vi TABLE OF CONTENTS CHAPTER NO. TITLE PAGE NO. ABSTRACT LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS AND ABBREVIATIONS iii x xi xvii 1 INTRODUCTION 1 1.1 INTRODUCTION 1 1.2 BACKGROUND 2 1.2.1 Types of DC-DC Buck Converters 3 1.2.1.1 Linear and switching converters 3 1.2.1.2 Isolated and non isolated switching buck converters 4 1.2.2 Feedback Control of Converter 6 1.2.3 Comparison between PWM and PSM 7 1.2.4 Nonlinear Phenomena in Buck Converters 8 1.2.5 Applications of Buck Converters 10 1.3 REVIEW OF RELEVANT LITERATURE 10 1.4 AIMS AND OBJECTIVES 15 1.5 ORGANISATION OF THE THESIS 16
vii CHAPTER NO. TITLE PAGE NO. 2 PWM AND PSM DC/DC BUCK CONVERTERS 18 2.1 PWM DC DC BUCK CONVERTER 18 2.1.1 Circuit Operation 19 2.1.2 Operating Modes of Converter 21 2.1.3 Voltage Mode Controlled Buck Converter 31 2.1.4 Simulation of Voltage Mode Controlled Converter under CCM 38 2.1.4.1 Results 39 2.1.5 Observations with Variation in Input Voltage/Load 42 2.1.6 Bifurcation and Chaos in PWM DC DC Converter 44 2.1.6.1 A Method to generate stepped input voltage variation 45 2.2 PSM DC DC BUCK CONVERTER 52 2.2.1 Circuit Operation 53 2.2.2 Operating Modes 55 2.2.2.1 Continuous conduction mode I 55 2.2.2.2 Continuous conduction mode II 56 2.2.2.3 Discontinuous conduction mode 57 2.2.2.4 Critical mode 58 2.2.3 Modeling of Converter under Continuous Conduction Mode 59 2.2.4 Simulation of PSM Buck Converter under CCM 62 2.2.5 Observations with Variation in Input Voltage/Load 65
viii CHAPTER NO. TITLE PAGE NO. 2.2.6 Bifurcation and Chaos in PSM DC DC Converter 66 2.7 CONCLUSION 70 3 PSM BUCK DC-DC CONVERTER UNDER DISCONTINUOUS CONDUCTION MODE 71 3.1 DISCONTINUOUS CONDUCTION MODE IN BUCK CONVERTER 72 3.2 MODELLING AND SIMULATION OF PSM CONVERTER UNDER DCM 74 3.2.1 Modelling 75 3.2.2 Simulation 81 3.3 MODELLING AND SIMULATION OF PSM CONVERTER UNDER FORCED DCM 85 3.3.1 Modelling converter under Forced DCM 85 3.4 OBSERVATIONS WITH VARIATION IN INPUT VOLTAGE 90 3.5 BIFURCATION AND CHAOS IN PSM CONVERTER UNDER DCM 91 3.6 BIFURCATION AND CHAOS IN PSM DC-DC VMC FDCM 94 3.7 CONCLUSION 96 4 IMPROVED PSM DC-DC BUCK CONVERTER 97 4.1 RIPPLE IN DC-DC BUCK CONVERTERS 97 4.2 FACTORS AFFECTING RIPPLE IN BUCK CONVERTERS 102 4.3 IMPROVED PSM DC-DC BUCK CONVERTER 110
ix CHAPTER NO. TITLE PAGE NO. 4.3.1 Skip Logic 111 4.3.2 Inductor Current Limit 113 4.3 APPLICATIONS OF PSM DC-DC BUCK CONVERTER 118 4.4.1 Regulated Power Supply 118 4.4.1.1 Simulation 119 4.4.1.2 Experimental evaluation 122 4.4.2 Chaos Free Operation with Mode Hopping 127 4.5 CONCLUSION 130 5 CONCLUSION AND FUTURE WORK 131 5.1 CONTRIBUTION OF THE THESIS 132 5.2 FUTURE SCOPE OF THE WORK 133 APPENDIX 136 REFERENCES 145 LIST OF PUBLICATIONS 151 CURRICULUM VITAE 153
x LIST OF TABLES TABLE NO. TITLE PAGE NO. 1.1 Comparison between linear and switching converters 3 2.1 Specifications of power stage 38 2.2 Parameter values considered for simulation 39 2.3 Parameter values considered for simulation 62 2.4 Pulses applied and skipped over the range of input voltage from 12V to 20V 69 3.1 Parameters considered for PSM DC/DC converter under DCM 81 3.2 Parameters considered for simulation of Forced Discontinuous Conduction Mode 90 4.1 Parameter values considered for the improved PSM buck converter 115
xi LIST OF FIGURES FIGURE NO. TITLE PAGE NO. 1.1 Power converter in an electric power system 2 1.2 Buck converter 5 1.3 Rapid decrease of both conduction and switching losses in skipping mode 12 1.4 The schematic of PWM/PSM dual-mode controller 13 1.5 The output voltage V O with modulation factor M 14 2.1 PWM Buck converter 19 2.2 Input voltage presented to LC filter due to switch action 20 2.3 Typical waveforms of inductor current i L and Capacitor voltage v C 21 2.4. Continuous conduction mode (a) Buck converter circuit (b) Switch open and voltage across inductor is (v in -v 0 ) (c) Switch closed and voltage across inductor is (-v 0 ) 22 2.5 Inductor voltage and current-continuous conduction mode 23 2.6 Inductor current -Discontinuous conduction mode 24 2.7 Third circuit configuration - Discontinuous conduction mode 25 2.8 Buck converter circuit 26 2.9 Equivalent circuit with (a) switch closed (b) switch open-for developing the state equations 27 2.10 Simulink actual model of the buck converter 30 2.11 State space averaged model of buck converter 30 2.12 SIMULINK PSB model of converter 31 2.13 Voltage mode controlled PWM buck converter 32 2.14 Closed loop with compensator 32
xii FIGURE NO. TITLE PAGE NO. 2.15 PWM generation 33 2.16 Step response of uncompensated system 35 2.17 Bode plot of uncompensated system 36 2.18 Step response of compensated system 37 2.19 Bode plot of compensated system 37 2.20 SIMULINK Model of PWM buck converter with PID Control 38 2.21 Inductor current and output voltage of converter 40 2.22 Output voltage ripple for VM controlled buck converter 41 2.23 Phase plot between vc and il showing period I operation 41 2.24 Response to a step change in input voltage PWM control 42 2.25 Response to a step change in input voltage PWM control 43 2.26 Response to a step change in load PWM control 43 2.27 Response to a step change in load PWM control simulated with PSIM 44 2.28 Schematic to generate a stepped input voltage variation 46 2.29 Stepped input voltage variation and sampling pulses 46 2.30 Phase portrait Switching map PWM converter 49 2.31 State trajectory PWM converter period I operation 50 2.32 State trajectory in state space PWM converter period II operation 50 2.33 Control voltage and ramp during period II operation 51 2.34 Bifurcation diagram for PWM converter input voltage in V is parameter 51 2.35 Stroboscopic map for PWM converter, at 22.6V 52
xiii FIGURE NO. TITLE PAGE NO. 2.36 Strange attractor at V in = 24V PWM converter 52 2.37 PSM DC/DC buck converter 53 2.38 Waveforms of output voltage, inductor current and gate pulses for a PSM converter 54 2.39 PSM control logic 55 2.40 Inductor current waveform in CCM I 56 2.41 Inductor current waveform in CCM II 57 2.42 Inductor current waveform in DCM 58 2.43 Inductor current waveform in critical mode 59 2.44 PSM buck converter SIMULINK PSB 63 2.45 Inductor current for continuous conduction and output voltage. Ripple is observed to be slightly greater than 10%. 63 2.46 Simulation output showing the ripple in v 0, inductor current and pulses applied and skipped. Ripple is slightly above 10% 64 2.47 Average model simulated with input voltage = 12V and D=0.8 64 2.48 Output voltage response to step change in (a) input and (b) load current 65 2.49 State trajectory in state space - plot between i L and v C 66 2.50 Phase portrait - Stroboscopic map PSM converter for V in =12V 67 2.51 Bifurcation diagram for PSM converter 67 2.52 Bifurcation diagram for PSM converter enlarged over 10V to 20V range 68 2.53 Stroboscopic map for PSM converter at V in = 17.6 V 68
xiv FIGURE NO. TITLE PAGE NO. 2.54. Inductor current in A with change in input voltage in 2V steps from 12V to 20V 69 3.1 K Vs D plot showing DCM/CCM regions separated by the borderline 72 3.2. Average inductor current or the load DC current equals half the inductor ripple 73 3.3 Modulation factor Vs V in (Increased skipping with V in ) 78 3.4 Modulation factor Vs R L. (Increased skipping with R L ) 79 3.5 PSM Buck converter waveforms for a load of 500mA 82 3.6 Step increase in load and response of output voltage. Load increased from 250mA to 500mA. (a) Load current and output voltage (b) Output voltage and inductor current 83 3.7 Step increase in load and response of output voltage 84 3.8 Inductor current and applied pulses 86 3.9 Typical current waveform in FDCM PSM converter 88 3.10 Forced Discontinuous conduction in PSM buck converter 89 3.11 Waveforms of Vin, v0 and il in PSM forced DCM showing discontinuous conduction with Ripple 6% 90 3.12 Bifurcation diagram for PSM DC/DC buck converter under DCM 93 3.13 Bifurcation diagram for PSM DC/DC buck converter under DCM-enlarged view 93 3.14 Inductor current and output voltage with V in = 12V for PSM buck converter under forced DCM Ripple 6% 94
xv FIGURE NO. TITLE PAGE NO. 3.15 Inductor current and output voltage with V in = 35V for PSM buck converter under forced DCM Ripple 6% 94 3.16 Phase plane trajectory i L Vs v C discontinuous current and no Chaos at V in = 12V for PSM converter under forced DCM 95 3.17 Phase plane trajectory i L Vs v C discontinuous current and no Chaos at V in = 35V 95 4.1 Inductor current in buck converter 98 4.2 Equivalent circuit of capacitor with ESR 101 4.3 Output voltage ripple Vs Frequency with C as parameter 103 4.4 Output voltage ripple Vs Frequency with L as parameter 103 4.5 Output voltage ripple Vs Frequency with D as parameter 104 4.6 Inductor current in DCM 105 4.7 Inductor current and output voltage in PSM converter under CCM 106 4.8 Inductor current in PSM converter under CCM 107 4.9 Improved PSM DC-DC buck converter-schematic 111 4.10 Skip logic sub circuit 112 4.11 Inductor current limit sub circuit 113 4.12 Typical output voltage and inductor current waveforms - Improved converter 114 4.13 CLK and pulses applied to switch 114 4.14 Output voltage and load current waveforms at nominal input voltage of 12V 115 4.15 Starting output and capacitor voltages and inductor current at 12V input voltage 116 4.16 Output Voltage and applied input voltage Response to a step increase in input voltage from 12V to 20V 116
xvi FIGURE NO. TITLE PAGE NO. 4.17 Output Voltage and load current response to a step decrease in load current from 1A to 0.5 A 117 4.18 Output Voltage Inductor current portrait. Average inductor current or Load current is 1A. Pulses skipped result in periodical inductor current discontinuity 117 4.19 Cascaded PSM and linear arrangement for power supply Block schematic 119 4.20 SIMPLIS schematic of PSM Buck regulator and linear regulator cascade 120 4.21 SIMPLIS simulation output showing reference and output voltage of PSM stage 121 4.22 Output voltage of linear regulator. The ripple reduced from 4% to less than 1% 121 4.23 Schematic of PSM converter with MOSFET IRF530 cascaded with linear regulator 122 4.24 Simulation output showing voltage output of PSM converter, linear regulator and Inductor current along with clock and applied pulses 122 4.25 Circuit schematic in express PCB 124 4.26 Component side of the board 125 4.27 Bottom copper layer 126 4.28 PWM/PSM hybrid mode with mode select for chaos free operation 128 4.29 Output voltage near transition to PSM from PWM 129 4.30 Bifurcation diagram - chaotic to non-chaotic transition at V in = 30V 129 5.1 Input current harmonic components PSM converter 134 5.2 Interleaved buck converter PWM 135 5.3 Control and output current signals PWM 135
xvii LIST OF SYMBOLS AND ABBREVIATIONS f a - Actual or effective frequency of the switch CLK - Clock CF-ZVS - Constant Frequency Zero Voltage Switching Quasi -QRC Resonant Converter v con - Control voltage V d - diode drop DCM - Discontinuous Conduction Mode d, D - Duty cycle EMI - Electro Magnetic Interference ESR - Equivalent Series Resistances I L - Inductor current ripple LIR - Inductor current ripple v in - Input voltage LDO - Low Drop Out V L - Lower voltage of ramp M - Modulation Factor M - Modulation factor p (or n) - Number of cycles during charging period q (or m) - Number of cycles during skipping period r - Number of cycles during which inductor current is zero T OFF - OFF state duration T ON - ON state duration v 0 - Output voltage PFM - Pulse Frequency Modulation PSM - Pulse Skipping Modulation PWM - Pulse Width Modulation v ramp - Ramp voltage
xviii Vref - Reference voltage x n - State vector n th sample f sw - Switching frequency T - Total duration V U - Upper voltages of ramp r - Voltage Ripple ZVS - Zero Voltage Switching