a very high frequency dc-dc converter based on a class pfi resonant inverter

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  • 1A Very High Frequency dc-dc Converter Based ona Class 2 Resonant Inverter

    Juan M. Rivas, Olivia Leitermann, Yehui Han, David J. PerreaultLABORATORY FOR ELECTROMAGNETIC AND ELECTRONIC SYSTEMS



    NISKAYUNA, NY 12309EMAIL: djperrea@mit.edu


    THIS paper introduces a new dc-dc converter suitable foroperation at very high frequencies under on-off control.The converter power stage is based on a resonant inverter(the 2 inverter) providing low switch voltage stress and fastsettling time. A new multi-stage resonant gate driver suited fordriving large, high-voltage rf MOSFETS at VHF frequencies is alsointroduced. Experimental results are presented from a prototypedc-dc converter operating at 30 MHz at input voltages up to200 V and power levels above 200 W. These results demonstratethe high performance achievable with the proposed design.

    Index Termsresonant dc-dc converter, very high frequency(VHF), class inverter, class phi inverter, class F power amplifier,class E inverter, resonant gate drive, resonant rectifier, harmonicpeaking, on-off control, burst-mode control, cycle skipping con-trol.


    POWER density and response speed are important per-formance metrics in dc-dc power converters. Increasesin switching frequency potentially enable improvement ofboth of these metrics: higher switching frequencies permitthe use of smaller-valued (and often physically smaller) pas-sive components having reduced energy storage requirements.Reduced intermediate energy storage, coupled with a shorterswitching period, permits more agile response to changes inoperating condition. There is thus strong motivation to moveto greatly increased switching frequencies if losses, switchdriving, control, and other design challenges can be addressed.

    Zero-voltage-switching (ZVS) resonant dc-dc convertersoffer the opportunity to operate at higher frequencies, butpose a number of design challenges. First, designs of thistype often suffer from high device voltage stress [1][11].Driving of transistors also becomes a challenge as frequenciesare increased, due to both loss considerations and the difficultyof achieving sufficiently fast switching transitions. Moreover, itis often difficult to achieve efficient operation of ZVS resonantconverters across a wide load range, owing to resonating losses(for ZVS operation) that do not scale with output powerdelivery.

    This paper introduces a new resonant dc-dc converter andassociated driving and control methods that address the above

    challenges. The converter power stage is based on a resonantinverter (the 2 inverter) that provides low switch voltagestress and fast settling time. The proposed power stage isoperated at fixed switching frequency and duty ratio. Toachieve output control and high efficiency across a wide loadrange, we adopt on/off control [8][14]. We also introducea new multi-stage resonant gate drive that provides low-lossdriving of high-voltage MOSFETS at VHF frequencies, and iswell suited to on/off control. Together, these circuit designsand methods yield extremely high performance.

    Section II of the paper introduces the system structureand control approach. Detailed descriptions of the proposedconverter and its constituent elements are also presented.The new multi-stage resonant gate drive system is treated inSection III. The results presented throughout this documentdemonstrate the efficacy of the proposed approach. Finally,Section IV concludes the paper.


    Figure 1 shows the general structure of the proposed dc-dc converter. The converter power stage comprises a resonantinverter, a transformation stage, and a resonant rectifier. Theresonant inverter accepts a dc input voltage, and generatesvery high frequency (VHF) ac, which is processed throughthe transformation stage to produce different ac voltage andcurrent levels. The resonant rectifier then converts the trans-formed ac power back to dc. A multi-stage resonant gate driveis employed to drive the inverter switch, enabling efficientoperation at much higher frequencies than would otherwisebe possible.

    Regulation of the converter output voltage can be achievedthrough on/off control of the inverter [8][14]. In this ap-proach, the power stage is gated on and off at a modulation fre-quency that is far lower than the inverter switching frequency.By controlling the fraction of time that the inverter stage runs(and delivers power to the output) the output voltage can beregulated to a desired reference level.

    Key advances in the system developed here are in thedesign of the power stage and the gate drive, and in how

  • 2Resonant Inverter


    ResonantRectifier & Filter

    On/Off Control






    Fig. 1. General structure of the proposed dc-dc converter.









    Fig. 3. Resonant rectifier.

    these elements are specifically optimized to achieve highperformance under on/off control. We focus on each of thesubsystems in turn and describe the design procedure of a200 W dc-dc converter operating at 30 MHz with an inputvoltage range of 160 V to 200 V and output voltage of 33 V.

    B. Rectification and Voltage transformationFigure 2 shows the schematic of the 2-based dc-dc con-

    verter introduced here. The figure outlines the different stagesof the converter corresponding to the general structure shownin Fig. 1. We begin by considering how the rectifier andvoltage transformation stages of the converter may be de-signed. For design purposes, the resonant rectifier can simplybe modeled as illustrated in Fig. 3, which shows the resonantrectifier driven from a sinusoidal current source and loadedwith a constant voltage at the output. Together, the large energystorage at the output and the on-off scheme regulating theoutput voltage of the converter allow us to treat the outputvoltage of the rectifier as constant for design purposes. Inthe figure, the rectifier is modeled as being driven by asinusoidal current source of magnitude Irec. The resonantinductor LR provides a path for the dc current and resonateswith the capacitances CD and CEXT shown in the Figure.CD represents the diode non-linear capacitance while CEXTaccounts for external capacitance added plus the parasiticinterwinding capacitance of inductor LR.

    It is possible to describe the voltage-current relationshipof a resonant rectifier in terms of an equivalent input im-pedance in a describing-function sense [9], [15]. In our designthe resonant elements were tuned to make the input looknearly resistive at the fundamental frequency (That is, thefundamental of the voltage vr is in phase with the drivecurrent irec). Alternatively, if the rectifier is tuned to appearappropriately reactive at the switching frequency, resonancebetween the interconnect network and the rectifier networkcan be used to provide voltage gain from the input to the

    output. The input current amplitude is selected to provide thedesired output power. The amplitude and conduction angleof the diode current depend on the component values. Byadjusting the net capacitance (CD CEXT ) in parallel with theresonant inductor, we can trade off the length of the conductioninterval and the peak reverse voltage across the diode. In someimplementations it is convenient to have a conduction angleclose to 50 percent, as this provides a good tradeoff betweenpeak diode forward current and reverse voltage. If additionalcapacitance is required, this can either be added externally orcan be solely provided by additional diode area, which canhave the added benefit of reducing the overall conduction lossin the rectifier. For the 200 W design presented here we usea pair of silicon carbide Schottky diodes (Cree CSD10030)in parallel1. In the design presented here, the correspondingresonant capacitance (CD CEXT ) of Fig. 3 is only providedby the non-linear capacitance of the diodes.

    The tuning of the rectifier stage was done numerically inSPICE, which required an accurate diode model. Parametersfor the non-linear diode capacitance were obtained by mea-suring the diode capacitance (CKA =548 pF, 163 pF, and119 pF , at fs=1 MHz) at three different bias voltages (VKA=0,11 V, and 23 V respectively) and solving for VJ and m inthe equation: CKA = Cj0/(1 + vKAVJ )

    m. For the CSD10030

    diode: Cj0 = 548.3 pF, VJ = 0.78 V, and m=0.45 for0 vKA < 100 V. The CSD10030 datasheet indicates that forvKA > 100 V the diode capacitance is approximately constant(CKA = 62.6 pF). In addition to the capacitance, the SPICEmodel of the diode incorporates 6 nH of lead inductance (be-tween lead and the back of the TO-220 package), and 0.15 ofequivalent series resistance. The forward characteristic of eachdiode is modeled as a constant forward drop (Vd,ON=507 mV)in series with a resistor (RS=89.7 m). With the appropriatemodel of the diodes, we proceeded to iteratively adjust thevalue of LR and Irec in SPICE and look for the values atwhich the fundamental of vr and irec were in phase, and forwhich the rectifier delivered sufficient output power.

    Figure 4 (a) shows a SPICE simulation of the rectifiershown in Fig. 3, tuned to appear resistive at the fundamentalfrequency. For the conditions shown in the figure, LR=75 nH,fs = 30 MHz and |Irec|= 7.15 A. The output power POUTdelivered to the 33 V load is 200 W. Figure 4 (b) shows thesinusoidal input current, and the fundamental component ofthe input voltage, from which the an equivalent resistance ofapproximately 8.4 can be extracted.

    Generally, the equivalent rectifier resistance will not cor-respond to the load resis


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