WIDE-RANGE 7-SWITCH FLYING CAPACITOR BASED DC-DC CONVERTER FOR POINT-OF-LOAD APPLICATIONS

WIDE-RANGE 7-SWITCH FLYING CAPACITOR BASED DC-DC CONVERTER FOR POINT-OF-LOAD APPLICATIONS By Parh Jain A hesis submied in conformiy wih he requiremens for he degree of Maser of Applied Science Graduae Deparmen of Elecrical and Compuer Engineering Universiy of Torono Copyrigh by Parh Jain 2015

WIDE-RANGE 7-SWITCH DC-DC CONVERTER FOR POINT-OF-LOAD APPLICATIONS Parh Jain Maser of Applied Science Graduae Deparmen of Elecrical and Compuer Engineering Universiy of Torono 2015 ABSTRACT In his hesis a dc-dc converer referred o as he 7-swich flying capacior (7SFC) based muli-level buck converer inended for poin-of-load applicaions is presened. The 7SFC operaes wih he principle of ransformabiliy which allows i o run in several swiching modes when paired wih a digial conroller. The mode is seleced based on inpu and oupu condiions by esimaing he highes efficiency mode. The 7SFC converer uilizes a flying capacior, which for cerain modes allows for a large reducion in swiching losses, especially when he converer is operaed wih highinpu volages. Compared o he convenional 2-phase inerleaved buck converer, he 7SFC is able o reduce he size of he oupu inducors and capacior by 33%. The 7SFC discree prooype is able o achieve efficiencies greaer han 90% over he majoriy of he operaing range. ii

ACKNOWLEDGEMENTS I would firs like o offer my graiude o he Universiy of Torono and he saff and faculy of he Deparmen of Elecrical and Engineering for providing a comforable and friendly environmen o perform my research over he pas wo years. I would also like o hank Alex Gerfer and Marin Haug of Wurh Elekronik for financially supporing my degree and providing useful feedback hrough he compleion of my projec. Mos of all, I would like o sincerely hank Prof. Aleksandar Prodic for his compassionae suppor hrough boh my undergraduae and graduae sudies. Prof. Prodic has gone beyond he call of duy on many occasions o provide me wih opporuniies o shine in he discipline and perform valuable research. Also, I would like o hank him for he many meaningful personal and professional connecions he has provided me wih. Finally, I would like o hank all of my lab maes who I have had he greaes pleasures of working wih over he course of my degree. Special hanks go ou o: Nenad Vukadinovic, Tim McRae, SM Ahsannuzaman, Behzad Mahdavikkah, Mahmoud Shousha, Amr Amin, Adrian Sraka, Jordan Kis, Jusin Blackman, Maryam Amouzandeh, Shadi Dashmiz and anyone who I have forgoen o menion here. Wihou heir company and suppor he lab environmen would no have been he same. iii

TABLE OF CONTENTS Chaper 1:... 1 1. Inroducion... 1 1.1 Poin-of-Load Converers... 1 1.2 Thesis Objecive... 3 1.3 Thesis Ouline... 3 Chaper 2:... 5 2. Prior Ar in Non-Isolaed Poin-of-Load Conversion... 5 2.1 Non-Isolaed Poin-of-Load Converer Topologies... 5 2.1.1 2-Phase Inerleaved Buck Converer... 6 2.1.2 Double Sep-Down Buck Converer... 8 2.1.3 2-Phase 3-Level Buck... 10 2.2 Digial Conrol... 13 Chaper 3:... 14 3. Novel Flying Capacior Based Dc-dc Topology... 15 3.1 Principle of Operaion... 17 3.1.1 7SFC: 2-Phase Inerleaved Buck Mode Operaion... 17 3.1.2 7SFC: High Sep-Down Mode Operaion... 19 3.1.3 7SFC: 3-Level Buck Mode Operaion... 21 3.1.4 Digial Conroller for he 7SFC Converer... 22 3.2 Loss Breakdown... 24 3.1.1 Conducion Losses... 24 3.1.2 Swiching Losses... 24 3.1.3 MOSFET Oupu Capacior Losses... 26 3.1.4 Gae Drive Losses... 27 3.1.5 Reverse Recovery Losses... 28 3.1.6 Inducor Core Loss... 29 3.3 Volume Esimaion... 30 3.4 Phase Shedding... 33 iv

3.5 Gae Driving... 35 Chaper 4:... 38 4. Experimenal Resuls and Comparison... 38 4.1 Reacive Componen Selecion and Volume Comparison... 40 4.1.1 Inducor Selecion... 40 4.1.2 Oupu Capacior Selecion... 41 4.1.3 Volume Comparison... 43 4.2 Power Loss Breakdown... 44 4.2.1 High Sep-Down Raio Loss Breakdown... 45 4.2.2 Medium Sep-Down Raio Loss Breakdown... 46 4.2.3 Loss Breakdown for Sep Down Raio Close o 0.5... 47 4.3 7SFC Seady-Sae Operaion... 48 4.3.1 7SFC: High Sep-Down Mode Waveforms... 48 4.3.2 7SFC: Inerleaved Buck Mode Waveforms... 49 4.3.3 7SFC: 3-Level Buck Mode Waveforms... 50 4.3.4 Convenional Inerleaved Buck Converer Waveforms... 51 4.4 Efficiency Resuls and Comparison... 52 Chaper 5:... 55 5. Conclusions and Fuure Work... 55 5.1 Major Accomplishmens... 55 5.2 Fuure Work... 56 References... 56 Appendix A:... 60 A. 2-Phase 3-Level Buck Converer Operaion for M > 0.5... 60 Appendix B:... 61 B. 7SFC Converer Conducion Losses... 62 B.1 Inerleaved Buck Mode... 62 B.2 High Sep-Down Mode... 64 v

B.3 3-Level Buck Mode... 69 Appendix C:... 72 C. Adding RMS Currens... 73 Appendix D:... 73 D. 2-Phase Inerleaved Buck Converer Loss Breakdown... 74 D.1 Conducion Losses... 74 D.2 Swiching Losses... 74 D.3 MOSFET Oupu Capacior Losses... 76 D.4 Gae Drive Losses... 76 D.5 Reverse Recovery Losses... 77 D.6 Inducor Core Loss... 77 Appendix E:... 77 E. Addiional Experimenal Seady-Sae Waveforms... 78 E.1 7SFC: High Sep-Down Mode Waveforms... 78 E.2 7SFC: Inerleaved Buck Mode... 79 E.3 7SFC 3-level buck mode... 80 E.4 Convenional Inerleaved Buck Converer... 81 Appendix F:... 83 F. Addiional Experimenal Efficiency Resuls... 83 vi

LIST OF TABLES Table 1. Experimenal Prooype Componens... 39 Table 2. Oupu capacior selecion based on oupu volage ripple... 42 Table 3. Oupu capacior selecion based on oupu volage deviaion... 43 Table 4. Toal silicon area comparison based on maximum inpu volage, V in,max... 44 vii

LIST OF FIGURES Figure 1-1: Inermediae bus power archiecure for poin-of-load applicaions... 2 Figure 2-1: Prior ar in non-isolaed poin-of-load conversion. a) Inerleaved buck converer, b) Double sep-down buck converer, c) 2-phase 3-level buck converer... 6 Figure 2-2: Swiching sequence and inducor waveforms for he inerleaved buck converer for D<0.5... 7 Figure 2-3: Swiching sequence and inducor waveforms for he double sep-down buck converer.. 9 Figure 2-4: DC equivalen circui for he double sep-down buck converer... 10 Figure 2-5: Swiching sequence and inducor waveforms for he 2-phase 3-level buck converer operaing in he M<0.5 mode... 12 Figure 3-1: Four quadrans of he operaing range... 15 Figure 3-2: Prior ar caegorized ino he four quadrans of he operaing range... 16 Figure 3-3: Novel 7-swich flying capacior (7SFC) based muli-level buck converer... 16 Figure 3-4: Swiching sequence and inducor waveforms for he inerleaved buck mode of he 7SFC converer operaing wih D<0.5... 18 Figure 3-5: Swiching sequence and inducor waveforms for he inerleaved buck mode of he 7SFC converer operaing wih D>0.5... 19 Figure 3-6: Swiching sequence and inducor waveforms for he high sep-down mode of he 7SFC converer... 20 Figure 3-7: Swiching sequence and inducor waveforms for he 3-level buck mode of he 7SFC converer... 22 Figure 3-8: Volage mode conroller for he 7SFC converer... 23 viii

Figure 3-9: Oupu capacior posiive charge for oupu volage ripple calculaion... 33 Figure 3-10: Swiching sequence and inducor waveforms for he single-phase inerleaved buck operaion of he 7SFC converer... 34 Figure 3-11: Swiching sequence and inducor waveforms for he single-phase 3-level buck operaion of he 7SFC converer... 35 Figure 3-12: Gae driving implemenaion of he 7SFC converer, a) charging of SW 5 boosrap circui, b) charging of SW 1 and SW 4 boosrap circuis... 37 Figure 4-1: Image of he op view of he experimenal prooype. The op PCB consiss of he power sage and he boom PCB is he conrol board wih sensing, ADCs and DACs... 38 Figure 4-2: Power loss breakdown for Vin=24V & Vou=1V, a) inerleaved buck converer, b) 7SFC converer... 46 Figure 4-3: Power loss breakdown for V in =7V & V ou =1V, a) inerleaved buck converer, b) 7SFC converer... 47 Figure 4-4: Power loss breakdown for V in =12V & V ou =5V, a) inerleaved buck converer, b) 7SFC converer, 3-level buck mode, c) 7SFC converer, inerleaved buck mode... 48 Figure 4-5: Experimenal waveforms for he 7SFC converer operaing in he high sep-down mode wih V in =12V & V ou =1V, a) displaying swiching nodes v x1 and v x2, b) displaying swiching node v x1 and oupu volage v ou... 49 Figure 4-6: Experimenal waveforms for he 7SFC converer operaing in he inerleaved buck mode wih V in =24V & V ou =12V, a) displaying swiching nodes v x1 and v x2, b) displaying swiching node v x1 and oupu volage v ou... 50 Figure 4-7: Experimenal waveforms for he 7SFC converer operaing in he 3-level buck mode wih V in =36V & V ou =12V, displaying swiching node v x and oupu volage v ou... 51 ix

Figure 4-8: Experimenal waveforms for he convenional inerleaved buck converer wih V in =12V & V ou =1V, a) displaying swiching nodes v x1 and v x2, b) displaying swiching node v x1 and oupu volage v ou... 51 Figure 4-9: Experimenal waveforms for he convenional inerleaved buck converer wih V in =36V & V ou =12V, a) displaying swiching nodes v x1 and v x2, b) displaying swiching node v x1 and oupu volage v ou... 52 Figure 4-10: Efficiency curves for V in =12V &V ou =1V for, a) convenional inerleaved buck converer, b) 7SFC converer... 53 Figure 4-11: Efficiency curves for V in =12V & V ou =5V for, a) inerleaved buck converer, b) 7SFC converer... 53 Figure 4-12: Efficiency curves for V in =15V & V ou =12V for, a) inerleaved buck converer, b) 7SFC converer... 54 Figure 5-1: Modes of he 7SFC converer caegorized based on he operaing range.... 56 Figure A-1: Swiching sequence and inducor waveforms for he 2-phase 3-level buck converer operaing in he M>0.5 mode... 61 Figure B-1: Swiching sequence and inducor waveforms for he inerleaved buck mode of he 7SFC converer for a) D<0.5 and b) D>0.5... 63 Figure B-2: Swiching sequence and inducor waveforms for he high sep-down mode of he 7SFC converer... 66 Figure B-3: Curren division during synchronous recificaion for he high sep-down mode of he 7SFC converer... 67 Figure B-4: Inducor and swich currens for he 3-level buck mode of he 7SFC converer... 71 Figure C-1: Typical inducor curren waveform... 73 Figure D-1: Inducor and swich currens for he inerleaved buck converer.... 75 x

Figure E-1: Experimenal waveforms for he high sep-down mode of he 7SFC converer wih V in =48V & V ou =3.3V... 78 Figure E-2: Experimenal waveforms for he high sep-down mode of he 7SFC converer wih V in =48V & V ou =11V... 78 Figure E-3: Experimenal waveforms for he inerleaved buck mode of he 7SFC converer wih V in =15V & V ou =12V... 79 Figure E-4: Experimenal waveforms for he inerleaved buck mode of he 7SFC converer wih V in =6V & V ou =5V... 79 Figure E-5: Experimenal waveforms for he 3-level buck mode of he 7SFC converer wih V in =48V & V ou =12V Figure E-6: Experimenal waveforms for he 3-level buck mode of he 7SFC converer wih V in =5V & V ou =3.3V... 80 Figure E-7: Experimenal waveforms for he convenional inerleaved buck converer wih V in =48V & V ou =3.3V... 81 Figure E-8: Experimenal waveforms for he convenional inerleaved buck converer wih V in =48V & V ou =12V... 81 Figure E-9: Experimenal waveforms for he convenional inerleaved buck converer wih V in =24V & V ou =12V... 81 Figure E-10: Experimenal waveforms for he convenional inerleaved buck converer wih V in =15V & V ou =12V... 82 Figure E-11: Experimenal waveforms for he convenional inerleaved buck converer wih V in =6V & V ou =5V... 82 Figure E-12: Experimenal waveforms for he convenional inerleaved buck converer wih V in =15V & V ou =3.3V... 82 Figure F-1: Efficiency curves for he 7SFC converer wih V ou =1V... 83 xi

Figure F-2: Efficiency curves for he 7SFC converer wih Vou=3.3V... 84 Figure F-3: Efficiency curves for he 7SFC converer wih V ou =5V... 85 Figure F-4: Efficiency curves for he 7SFC converer wih V ou =12V... 85 xii

1 CHAPTER 1: 1. INTRODUCTION In almos all elecronics oday, poin-of-load (PoL) dc-dc converers are needed o provide regulaed dc volages o various funcional blocks in a sysem. Generally, hese funcional blocks require differen volage and power levels and, herefore, dedicaed PoL converers are used for each block. For hese sysems, cusom designs of he buck converer are almos exclusively used as he PoL of choice. The use of cusom PoL designs allows he designer o maximize efficiency and minimize volume for each converer, and opimize he full sysem performance. However, his increases sysem-level design complexiy, could influence reliabiliy, and increases manufacuring cos [1]. For example, o design, verify and implemen up o 10 dedicaed PoLs would heavily burden he designer and increase he ime-o-marke significanly. For hese reasons, i is beneficial o have a sand-alone wide-range universal converer ha can provide a large range of volages and power levels suiable for all applicaions, raher han specific ones. For many applicaions he success of a PoL is deermined by is abiliy o provide a regulaed volage and power wih high power processing efficiency, low volume, and good dynamic performance. The main objecive of his hesis is o propose a opology ha will ac as he aforemenioned universal converer and mee he necessary requiremens for wide-range PoL applicaions. 1.1 Poin-of-Load Converers Poin-of-load converers are used expansively in elecronic sysems o efficienly disribue power o all of he necessary loads, from communicaions and compuer applicaions o medical and miliary areas. PoLs are dc-dc converers ha are placed close o he loads hey are supplying power o, and provide conversion, regulaion and in some cases isolaion [2]. A diagram of he inermediae bus power archiecure is presened in Figure 1-1. In his sysem, an ac-dc fron-end converer is uilized o provide basic isolaion and conversion o a high-volage bus (generally 48V o 380V). Following his, an isolaed dc-dc converer is used o supply an inermediae bus a a lower volage (ypically 3.3V o 48V) from which he PoLs operae. This power archiecure

2 has gained populariy over he las fifeen years and is he main archiecure for poin-of-load sysems [3]. Inermediae bus volages are heavily ied o paricular applicaions: 8V or 12V for he communicaions segmen, 12V and 24V for compuer sysems, 3.3V, 5V, 12V and 48V for medical, and volages even higher for miliary and aerospace applicaions [4]. Since isolaion is already provided by he previous conversion sages, he PoLs can be non-isolaed. AC Power ( 90V o 265V ) AC-DC Fron-End Converer High Volage Bus ( 48V o 380V ) Isolaed Inermediae Bus Converer Inermediae Bus ( 3.3V o 48V ) Non-Isolaed POL Non-Isolaed POL Non-Isolaed POL Non-Isolaed POL 1V 3.3V 5V 12V Figure 1-1: Inermediae bus power archiecure for poin-of-load applicaions According o marke research performed by Darnell [4,5], he oal marke revenue for dc-dc converer modules in 2016 is expeced o be $4.3 billion and, for dc-dc converer IC soluions, he marke sales are expeced o be 32 billion unis; boh being rapidly growing markes. Paricular aenion in he sudies is given o he non-isolaed PoL applicaion segmen where he inermediae bus power archiecure has gained populariy due o increased sysem performance. The growh of his marke segmen relies on he improvemens of PoL converers compared o he convenional buck soluion. By increasing power processing efficiency, lowering cos, reducing size, and improving configurabiliy, he use of he PoL can be expanded. In a convenional PoL sysem each non-isolaed PoL block in Figure 1-1 would be a cusom buck converer designed based on he inermediae bus volage and required oupu volage and power. In a large sysem, he design complexiy increases direcly wih he number of required PoLs.

3 Anoher drawback of he convenional buck soluion is he dependence of sysem performance on he inpu and oupu operaing condiions. For high inermediae bus volages, he power processing efficiency of he buck converer significanly degrades. Due o hese limiaions, he focus of his hesis will be on he design of a novel non-isolaed PoL converer ha can operae for a wide range of operaing condiions wih high power processing efficiency and low volume compared o he convenional buck converer. 1.2 Thesis Objecive The objecive of his hesis is o analyze he limiaions of exising PoL soluions and o propose a new soluion ha can improve on hem. The specific limiaions ha are being addressed are wide-range conversion, overall volume and power processing efficiency. This is done by inroducing a novel non-isolaed opology ha uilizes specific advanages of several pre-exising opologies and combining hem ino a single low-volume high-efficiency converer. Compared o he convenionally used 2-phase inerleaved buck converer, his new opology improves in he following ways: Taking advanage of muli-level dc-dc conversion Muli-mode converer operaion for efficiency opimizaion Significan reducion in reacive componen volume Reducing silicon area needed for implemenaion 1.3 Thesis Ouline The maerial of his hesis is presened in he following sequence: In Chaper 2 pre-exising opologies for non-isolaed PoL applicaions are presened. These opologies include he convenional 2-phase inerleaved buck converer, as well as previously proposed alernaives, he double sep-down buck [6] and he 3-level buck converer [7]. The opology limiaions are discussed, clearly saing specific areas of improvemen, which are addressed in Chaper 3 wih he inroducion of he new opology. Following his discussion, prior ar for conrol is presened including digial conrol echniques for dc-dc converers.

4 Chaper 3 begins by oulining he design sraegy used o come up wih he novel 7-swich flying capacior (7SFC) based muli-level buck converer. Then, he principle of operaion and full analyses of converer losses and volume esimaions are presened. Conrol echniques are discussed for he 7SFC converer and he conroller complexiy is analyzed. In Chaper 4 an experimenal prooype ha was designed, buil and esed is inroduced wih he following specificaions: 3V < V in < 48V, 1V < V ou < 12V, I load < 6A. Power loss breakdowns for he 7SFC converer and he convenional inerleaved buck converer are compared over his operaing range. Efficiency resuls for he 7SFC muli-level buck are presened for many operaing poins. The volume comparison for reacive componens is verified hrough inducor curren ripple and ransien comparisons. The hesis conclusion as well as possible fuure work wih regards o he 7SFC muli-level buck converer is presened in Chaper 5.

5 CHAPTER 2: 2. PRIOR ART IN NON-ISOLATED POINT-OF-LOAD CONVERSION This secion is a review of he convenional and previously proposed echnologies for nonisolaed poin-of-load conversion in erms of boh opologies and complemenary conrol mehods. Single-sage opologies are preferred for his applicaion due o he design simpliciy, and he efficiency improvemens by neglecing a fron-end conversion sage. Firs, hree opologies will be examined as background in non-isolaed PoL opologies, he 2-phase inerleaved buck converer, he double sep-down buck converer [6], and he 2-phase 3-level buck converer [7]. In he second par of his secion digial conrol mehods are discussed as a means of conrolling PoLs. 2.1 Non-Isolaed Poin-of-Load Converer Topologies The buck converer opology is he mos widely used opology for non-isolaed PoLs due o he exensive research wih regards o is design and conrol [8]. Also, o improve on he buck converer s performance, many opologies and conrol mehods have been derived o opimize efficiency for paricular applicaions of PoLs [9-13]. In hese opologies, he rade-off for design simpliciy over flexibiliy for a wide range of conversion raios is made. Muli-level converers have also been adoped for high-power converers [7], and recenly proposed for low-power applicaions as well [14]. Muli-level opologies have gained aenion over recen years due o heir improvemens in efficiency and volume over convenional buck opologies a he cos of added design complexiy. Three opologies will be discussed in his secion as a review of prior ar in non-isolaed PoL conversion, 1) he 2-phase inerleaved buck, 2) he double sep-down buck proposed by Nishijima [6] and 3) he 2-phase 3-level buck converer, whose single-phase counerpar was proposed by Meynard [7]. The hree opologies are shown in Figure 2-1.

6 SW 1 L 1 i L1 () V in SW 2 SW 3 SW 4 V x1 V x2 L 2 i L2 () C R V ou V in SW 1 V Cfly L 1 C fly SW V x1 2 SW 3 SW 4 V x2 L 2 i L1 () i L2 () C R V ou SW 2 SW 3 V Cfly1 SW 1 L 1 C fly1 SW 4 V x1 SW 6 SW 5 V Cfly2 SW 7 L 2 C fly2 SW 8 i L1 () C R V ou V in V x2 i L2 () Figure 2-1: Prior ar in non-isolaed poin-of-load conversion. a) Inerleaved buck converer, b) Double sep-down buck converer, c) 2-phase 3-level buck converer 2.1.1 2-Phase Inerleaved Buck Converer Along wih is single-phase counerpar, he 2-phase inerleaved buck converer of Figure 2-1a) is a popular choice for power modules and wide-range sep-down conversion. The buck converer is very well undersood, and a plehora of research has been done modeling is losses and conrol [8]. This makes i an aracive, simple soluion for many designers. However, i has significan drawbacks when i comes o high sep-down conversions, which is required in a large number of applicaions. For he sake of convenience he swiching sequence and inducor waveforms for he 2-phase inerleaved buck converer operaing wih a duy raio of D < 0.5 is shown in Figure 2-2. The conversion raio for his converer is M(D)=D, and i can operae from 0 < D < 1.

7 The firs limiaion of he buck converer for high sep-down conversion raios is in he range of duy raio values. Since he conversion raio is direcly relaed o he duy raio, he highes possible sep-down conversion depends on he lowes duy raio possible in he converer. In high-frequency converers, which are common for low-volume applicaions, low duy raio values become more difficul o produce. Sae 1: 0 < < DT s Sae 2 (& 4): DT s < < T s /2 (T s /2+DT s < < T s ) SW 1 L 1 SW 1 L 1 V in V L1 SW 2 i L1 () SW i L1 () 2 SW L 2 3 C SW L 2 3 C R V ou R V V ou SW L2 i L2 () V L2 i L2 () 4 V in SW 4 V L1 V in Sae 3: T s /2 < < DT s +T s /2 SW 1 SW 2 SW 3 SW 4 L 1 V L1 L 2 V L2 i L1 () C i L2 () R V ou V L1 () i L1 () V L2 () i L2 () 0 Sae 1 Sae 2 Sae 3 Sae 4 V in -V ou -V ou V in -V ou -V ou DT s T s /2 (½+D)T s T s Figure 2-2: Swiching sequence and inducor waveforms for he inerleaved buck converer for D<0.5 Oher disadvanages of he buck converer relae o he power densiy and volume limiaions of he opology. The buck converer swiches mus all be raed o block he full inpu volage of he converer which impacs he silicon area aken up by he swiches. Along wih his, he swiching losses of he converer are direcly relaed o he volage across he swiches. For high inpu volages he swiching losses dominae he oal losses of he converer, hus reducing he efficiency and power densiy. For dc-dc converers wih swiching frequencies in he hundreds of

8 kiloherz, as argeed in his hesis, he reacive componens ake up he majoriy of he volume. Generally, he inducor is chosen o achieve a paricular curren ripple specificaion, as shown in Eq. (2-1) for he 2-phase inerleaved buck converer where V in is he inpu volage, V ou is he oupu volage, I load,max is he maximum load curren of he converer, Δi L is he desired peakpeak curren ripple, and f s is he swiching frequency. L = Vou (1 ) V V ou I load,max in 2 i f s ( L ) I load,max. (2-1) The volume of he inducor is relaed o he energy sorage requiremen [15] based on Eq. (2-2), Inducor Volume L (i) 2, (2-2) where L is he chosen inducance value from (1) and i is he maximum curren in he inducor. For high inpu volages, and conversion raios close o M(D)=0.5, he required inducance value will be large, hus presening a major conribuion o he overall converer volume. 2.1.2 Double Sep-Down Buck Converer The double sep-down buck converer of Figure 2-1,b) was proposed by Nishijima e al. [6] as an alernaive o he 2-phase inerleaved buck converer inended for high sep-down raios. Since i incorporaes a flying capacior, C fly, i is able o reduce he swiching losses and volage raings of he swiches wihou increasing he number of swiches. This converer has been analyzed in deail in previous work [16] and has been shown o achieve higher efficiencies han he 2-phase inerleaved buck converer over is operaing range. The conversion raio for his opology is M(D)=D/2 and i operaes over he range of duy raios of 0<D<0.5. For compleeness, he swiching sequence and relevan inducor waveforms for he double sep-down buck are provided in Figure 2-3. When operaing in seady-sae, he flying capacior has approximaely half of he inpu volage across i.

9 Sae 1: 0 < < DT s Sae 2 (& 4): DT s < < T s /2 (T s /2+DT s < < T s ) SW 1 V Cfly C fly SW 2 L 1 V L1 i L1 () SW 1 V Cfly L 1 C fly SW 2 V L1 i L1 () V in SW 3 SW 4 L 2 V L2 i L2 () C R V ou V in SW 3 SW 4 L 2 V L2 i L2 () C R V ou V in Sae 3: T s /2 < < DT s +T s /2 SW 1 V Cfly C fly SW 3 SW 4 SW 2 L 1 V L1 L 2 V L2 i L1 () C i L2 () R V ou Sae 1 Sae 2 Sae 3 Sae 4 V L1 () V in -V Cfly -V ou i L1 () V L2 () i L2 () 0 -V ou V Cfly -V ou -V ou -V ou DT s T s /2 (1/2+D)T s T s Figure 2-3: Swiching sequence and inducor waveforms for he double sep-down buck converer. As can be seen from Figure 2-3, hree ou of four of he swiches, all excep for SW 3, are only required o block half of he full inpu volage. This will significanly reduce he silicon area requiremen for his opology compared o he 2-phase inerleaved buck. In erms of power densiy, all four of he swiches experience swiching losses proporional o half of he inpu volage, as opposed o he full inpu volage in he convenional buck converer. This explains he efficiency and power densiy improvemens of he double sep-down buck. Furhermore, he oupu inducors can be reduced in size compared o he inerleaved buck converer for he same curren ripple requiremen. The equaion for he selecion of inducance for he double sep-down buck converer is shown in Eq. (2-3), L = 2 Vou (1 ) V V ou I load,max in 2 i f s ( L ) I load,max, (2-3) where V in is he inpu volage, V ou is he oupu volage, I load,max is he maximum load curren, Δi L is he desired peak-peak curren ripple, and f s is he swiching frequency.

10 The main limiaion of he opology is a much reduced operaing range compared o he 2-phase inerleaved buck converer. Given he duy raio range of 0<D<0.5, he converer can only provide conversion raios up o ¼. Thus, for a wide-range converer which requires volage conversion above ¼, he double sep-down buck is no suiable as a full soluion. The double sep-down buck converer also has he advanage of inheren inducor curren balancing. Observing he dc equivalen circui of he converer shown in Figure 2-4, i can be seen ha he inducor currens, I L1 and I L2, are forced equal if he duy raios for Sae 1 and Sae 3 are he same. Also, if we assume he equivalen phase resisances for L 1 and L 2, R eq1 and R eq2, are close, hen he flying capacior, C fly, will also be approximaely half of he inpu volage wihou he need for addiional conrol. D V in R eq1 I L1 V Cfly V in D I L1 D V Cfly R eq2 I L2 D V Cfly C R Vou C fly D I L1 D I L2 Figure 2-4: DC equivalen circui for he double sep-down buck converer 2.1.3 2-Phase 3-Level Buck The 2-phase 3-level buck converer shown in Figure 2-1c) and is single-phase counerpar are less convenional opologies for low o medium power levels of PoL conversion. The original research on he 3-level buck converer was performed by Meynard and Foch [7] where hey model several variaions of he mulilevel converer. The 3-level buck was originally proposed as a high volage inverer since he high volage across he power swiches in his applicaion was a serious reliabiliy issue [17]. As shown in [7], wih he addiion of a single flying capacior he convenional buck converer becomes a 3-level converer ha can be used for sep-down dc-dc conversion. As a resul, he blocking volage requiremen for all of he swiches is reduced by

11 half, and hus reduces swiching losses for each swich as well. The 3-level buck can be operaed wih wo disinc swiching sequences o achieve conversion for all sep-down cases. The firs sequence achieves a conversion raio of M(D)=D wih a duy raio range of 0<D<0.5 and he second sequence achieves a conversion raio of M(D)=½+D wih he same duy raio range. In his hesis we are ineresed in 2-phase converers so he swiching sequence and relevan inducor waveforms for he 2-phase 3-level buck is provided in Figure 2-5 for M<0.5. The swiching sequence and inducor waveforms for he M>0.5 case has been referred o Appendix A. The 2-phase 3-level buck converer has wo flying capaciors, C fly1 and C fly2, which have approximaely half of he inpu volage across hem in seady-sae. The main advanage of he 2-phase 3-level buck is he reducion in oupu inducor volume based on he curren ripple requiremen. The inducor selecion for he 2-phase 3-level buck based on he curren ripple requiremen is shown in Eq. (2-4), L = (1 2 Vou ) V V ou I load,max in 2 i f s ( L ) I load,max, (2-4) where V in is he inpu volage, V ou is he oupu volage, I load,max is he maximum load curren, Δi L is he desired peak-peak curren ripple, and f s is he swiching frequency. Compared o he 2- phase inerleaved buck converer he oupu inducors can be reduced by more han half, and compared o he double sep-down buck converer he inducors are halved, using Eq. (2-2) for inducor energy sorage capaciy. Since he reacive componens are he major conribuors for volume in dc-dc converers operaing in he hundreds of kiloherz, his reducion is a significan benefi of he 2-phase 3-level buck converer. A he same ime, however, core losses for each inducor are doubled due o he increased apparen frequency in he inducor. The drawbacks for he 2-phase 3-level buck converer appear mainly due o he increased number of swiches i requires o operae. The swiching losses for each swich is reduced, however, he fac ha eigh swiches are operaed in every swiching cycle, as opposed o four in he inerleaved buck converer, diminishes his advanage significanly. The resul is an overall efficiency ha is comparable o he inerleaved buck converer, wih he clear advanage of significanly reduced volume as menioned earlier. Along wih he addiional swiches, he 2-

12 phase 3-level buck requires wo flying capaciors, increasing volume furher. Unlike he double sep-down buck converer, he 2-phase 3-level buck does no have inheren curren balancing. Sae 1: 0 < < DTs SW2 Sae 2: DTs < < Ts/4 SW2 Vin SW1 SW5 VCfly1 Cfly1 SW6 VCfly2 Cfly2 SW8 SW3 SW4 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Vin SW1 SW5 VCfly1 Cfly1 SW6 SW4 VCfly2 Cfly2 SW8 SW3 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Sae 3: Ts/4 < < Ts (D+¼) SW2 Sae 4: Ts (D+¼) < < Ts/2 SW2 SW1 VCfly1 SW3 L1 SW1 VCfly1 SW3 L1 Vin SW5 Cfly1 SW4 SW6 VCfly2 Cfly2 SW7 SW8 VL1 L2 VL2 il1() C il2() R Vou Vin SW5 Cfly1 SW6 SW4 VCfly2 Cfly2 SW8 SW7 VL1 L2 VL2 il1() C il2() R Vou Sae 5: Ts/2 < < Ts (D+½) SW2 Sae 6: Ts (D+½) < < Ts 3/4 SW2 Vin SW1 SW5 VCfly1 Cfly1 SW6 SW4 VCfly2 Cfly2 SW8 SW3 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Vin SW1 SW5 VCfly1 Cfly1 SW6 SW4 VCfly2 Cfly2 SW8 SW3 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Sae 7: Ts 3/4 < < Ts (D+¾) SW2 Sae 8: Ts (D+¾) < < Ts SW2 Vin SW1 SW5 VCfly1 Cfly1 SW6 SW4 VCfly2 Cfly2 SW8 SW3 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Vin SW1 SW5 VCfly1 Cfly1 SW6 SW4 VCfly2 Cfly2 SW8 SW3 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Sae 1 Sae 3 Sae 5 Sae 7 Sae 2 Sae 4 Sae 6 Sae 8 VL1() il1() il2() 0 Vin-VCfly-Vou -Vou -Vou Vin-VCfly-Vou VCfly-Vou -Vou -Vou VCfly-Vou -Vou Iload/2 Iload/2 DTs Ts/4 Ts/2 Ts 3/4 Ts Ts/4+DTs Ts/2+DTs Ts 3/4+DTs Figure 2-5: Swiching sequence and inducor waveforms for he 2-phase 3-level buck converer operaing in he M<0.5 mode

13 This implies ha he flying capaciors are no guaraneed o be balanced a half of he inpu volage. Some previous work has been done ha suggess he flying capaciors can be moniored, and conrolled o achieve he desired volage [18,19], however, his increases he conroller complexiy for his opology. 2.2 Digial Conrol Digial conrol has gained increasing aenion over he las en years for low-cos volumesensiive applicaions. In mos cases a digial conroller can be fully inegraed on-chip and consume a fracion of he volume and power of he converer iself [20-21]. Compared o is analog alernaive, a digial conroller does no require large capaciors and resisors o make up he conrol feedback nework. Anoher advanage of digial conrol is he increase in flexibiliy for he conroller compared o an analog conroller. In a digial conroller, since he compensaor is implemened using digial arihmeic, wih he change of a single number he compensaor design can be adjused. In an analog implemenaion, his degree of flexibiliy would require a large bank of capacior and resisor values, and addiional circuiry o selec desired values, which would increase he conroller volume. This makes digial conrol an aracive soluion for a wide-range converer ha has varying inpu volage, oupu volage and load curren. To deal wih sudden changes in he load curren, a frequen occurrence for PoLs, several digial conrol mehods exis. The mos convenional mehod is by uning he PID coefficiens in he digial compensaor o achieve a good ransien response. This, however, has limiaions when dealing wih a wide range of inpu volages, oupu volages and load currens since he PID can only be opimized for a cerain range. Time-opimal conrol [22] is a non-linear soluion o he issue of ransiens ha can funcion for any variaion of inpu volage, oupu volage and load curren. In a ime-opimal conroller, when a load ransien occurs, he PID is bypassed and he inducor curren is eiher ramped up or ramped down unil he charge in he oupu capacior is recovered and has seled o he desired oupu volage. Once his has compleed, he PID is reiniialized and resumes operaion. The advanages of a ime-opimal conrol oher han flexibiliy for converer parameers are a fas dynamic response, in one swiching cycle, and reduced oupu volage deviaion compared o a uned PID conroller. This allows for a reducion in he oupu

14 capaciance, one of he mos spacious elemens of he converer. This mehod is used as he benchmark for ransien conrol in Chaper 3 for oupu capacior sizing. CHAPTER 3:

15 3. A NOVEL FLYING CAPACITOR BASED DC-DC TOPOLOGY This secion proposes a novel dc-dc converer as a soluion o he wide-range universal dc-dc converer issue. To address he design issue of a novel dc-dc converer for a wide-range applicaion he operaing range was divided ino four caegories: 1) high volage, low curren, 2) high volage, high curren, 3) low volage, low curren, and 4) low volage high curren, as shown in Figure 3-1, where he volage is he inpu volage V in and he oupu curren is I load. For high inpu volages swiching loss should be avoided, and for high oupu currens swich conducion loss is miigaed. For low volage and low oupu curren condiions, gae drive losses are avoided and specialized conrol echniques such as phase shedding can be used. High Inpu Volage, Low Oupu Curren - Trade-off swiching loss wih conducion loss Low Inpu Volage, Low Oupu Curren - Low gae drive losses - Conrol echniques High Inpu Volage, High Oupu Curren - Low swiching loss and low conducion loss Low Inpu Volage, High Oupu Curren - Low conducion loss where here can be swiching loss Figure 3-1: Four quadrans of he operaing range By looking a he problem in his way, differen opologies, such as he ones in Chaper 2, could be caegorized o achieve high efficiency in one caegory bu no he ohers. For example, he inerleaved buck converer has good efficiency for low inpu volages where swiching losses are less dominan, and he double sep-down buck converer has high efficiency for high sep-down cases. A summary of he prior ar of Chaper 2 caegorized ino he four quadrans of he operaing range is shown in Figure 3-2.

16 High Inpu Volage, Low Oupu Curren High Inpu Volage, High Oupu Curren - 2-phase, 3-level buck - Double sep-down buck - 2-phase 3-level buck Low Inpu Volage, Low Oupu Curren - Single-phase buck - Single-phase, 3-level buck Low Inpu Volage, High Oupu Curren - Inerleaved buck Figure 3-2: Prior ar caegorized ino he four quadrans of he operaing range The new opology, referred o as he 7-swich flying capacior muli-level buck converer, or 7SFC, is shown in Figure 3-3. As he name suggess, i has an increased number of swiches compared o he convenional inerleaved buck converer and double sep-down converer. Paired wih a digial conroller, he added benefis of he 7SFC converer are manifold in erms of efficiency, volume, and flexibiliy. V in V Cfly SW 1 SW 3 L 1 C fly SW SW 7 2 V x1 SW 4 SW 5 SW 6 V x2 L 2 C R V ou Figure 3-3: Novel 7-swich flying capacior (7SFC) based muli-level buck converer I uilizes specific advanages from he prior ar, such as he wide conversion range of he inerleaved buck converer, he high sep-down advanages of he double sep-down buck, and he reduced swich raings and swiching volages of he 3-level converer, o form a complee soluion ha can provide high efficiency and high power densiy for a wide range of conversion raios. The principle of operaion is discussed nex, followed by a complee loss breakdown for each mode, converer volume esimaion and some implemenaion deails. The conroller is hen discussed and general conrol issues are summarized.

17 3.1 Principle of Operaion The 7-swich flying capacior (7SFC) muli-level buck converer operaes on he principle of ransformabiliy, which refers o is abiliy o choose is mode of operaion based on operaing condiions. This mode changing characerisic is faciliaed by a complemenary digial conroller. The hree modes of operaion being presened here are: 1) inerleaved buck mode, 2) high sep-down mode, and 3) 3-level buck mode. The inerleaved buck mode is derived from he 2-phase inerleaved buck converer, he high sep-down mode from he double sep-down buck converer and he 3-level buck mode from he 3-level buck. To mainain he reduced swich raings of half of he maximum inpu volage across all of he swiches, an advanage of he double sep-down buck and 3-level buck, he modes mus be operaed accordingly. The mode wih he highes efficiency is seleced by he digial conroller based on a look-up able. The following sub-secions presen he swich operaion and paricular deails of each of he modes of he 7SFC based muli-level buck converer followed by a descripion of he digial conroller implemenaion. 3.1.1 7SFC: 2-Phase Inerleaved Buck Mode Operaion In he 7SFC based muli-level buck converer he inerleaved buck mode can only be used for a reduced inpu volage range. This is due o he fac ha we require ha all of he swiches are raed for a maximum blocking volage of V in,max /2, where V in,max is he highes inpu volage of he operaing range. In he inerleaved buck mode of operaion all of he swiches are exposed o he full inpu volage so he maximum inpu volage o operae his mode would be V in,max /2. The inerleaved buck mode is mainly used for conversion raios close o and greaer han 0.5, and i is he only mode ha can provide a conversion raio greaer han 0.5. The conversion raio for he inerleaved buck mode is shown in Eq. (3-1), M(D) = D, (3-1) where M(D) is he conversion raio and D is he duy raio for he mode.

18 The swiching sequence for he 7SFC inerleaved buck mode wih D > 0.5 is shown in Figure 3-4. SW 1, SW 2 and SW 4 remain ON which holds he inermediae capacior volage, V Cfly, a he inpu volage. This mode operaes he same as a convenional inerleaved buck converer, where SW 7 and SW 5 ac as he main swiches, and SW 3 and SW 6 ac as he synchronous recifiers, for he L 1 and L 2 phases respecively. One difference incurred from uilizing he inerleaved buck converer mode in he 7SFC which is no presen in he convenional inerleaved buck converer is he increased curren in SW 1, and SW 4 during Sae 1. In his sae he swiches mus conduc he full load curren, which increases conducion losses in hese ransisors. Sae 1 (& 3): 0 < < (D-½)T s (T s /2 < < T s /2+(D-½)T s ) Sae 2: (D-½)T s < < T s /2 V in V Cfly SW 1 SW L 1 3 C fly V SW L1 2 SW 7 SW4 SW 5 SW 6 i L1 () SW 1 SW L 1 3 C fly SW 2 L 2 C V SW4 L 2 V L2 i L2 () R in C V ou SW 5 V L2 i L2 () R V ou V Cfly SW 7 V L1 SW 6 i L1 () Sae 4: V in T s /2+(D-½)T s < < T s V Cfly SW 1 SW L 1 3 C fly SW 2 SW 7 SW4 SW 5 V L1 L 2 V L2 SW 6 i L1 () i L2 () C R V ou V L1 () i L1 () V L2 () i L2 () 0 Sae 1 Sae 2 Sae 3 Sae 4 V in -V ou V in -V ou V in -V ou -V ou (D-½)T s T s /2 DT s -V ou T s Figure 3-4: Swiching sequence and inducor waveforms for he inerleaved buck mode of he 7SFC converer operaing wih D<0.5

19 The swiching sequence for D < 0.5 is shown in Figure 3-5 where he swiches have he same funcions as for he D > 0.5 case, however, SW 1 and SW 4 do no conduc increased curren a any poin during he swiching cycle. V in Sae 1: 0 < < DT s V Cfly SW 1 SW L 1 3 C fly SW 7 SW4 SW 2 SW 5 V L1 SW 2 L 2 C V L2 i L2 () R V SW4 L 2 in C V ou SW 5 V L2 i L2 () R V ou SW 6 i L1 () Sae 2 (& 4): DT s < < T s /2 (T s /2+DT s < < T s ) V Cfly SW 1 SW L 1 3 C fly SW 7 VL1 SW 6 i L1 () Sae 3: T s /2 < < DT s +T s /2 V in V Cfly SW 1 SW L 1 3 C fly V L1 SW 7 SW4 SW 2 SW 5 L 2 V L2 SW 6 i L1 () i L2 () C R V ou V L1 () i L1 () V L2 () i L2 () 0 Sae 1 Sae 2 Sae 3 Sae 4 V in -V ou -V ou V in -V ou (D-½)T s T s /2 DT s -V ou T s Figure 3-5: Swiching sequence and inducor waveforms for he inerleaved buck mode of he 7SFC converer operaing wih D>0.5 The inducor curren ripple for he inerleaved buck mode is represened by Δi L-IB, and shown in Eq. (3-2), i L IB = (V in V ou ) ( Vou ) T V s in, (3-2) L where V in is he inpu volage, V ou is he oupu volage, T s is he swiching period and L is he inducance value. 3.1.2 7SFC: High Sep-Down Mode Operaion

20 The high sep-down mode of he 7SFC is derived from he double sep-down buck converer presened in Chaper 2, and provides he highes efficiency for high sep-down cases, as he name suggess. Like he double sep-down buck, his mode of operaion has a limied range of operaion of 0<D<0.5 and conversion raio shown in (3-3), M(D) = D 2, (3-3) where M(D) is he conversion raio, and D is he duy raio. The main advanage of he high sepdown mode of he 7SFC from he double sep-down buck converer is ha wih he addiion of wo swiches, SW 7 and SW 5, all 7 of he swiches in he 7SFC can be raed a half of he full inpu volage. The benefi of a lower volage raing for a swich is a reduced volume and figure of meri compared o a higher volage swich [23]. Figure of meri is a measure of he qualiy of a specific semiconducor device, used o compare differen devices. The swiching sequence for he 7SFC operaing in he high sep-down mode is shown in Figure 3-6. V in Sae 1: 0 < < DT s V Cfly SW 1 SW L 1 3 C fly SW 7 SW4 SW 2 SW 5 V L1 i L1() V L1 SW 2 i SW L1 () L 7 2 L C 2 V L2 i L2 () R V SW4 in C V ou SW 5 V L2 i L2 () R V ou SW 6 Sae 2 (& 4): DT s < < T s /2 (T s /2+DT s < < T s ) V Cfly SW 1 SW L 1 3 C fly SW 6 V in Sae 3: T s /2 < < DT s +T s /2 V Cfly SW 1 SW L 1 3 C fly V L1 SW 7 SW4 SW 2 SW 5 L 2 V L2 SW 6 i L2() i L1 () C R V ou Sae 1 Sae 2 Sae 3 Sae 4 V L1 () V in -V Cfly -V ou i L1 () V L2 () i L2 () 0 -V ou V Cfly -V ou -V ou -V ou DT s T s /2 T s /2+DT s T s Figure 3-6: Swiching sequence and inducor waveforms for he high sep-down mode of he 7SFC converer

21 Observing he swiching sequence i can be seen ha anoher difference from he double sepdown converer of Chaper 2 is he curren division during Sae 2 and 4. In hese synchronous recificaion saes he inducor currens are divided amongs SW 2, SW 3, SW 5, SW 6 and SW 7 based on heir on-resisances. This disribues he curren amongs he swiches o achieve lowes power losses naurally compared o if SW 5 and SW 7 were no presen. The inducor curren ripple for he high sep-down mode is represened by Δi L-HSD, and shown in Eq. (3-4), i L HSD = (Vin 2 V ou) ( 2 V ou) T V s in L, (3-4) where V in is he inpu volage, V ou is he oupu volage, T s is he swiching period and L is he inducance value. 3.1.3 7SFC: 3-Level Buck Mode Operaion The 3-level buck mode of he 7SFC converer is a simplified version of he wo-phase 3-level buck inroduced in Chaper 2. This mode is operaed wih boh inducors in parallel by keeping SW 5 and SW 7 on over he full swiching cycle. This allows he load curren o be spli beween he wo inducors, reducing he volume requiremen and losses of he inducors, as would be seen in any 2-phase opology. This mode operaes wih a duy raio range of 0<D<0.5 and a conversion raio of M(D) = D, where M(D) is he conversion raio, and D is he duy raio. Similar o he high sep-down mode he swiches are swiched a half of he inpu volage, reducing swiching losses as well. The 3-level buck mode has many poenial savings in erms of efficiency however here are also several conrol issues, such as inermediae capacior balancing and inducor curren balancing, which make i more difficul o use. The swiching sequence and inducor volage and curren waveforms for he 3-level buck mode are shown in Figure 3-7. The curren division during synchronous recificaion is similar o ha of he high sep-down mode as well since several swiches are presen in he conducion pah.

22 V in Sae 1: 0 < < DT s V Cfly SW 1 SW L 1 3 C fly V L1 SW 7 SW4 SW 2 SW 5 SW 2 L 2 C V L2 i L2 () R V SW4 L 2 in C V ou SW 5 V L2 i L2 () R V ou SW 6 i L1 () Sae 2 (& 4): DT s < < T s /2 (T s /2+DT s < < T s ) V Cfly SW 1 SW L 1 3 C fly V L1 SW 7 SW 6 i L1 () V in Sae 3: T s /2 < < DT s +T s /2 V Cfly SW 1 SW L 1 3 C fly V L1 SW 7 SW4 SW 2 SW 5 L 2 V L2 SW 6 i L2 () i L1 () C R V ou Sae 1 Sae 2 V L1 () V in -V Cfly -V ou Sae 3 V Cfly -V ou Sae 4 -V ou -V ou i L1 () V L2 () V in -V Cfly -V ou V Cfly -V ou i L2 () 0 -V ou -V ou DT s T s /2 T s /2+DT s T s Figure 3-7: Swiching sequence and inducor waveforms for he 3-level buck mode of he 7SFC converer For his mode of operaion, since he inducors are in parallel, he advanages of inerleaved operaion from he 2-phase 3-level buck of Chaper 2 are los. The consequence of his is an increased oupu capacior value for he same oupu volage ripple compared o ha opology. Also, some of he swiches, such as SW 1, SW 2, SW 3 and SW 4, are exposed o he full load curren during cerain periods of he swiching cycle, hus increasing conducion losses compared o he 2-phase 3-level buck converer. The inducor curren ripple for he 3-level buck mode is represened by Δi L-3LB, and shown in Eq. (3-5), i L 3LB = (Vin 2 V ou) ( V ou) T V s in, (3-5) L where V in is he inpu volage, V ou is he oupu volage, T s is he swiching period and L is he inducance value. 3.1.4 Digial Conroller for he 7SFC Converer

23 A digial conroller was chosen for he 7SFC based muli-level buck converer since i easily allows for he conrol of muliple modes of operaion, where he swiches are operaed differenly for each mode. Compared o convenional conrollers he conrol sysem for he 7SFC converer requires addiional feaures. The full conrol sysem for a volage mode conroller is shown in Figure 3-8. The oupu volage regulaion conrol loop consiss of an oupu volage sensor, whose gain is represened by H(s), followed by an analog-o-digial converer (ADC) o ranslae he oupu volage ino he digial domain. In he digial volage conroller he sensed oupu volage, Vou[n], is compared o a desired oupu volage, or reference, Vref[n], o produce an error signal, error[n], which is sen o he digial compensaor. The digial volage compensaor produces a duy raio command, D[n], based on curren and previous error values and previous duy raios, o be modulaed by he digial pulse widh modulaor (DPWM) o conrol he swiches of he dc-dc converer. This is a ypical volage mode conrol loop for dc-dc converers. V in V Cfly SW 1 SW 3 L 1 C fly SW 2 SW 7 SW 5 L 2 SW 4 SW 6 C R V ou H(s) ADC Vin[n] Mode Digial Pulse Widh Modulaor Mode Selec D[n] Digial Volage Conroller Digial Volage Compensaor Gae Signals Figure 3-8: Volage mode conroller for he 7SFC converer error[n] Vref[n] Iref[n] Vou[n] The imporan blocks of he digial conroller, designed for he 7SFC converer, are he DPWM and he Mode Selec blocks. The Mode Selec block akes he inpu volage V in, desired oupu volage V ref, and informaion abou he required oupu curren I ref, o deermine he operaing mode. In a final produc for a power module he user should be able o selec he operaing condiions, so his informaion is assumed o be available o he conroller. The Mode Selec H(s) ADC

24 block conains a look-up able ha sores which modes have he highes efficiency for specific operaing condiions, and herefore he highes efficiency mode can always be seleced. The Mode Selec block sends he required mode of operaion, Mode, o he DPWM which conains swiching sequences for each mode. Using he duy raio, D[n], from he compensaor, and he Mode inpu from he Mode Selec block, he DPWM modulaes he swiches accordingly. 3.2 Loss Breakdown A loss breakdown for all of he modes of he 7SFC based muli-level buck converer is provided in he following secions. Once he losses have all been modeled, numerical comparisons can be made o he alernaive opologies presened in Chaper 2. 3.1.1 Conducion Losses The conducion losses in he converer are governed by he resisive losses in he MOSFETs and he inducors. The equivalen series resisance (ESR) of he oupu capacior and he flying capacior is considered negligible and ignored in his analysis. The equaion for conducion loss, represened by P cond, is well undersood [8] and shown in Eq. (3-6), P cond = i 2 RMS R, (3-6) where i RMS is he RMS curren hrough a resisor, and R is he resisor value. This mehod applies for all of he resisive elemens of he converer, and since he analysis is repeiive, he full conducion loss breakdown for each mode of he 7SFC converer is referred o Appendix B. Deails wih regards o adding RMS currens is provided in Appendix C. 3.1.2 Swiching Losses The swiching losses are caused by he curren-volage overlap during he swiching ransiions of he MOSFETs. For a urn-on ransiion, as he inpu capaciance of he MOSFET is charged, he drain curren will rise and he volage across he MOSFET will fall. Similarly, for a urn-off ransiion, he inpu capaciance is discharged and he curren reduces as he drain-source volage rises. This is known as a hard swiching ransiion. A sof ransiion, which does no cause swiching losses, uilizes he body-diode of he MOSFET o conduc prior o a swiching

25 ransiion. This causes he volage o be equal o he diode forward volage drop, which is considered negligible here, as he curren rises or falls in he MOSFET. For he inerleaved buck mode of operaion he only wo swiches experiencing hard swiching ransiions are SW 7 and SW 5. The remaining swiches do no demonsrae his caegory of loss because SW 1, SW 2 and SW 4 are always on, and SW 3 and SW 6 have sof-swiching ransiions. The equaions for urn-on swiching losses for SW 7 and SW 5, i.e. P SW7,ON-IB and P SW5,ON-IB, are shown in Eq. (3-7), P SW5,ON IB = P SW7,ON IB = 1 2 V in ( I load 2 i L IB ) f 2 s on, (3-7) where V in is he inpu volage, I load is he load curren, Δi L-IB is he inducor curren ripple for he inerleaved buck mode, f s is he swiching frequency, and on is he overlap ime of he volage and curren during he urn-on ransiion. The urn-off swiching losses, P SW7,OFF-IB and P SW5,OFF- IB are shown in Eq. (3-8), P SW5,OFF IB = P SW7,OFF IB = 1 2 V in ( I load 2 + i L IB ) f 2 s off, (3-8) where off is he overlap ime of he volage and curren in he MOSFET during he urn-off ransiion. The swiching loss analysis for he high sep-down mode of operaion is more involved han he inerleaved buck mode, considering six ou of seven of he swiches are operaed in one swiching cycle. As expeced SW 3 will no experience any swiching losses since i remains on hrough he whole cycle. The analysis is performed by observing he ransiion beween each sae, saring wih Sae 1 o Sae 2. For his ransiion SW 1 experiences a hard urn-off and o mainain he coninuous curren in he inducor he body diodes of SW 2 and SW 5 are forced o conduc. Therefore he urn-on ransiion for SW 2 and SW 5 is sof, and will no incur swiching losses. The ransiion beween Sae 2 and Sae 3 begins wih he urn-off of SW 6 and SW 7. Once again, o mainain he coninuous curren in each inducor heir body diodes will begin conducing producing sof urn-off ransiions. Then, SW 4 is urned on wih a hard ransiion o sar ramping up he inducor curren, producing urn-on swiching losses. The ransiion o Sae 4 has he opposie effec, wih SW 4 urning off wih a hard ransiion, followed by he sof urn-on

26 of SW 7 and SW 6. The final ransiion back o Sae 1 consiss of he sof urn-off ransiion of SW 2 and SW 5 followed by he hard urn-on of SW 1. The relevan swiching losses for SW 1 and SW 4, he only hard-swiched swiches, i.e. P SW1,ON-HSD, P SW4,ON-HSD and P SW1,OFF-HSD, P SW4,OFF-HSD, are shown in Eqs. (3-9,3-10), P SW1,ON HSD = P SW4,ON HSD = 1 2 (V in ) 2 (I load 2 i L HSD ) f 2 s on, (3-9) P SW1,OFF HSD = P SW4,OFF HSD = 1 2 (V in ) 2 (I load 2 where Δi L-HSD is he inducor curren ripple for he high sep-down mode. + i L HSD ) f 2 s off, (3-10) The swiching loss breakdown for he 3-level buck mode of operaion follows ha of he high sep-down buck closely, however, here are fewer swiching elemens. SW 5 and SW 7 remain on hrough he whole swiching cycle connecing boh inducors in parallel. The only swiches experiencing hard swiching ransiions are SW 1 and SW 4 once again, where he remaining swiches have sof-swiching characerisics for boh urn-on and urn-off. The swiching losses for SW 1 and SW 4, i.e. P SW1,ON-3LB, P SW4,ON-3LB and P SW1,OFF-3LB, P SW4,OFF-3LB, are shown in Eqs. (3-11,3-12), P SW1,ON 3LB = P SW4,ON 3LB = 1 2 (V in ) 2 (I load 2 i L 3LB ) f 2 s on, (3-11) P SW1,OFF 3LB = P SW4,OFF 3LB = 1 2 (V in ) 2 (I load 2 where Δi L-3LB is he inducor curren ripple for he 3-level buck mode. 3.1.3 MOSFET Oupu Capacior Losses + i L 3LB ) f 2 s off, (3-12) The MOSFET oupu capacior losses are incurred from he charging and discharging of he oupu capacior of he MOSFET, C oss, during swiching ransiions. The oupu capacior losses for each mode are derived based on he assumpion ha he inducor curren remains posiive over he swiching period. For he inerleaved buck mode of operaion, all four swiches ha are operaed, i.e. SW 7, SW 3, SW 5, and SW 6, experience oupu capacior losses, P Coss-IB, as shown in Eq. (3-13),

27 P Coss IB = 1 2 C oss V in 2 f s, (3-13) where V in is he inpu volage and f s is he swiching frequency. For he high sep-down mode he oupu capacior losses are much lower due o he lower blocking volages of he swiches. Since SW 3 remains on i does no experience hese losses. The oupu capaciance loss in each of he remaining six swiches, P Coss-HSD, is represened by Eq. (3-14), P Coss HSD = 1 2 C oss ( V in 2 )2 f s. (3-14) The oupu capacior losses for he 3-level buck mode of operaion are expeced o be higher han ha of he high sep-down mode bu lower han he inerleaved buck mode. Even hough SW 5 and SW 7 do no experience any losses of his ype, he oupu capaciors of SW 3 and SW 6 are charged and discharged o V in /2 a wice he frequency of he oher swiches, hus doubling heir respecive oupu capacior loss. The remaining swiches, however, experience loss a he swiching frequency according o he high sep-down mode equaion given in Eq. (3-14). The equaion for he oupu capacior loss for SW 3 and SW 6, P Coss-3LB, is shown in Eq. (3-15), 3.1.4 Gae Drive Losses P Coss 3LB = 1 2 C oss ( V in 2 )2 (2 f s ). (3-15) The gae drive losses for he swiches come from charging and discharging he inpu capaciance of a swich o urn i on. The gae drive loss of a swich, P gae, can be calculaed uilizing he gae charge, Q g, gae drive volage, V drive, and swiching frequency, f s, as shown in Eq. (3-16), P gae = Q g V drive f s. (3-16) I is assumed ha hese parameers are consisen for all hree modes, so he losses are compared based on he number of swiches being operaed. I is clear ha he inerleaved buck mode would have he lowes gae drive losses, since only four swiches are operaed. The high sep-down mode has a higher gae drive loss since here are six operaing swiches.

28 The 3-level buck mode can be operaed in wo ways depending on he efficiency rade-off due o he double swiching of SW 6. A low currens, where gae drive losses become more dominan, we can choose o gae SW 6 eiher once during he swiching cycle or o no gae i a all, o save on gae drive losses. The resul would be higher curren flowing in SW 5 and SW 7 bu a low currens his effec should no be a large facor. Therefore, if we choose o gae SW 6 wice during he swiching period hen he gae drive losses would be equivalen o ha of he high sep-down mode, and if we were o no gae SW 6 a all he losses would be equivalen o he inerleaved buck mode. 3.1.5 Reverse Recovery Losses Reverse recovery losses are caused during he urn-off swiching ransiion of a conducing body diode when anoher swich begins conducing he inducor curren [8]. These losses come from he removal of charge from he body diode, where he recovered charge is represened by Q rr. Reverse recovery loss informaion is highly influenced by he es condiions and for differen condiions his informaion can vary significanly. Knowing his, we can assume he reverse recovery loss calculaion is simply a basic esimaion ha we can use o compare opologies on a basic level. The reverse recovery losses in he inerleaved buck mode come from he main-swich urn-on, SW 7 or SW 5, while he body diode of he low-side swich, SW 3 or SW 6 respecively, is conducing. The resuling reverse recovery loss corresponding o SW 3 and SW 6, i.e. P rr-ib, is shown in Eq. (3-17), P rr IB = Q rr V in f s, (3-17) Where V in is he inpu volage and f s is he swiching frequency. The reverse recovery losses for he high sep-down mode are higher han he oher modes of operaion. This is due o he fac ha here are more swiches whose body diodes conduc in one swiching cycle. When he SW 1 urn-on ransiion occurs, boh SW 2 and SW 5 experience reverse recovery losses. Similarly, when SW 4 urns on, boh SW 6 and SW 7 experience reverse recovery loss. The equaion for reverse recovery loss in he high sep-down mode, P rr-hsd is given in Eq. (3-18),

29 P rr HSD = Q rr ( V in 2 ) f s. (3-18) For he 3-level buck mode of operaion we will look a he case where SW 6 is operaed wice in one swiching cycle. Therefore, for he urn-on ransiion of SW 1, SW 2 and SW 6 experience reverse recovery losses, and for he urn-on ransiion of SW 4, SW 3 and SW 6 experience reverse recovery losses. The equaion for reverse recovery loss in he 3-level buck mode, P rr-3lb, is he same as he high sep-down mode, and shown in Eq. (3-19), The specific reverse recovery loss for SW 6 is equal o 2 P rr-3lb. 3.1.6 Inducor Core Loss P rr 3LB = Q rr ( V in 2 ) f s. (3-19) Inducor core losses are based on magneic losses dependen on he frequency and magniude of he inducor curren ripple. The equaion ha defines he core loss, P core, in an inducor is shown in Eq. (3-20), P core = K (f ind ) α ( i) β, (3-20) where f ind is he effecive frequency of he curren in he inducor, Δi is he curren ripple magniude, and K, α, and β are inducor design consans specific o each inducor. For he inerleaved buck mode he inducor curren frequency is equal o he swiching frequency, and he curren ripple has a magniude previously defined in Eq. (3-2). Thus he equaion for core loss, P core-ib, becomes ha of Eq. (3-21), V in ) T s P core IB = K (f s ) α ( (V in V ou ) ( Vou L ) β, (3-21) where V in is he inpu volage, V ou is he oupu volage, T s is he swiching period, f s is he swiching frequency and L is he inducance value.

30 In he high sep-down mode he inducor frequency is also equal o he swiching frequency, and by subsiuing he equaion for inducor curren ripple from Eq. (3-4), he core loss equaion, P core-hsd, becomes ha of Eq. (3-22), P core HSD = K (f s ) α ( (Vin 2 V ou) ( 2 V ou) T V s in L ) β. (3-22) The core losses for he 3-level buck mode are higher han he oher modes due o he higher effecive frequency of he curren in each inducor. Given he curren ripple of Eq. (3-5), he core loss for his mode, P core-3lb, is shown in Eq. (3-23), P core,3lb = K (2 f s ) α ( ( V in 2 V ou) ( V ou L V in ) T s ) β. (3-23) 3.3 Volume Esimaion The volume esimaion for he 7SFC based muli-level buck converer is done by observing he wors case inducor curren ripple, he blocking volages of he swiches, and he wors case oupu capacior volage ripple and volage deviaion in response o a ransien. Inducor volume is governed by he relaion shown in Eq. (3-24), Inducor Volume L i raed 2 (3-24) where L is he inducance value, and i raed is he inducor raed curren. I is clear ha he inducor volume is proporional o he inducance value direcly and he curren raing wih a squared relaion [15]. Since all of he opologies have he same inducor curren raings we can use he inducance value o compare he volumes. Similar o he inducor volume equaion, he oupu capacior volume is governed by he relaion of Eq. (3-25), 2 Capacior Volume C v raed (3-25)

31 where C is he capacior value, and v raed is he volage raing for he capacior [15]. Here we noice he volume is proporional o he capacior value direcly, and he volage raing wih a squared relaion. The wors case inducor curren ripple analysis is done by observing he wors case curren ripple for each mode, given he specific operaing range of he mode. Depending on he specificaions of he power module being designed, he analysis can help deermine how he inducor should be sized. For he inerleaved buck converer he inducor curren ripple is proporional o he inpu and oupu volages according o Eq. (3-26), IB curren ripple (V in V ou ) ( V ou V in ) (3-26) where V in is he inpu volage and V ou is he oupu volage. Thus he wors case inducor curren ripple for he inerleaved buck mode is for he highes inpu volage, V in =V in,max /2 and for a conversion raio of V ou /V in =0.5, where V in,max is he highes inpu volage in he operaing range. For he high sep-down mode of operaion he inducor curren ripple depends on he inpu and oupu volages hrough he equaion of Eq. (3-27), HSD curren ripple ( V in 2 V ou) ( 2 V ou V in ). (3-27) For his mode he highes curren ripple occurs for he highes inpu volage, which in his case is V in =V in,max, and for a conversion raio of V ou /V in =0.25 since his is he conversion raio limi. For he 3-level buck mode he inducor ripple is defined by Eq. (3-28), 3LB curren ripple ( V in 2 V ou) ( V ou V in ). (3-28) The wors case curren ripple occurs for he highes inpu volage, V in =V in,max and conversion raio V ou /V in =0.5.

32 For he analysis of MOSFET silicon area usage we will simply look a he maximum blocking volage for each swich and oal number of swiches. In [23] i is saed ha he on-resisance for a MOSFET per uni silicon area, R on /(uni silicon area), is defined by Eq. (3-29), R on uni silicon area = γ (V B) 2, (3-29) where R on is he on-resisance of he MOSFET, γ is a echnology dependen facor, and V B is he MOSFET breakdown volage. Using his principle, he MOSFET on-resisance increases wih a squared relaion o he blocking volage, for a fixed silicon area specificaion. From his relaion i can be inferred ha, by increasing he silicon area, he on-resisance can be normalized, allowing for a silicon area evaluaion of muliple converers. For example, by increasing he silicon area in a squared proporion o he blocking volage, he on-resisance is held consan. To deermine he oal silicon area used by he MOSFETs in he 7SFC converer we observe he necessary blocking volages for all of he swiches. Since he swiches are all raed for V in,max /2, he oal silicon area for he 7SFC can be approximaed by Eq. (3-30), Toal Silicon Area (7SFC) 7 4 (V in,max) 2. (3-30) This is equivalen o he double sep-down buck converer and less han he inerleaved buck converer and 2-phase 3-level buck converer from Chaper 2. The oupu capacior selecion was performed by observing he wo specificaions below and selecing he larger capaciance value requiremen, saisfying boh condiions: 1) Maximum oupu volage ripple, Δv ou, as a fracion of he dc oupu volage, V ou 2) Maximum oupu volage deviaion, V ou,dev, o a maximum load ransien of I ran,max This mehod was proposed in [24] assuming ime-opimal conrol was used o conrol ransiens. For he oupu volage ripple specificaion he posiive curren of he capacior is inegraed o find he added charge, ΔQ C, in he oupu capacior in one swiching cycle, shown in Figure 3-9.

33 i C () ΔQ C 0 DT s T s /2 T s /2+DT s T s Figure 3-9: Oupu capacior posiive charge for oupu volage ripple calculaion The oupu capacior value, C, based on his specificaion, is found using Eq. (3-31), C Q C V ou ( v ou V ou ). (3-31) To find he oupu capacior value according o oupu volage deviaion specificaion we observe he oupu volage deviaion in response o sep-up and sep-down ransiens. The required oupu capacior, C, for a sep-down ransien is found using Eq. (3-32), C L (I ran,max+( i 2 )2 ) 2 V ou V ou,dev, (3-32) where L is he inducance value and Δi is he inducor curren ripple. For a sep-up ransien he capacior value is seleced using Eq. (3-33), where M is he conversion raio. C L (I ran,max+( i 2 )2 ) M, (3-33) 2 V ou V ou,dev 1 M In Chaper 4 a volume comparison is performed beween he inerleaved buck converer of Chaper 2 and he 7SFC converer for a real prooype. Here we are able o compare real componen values and compuaionally verify he wors case condiions given a specific converer operaing range. 3.4 Phase Shedding

34 Similar o he inerleaved buck converer and he 2-phase 3-level buck converer of Chaper 2, he 7SFC converer has he abiliy o perform phase shedding o furher increase efficiency a low currens. This can be done for he inerleaved buck mode and he 3-level buck mode of he 7SFC. The swiching sequence and corresponding inducor waveforms for he single phase buck mode is provided in Figure 3-10. V in Sae 1: Sae 2: 0 < < DT s DT s < < T s V Cfly SW 1 SW L 1 3 C fly V L1 SW 2 SW 7 SW4 SW 5 SW 6 i L1 () SW 1 SW L 1 3 C fly V L1 SW 7 SW 2 L 2 C V SW4 L 2 V L2 R in C V ou SW 5 V L2 R V ou V Cfly SW 6 i L1 () V L1 () i L1 () 0 Sae 1 Sae 2 V in -V ou T s /2 DT s -V ou T s Figure 3-10: Swiching sequence and inducor waveforms for he single-phase inerleaved buck operaion of he 7SFC converer The same for he single-phase 3-level buck mode is provided in Figure 3-11.

35 V in Sae 1: 0 < < DT s V Cfly SW 1 SW L 1 3 C fly SW 7 SW4 SW 2 SW 5 V L1 SW 2 L 2 C V L2 R V SW4 L 2 in C V ou SW 5 V L2 R V ou SW 6 i L1 () Sae 2 (& 4): DT s < < T s /2 (T s /2+DT s < < T s ) V Cfly SW 1 SW L 1 3 C fly SW 7 V L1 SW 6 i L1 () V in Sae 3: T s /2 < < DT s +T s /2 V Cfly SW 1 SW L 1 3 C fly SW 2 SW 7 SW4 SW 5 V L1 L 2 V L2 SW 6 i L1 () C R V ou Sae 1 Sae 2 Sae 3 Sae 4 V L1 () V in -V Cfly -V ou V Cfly -V ou i L1 () 0 -V ou -V ou DT s T s /2 T s /2+DT s T s Figure 3-11: Swiching sequence and inducor waveforms for he single-phase 3-level buck operaion of he 7SFC converer 3.5 Gae Driving The gae driving sraegy for he 7SFC based muli-level buck converer follows wo schemes ha have been previously proposed. The firs is he convenional boosrapping scheme for highside swiches, mainly used for he buck converer [25], and he second is a gae driving scheme proposed for he double sep-down buck converer by Nishijima [26]. These wo mehods are used accordingly o drive he MOSFETs in all of he modes of operaion in he 7SFC converer. The full gae drive seup is as follows. SW 2 and SW 6 are driven wih low-side gae drivers supplied by he gae drive volage, V drive. SW 3 and SW 7 uilize he convenional boosrapping echnique from he drain node of SW 2 wih high-side gae drivers, and SW 5 has he same gae driving echnique boosrapped off of he drain node of SW 6. Lasly SW 4 and SW 1 uilize he second gae driving echnique where here boosrap capaciors are charged from he boosrap capacior of SW 5 when heir source nodes are conneced. The wo gae driving echniques will be described by example by analyzing he high sep-down mode of operaion of he 7SFC converer. As described in Secion 3.1.2, in Sae 1 of he high sep-down buck mode inducor L 1 is charging wih V in -V Cfly -V ou and L2 is discharging wih V ou. The gae driving analysis for Sae 1

36 is shown in Figure 3-12a). In his sae he boosrap capacior of SW 5, C b5, is able o charge since he source node of SW 5 is grounded by he SW 6 urn-on. The boosrap capaciors of SW 4 and SW 1 are no charged during his sae. The nex porion of he gae driving scheme occurs during Sae 3, shown in Figure 3-12b). In his sae when SW 5 is urned on he source nodes of SW 4 and SW 5 are conneced. This allows he boosrap capacior C b4 o be charged off of he SW 5 boosrap capacior C b5. Then SW 4 is able o urn-on, hus connecing he source nodes of SW 4 and SW 1 allowing he boosrap capacior of SW 1, C b1, o be charged as well. This shows ha all of he swiches are able o be driven given his gae driving scheme.

37 C SW fly 1 SW 3 L 1 SW 7 V in SW 1 Driver SW 2 SW4 V in /2 SW 5 C b1 D b1 SW 4 Driver C b4 D b4 SW 6 0V L 2 SW 5 Driver C C b5 D b5 R V ou V dr C SW fly 1 SW 3 L 1 SW 7 V in SW 1 Driver SW 2 SW4 V in /2 SW 5 C b1 D b1 SW 4 Driver C b4 D b4 SW 6 L 2 SW 5 Driver C C b5 D b5 R V ou V dr Figure 3-12: Gae driving implemenaion of he 7SFC converer, a) charging of SW 5 boosrap circui, b) charging of SW 1 and SW 4 boosrap circuis

38 CHAPTER 4: 4. EXPERIMENTAL RESULTS AND COMPARISON This secion of he hesis deails he experimenal prooype ha was buil o verify he novel 7SFC based muli-level buck converer as well as compare o convenional and alernaive opologies. Using he same prooype, he convenional inerleaved buck converer of Chaper 2 was also buil o compare resuls. A wide range of operaing condiions was esed o fully characerize he 7SFC converer s advanages. The prooype was buil o operae wih inpu volages of 3V < V in < 48V and oupu volages of 1V < V ou < 12V, wih only sep-down operaion. The load curren range he prooype was designed for is I load < 6A. The prooype was designed and esed for a swiching frequency of f s =800kHz. Figure 4-1: Image of he op view of he experimenal prooype. The op PCB consiss of he power sage and he boom PCB is he conrol board wih sensing, ADCs and DACs

39 The componens used in he power sage of he 7SFC converer as well as he convenional inerleaved buck converer are provided in Table 1. The prooype was buil on a 4-layer PCB board and separaed ino a power sage board (op) and conrol board (boom). An image of he prooype is provided in Figure 4-1. Table 1. Experimenal Prooype Componens Par Role CSD88539 MOSFET 7SFC: SW 1, SW 4, SW 5, SW 7 Inerleaved Buck: SW 1, SW 3 AO4264 MOSFET 7SFC: SW 2, SW 3, SW 6 Inerleaved Buck: SW 2, SW 4 MCP1407 low-side gae driver 7SFC: SW 2, SW 6 Inerleaved Buck: SW 2, SW 4 LTC4440 high-side gae driver 7SFC: SW 1, SW 3, SW 4, SW 5, SW 7 Inerleaved Buck: SW 1, SW 2 Wurh 1uH inducor: 744 373 490 10 Wurh 1.5uH inducor: 744 373 490 15 2x10uF ceramic capacior 2x100uF ceramic capacior 7SFC inducors Inerleaved buck inducors C fly for 7SFC C for boh converers (oupu capacior) Curren sense wire for L 1 phase: 15mΩ Curren sense wire for L 2 phase: 14mΩ

40 The following subsecions discuss he experimenal verificaion of he 7SFC based muli-level converer and is comparisons o convenional opologies. The double sep-down buck converer is negleced here since i canno funcion as a full soluion given he operaing range. Firs he inducor and capacior selecion for he 7SFC is performed given he operaing condiions. From his we can compare he volume of he 7SFC wih he inerleaved buck converer and 2-phase 3- level buck converer. Nex, a power loss breakdown is shown for he convenional inerleaved buck converer and compared o he power loss of he 7SFC converer for several operaing poins. In he final secions experimenal waveforms are shown for he prooype and efficiency resuls are discussed. 4.1 Reacive Componen Selecion and Volume Comparison Based on he operaing range of he prooype we are able o choose and compare he inducors and capaciors for he 7SFC based muli-level buck, he convenional 2-phase inerleaved buck and he 2-phase 3-level buck opologies. Along wih his, he oal silicon area of he swiches is considered for each opology. Using his informaion, a oal converer volume comparison is made for he hree opologies. 4.1.1 Inducor Selecion Since his hesis arges low-volume PoL applicaions, he 7SFC converer inducors were chosen o have values of 1uH each. This value is chosen because wih curren inducor echnology, inducors in his range sar o be considered for inegraed applicaions. Given he 1uH inducor selecion we can solve for he wors case curren ripple for he 7SFC converer, which is equal for he high sep-down mode and he inerleaved buck mode. The equaion for wors case inducor ripple of he 7SFC is shown in Eq. (4-1), i 7SFC,wors = (48V 2 12V) (2 12V 48V ) = 7.5A, (4-1) 1uH 800kHz by subsiuing he parameers for he wors case, i.e. inpu volage of V in =48V, oupu volage of V ou= 12V as well as converer parameers, inducance of L=1uH and swiching frequency of f s =800kHz, ino Eq. (3-4) for he high sep-down mode.

41 Using he 1uH inducance of he 7SFC as a benchmark we can solve for he necessary inducance value for he convenional inerleaved buck converer and 2-phase 3-level buck converer o achieve he same wors case inducor curren ripple. For he convenional inerleaved buck converer we can solve for he inducance value by subsiuing he benchmark curren ripple of 7.5A and swiching frequency of f s =800kHz, as well as he wors case curren ripple condiions of V in =48V and V ou =12V ino Eq. (3-2), o ge he inducance value L IB of Eq. (4-2): L IB = (48V 12V) (12V 48V ) = 1.5uH. (4-2) 7.5A 800kHz I is clearly shown ha for his operaing range he inerleaved buck converer requires 1.5 imes larger inducors o achieve he same wors case curren ripple as he 7SFC converer. For he 2-phase 3-level buck converer, he chosen inducor is represened by L 2Ph-3LB and shown in Eq. (4-3), L 2Ph 3LB = (48V 2 12V) (12V 48V ) = 0.5uH, (4-3) 7.5A 800kHz where he wors case curren ripple is 7.5A, he swiching frequency is f s =800kHz, and he wors case operaing condiions are V in =48V and V ou =12V. As expeced, he 2-phase 3-level buck converer only requires half of he inducance of he 7SFC converer o achieve he same curren ripple specificaion as he 7SFC converer. 4.1.2 Oupu Capacior Selecion The pracical oupu capacior selecion for each converer was found using he wo specificaions below and selecing he larger capaciance value requiremen: 1) Oupu volage ripple of 1% of he oupu volage, i.e. v ou V ou = 0.01 2) Oupu volage deviaion of V ou,dev =50mV o a maximum load ransien of I ran,max =3A To find he wors case condiions for each specificaion for he hree opologies, a MATLAB scrip was wrien. In he analyses he inducor values derived in he previous secion were uilized for he corresponding opologies.

42 The oupu capacior value, C, based on he firs specificaion, is found using Eq. (4-4), C Q C V ou 0.01, (4-4) where he 0.01 facor appears from he 1% oupu volage ripple requiremen. Table 2 oulines he resuls for he convenional inerleaved buck converer, 2-phase 3-level buck converer and he 7SFC converer based on he oupu volage ripple specificaion. Clearly shown in he resuls, he 7SFC converer requires a larger oupu capacior value by approximaely 43% compared o he convenional inerleaved buck opology for he wors case condiions. Compared o he 2- phase 3-level buck converer he required oupu capacior is wice as large o mainain he same oupu volage ripple. Table 2. Oupu capacior selecion based on oupu volage ripple Topology Operaing Condiions Capacior Value Convenional Inerleaved Buck Converer V in = 48V, V ou = 1V 6.239uF 2-Phase 3-Level Buck Converer V in = 48V, V ou = 1V 4.476uF 7SFC based Muli-level Buck Converer High Sep-Down Mode V in = 48V, V ou = 1V 8.952uF For he oupu volage deviaion specificaion, he resuls are oulined in Table 3, for sep-down and sep-up ransiens, uilizing Eq. (4-5) and Eq. (4-6) respecively, C L (3A+( i 2 )2 ) 2 V ou 50mV, (4-5) C L (3A+( i 2 )2 ) M, (4-6) 2 V ou 50mV 1 M

43 where L is he inducance value and Δi is he inducor curren ripple depending on he converer being analyzed. For he sep-up ransiens, we assume he maximum seady-sae conversion raio is 96% or else he inducor slope would be zero and he ransien would no be possible. We can see for he ransien specificaion he requiremens for oupu capacior value are much larger o achieve a 50mV volage deviaion wih a maximum load ransien of 3A. Therefore, for a PoL applicaion his specificaion will be he dominan one. The 7SFC converer is able o achieve a 33% reducion in oupu capaciance compared o he convenional inerleaved buck, furher improving on he volume. Compared o he 2-phase 3-level buck, however, he 7SFC converer will require an oupu capacior of wice he value, hus having a larger volume. Table 3. Oupu capacior selecion based on oupu volage deviaion Topology Transien Type Operaing Condiions Capacior Value Convenional Inerleaved Buck Converer 2-Phase 3-Level Buck Converer Sep-Down V in = 48V, V ou = 1V 71.81uF Sep-Up V in = 3V, V ou = 2.875V 544uF Sep-Down V in = 48V, V ou = 1V 24.57uF Sep-Up V in = 3V, V ou = 2.875V 182uF 7SFC based Muli-level Sep-Down High Sep-Down Mode V in = 48V, V ou = 1V 49.15uF Buck Converer Sep-Up Inerleaved Buck Mode V in = 3V, V ou = 2.875V 364uF 4.1.3 Volume Comparison Using he inducor and capacior values from he previous secion as well as he MOSFET silicon area analyses from Chaper 3, he volume of he various opologies can be compared. Referring back o Eq. (3-24), i is clear he 7SFC converer will have a 33% smaller inducor volume han he inerleaved buck converer bu a he same ime double he inducor volume of

44 he 2-phase 3-level buck converer. Similar o he inducor volume resuls, observing Eq. (3-25) shows ha he 7SFC converer can have a 33% reducion in oupu capacior volume as well compared o he inerleaved buck converer bu requires wice he volume of oupu capacior when compared o he 2-phase 3-level buck converer. Uilizing he silicon area analysis of Chaper 3 for he 7SFC converer on he inerleaved buck converer and he 2-phase 3-level buck converer, he oal silicon area for he hree opologies can be compared, as shown in Table 4. The resuls show ha he 7SFC converer uilizes less han half of he silicon area of he inerleaved buck converer and has a 1/8 reducion of silicon area compared o he 2-phase 3-level buck converer. Table 4. Toal silicon area comparison based on maximum inpu volage, V in,max Topology Toal Silicon Area Represenaion Convenional Inerleaved Buck Converer 4 (V in,max ) 2 2-Phase 3-Level Buck Converer 7SFC based Muli-level Buck Converer 2 (V in,max ) 2 7 4 (V in,max) 2 Thus, in general, he oal volume savings of he 7SFC based muli-level converer make i an aracive soluion compared o alernaive ones as long as he efficiency resuls agree. 4.2 Power Loss Breakdown In his secion power loss breakdowns are provided for specific operaing poins for he inerleaved buck converer and he 7SFC converer. The loss breakdown for he 7SFC converer was presened in Chaper 3, and he loss breakdown for he convenional 2-phase inerleaved buck converer is provided in Appendix D. By doing his i is easy o observe where he 7SFC converer provides savings in erms of specific loss elemens. The operaing poins ha will be

45 analyzed are a high sep-down conversion wih inpu volage, V in =24V, and oupu volage, V ou =1V, a medium sep-down conversion wih lower inpu volage of V in =7V o V ou =1V and a sep-down raio close o 0.5 of V in =12V o V ou =5V. We will no show a comparison of sepdown raios of M > 0.5 because he 7SFC converer always operaes in he inerleaved buck mode in his operaing range, hus having similar losses and performance. 4.2.1 High Sep-Down Raio Loss Breakdown The power loss breakdown for he inerleaved buck converer and he 7SFC converer for V in =24V and V ou =1V is provided in Figure 4-2a) and b). A major difference ha is clearly noiceable for his operaing poin is he large difference in swiching losses for he wo converers. The inerleaved buck converer has approximaely double he swiching losses over he enire load curren range due o he swiching ransiions wih he full inpu volage, V in, which in his case is very high (24V). A his operaing poin he conducion losses are lower because of he low inducor curren ripple. Anoher difference beween he wo converers is he slighly larger swich conducion losses for he 7SFC converer. This is due o he increased number of swiches, which also explains he increased gae drive losses. The inducor core loss is negligible for boh converers.

Power Loss (W) Power Loss (W) 46 2 Inerleaved Buck Converer Power Loss Breakdown for V in = 24V & V ou = 1V 2 7SFC: High Sep-Down Mode Power Loss Breakdown for V in = 24V & V ou = 1V 1.8 1.6 1.4 1.2 Swich Conducion Loss Swiching Loss Oupu Capacior Loss Inducor Conducion Loss Inducor Core Loss Gae Loss 1.8 1.6 1.4 1.2 Swich Conducion Loss Swiching Loss Oupu Capacior Loss Inducor Conducion Loss Inducor Core Loss Gae Loss 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 1 2 3 4 5 6 Oupu Curren (A) 0 0 1 2 3 4 5 6 Oupu Curren (A) Figure 4-2: Power loss breakdown for Vin=24V & Vou=1V, a) inerleaved buck converer, b) 7SFC converer 4.2.2 Medium Sep-Down Raio Loss Breakdown The power loss breakdown for a medium sep-down raio wih V in =7V and V ou =1V for he inerleaved buck converer and he 7SFC converer is provided in Figure 4-3a) and b). For he inerleaved buck converer we can see ha even for his operaing poin he swiching losses are dominan, along wih he gae drive losses. For he 7SFC converer, however, since he swiching losses are basically halved, hey are comparable o he conducion losses of he swiches and inducors. The gae drive losses for he 7SFC converer remain high a he operaing poin. Core losses are negligible for boh opologies once again. We can once again see he main advanage of inroducing he high sep-down mode of operaion for he 7SFC converer, he large reducion in swiching losses and is effeciveness for conversion raios less han 0.25.

Power Loss (W) Power Loss (W) 47 0.7 0.6 0.5 0.4 Inerleaved Buck Converer Power Loss Breakdown for V in = 7V & V ou = 1V Swich Conducion Loss Swiching Loss Oupu Capacior Loss Inducor Conducion Loss Inducor Core Loss Gae Loss 0.7 0.6 0.5 0.4 7SFC: High Sep-Down Mode Power Loss Breakdown for V in = 7V & V ou = 1V Swich Conducion Loss Swiching Loss Oupu Capacior Loss Inducor Conducion Loss 0.3 0.3 Inducor Core Loss Gae Loss 0.2 0.2 0.1 0.1 0 0 1 2 3 4 5 6 Oupu Curren (A) 0 0 1 2 3 4 5 6 Oupu Curren (A) Figure 4-3: Power loss breakdown for V in =7V & V ou =1V, a) inerleaved buck converer, b) 7SFC converer 4.2.3 Loss Breakdown for Sep Down Raio Close o 0.5 The loss breakdown for he inerleaved buck converer and he 7SFC converer for he operaing poin of V in =12V and V ou =5V is shown in Figure 4-4a), b) and c). A his operaing poin he 7SFC converer can operae in he inerleaved buck mode and 3-level buck mode, so loss breakdowns for boh modes are shown. A his operaing poin he inerleaved buck converer and he 7SFC converer operaing in he 3-level buck mode have differen dominan losses alogeher. For he inerleaved buck converer, i is no surprising o see ha he swiching loss is he larges componen. For he 7SFC converer operaing in he 3-level buck mode he swich conducion losses become very subsanial a high currens. This is also expeced, since cerain swiches in he 3-level buck mode are exposed o he full load curren, and he number of swiches has increased. Along wih he reducion in swiching losses for he 3-level buck mode, inducor conducion losses are significanly reduced compared o he inerleaved buck converer due o he decrease in inducor curren ripple. For he 7SFC converer operaing in he inerleaved buck mode we noice mos of he losses are very similar o he inerleaved buck converer, excep for he swich conducion losses. This is again due o he increased number of swiches from 4 in he inerleaved buck converer o 7 in he 7SFC converer.

Power Loss (W) Power Loss (W) Power Loss (W) 48 1.4 1.2 1 0.8 0.6 Inerleaved Buck Converer Power Loss Breakdown for V in = 12V & V ou = 5V Swich Conducion Loss Swiching Loss Oupu Capacior Loss Inducor Conducion Loss Inducor Core Loss Gae Loss 1.4 1.2 1 0.8 0.6 7SFC: 3-Level Buck Mode Power Loss Breakdown for V in = 12V & V ou = 5V Swich Conducion Loss Swiching Loss Oupu Capacior Loss Inducor Conducion Loss Inducor Core Loss Gae Loss 0.4 0.4 0.2 0.2 0 0 1 2 3 4 5 6 Oupu Curren (A) 0 0 1 2 3 4 5 6 Oupu Curren (A) 1.4 1.2 1 0.8 7SFC: Inerleaved Buck Mode Power Loss Breakdown for V in = 12V & V ou = 5V Swich Conducion Loss Swiching Loss Oupu Capacior Loss Inducor Conducion Loss Inducor Core Loss Gae Loss 0.6 0.4 0.2 0 0 1 2 3 4 5 6 Oupu Curren (A) Figure 4-4: Power loss breakdown for V in =12V & V ou =5V, a) inerleaved buck converer, b) 7SFC converer, 3-level buck mode, c) 7SFC converer, inerleaved buck mode 4.3 7SFC Seady-Sae Operaion In his secion operaing waveforms of he 7SFC converer are provided o demonsrae is funcionaliy for several operaing poins on he experimenal prooype. For each mode, one operaing poin is seleced ha he specific mode is designed for. Since he convenional inerleaved buck converer was also esed using he same prooype, operaing waveforms for his opology are also shown. Waveforms for several oher operaing poins for boh he 7SFC converer and he convenional inerleaved buck converer are provided in Appendix E. 4.3.1 7SFC: High Sep-Down Mode Waveforms

49 The waveforms shown in Figure 4-5a) and b) are for he swiching nodes, v x1 and v x2, inducor currens, i L1 and i L2, and he oupu volage, v ou, for he operaing poin of inpu volage, V in =12V, oupu volage, V ou =1V and load curren, I load =1A. Figure 4-5a) shows ha he volage a he swiching nodes, v x1 and v x2, are alernaing beween 6V and 0V, as expeced for he high sep-down mode. We also noice ha he inducor currens are balanced and since he volages a he v x1 and v x2 nodes are close, i means he flying capacior C fly is approximaely equal o V in /2. The oupu volage shown in Figure 4-5b) confirms ha we are operaing wih a conversion raio of 12V-o-1V. Figure 4-5: Experimenal waveforms for he 7SFC converer operaing in he high sep-down mode wih V in =12V & V ou =1V, a) displaying swiching nodes v x1 and v x2, b) displaying swiching node v x1 and oupu volage v ou 4.3.2 7SFC: Inerleaved Buck Mode Waveforms Waveforms for he inerleaved buck mode of he 7SFC converer are shown in Figure 4-6a) and b). for he operaing poin of inpu volage, V in =24V, oupu volage, V ou =12V and load curren, I load =1A. We noice ha he swiching nodes v x1 and v x2 swich a 24V, or he full inpu volage. We can also expec he proper conversion raio by observing he duy raio of approximaely 0.5 in Fig. 36.a. Fig. 36.b. confirms he oupu volage of V ou =12V is achieved.

50 Figure 4-6: Experimenal waveforms for he 7SFC converer operaing in he inerleaved buck mode wih V in =24V & V ou =12V, a) displaying swiching nodes v x1 and v x2, b) displaying swiching node v x1 and oupu volage v ou 4.3.3 7SFC: 3-Level Buck Mode Waveforms Waveforms for he 7SFC converer operaing in he 3-level buck mode are shown in Figure 4-7 for inpu volage, V in =36V, oupu volage, V ou =12V and load curren, I load =1A. Since he inducors are conneced in parallel only one swiching node is displayed, which is referred o as v x for his mode. The v x node swiches beween approximaely 18V and 0V which implies he flying capacior C fly volage is balanced a V in /2. There is a sligh curren imbalance for he curren waveforms, i L1 and i L2. Unlike he high sep-down mode here is no inheren loop mainaining balance beween he inducor currens for he 3-level buck mode of he 7SFC converer. The oupu volage signal, v ou, a he op of he Figure confirms ha he 7SFC is operaing wih V ou =12V. v v i i

51 Figure 4-7: Experimenal waveforms for he 7SFC converer operaing in he 3-level buck mode wih V in =36V & V ou =12V, displaying swiching node v x and oupu volage v ou 4.3.4 Convenional Inerleaved Buck Converer Waveforms Two operaing poins are seleced o demonsrae he inerleaved buck converer operaion, 1) inpu volage, V in =12V, oupu volage, V ou =1V and load curren, I load =1A and 2) V in =36V, V ou =12V and I load =1A. The convenional inerleaved buck converer was operaed wih an increased inducor value of 1.5uH according o he inducor selecion of Secion 4.1. Figures for he wo operaing poins described are shown in Figure 4-8 and Figure 4-9. For he 12V-o-1V operaing poin he required duy raio for he convenional inerleaved buck converer is half of ha of he 7SFC high sep-down mode. The resul is increased volage spiking. The fac ha he swiching node is beween he full inpu volage of 12V and 0V confirms he inerleaved buck converer operaion. The oupu volage in Figure 4-8b) confirms he operaing poin of V ou =1V. v x2 v i i v v i i Figure 4-8: Experimenal waveforms for he convenional inerleaved buck converer wih V in =12V & V ou =1V, a) displaying swiching nodes v x1 and v x2, b) displaying swiching node v x1 and oupu volage v ou For he second operaing poin he swiching nodes, v x1 and v x2, are swiching beween approximaely 36V and 0V. The currens are slighly imbalanced since here is no inheren curren balancing wih a volage mode conroller. Comparing he inducor curren ripple o he 3- level buck mode of he 7SFC converer of he previous secion shows ha he inducor curren ripple is approximaely hree imes he magniude, which is a major loss conribuion of he

52 inerleaved buck converer a his operaing poin. Finally, he oupu volage can be confirmed in Figure 4-9b) as V ou =12V. Figure 4-9: Experimenal waveforms for he convenional inerleaved buck converer wih V in =36V & V ou =12V, a) displaying swiching nodes v x1 and v x2, b) displaying swiching node v x1 and oupu volage v ou 4.4 Efficiency Resuls and Comparison To verify he expeced efficiency improvemens of he 7SFC based muli-level converer over he convenional inerleaved buck converer, efficiency measuremens were aken for boh converers a various operaing poins. In his secion, efficiency resuls for hree operaing poins are presened and compared beween he wo converers, 1) inpu volage, V in =12V, oupu volage, V ou =1V, 2) V in =12V, V ou =5V and 3) V in =15V, V ou =12V. Addiional efficiency curves are provided in Appendix F. In he firs operaing poin he benefi of he high-sep down mode of he 7SFC converer, whose purpose is o achieve highes efficiency for high sep-down raios, is demonsraed. Efficiency curves for he convenional inerleaved buck converer and he 7SFC converer operaing in he high sep-down mode are presened in Figure 4-10 for his operaing poin. A his operaing poin he 7SFC converer improves on he efficiency of he inerleaved buck converer for he enire range of load currens. The previously shown loss breakdown clearly demonsraed ha swiching losses are he major componen ha is reduced by moving o he high sep-down mode of he 7SFC converer. Thus, for his operaing poin, he 7SFC converer is a very aracive opion.

Efficiency (%) Efficiency (%) Efficiency (%) Efficiency (%) 53 90% Inerleaved Buck Converer Experimenal Efficiency for V in = 12V & V ou = 1V 90% 7SFC: Experimenal Efficiency Resuls wih V in = 12V & V ou = 1V 85% 85% 80% 80% 75% 75% 70% 70% 65% 60% Vin = 12V 65% 60% Vin = 12V (HSD Mode) 55% 0 1 2 3 4 5 6 Oupu Curren (A) 55% 0 1 2 3 4 5 6 Oupu Curren (A) Figure 4-10: Efficiency curves for V in =12V &V ou =1V for, a) convenional inerleaved buck converer, b) 7SFC converer Efficiency curves for he second operaing poin are presened in Figure 4-11. For his operaing poin we can see how he highes efficiency mode of he 7SFC converer depends on load curren. 100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% Inerleaved Buck Converer Experimenal Efficiency for V in = 12V & V ou = 5V Vin = 12V 35% 0 1 2 3 4 5 6 Oupu Curren (A) 100% 95% 90% 85% 80% 75% 70% 65% 60% 55% 50% 45% 40% 7SFC: Experimenal Efficiency Resuls wih V in = 12V & V ou = 5V Vin = 12V (3LB Mode) Vin = 12V (IB Mode) 35% 0 1 2 3 4 5 6 Oupu Curren (A) Figure 4-11: Efficiency curves for V in =12V & V ou =5V for, a) inerleaved buck converer, b) 7SFC converer A he low end of currens, up o approximaely 3A, he 3-level buck mode has significanly higher efficiency. Even when compared o he convenional inerleaved buck converer he

Efficiency (%) Efficiency (%) 54 efficiency is much improved. As he load curren is increased pas 3A he inerleaved buck mode becomes he highes efficiency mode. For his segmen of he efficiency curve he 7SFC converer achieves almos equivalen efficiency compared o he convenional inerleaved buck. The higher conducion losses of he inerleaved buck mode of he 7SFC compared o he inerleaved buck converer are wha cause he efficiency o be slighly reduced. The hird operaing poin is a direc comparison beween he inerleaved buck converer and he inerleaved buck mode of he 7SFC converer as shown in Figure 4-12. Here, over he full operaing range, he inerleaved buck converer has slighly higher efficiency, peaking a 97% where he inerleaved buck mode of he 7SFC only reaches 96.5% wih a higher efficiency dropoff a high currens. However, he benefis gained by inroducing he oher modes of he converer for oher operaing poins make he radeoff very worhwhile. 100% Inerleaved Buck Converer Experimenal Efficiency for V in = 15V & V ou = 12V 100% 7SFC: Experimenal Efficiency Resuls wih V in = 15V & V ou = 12V 95% 95% 90% 90% 85% 85% 80% 80% 75% 75% 70% Vin = 15V 70% Vin = 15V (IB Mode) 65% 0 1 2 3 4 5 6 Oupu Curren (A) 65% 0 1 2 3 4 5 6 Oupu Curren (A) Figure 4-12: Efficiency curves for V in =15V & V ou =12V for, a) inerleaved buck converer, b) 7SFC converer

55 CHAPTER 5: 5. CONCLUSIONS AND FUTURE WORK This hesis presened a novel soluion for a wide-range dc-dc converer, he 7-swich flying capacior (7SFC) based muli-level buck converer, ha improves on he convenional soluion, he 2-phase inerleaved buck converer, in several ways. The meris of he 7SFC converer were evaluaed in erms of efficiency, volume, and conroller complexiy. The major accomplishmens of his work and fuure research are provided in he following secions. 5.1 Major Accomplishmens This work was able o show ha he 7SFC based muli-level converer is a suiable alernaive o he convenional 2-phase inerleaved buck converer in erms of efficiency and volume over he majoriy of he operaing range for a wide-range converer. The increased number of swiches in he converer, for he cos of no addiional volume, and paired wih a digial conroller, provides flexibiliy ha is no presen in convenional opologies. The following lis summarizes he advanages of he 7SFC converer: Muli-mode swich operaion faciliaed by a digial conroller Operaing poin based efficiency opimizaion High-sep down raio efficiency significanly improved over he convenional inerleaved buck by significanly reducing swiching losses Reduced volume inducor volume requiremen by 33% Reduced oupu capacior requiremen by 33% Less han 50% of he silicon area for he MOSFETs compared o he inerleaved buck The modes of operaion of he 7SFC converer are caegorized ino operaing range based on Figure 5-1.

56 High Inpu Volage, Low Oupu Curren - High sep-down mode - 3-level buck mode Low Inpu Volage, Low Oupu Curren - Single-phase buck mode - Single-phase, 3-level buck mode High Inpu Volage, High Oupu Curren - High sep-down mode - 3-level buck mode Low Inpu Volage, High Oupu Curren - High sep-down mode - Inerleaved buck mode Figure 5-1: Modes of he 7SFC converer caegorized based on he operaing range. 5.2 Fuure Work The fuure work for he 7SFC based muli-level buck converer relaes mainly wih puing all of he conrol feaures ogeher. This hesis has shown ha he swich configuraion can be used o operae in many modes, bu selecing modes and changing modes during he converer operaion can presen a new se of design challenges. For example, in response o a load ransien, i becomes complicaed o move beween he inerleaved buck mode and he 3-level buck mode while mainaining balanced inducor currens and no allowing a large oupu volage deviaion. Specialized conrol wih regards o he flying capacior should be addressed o make he mode changing possible. In general, load ransiens should be esed for his converer o confirm he heoreical claims made here wih regards o he oupu capacior selecion. Furhermore, some conrol issues peraining o he specific operaing modes haven been solved in previous research. For example, for he 3-level buck mode, he capacior balancing issue remains a challenge for a wide range converer. REFERENCES

57 [1] Mifakhudinov, R., Improving Sysem Efficiency wih a New Inermediae-Bus Archiecure, Texas Insrumens Inc. Seminar, 2009 [2] Culberson, L., The Modern Disrbued Power Archiecure, Mouser Elecronics [3] D. Morrison, Disribued power moves o inermediae-bus volage, Elecronic Design, pp. 55 62, Sep. 16, 2002 [4] Darnell. (2014), Worldwide DC-DC Converer Module Forecass: Power Archiecures, Produc Types, Volage Trends and Applicaions, Feb. 2014. [5] Darnell. (2011), Worldwide DC-DC Converer IC Forecass: Applicaions, Amperages and Emerging Applicaions Elevenh Ediion,April 2014. [6] Nishijima, K.; Harada, K.; Nakano, T.; Nabeshima, T.; Sao, T., "Analysis of Double Sep-Down Two-Phase Buck Converer for VRM," Telecommunicaions Conference, 2005. INTELEC '05. Tweny-Sevenh Inernaional, pp.497,502, Sep. 2005 [7] Meynard, T.A.; Foch, H., "Muli-level conversion: high volage choppers and volagesource inverers," Power Elecronics Specialiss Conference, 1992. PESC '92 Record., 23rd Annual IEEE, pp.397,403 vol.1, 29 Jun-3 Jul [8] Erickson, Rober W., and Dragan Maksimovic. Fundamenals of power elecronics. Springer Science & Business Media, 2007. [9] David Reusch, High Frequency, High Power Densiy Inegraed Poin of Load and Bus Converers, Ph.D. Disseraion, Virginia Tech, 2012 [10] Cosabeber, A.; Maavelli, P.; Saggini, S., "Digial Time-Opimal Phase Shedding in Muliphase Buck Converers," Power Elecronics, IEEE Transacions on, vol.25, no.9, pp.2242,2247, Sep. 2010 [11] Wang, J.; Ng, K.; Kawashima, T.; Sasaki, M.; Nishio, H.; Prodic, A.; Ng, W.T., "A digially conrolled inegraed DC-DC converer wih ransien suppression," Power

58 Semiconducor Devices & IC's (ISPSD), 2010 22nd Inernaional Symposium on, pp.277,280, 6-10 June 2010 [12] Reusch, D.; Lee, F.C.; Gilham, D.; Yipeng Su, "Opimizaion of a high densiy gallium niride based non-isolaed poin of load module," Energy Conversion Congress and Exposiion (ECCE), 2012 IEEE, pp.2914,2920, 15-20 Sep. 2012 [13] Shirazi, M.; Zane, R.; Maksimovic, D.; Corradini, L.; Maavelli, P., "Auouning echniques for digially-conrolled poin-of-load converers wih wide range of capaciive loads," Applied Power Elecronics Conference, APEC 2007 - Tweny Second Annual IEEE, pp.14,20, Feb. 25 2007-March 1 2007 [14] Lei, Y.; Liu,W-C.; Pilawa-Podgurski, R., An Analyical Mehod o Evaluae Flying Capacior Mulilevel Converers and Hybrid Swiched-Capacior Converors for Large Volage Conversion Raios, COMPEL, 2015 [15] M. D. Seeman, A Design Mehodology for Swiched-Capacior DC-DC Converers, Ph.D. Disseraion, Universiy of California a Berkeley, 2009 [16] Shenoy, P.S.; Amaro, M.; Freeman, D.; Morroni, J., "Comparison of a 12V, 10A, 3MHz buck converer and a series capacior buck converer," Applied Power Elecronics Conference and Exposiion (APEC), 2015 IEEE, vol., no., pp.461,468, 15-19 March 2015 [17] Villar-Pique, G., & Alarcón, E. (2011). CMOS inegraed swiching power converers. [18] Reshma, PS.; Jose,R., "Three level buck converer wih improved dynamic performance using linear-non linear conrol," Inernaional Journal of Innovaive Research in Elecrical, Elecronics, Insrumenaion and Conrol Engineering, vol. 2, Issue 3, March 2014, pp. 1189-1192 [19] Reusch, D.; Lee, F.C.; Ming Xu, "Three level buck converer wih conrol and sof sarup," Energy Conversion Congress and Exposiion, 2009. ECCE 2009. IEEE, pp.31,35, 20-24 Sep. 2009

59 [20] Prodic, A.; Maksimovic, D.; Erickson, R.W., "Design and implemenaion of a digial PWM conroller for a high-frequency swiching DC-DC power converer," in Indusrial Elecronics Sociey, 2001. IECON '01. The 27h Annual Conference of he IEEE, vol.2, no., pp.893-898 vol.2, 2001 [21] A. Radic, Pracical Volume-Reducion Sraegies for Low-Power High-Frequency Swich Mode Power Supplies. PhD hesis, Universiy of Torono, Canada, 2014. [22] Cosabeber, A.; Corradini, L.; Maavelli, P.; Saggini, S., "Time opimal, parameersinsensiive digial conroller for DC-DC buck converers," in Power Elecronics Specialiss Conference, 2008. PESC 2008. IEEE, vol., no., pp.1243-1249, 15-19 June 2008 [23] Baliga, B. Jayan. Fundamenals of power semiconducor devices. Springer Science & Business Media, 2010. [24] Bjeleic, A.; Corradini, L.; Maksimovic, D.; Zane, R., "Specificaions-driven design space boundaries for Poin-of-Load converers," Applied Power Elecronics Conference and Exposiion (APEC), 2011 Tweny-Sixh Annual IEEE, pp.1166,1173, 6-11 March 2011 [25] Bazine, J. P., & O'connor, J. A. (1997). U.S. Paen No. 5,627,460. Washingon, DC: U.S. Paen and Trademark Office. [26] Abe, K.; Nishijima, K.; Harada, K.; Nakano, T.; Nabeshima, T.; Sao, T., "A Novel Three-Phase Buck Converer wih Boosrap Driver Circui," in Power Elecronics Specialiss Conference, 2007. PESC 2007. IEEE, vol., no., pp.1864-1871, 17-21 June 2007 APPENDICES

60 APPENDIX A: A. 2-PHASE 3-LEVEL BUCK CONVERTER OPERATION FOR M > 0.5 The swiching sequence and inducor volage and curren waveforms for he 2-phase 3-level buck converer for conversion raio, M > 0.5, is shown in Figure A-1. Sae 1: 0 < < DTs SW2 Sae 2: DTs < < Ts/4 SW2 Vin SW1 SW5 VCfly1 Cfly1 SW6 VCfly2 Cfly2 SW8 SW3 SW4 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Vin SW1 SW5 VCfly1 Cfly1 SW6 SW4 VCfly2 Cfly2 SW8 SW3 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Sae 3: Ts/4 < < Ts (D+¼) SW2 Sae 4: Ts (D+¼) < < Ts/2 SW2 Vin SW1 SW5 VCfly1 Cfly1 SW4 SW6 VCfly2 Cfly2 SW3 SW7 SW8 L1 VL1 L2 VL2 il1() C il2() R Vou Vin SW1 SW5 VCfly1 Cfly1 SW6 SW4 VCfly2 Cfly2 SW8 SW3 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Sae 5: Ts/2 < < Ts (D+½) SW2 Sae 6: Ts (D+½) < < Ts 3/4 SW2 Vin SW1 SW5 VCfly1 Cfly1 SW4 SW6 VCfly2 Cfly2 SW8 SW3 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Vin SW1 SW5 VCfly1 Cfly1 SW6 SW4 VCfly2 Cfly2 SW8 SW3 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Sae 7: Ts 3/4 < < Ts (D+¾) SW2 Sae 8: Ts (D+¾) < < Ts SW2 Vin SW1 SW5 VCfly1 Cfly1 SW6 SW4 VCfly2 Cfly2 SW8 SW3 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Vin SW1 SW5 VCfly1 Cfly1 SW6 SW4 VCfly2 Cfly2 SW8 SW3 SW7 L1 VL1 L2 VL2 il1() C il2() R Vou Sae 1 Sae 3 Sae 5 Sae 7 Sae 2 Sae 4 Sae 6 Sae 8 VL1() Vin-Vou Vin-Vou il1() il2() 0 VCfly-Vou Vin-VCfly-Vou Vin-Vou Vin-VCfly-Vou VCfly-Vou Vin-Vou Iload/2 Iload/2 DTs Ts/4 Ts/2 Ts 3/4 Ts Ts/4+DTs Ts/2+DTs Ts 3/4+DTs VCfly-Vou

61 Figure A-1: Swiching sequence and inducor waveforms for he 2-phase 3-level buck converer operaing in he M>0.5 mode APPENDIX B:

62 B. 7SFC CONVERTER CONDUCTION LOSSES This Appendix deails he conducion losses for each mode of he 7SFC based muli-level buck converer. B.1 Inerleaved Buck Mode The inducor and swich currens for he inerleaved buck mode for boh D < 0.5 and D > 0.5 are shown in Fig. 22.a. and b. respecively. For he D < 0.5 case of Fig. 22.a. he RMS currens for boh inducors, i L1,RMS and i L2,RMS as well as all of he swiches i SW1,RMS, i SW4,RMS, i SW2,RMS, i SW3,RMS, i SW6,RMS, i SW5,RMS and i SW7,RMS are shown in Eqs. (B-1 o B-4), i L1,RMS = i L2,RMS = I load 2 1 + 1 12 ( i L IB I load ) 2, (B-1) i SW1,RMS = i SW4,RMS = I load 2 2 D 1 + 1 3 ( i L IB I load ) 2, (B-2) i SW2,RMS = i SW3,RMS = i SW6,RMS = I load 2 (1 D) 1 + 1 3 ( i L IB I load ) 2, (B-3) i SW5,RMS = i SW7,RMS = I load 2 D 1 + 1 3 ( i L IB I load ) 2, (B-4) where I load is he load curren, Δi L-IB is he inducor curren ripple from Eq. (3-2), and D is he duy raio. In he D > 0.5 case he RMS curren value for SW 1 is found by looking a wo porions of he swiching cycle, for Sae 1 (or Sae 3) and Sae 2 (or Sae 4). For his mode of operaion SW 4 and SW 1 have he same curren, so o simplify we will look a he curren hrough SW 1.

63 V in i SW1 () SW 1 C fly i SW3 () SW3 L 1 i L1 () i SW2 () i SW SW7 () 2 SW 7 SW 5 L 2 SW 4 i SW4 () i SW5 () isw6 () i L2 () C R V ou SW 6 i L1 () Sae 1 Sae 2 Sae 3 Sae 4 Δi i L2 () Δi i SW1 () Δi i SW2 () Δi i SW3 () Δi i SW4 () Δi i SW5 () Δi i SW6 () Δi i SW7 () Δi 0 DT s T s /2 T s /2+DT s T s i L1 () i L2 () i SW1 () i SW2 () i SW3 () i SW4 () i SW5 () i SW6 () Sae 1 Sae 2 Sae 3 Sae 4 Δi Δi Δi SW1a Δi SW1b Δi Δi Δi SW4a Δi SW4b Δi Δi i SW7 () Δi 0 DT s T s /2 T s /2+DT s T s I load I load Figure B-1: Swiching sequence and inducor waveforms for he inerleaved buck mode of he 7SFC converer for a) D<0.5 and b) D>0.5 In Sae 1 he average curren hrough SW 1 is I load and wih a curren ripple of Δi SW1a. The value of Δi SW1a is shown in Eq. (B-5), i SW1a = i SW4a = 2 (V in V ou ) (D 1 2 ) T s L, (B-5)

64 where V in is he inpu volage, V ou is he oupu volage, T s is he swiching period and L is he inducance value. In Sae 2 he average curren hrough SW 1 and SW 4 is wih a curren ripple of Δi SW1b shown in Eq. (B-6), i SW1b = i SW4b = (V in V ou ) (1 D) T s L. (B-6) The oal RMS curren of SW 1 and SW4, i.e. i SW1,RMS and i SW4,RMS, is provided in Eq. (B-7), i SW1,RMS = i SW4,RMS = 2 [ (D 1 2 )2 I load 2 (1 + 1 3 ( i SW1a 2 I load ) 2 ) + + (1 D) 2 ( I load 2 )2 (1 + 1 3 ( i SW1b I load ) 2 ) ]. (B-7) For a more deailed explanaion of adding RMS values proceed o Appendix C. The RMS currens for he remaining swiches for he inerleaved buck mode operaing wih D > 0.5 are he same as for he D < 0.5 case and have been provided in Eqs. (B-1, B-3, B-4) previously. B.2 High Sep-Down Mode The inducor and swich currens for he 7SFC converer operaing in he high sep-down mode of operaion are shown in Fig. 23. The RMS curren values for he inducors, i.e. i L1,RMS and i L2,RMS, are shown in Eq. (B-8), i L1,RMS = i L2,RMS = I load 2 1 + 1 12 ( i L HSD I load ) 2, (B-8) where I load is he load curren and Δi L-HSD is he inducor curren ripple from Eq. (3-4). The RMS currens for SW 1 and SW 4, i.e. i SW1,RMS and i SW4,RMS, where he effec of curren division is no a conribuing facor, are provided in Eq. (B-9), i SW1,RMS = i SW4,RMS = I load 2 D 1 + 1 3 ( i I load ) 2, (B-9)

65 where D is he duy raio. The RMS currens for he res of he swiches are found using he mehod in Appendix C. The curren ripple for he swiches where only one phase is in synchronous recificaion, i.e. SW 2 and SW 3 during Sae 3, and SW 6 during Sae 1, is given in Eq. (B-10) and denoed by Δi sr,γ : i sr,γ = (V ou ) D T s L, (B-10) Where V ou is he oupu volage, T s is he swiching period and L is he inducance value.

66 V in i SW1 () SW 1 C fly i SW3 () SW3 L 1 i L1 () i SW2 () i SW SW7 () 2 SW 7 SW 5 L 2 SW 4 i SW4 () i SW5 () isw6 () i L2 () C R V ou SW 6 i L1 () i L2 () i SW1 () i SW2 () i SW3 () i SW4 () i SW5 () i SW6 () i SW7 () Δi Sae 1 Sae 2 Sae 3 Sae 4 Δi Δi Δi Δi SW2,sr Δi SW3,sr Δi SW5,sr Δi SW6,sr Δi sr,γ Δi SW7,sr I SW2,srα I SW3,srα I SW5,srα I SW6,srα I SW7,srα Δi sr,γ Δi sr,γ Δi Δi 0 DT s T s /2 T s /2+DT s T s I SW2,srβ I SW3,srβ I SW5,srβ I SW6,srβ I SW7,srβ Figure B-2: Swiching sequence and inducor waveforms for he high sep-down mode of he 7SFC converer

67 To complee he RMS curren calculaions he curren division during he synchronous recificaion saes, Sae 2 and Sae 4, are analyzed. The simplified curren division circui considering he on-resisances of he swiches ha are involved is shown in Fig. 24. I should be noed ha he averages of he inducor currens i L1 () and i L2 () during each synchronous recificaion sae are differen. R on3 i L1 () R on2 I SW5,sr i L2 () R on5 R on7 R on6 I SW2,sr I SW6,sr I load Figure B-3: Curren division during synchronous recificaion for he high sep-down mode of he 7SFC converer The average currens during he firs synchronous recificaion sae, Sae 2, are denoed wih he subscrip srα and for he second one, Sae 4, wih he subscrip srβ. These average currens and heir respecive curren ripples over he sae are shown in Eqs. (B-11 o B-23): I L1,srα = I load 2 + 1 4 (V ou T s ), (B-11) L I L2,srα = I load 2 1 4 (V ou T s ), (B-12) L I SW2,srα = I SW3,srα = I L1,srα (R on7 +R on5 )+I load R on6 R on2 +R on3 +R on5 +R on6 +R on7, (B-13) I SW5,srα = I SW7,srα = I load R on6 I L1,srα (R on2 +R on3 +R on6 ) R on2 +R on3 +R on5 +R on6 +R on7, (B-14) I SW6,srα = I load (R on2 +R on3 +R on5 +R on7 ) I L1,srα (R on5 +R on7 ) R on2 +R on3 +R on5 +R on6 +R on7, (B-15) I L1,srβ = I load 2 1 4 (V ou T s ), (B-16) L

68 I L2,srβ = I load 2 + 1 4 (V ou T s ), (B-17) L I SW2,srβ = I SW3,srβ = I L1,srβ (R on7 +R on5 )+I load R on6 R on2 +R on3 +R on5 +R on6 +R on7, (B-18) I SW5,srβ = I SW7,srβ = I load R on6 I L1,srβ (R on2 +R on3 +R on6 ) R on2 +R on3 +R on5 +R on6 +R on7, (B-19) I SW6,srβ = I load (R on2 +R on3 +R on5 +R on7 ) I L1,srβ (R on5 +R on7 ) R on2 +R on3 +R on5 +R on6 +R on7, (B-20) i SW2,sr = i SW3,sr = (V ou ) (1 2 D) T s L R on5 +2 R on6 +R on7 ( ), R on2 +R on3 +R on5 +R on6 +R on7 (B-21) i SW5,sr = i SW7,sr = (V ou ) (1 2 D) T s L R on2 +R on3 R on6 ( ), R on2 +R on3 +R on5 +R on6 +R on7 (B-22) i SW6,sr = (V ou ) (1 2 D) T s L ( 2 (R on2+r on3 )+R on5 +R on7 R on2 +R on3 +R on5 +R on6 +R on7 ), (B-23) wih he labelling corresponding o Figure B-3. The curren ripples for boh synchronous recificaion saes are equal. The RMS currens for he remaining swiches, i.e. i SW2,RMS, i SW3,RMS, i SW5,RMS, i SW6,RMS, i SW7,RMS, are hen calculaed and given in Eqs. (B-24 o B-28), 2 ) 2 I SW2,srα ( 1 2 D)2 I 2 SW2,srα (1 + 1 ( i SW2,sr 3 i SW2,RMS = ) + ( 1 2 D)2 I 2 SW2,srβ, (B-24) (1 + 1 ( i 2 SW2,sr ) ) + D 2 ( I load 3 2 I SW2,srβ 2 )2 (1 + 1 3 ( i sr,γ ) 2 ) I load i SW3,RMS = ( 1 2 D)2 I 2 SW3,srα (1 + 1 ( i 2 SW3,sr ) ) + ( 1 3 2 I SW3,srα 2 D)2 I 2 SW3,srβ (1 + 1 3 ( i SW3,sr 2 I SW3,srβ ) 2 ) + D 2 ( I load 2 )2 (2 + 1 i (( ) 2 + ( i sr,γ ) 2 ) ) 3 I load I load, (B- 25)

69 2 ) 2 I SW5,srα ( 1 2 D)2 I 2 SW5,srα (1 + 1 ( i SW5,sr 3 i SW5,RMS = ) + ( 1 2 D)2 I 2 SW5,srβ, (B-26) (1 + 1 ( i 2 SW5,sr ) ) + D 2 ( I load 3 2 I SW5,srβ 2 )2 (1 + 1 ( i ) 2 ) 3 I load 2 ) 2 I SW6,srα ( 1 2 D)2 I 2 SW6,srα (1 + 1 ( i SW6,sr 3 i SW6,RMS = ) + ( 1 2 D)2 I 2 SW6,srβ, (B-27) (1 + 1 ( i 2 SW6,sr ) ) + D 2 ( I load 3 2 I SW6,srβ 2 )2 (1 + 1 3 ( i sr,γ ) 2 ) I load ( 1 2 D)2 I 2 SW7,srα (1 + 1 ( i 2 SW7,sr ) ) + ( 1 3 2 I SW7,srα 2 D)2 I 2 SW7,srβ i SW7,RMS =. (B-28) (1 + 1 ( i 2 SW7,sr ) ) 3 2 I SW7,srβ B.3 3-Level Buck Mode The 3-level buck mode of operaion of he 7SFC converer demonsraes higher conducion losses han he oher modes of operaion due o he fac ha some of he swiches experience he full load curren over a porion of he swiching cycle. The waveforms for he currens of he inducors and swiches are shown in Fig. 25. The RMS currens for each inducor, i L1,RMS and i L2,RMS, as well as SW 1 and SW 4, i SW1,RMS and i SW2,RMS, are simply calculaed in Eq. (B-29) and (B- 30), i L1,RMS = i L2,RMS = I load 2 1 + 1 12 ( i L 3LB I load ) 2, (B-29) i SW1,RMS = i SW4,RMS = I load 2 D 1 + 1 3 ( i L 3LB I load ) 2, (B-30) where I load is he load curren, Δi L-3LB is he inducor curren ripple for he 3-level buck mode from Eq. (3-5), and D is he duy raio. The RMS curren calculaions for he oher swiches are more cumbersome. For hese swiches he curren is divided during he synchronous recificaion saes, Sae 2 and Sae 4. The curren division circui is he same as ha of he high sep-down case shown previously in Figure B-4, bu he inducor currens when enering synchronous

70 recificaion have changed. Assuming he flying capacior, C fly, is balanced a half of he inpu volage, we can assume he average currens and curren ripple for each individual swich is equal beween boh synchronous recificaion saes. These currens are denoed wih he subscrip srσ and are shown in Eqs. (B-31 o B-37):

71 V in i SW1 () SW 1 C fly i SW3 () SW3 L 1 i L1 () i SW2 () i SW SW7 () 2 SW 7 SW 5 L 2 SW 4 i SW4 () i SW5 () isw6 () i L2 () C R V ou SW 6 i L1 () i L2 () i SW1 () i SW2 () Sae 1 Sae 2 Sae 3 Sae 4 Δi Δi 2 Δi I load i SW3 () Δi SW2,srσ 2 Δi I load I SW2,srσ i SW4 () 2 Δi Δi SW3,srσ I load I SW3,srσ 2 Δi I load i SW5 () i SW6 () Δi SW5,srσ Δi I SW5,srσ i SW7 () Δi SW6,srσ Δi SW7,srσ 0 DT s T s /2 Δi T s /2+DT s T s I SW6,srσ I SW7,srσ Figure B-4: Inducor and swich currens for he 3-level buck mode of he 7SFC converer I L1,sr = I L2,sr = I load 2, (B-31)

72 I SW2,srσ = I SW3,srσ = I load ( R on7+r on5 )+R 2 on6, R on2 +R on3 +R on5 +R on6 +R on7 (B-32) I SW5,srσ = I SW7,srσ = I load ( R on2+ron3 Ron6 ) 2, R on2 +R on3 +R on5 +R on6 +R on7 (B-33) I SW6,srσ = I load R on2 +R on3 +( R on5 +R on7 ) 2, R on2 +R on3 +R on5 +R on6 +R on7 (B-34) i SW2,srσ = i SW3,srσ = (V ou ) (1 2 D) T s L R on5 +2 R on6 +R on7 ( ), R on2 +R on3 +R on5 +R on6 +R on7 (B-35) i SW5,srσ = i SW7,srσ = (V ou ) (1 2 D) T s L R on2 +R on3 R on6 ( ), R on2 +R on3 +R on5 +R on6 +R on7 (B-36) i SW6,srσ = (V ou ) (1 2 D) T s L ( 2 (R on2+r on3 )+R on5 +R on7 R on2 +R on3 +R on5 +R on6 +R on7 ), (B-37) where he curren and on-resisance labels are presen in Fig. X and X. respecively. Using he RMS curren adding mehod of Appendix C, he RMS currens for he remaining swiches, i SW2,RMS, i SW3,RMS, i SW5,RMS, i SW7,RMS, i SW6,RMS, are calculaed wih Eqs. (B-38 o B-40): D 2 I 2 load (1 + 1 ( i ) 2 ) + 2 ( 1 3 I load 2 D)2 I 2 SW2,srσ i SW2,RMS = i SW3,RMS = (1 + 1 ( i 2 SW2,srσ ) ) 3 2 I SW2,srσ, (B-38) 2 D 2 ( I load 2 )2 (1 + 1 ( i ) 2 ) + 2 ( 1 3 I load 2 D)2 I 2 SW5,srσ i SW5,RMS = i SW7,RMS = (1 + 1 ( i 2 SW5,srσ ) ) 3 2 I SW5,srσ, (B- 39) APPENDIX C: i SW6,RMS = 2 ( 1 2 D)2 I 2 SW6,srσ (1 + 1 ( i 2 SW6,srσ ) ). (B-40) 3 2 I SW6,srσ

73 C. ADDING RMS CURRENTS This Appendix oulines he general echnique for adding RMS currens. A ypical inducor curren waveform is provided in Fig. 45. To find he oal RMS curren of i() he period is separaed ino hree porions: 1) 0<<DT s, 2) DT s <<T s /2, and 3) (1/2+D)T s <<T s, where D is he duy raio, and T s is he swiching period. The oal RMS curren can be found by performing a weighed sum of he squared RMS currens of each porion, followed by a square roo operaion as in Eq. (C-1). i() Δi I ave 0 DT s T s /2 (½ + D)T s T s Figure C-1: Typical inducor curren waveform I RMS,oal = D I RMS,1 2 + ( 1 2 D) I RMS,2 2 + ( 1 2 D) I RMS,3 2 (C-1) I is simple o find he RMS values of each individual porion, I RMS,1, I RMS,2, and I RMS,3, as shown in Eqs. (C-2 o C-3): I RMS,1 = I ave D 1 + 1 3 ( i 2 I ave ) 2, (C-2) I RMS,2 = I RMS,3 = I ave ( 1 2 D) 1 + 1 3 ( i 2 I ave ) 2, (C-3) Thus, he oal RMS curren, I RMS,oal is calculaed wih Eq. (C-4), I RMS,oal = D 2 I ave 2 (1 + 1 3 ( i 2 I ave ) 2 ) + 2 ( 1 2 D)2 I ave 2 (1 + 1 3 ( i 2 I ave ) 2 ). (C-4) APPENDIX D:

74 D. 2-PHASE INTERLEAVED BUCK CONVERTER LOSS BREAKDOWN This Appendix presens a breakdown of he major loss conribuions for he convenional 2- phase inerleaved buck converer. D.1 Conducion Losses The inducor curren ripple for he inerleaved buck, Δi L, is shown in Eq. (D-1), i L = (V in V ou ) D T s L, (D-1) where V in is he inpu volage, V ou is he oupu volage, D is he duy raio, T s is he swiching period, and L is he inducance value. The RMS curren values for each inducor, i L1,RMS and i L2,RMS, are found using Eq. (D-2), i L1,RMS = i L2,RMS = I load 2 1 + 1 12 ( i L I load ) 2, (D-2) where I load is he load curren. The RMS curren values for he swiches, i SW1,RMS, i SW3,RMS, i SW2,RMS, and i SW4,RMS, are provided in Eqs. (D-3,D-4), i SW1,RMS = i SW3,RMS = I load 2 D 1 + 1 3 ( i I load ) 2, (D-3) D.2 Swiching Losses i SW2,RMS = i SW4,RMS = I load 2 (1 D) 1 + 1 3 ( i I load ) 2. (D-4)

75 In he inerleaved buck opology, only he wo high-side swiches, i.e. SW 1 and SW 3, experience hard-swiching ransiions. The low-side swiches, SW 2 and SW 4, have sof ransiions due o he body diode conducion which resuls in no losses in his caegory. i SW1 () L 1 i L1 () V in SW 1 SW 2 i SW3 () SW 3 SW 4 i SW2 () i SW4 () L 2 i L2 () C R V ou i L1 () i SW1 () i SW2 () i L2 () i SW3 () i SW4 () 0 Sae 1 Sae 2 Sae 3 Sae 4 Δi Δi Δi Δi Δi Δi DT s T s /2 (½ + D)T s T s Figure D-1: Inducor and swich currens for he inerleaved buck converer.

76 The equaions for urn-on and urn-off swiching losses for SW 1 and SW 3, i.e. P SW1,ON, P SW3,ON, P SW1,OFF and P SW3,OFF, are shown in Eq. (D-5) and (D-6), P SW1,ON = P SW3,ON = 1 2 V in ( I load 2 i L 2 ) f s on, (D-5) P SW1,OFF = P SW3,OFF = 1 2 V in ( I load 2 + i L 2 ) f s off, (D-6) where V in is he inpu volage, I load is he load curren, Δi L is he inducor curren ripple for he convenional inerleaved buck converer, f s is he swiching frequency, on is he curren and volage overlap during a urn-on ransiion, and off is he overlap during a urn-off ransiion. Equaions (D-5) and (D-6) show ha swiching losses presen a significan drawback for he inerleaved buck converer. This converer has he full inpu volage, V in, frequenly appearing across he MOSFETs, and a high inpu volages, as will be seen in Chaper 4, he majoriy of he losses of his converer come from swiching losses. D.3 MOSFET Oupu Capacior Losses Assuming a posiive inducor curren over he full swiching period, each of he four swiches of he inerleaved buck converer will experience oupu capacior losses. The equaion for oupu capacior loss, P Coss, is shown in Eq. (D-7), P Coss = 1 2 C oss V in 2 f s, (D-7) where C oss is he oupu capaciance, V in is he inpu volage and f s is he swiching frequency. Once again, for he inerleaved buck converer, he oupu capacior losses will be very significan a high inpu volages due o he V 2 in facor. D.4 Gae Drive Losses

77 The gae drive losses, P gae, are found uilizing he gae charge, Q g, gae drive volage, V drive, and swiching frequency, f s, as shown in Eq. (D-8). P gae = Q g V drive f s (D-8) Wih four swiches, he gae drive losses are fairly low in he inerleaved buck for a wo-phase opology. D.5 Reverse Recovery Losses The reverse recovery losses in he inerleaved buck come from he main-swich urn-on (SW 1 or SW 3 ) while he body diode of he low-side swich (SW 2 or SW 4 ) is conducing. The reverse recovery losses, P rr, are calculaed using Eq. (D-9), P rr = Q rr V in f s, (D-9) where Q rr is he recovered charge from he low-side diode, V in is he inpu volage, and f s is he swiching frequency. D.6 Inducor Core Loss For he inerleaved buck converer he inducor curren frequency is equal o he swiching frequency, and he curren ripple has a magniude previously defined in Eq. (D-1). By subsiuing he swiching frequency, f s, as he inducor frequency, and curren ripple, Δi L, ino Eq. (3-20), he core loss equaion becomes Eq. (D-10), P core = K (f s ) α ( (V in V ou ) D T s ) β. (D-10) L APPENDIX E:

78 E. ADDITIONAL EXPERIMENTAL STEADY-STATE WAVEFORMS This Appendix simply conains addiional seady-sae operaion waveforms for boh he 7SFC based muli-level buck converer and he convenional inerleaved buck converer. E.1 7SFC: High Sep-Down Mode Waveforms v x2 v i i v v i i Figure E-1: Experimenal waveforms for he high sep-down mode of he 7SFC converer wih V in =48V & V ou =3.3V v x2 v i i v v i i Figure E-2: Experimenal waveforms for he high sep-down mode of he 7SFC converer wih V in =48V & V ou =11V

79 E.2 7SFC: Inerleaved Buck Mode v x2 v i i v v i i Figure E-3: Experimenal waveforms for he inerleaved buck mode of he 7SFC converer wih V in =15V & V ou =12V v x2 v i i v v i i Figure E-4: Experimenal waveforms for he inerleaved buck mode of he 7SFC converer wih V in =6V & V ou =5V

80 E.3 7SFC 3-level buck mode v v i i Figure E-5: Experimenal waveforms for he 3-level buck mode of he 7SFC converer wih V in =48V & V ou =12V Figure E-6: Experimenal waveforms for he 3-level buck mode of he 7SFC converer wih V in =5V & V ou =3.3V v v i i

81 E.4 Convenional Inerleaved Buck Converer Figure E-7: Experimenal waveforms for he convenional inerleaved buck converer wih V in =48V & V ou =3.3V Figure E-8: Experimenal waveforms for he convenional inerleaved buck converer wih V in =48V & V ou =12V Figure E-9: Experimenal waveforms for he convenional inerleaved buck converer wih V in =24V & V ou =12V

82 Figure E-10: Experimenal waveforms for he convenional inerleaved buck converer wih V in =15V & V ou =12V v v x2 v i i v i i Figure E-11: Experimenal waveforms for he convenional inerleaved buck converer wih V in =6V & V ou =5V v x2 v i i v v i i Figure E-12: Experimenal waveforms for he convenional inerleaved buck converer wih V in =15V & V ou =3.3V