Quasi-Resonant Converters Introduction 20.1 The - PowerPoint PPT Presentation

Chapter 20 Quasi-Resonant Converters Introduction 20.1 The zero-current-switching quasi-resonant switch cell 20.1.1 Waveforms of the half-wave ZCS quasi-resonant switch cell 20.1.2 The average terminal waveforms 20.1.3 The full-wave ZCS quasi-resonant switch cell 20.2 Resonant switch topologies 20.2.1 The zero-voltage-switching quasi-resonant switch 20.2.2 The zero-voltage-switching multiresonant switch 20.2.3 Quasi-square-wave resonant switches 20.3 Ac modeling of quasi-resonant converters 20.4 Summary of key points Fundamentals of Power Electronics 1 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 PWM switch cell L i 1 ( t ) i 2 ( t ) i ( t ) i 1 ( t ) i 2 ( t ) + + + + + Switch + cell v 1 ( t ) v 2 ( t ) v g ( t ) v 1 ( t ) C R v ( t ) v 2 ( t ) – – – – – – Fundamentals of Power Electronics 2 Chapter 20: Quasi-Resonant Converters

Two quasi-resonant switch cells D 1 L r D 1 Q 1 L r i 2 ( t ) i 1 ( t ) i 2 r ( t ) i 1 ( t ) i 2 r ( t ) i 2 ( t ) + + + + + + Q 1 v 1 ( t ) v 1 r ( t ) v 2 ( t ) v 1 ( t ) v 1 r ( t ) v 2 ( t ) D 2 C r D 2 C r – – – – – – Switch network Switch network Full-wave ZCS quasi-resonant switch cell Half-wave ZCS quasi-resonant switch cell Insert either of the above switch L i 1 ( t ) cells into the buck converter, to i 2 ( t ) i ( t ) + + + obtain a ZCS quasi-resonant version of the buck converter. L r Switch + cell v g ( t ) v 1 ( t ) v 2 ( t ) C R v ( t ) and C r are small in value, and – their resonant frequency f 0 is – – – greater than the switching frequency f s . = ω 0 1 f 0 = 2 π 2 π L r C r Fundamentals of Power Electronics 3 Chapter 20: Quasi-Resonant Converters

20.1 The zero-current-switching quasi-resonant switch cell L r D 1 Q 1 i 2 ( t ) i 1 ( t ) i 2 r ( t ) Tank inductor L r in series with transistor: + + + transistor switches at zero crossings of inductor current waveform v 1 ( t ) v 1 r ( t ) v 2 ( t ) D 2 C r Tank capacitor C r in parallel with diode D 2 : diode switches at zero crossings of capacitor voltage – – – waveform Switch network Half-wave ZCS quasi-resonant switch cell Two-quadrant switch is required: Half-wave: Q 1 and D 1 in series, transistor D 1 turns off at first zero crossing of current L r i 1 ( t ) i 2 r ( t ) i 2 ( t ) waveform + + + Full-wave: Q 1 and D 1 in parallel, transistor Q 1 v 1 ( t ) v 1 r ( t ) v 2 ( t ) turns off at second zero crossing of current D 2 C r waveform – – – Performances of half-wave and full-wave cells Switch network differ significantly. Full-wave ZCS quasi-resonant switch cell Fundamentals of Power Electronics 4 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: i 2 ( t ) ≈ i 2 ( t ) T s v 1 ( t ) ≈ v 1 ( t ) T s In steady state, we can further approximate these quantities by their dc values: i 2 ( t ) ≈ I 2 v 1 ( t ) ≈ V 1 Modeling objective: find the average values of the terminal waveforms 〈 v 2 ( t ) 〉 Ts and 〈 i 1 ( t ) 〉 Ts Fundamentals of Power Electronics 5 Chapter 20: Quasi-Resonant Converters

The switch conversion ratio µ L r D 1 Q 1 A generalization of the duty cycle i 1 ( t ) i 2 r ( t ) + + d ( t ) The switch conversion ratio µ is 〈 v 1 ( t ) 〉 T s + 〈 i 2 ( t ) 〉 T s v 1 r ( t ) v 2 ( t ) C r D 2 – the ratio of the average terminal – – voltages of the switch network. It Switch network can be applied to non-PWM switch Half-wave ZCS quasi-resonant switch cell networks. For the CCM PWM case, µ = d . i 2 ( t ) ≈ i 2 ( t ) v 2 ( t ) i 1 ( t ) If V/V g = M ( d ) for a PWM CCM µ = T s T s T s converter, then V/V g = M ( µ ) for the = v 1 ( t ) ≈ v 1 ( t ) v 1 r ( t ) i 2 r ( t ) same converter with a switch T s T s T s network having conversion ratio µ . In steady state: Generalized switch averaging, and i 2 ( t ) ≈ I 2 µ , are defined and discussed in µ = V 2 = I 1 v 1 ( t ) ≈ V 1 Section 10.3. V 1 I 2 Fundamentals of Power Electronics 6 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 Waveforms: cell, driven by the terminal quantities 〈 v 1 ( t ) 〉 Ts and 〈 i 2 ( t ) 〉 Ts . i 1 ( t ) I 2 L r D 1 Q 1 V 1 i 1 ( t ) i 2 r ( t ) L r + + θ = ω 0 t 1 2 3 4 Subinterval: 〈 v 1 ( t ) 〉 T s + 〈 i 2 ( t ) 〉 T s v 2 ( t ) v 1 r ( t ) v 2 ( t ) C r D 2 – – I 2 V c 1 – – C r Switch network α β δ ξ Half-wave ZCS quasi-resonant switch cell ω 0 T s Q 1 Q 1 X D 2 Conducting Each switching period contains four devices: D 1 D 1 subintervals D 2 Fundamentals of Power Electronics 7 Chapter 20: Quasi-Resonant Converters

Subinterval 1 Diode D 2 is initially conducting the filter Circuit equations: inductor current I 2 . Transistor Q 1 turns on, di 1 ( t ) = V 1 with i 1 (0) = 0 and the tank inductor current i 1 starts to dt L r increase. So all semiconductor devices i 1 ( t ) = V 1 L r t = ω 0 t V 1 conduct during this subinterval, and the Solution: R 0 circuit reduces to: L r R 0 = where L r C r i 1 ( t ) + This subinterval ends when diode D 2 + V 1 v 2 ( t ) I 2 becomes reverse-biased. This occurs – at time ω 0 t = α , when i 1 ( t ) = I 2 . – i 1 ( α ) = α V 1 α = I 2 R 0 R 0 = I 2 V 1 Fundamentals of Power Electronics 8 Chapter 20: Quasi-Resonant Converters

Subinterval 2 Diode D 2 is off. Transistor Q 1 conducts, and The solution is the tank inductor and tank capacitor ring i 1 ( ω 0 t ) = I 2 + V 1 R 0 sin ω 0 t – α sinusoidally. The circuit reduces to: L r i 1 ( t ) v 2 ( ω 0 t ) = V 1 1 – cos ω 0 t – α + i c ( t ) + V 1 v 2 ( t ) C r I 2 – The dc components of these waveforms are the dc – solution of the circuit, while the sinusoidal components The circuit equations are have magnitudes that depend di 1 ( ω 0 t ) = V 1 – v 2 ( ω 0 t ) v 2 ( α ) = 0 L r on the initial conditions and dt dv 2 ( ω 0 t ) on the characteristic i 1 ( α ) = I 2 = i 1 ( ω 0 t ) – I 2 C r impedance R 0 . dt Fundamentals of Power Electronics 9 Chapter 20: Quasi-Resonant Converters

Subinterval 2 continued i 1 ( ω 0 t ) = I 2 + V 1 i 1 ( t ) R 0 sin ω 0 t – α Peak inductor current: I 1 pk = I 2 + V 1 I 2 v 2 ( ω 0 t ) = V 1 1 – cos ω 0 t – α V 1 R 0 L r θ = ω 0 t Subinterval: 1 2 3 4 This subinterval ends at the first zero α β δ ξ crossing of i 1 ( t ). Define β = angular length of ω 0 T s subinterval 2. Then i 1 ( α + β ) = I 2 + V 1 R 0 sin β = 0 Hence β = π + sin – 1 I 2 R 0 sin β = – I 2 R 0 V 1 V 1 – π 2 < sin – 1 x ≤ π Must use care to select the correct 2 branch of the arcsine function. Note (from the i 1 ( t ) waveform) that β > π . I 2 < V 1 R 0 Fundamentals of Power Electronics 10 Chapter 20: Quasi-Resonant Converters

Boundary of zero current switching If the requirement I 2 < V 1 R 0 is violated, then the inductor current never reaches zero. In consequence, the transistor cannot switch off at zero current. The resonant switch operates with zero current switching only for load currents less than the above value. The characteristic impedance must be sufficiently small, so that the ringing component of the current is greater than the dc load current. Capacitor voltage at the end of subinterval 2 is 2 1 – I 2 R 0 v 2 ( α + β ) = V c 1 = V 1 1 + V 1 Fundamentals of Power Electronics 11 Chapter 20: Quasi-Resonant Converters

Subinterval 3 All semiconductor devices are off. The Subinterval 3 ends when the circuit reduces to: tank capacitor voltage reaches zero, and diode D 2 + becomes forward-biased. Define δ = angular length of v 2 ( t ) I 2 C r subinterval 3. Then – v 2 ( α + β + δ ) = V c 1 – I 2 R 0 δ = 0 The circuit equations are dv 2 ( ω 0 t ) 2 δ = V c 1 = V 1 1 – I 2 R 0 C r = – I 2 1 – dt V 1 v 2 ( α + β ) = V c 1 I 2 R 0 I 2 R 0 The solution is v 2 ( ω 0 t ) = V c 1 – I 2 R 0 ω 0 t – α – β Fundamentals of Power Electronics 12 Chapter 20: Quasi-Resonant Converters

Subinterval 4 Subinterval 4, of angular length ξ , is identical to the diode conduction interval of the conventional PWM switch network. Diode D 2 conducts the filter inductor current I 2 The tank capacitor voltage v 2 ( t ) is equal to zero. Transistor Q 1 is off, and the input current i 1 ( t ) is equal to zero. The length of subinterval 4 can be used as a control variable. Increasing the length of this interval reduces the average output voltage. Fundamentals of Power Electronics 13 Chapter 20: Quasi-Resonant Converters