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Fundamentals of Power Electronics 1 Chapter 20: Quasi-Resonant Converters Chapter 20 Quasi-Resonant Converters Introduction 20.1The zero-current-switching quasi-resonant switch cell 20.1.1Waveforms of the half-wave ZCS quasi-resonant switch cell 20.1.2The average terminal waveforms 20.1.3The full-wave ZCS quasi-resonant switch cell 20.2Resonant switch topologies 20.2.1The zero-voltage-switching quasi-resonant switch 20.2.2The zero-voltage-switching multiresonant switch 20.2.3Quasi-square-wave resonant switches 20.3Ac modeling of quasi-resonant converters 20.4Summary of key points

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Fundamentals of Power Electronics 4 Chapter 20: Quasi-Resonant Converters The resonant switch concept A quite general idea: 1.PWM switch network is replaced by a resonant switch network 2.This leads to a quasi-resonant version of the original PWM converter Example:realization of the switch cell in the buck converter

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Fundamentals of Power Electronics 5 Chapter 20: Quasi-Resonant Converters 20.1 The zero-current-switching quasi-resonant switch cell Tank inductor L r in series with transistor: transistor switches at zero crossings of inductor current waveform Tank capacitor C r in parallel with diode D 2 : diode switches at zero crossings of capacitor voltage waveform Two-quadrant switch is required: Half-wave: Q 1 and D 1 in series, transistor turns off at first zero crossing of current waveform Full-wave: Q 1 and D 1 in parallel, transistor turns off at second zero crossing of current waveform Performances of half-wave and full-wave cells differ significantly.

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Fundamentals of Power Electronics 6 Chapter 20: Quasi-Resonant Converters The switch conversion ratio µ In steady state: A generalization of the duty cycle d(t) The switch conversion ratio µ is the ratio of the average terminal voltages of the switch network. It can be applied to non-PWM switch networks. For the CCM PWM case, µ = d. If V/V g = M(d) for a PWM CCM converter, then V/V g = M(µ) for the same converter with a switch network having conversion ratio µ. Generalized switch averaging, and µ, are defined and discussed in Section 10.3.

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Fundamentals of Power Electronics 7 Chapter 20: Quasi-Resonant Converters Averaged switch modeling of ZCS cells It is assumed that the converter filter elements are large, such that their switching ripples are small. Hence, we can make the small ripple approximation as usual, for these elements: In steady state, we can further approximate these quantities by their dc values: Modeling objective: find the average values of the terminal waveforms v 2 (t) T s and i 1 (t) T s

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Fundamentals of Power Electronics 8 Chapter 20: Quasi-Resonant Converters 20.1.1 Waveforms of the half-wave ZCS quasi-resonant switch cell The half-wave ZCS quasi-resonant switch cell, driven by the terminal quantities v 1 (t) Ts and i 2 (t) Ts. Waveforms: Each switching period contains four subintervals

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Fundamentals of Power Electronics 16 Chapter 20: Quasi-Resonant Converters

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Fundamentals of Power Electronics 17 Chapter 20: Quasi-Resonant Converters

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Fundamentals of Power Electronics 18 Chapter 20: Quasi-Resonant Converters

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Fundamentals of Power Electronics 19 Chapter 20: Quasi-Resonant Converters

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Fundamentals of Power Electronics 20 Chapter 20: Quasi-Resonant Converters Analysis result: switch conversion ratio µ Switch conversion ratio: with This is of the form

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Fundamentals of Power Electronics 21 Chapter 20: Quasi-Resonant Converters Characteristics of the half-wave ZCS resonant switch J s ≤ 1 Switch characteristics: Mode boundary:

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Fundamentals of Power Electronics 22 Chapter 20: Quasi-Resonant Converters Buck converter containing half-wave ZCS quasi-resonant switch Conversion ratio of the buck converter is (from inductor volt-second balance): For the buck converter, ZCS occurs when Output voltage varies over the range

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Fundamentals of Power Electronics 23 Chapter 20: Quasi-Resonant Converters Boost converter example For the boost converter, Half-wave ZCS equations:

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Fundamentals of Power Electronics 24 Chapter 20: Quasi-Resonant Converters

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Fundamentals of Power Electronics 25 Chapter 20: Quasi-Resonant Converters 20.1.3 The full-wave ZCS quasi-resonant switch cell Half wave Full wave

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Fundamentals of Power Electronics 26 Chapter 20: Quasi-Resonant Converters

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Fundamentals of Power Electronics 27 Chapter 20: Quasi-Resonant Converters Analysis: full-wave ZCS Analysis in the full-wave case is nearly the same as in the half-wave case. The second subinterval ends at the second zero crossing of the tank inductor current waveform. The following quantities differ: In either case, µ is given by

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Fundamentals of Power Electronics 28 Chapter 20: Quasi-Resonant Converters Full-wave cell: switch conversion ratio µ Full-wave case: P 1 can be approximated as so

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Fundamentals of Power Electronics 29 Chapter 20: Quasi-Resonant Converters 20.2 Resonant switch topologies Basic ZCS switch cell: SPST switch SW : Voltage-bidirectional two-quadrant switch for half-wave cell Current-bidirectional two-quadrant switch for full-wave cell Connection of resonant elements: Can be connected in other ways that preserve high-frequency components of tank waveforms

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Fundamentals of Power Electronics 30 Chapter 20: Quasi-Resonant Converters Connection of tank capacitor Connection of tank capacitor to two other points at ac ground. This simply changes the dc component of tank capacitor voltage. The ac high- frequency components of the tank waveforms are unchanged.

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Fundamentals of Power Electronics 31 Chapter 20: Quasi-Resonant Converters A test to determine the topology of a resonant switch network Replace converter elements by their high-frequency equivalents: Independent voltage source V g : short circuit Filter capacitors: short circuits Filter inductors: open circuits The resonant switch network remains. If the converter contains a ZCS quasi-resonant switch, then the result of these operations is

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