Contents
1 Introduction 1
1.1 Objective of the Thesis . . . . 1
2 Electrical Power Losses in a DC-DC Converter 3 2.1 Simulations . . . . 4
2.2 Electric Losses . . . . 6
3 Differential Equation of the Converter 8 3.1 Buck Converter . . . . 8
3.1.1 Equations and Block Diagram with Mosfet on . . . . 9
3.1.2 Equations and Block Diagram with Mosfet off . . . 10
3.1.3 Block Diagram of the whole Circuit . . . 11
3.2 Boost Converter . . . 12
3.2.1 Equations and Block Diagram with Mosfet on . . . 13
3.2.2 Equations and Blocks Diagram with Mosfet off . . . 14
3.2.3 Blocks Diagram of the whole Circuit . . . 15
4 More Accurate Formulae for a Chopper 17 4.1 More Accurate Formula for a Buck Converter . . . 17
4.1.1 Continuous-conduction Mode . . . 17
4.1.2 Boundary between Continuous and Discontinuous-conduction Mode . 19 4.1.3 Discontinuous-Conduction Mode . . . 21
4.2 Initial Condition in a Buck Converter . . . 23
4.2.1 Initial condition in the main inductance . . . 23
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4.2.2 Initial Condition in the Output Capacitor . . . 24
4.2.3 Output voltage ripple . . . 24
4.3 A More Accurate Formula for a Boost-Converter . . . 25
4.3.1 continuous-conduction mode . . . 25
4.3.2 Boundary between Continuous and Discontinuous-Conduction Mode . 28 4.3.3 Discontinuous-Conduction Mode . . . 29
4.4 Initial Condition in a Boost-converter . . . 31
4.4.1 Initial condition in the main inductance . . . 31
4.4.2 Initial Condition in the Output Capacitor . . . 32
4.4.3 Output Voltage Ripple . . . 33
5 Simulation and Results 34 5.1 MOSFET . . . 35
5.2 Energy Balance of the Converter . . . 35
5.2.1 Calculation of the Efficiency . . . 36
5.3 Simulation using Simulink . . . 37
5.3.1 Braking Step-Down . . . 37
5.3.2 Motoring Step-Up . . . 45
5.4 Simulation using Simplorer . . . 49
5.4.1 Braking Step-down . . . 50
5.4.2 Motoring step-up . . . 50
6 Three-Phase Converter 51 6.1 Three-Phase Step-down Converter . . . 52
6.2 Three-Phases Step-up Converter . . . 53
6.3 Simulations . . . 54
6.3.1 Braking Step-down . . . 55
6.3.2 Motoring Step-up . . . 56
7 Conclusions 60
list of pictures 65
Bibliography 66
