Trans. Power Electron., 2003, 18, (5), pp. 105– 1121 23Luo F.L., and Ye H.: ‘Positive output multiple-lift push–pull switching capacitor Luo-converters’, IEEE Trans. Power Electron., 2004, 51, (3), pp. 594– 602 24Wismer M.G.: ‘Steady-state operation of a high-voltage multi-resonant converter in a high-temperature environment’, IEEE Trans. Power Electron., 2003, 18, (3), pp. 740– 748 (doi: http://doi.org/10.1109/TPEL.2003.810853) 25Erickson R.W., and Maksimovic D.: ‘ Fundamentals of power electronics’ (Kluwer, Norwell, MA, 2001, 2nd edn.) 26Saggini S., Trevisan D., Mattavelli P., and Ghioni M.: ‘Synchronous–asynchronous digital voltage-mode control for DC–DC converters’, IEEE Trans. Power Electron., 2007, 22, (4), pp. 1261– 1268 (doi: http://doi.org/10.1109/TPEL.2007.900554) 27Saggini S., Costabeber A., and Mattavelli P.: ‘A simple digital autotuning for analog controller in SMPS’, IEEE Trans. Power Electron., 2010, 25, (8), pp. 2170– 2178 (doi: http://doi.org/10.1109/TPEL.2010.2041011) 28Costabeber A., Mattavelli P., Saggini S., and Bianco A.: ‘Digital autotuning of DC–DC converters based on a model reference impulse response’, IEEE Trans. Power Electron., 2011, 26, (10), pp. 2915– 2924 (doi: http://doi.org/10.1109/TPEL.2011.2122271) Citing Literature Volume6, Issue6July 2013Pages 1100-1110 FiguresReferencesRelatedInformation