Abstract – Averaged switch approach is extended to the modeling of boundary conduction mode (BCM) dc-to-dc converters that operate at the boundary between continuous conduction mode (CCM) and discontinuous conduction mode (DCM). BCM dc-to-dc converters have smaller inductor size and reduced switching losses compared to CCM, and lower peak current compared to DCM. The large-signal BCM averaged switch model shows that several BCM converters with input voltage feedforward exhibit resistive or nearly resistive input characteristic, which is well suited for realization of power factor correctors. It is shown that BCM converters exhibit simpler dynamics compared to CCM current programmed control (CPM). Small-signal frequency responses predicted by the averaged switch model are verified by simulation and experiments.I.INTRODUCTIONPulse-width modulation (PWM) at constant switching frequency is a common technique applied in electrical power conversion circuits. Switching converters are usually operated in continuous conduction mode (CCM) for higher power applications or at full load, and in discontinuous conduction mode (DCM) for lower power application or at light load. Averaged models for constant-frequency CCM or DCM converters are well known and accepted in practice.Converters controlled to operate at the CCM/DCM boundary are said to operate in boundary conduction mode (BCM) or critical conduction mode. As an example, circuit diagram of a BCM boost converter is shown in Fig. 1. A switching cycle is initiated by turning the transistor on when the diode current drops to zero, while the turn-off transition is triggered when the peak transistor current reaches a desired value. The diode recovery problem is removed because the diode current is zero at the time when the transistor turned on.In contrast to constant-frequency PWM, the switching frequency of BCM converter varies with changes in the load current or the input voltage. BCM is frequently used in low-power power-factor-correction (PFC) rectifier applications [1-4].In this paper, the averaged switch modeling approach is extended to modeling of BCM converters. The averaged switch modeling is briefly reviewed in Section II. In Section III, we consider BCM converters without input voltage feedforward. Large-signal averaged models are derived for basic converter configurations. Parameters of linearized,small-signal averaged switch models are derived and used toobtain expressions for salient features of frequency responses of BCM converters. Modeling of BCM converters with input voltage feedforward is described in Section IV. The averaged models lead to simple explanation of how BCM converters can be well suited for PFC applications. In Section V,computer simulations and experimental results are used to illustrate applications and validate the BCM averaged switch models.Averaged Switch Modeling of Boundary Conduction Mode Dc-to-Dc Converters-LQJTXDQ &KHQ 5REHUW (ULFNVRQ DQG 'UDJDQ 0DNVLPRYLüColorado Power Electronics CenterDepartment of Electrical and Computer EngineeringUniversity of Colorado at Boulder Boulder, CO 80309-0425, USA+-)(t v g)(t v )(t i )(t v ref Fig. 1 Boundary conduction mode incorporating input voltagefeedforword.Fig. 2 Averaged switch modeling: a switch network, containing only theconverter switching elements.IECON'01: The 27th Annual Conference of the IEEE Industrial Electronics Society0-7803-7108-9/01/$10.00 (C)2001 IEEE 844
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