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ISTANBUL TECHNICAL UNIVERSITY  GRADUATE SCHOOL OF SCIENCE ENGINEERING AND TECHNOLOGY

Ph.D. THESIS

DIGITALLY CONTROLLED BUCK CONVERTERS FOR CURRENT REGULATED APPLICATIONS

Abdulkerim UĞUR

NOVEMBER 2019

Department of Electrical Engineering Electrical Engineering Programme

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Department of Electrical Engineering Electrical Engineering Programme

ISTANBUL TECHNICAL UNIVERSITY  GRADUATE SCHOOL OF SCIENCE ENGINEERING AND TECHNOLOGY

NOVEMBER 2019

DIGITALLY CONTROLLED BUCK CONVERTERS FOR CURRENT REGULATED APPLICATIONS

Ph.D. THESIS Abdulkerim UĞUR

(504122007)

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Elektrik Mühendisliği Anabilim Dalı Elektrik Mühendisliği Programı

KASIM 2019

İSTANBUL TEKNİK ÜNİVERSİTESİ  FEN BİLİMLERİ ENSTİTÜSÜ

AKIM REGÜLASYONLU UYGULAMALAR İÇİN SAYISAL KONTROLLÜ ALÇALTICI ÇEVİRİCİLER

DOKTORA TEZİ Abdulkerim UĞUR

(504122007)

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Thesis Advisor : Asst. Prof. Dr. Murat YILMAZ ... Istanbul Technical University

Jury Members : Asst. Prof. Dr. Deniz YILDIRIM ... Istanbul Technical University

Assoc. Prof. Dr. Lale TÜKENMEZ ERGENE

Istanbul Technical University ...

Prof. Dr. Ahmet Faruk BAKAN ... Yildiz Technical University

Prof. Dr. Abdulkadir BALIKÇI ... Gebze Technical University

Abdulkerim UĞUR, a Ph.D. student of ITU Graduate School of Science Engineering and Technology, 504122007, successfully defended the thesis entitled “DIGITALLY CONTROLLED BUCK CONVERTERS FOR CURRENT REGULATED APPLICATIONS”, which he prepared after fulfilling the requirements specified in the associated legislations, before the jury whose signatures are below.

Date of Submission : 13 September 2019 Date of Defense : 07 November 2019

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FOREWORD

I would like to express my sincerely thanks to my thesis advisor Asst. Prof. Dr. Murat YILMAZ for all his guidance and support during my Ph.D. studies. His mentoring was invaluable for me.

I want to thank my friends in TÜBİTAK BİLGEM; Emre Adem BAYAR for his helps on prototyping and Dr. Salih Kağan KALYONCU for our inspiring discussions during my studies.

Moreover, I would like to give my special thanks to my mother, my father and my brother. Without their blessings and encouragement to do my best, this work could not be accomplished.

Finally, I would like to thank to my dear wife Melike. She was always there to support and encourage me during my desperate moments. She and my little daughter Nihan boosted my morale whenever I needed.

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TABLE OF CONTENTS Page FOREWORD ... ix TABLE OF CONTENTS ... xi ABBREVIATIONS ... xiii SYMBOLS ... xv

LIST OF TABLES ... xvii

LIST OF FIGURES ... xix

SUMMARY ... xxiii

ÖZET ... xxv

INTRODUCTION ... 1

Literature Review ... 2

1.1.1 Analog control methods ... 2

1.1.2 Digital control methods ... 3

1.1.3 GaN-based switching devices for power electronic circuits ... 7

1.1.4 Multi-level flying capacitor converters ... 9

Purpose of the Thesis ... 11

Contributions of the Thesis ... 11

Thesis Outline ... 12

ANALOG CURRENT MODE CONTROL FOR BUCK CONVERTER ... 15

An Overview to Buck Converter ... 15

Current Mode Control Methods ... 16

2.2.1 Peak current mode control and modeling ... 16

2.2.2 Average current mode control and modeling ... 19

2.2.3 I2 average current mode control and modeling ... 21

Comparison of Current Mode Control Methods for Buck Converter ... 23

An Analog Controlled Buck Converter Prototype ... 27

GAN-BASED SYNCHRONOUS BUCK CONVERTER ... 29

Introduction ... 29

Analysis Si-Based and GaN-Based Synchronous Buck Converters ... 30

3.2.1 Loss estimation ... 31

3.2.2 Converter design ... 33

3.2.3 Comparison of Si-based and GaN-based synchronous buck converters ... 33

Experimental Study ... 34

DIGITAL CURRENT MODE CONTROL ... 39

An Overview to Digital Control in Power Electronics ... 39

Digital Peak Current Mode Control ... 41

4.2.1 Modeling of the digital peak current mode control ... 43

4.2.2 Implementation of DPCM ... 45

4.2.2.1 Compensator design ... 45

4.2.2.2 Timing Scheme ... 47

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Digital Average Current Mode Control ... 49

4.3.1 Modeling of the digital average current mode control ... 51

4.3.2 Implementation of DACM ... 51

4.3.2.1 Compensator design ... 52

4.3.2.2 Timing scheme ... 55

4.3.3 Simulation and experimental study of DACM control ... 55

DIGITAL HYBRID CURRENT MODE CONTROL ... 61

Modeling of the Digital Hybrid Current Mode Control ... 63

5.1.1 Continuous-time model of the DHCM control ... 63

5.1.2 Discrete-time model of the DHCM control... 64

Implementation of the Digital Hybrid Current Mode Control ... 66

5.2.1 Compensator design algorithm for DHCM ... 66

5.2.2 Timing scheme ... 68

Simulation and Experimental Study of DHCM Control ... 70

Comparison of DHCM and DACM Control Methods ... 75

Conclusion ... 75

THREE-LEVEL FLYING CAPACITOR BUCK CONVERTER AND DIGITAL CONTROL ... 79

Introduction ... 80

DHCM control with Proposed Asymmetric Slope Compensation ... 83

6.2.1 Description of DHCM control with ASC for 3LFC buck converter ... 84

6.2.2 Analysis of asymmetric slope compensation ... 85

Hardware Implementation and Digital Controller ... 89

6.3.1 Description of the hardware ... 89

6.3.2 Timing scheme ... 91

6.3.3 Compensator design ... 93

Simulations and Experimental Results ... 93

6.4.1 Verification of ASC with simulations ... 94

6.4.2 Simulation of DHCM control with ASC ... 96

6.4.3 Experimental verification of DHCM control with ASC ... 98

Discussions ... 102 CONCLUSION ... 105 Summary... 105 Future Work... 107 Acknowledgement ... 108 REFERENCES ... 109 CURRICULUM VITAE ... 117

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ABBREVIATIONS

ACM : Average Current Mode

ASC : Asymmetric Slope Compensation ADC : Analog to Digital Converter CCM : Continuous Conduction Mode CMC : Current Mode Control

DC : Direct Current

DAC : Digital to Analog Converter DACM : Digital Average Current Mode DHCM : Digital Hybrid Current Mode DPCM : Digital Peak Current Mode DPWM : Digital Pulse Width Modulator ESR : Equivalent Series Resistance FPGA : Field Programming Gate Array FOM : Figure of Merit

GaN : Gallium Nitride

HDPCM : Hybrid Digital Peak Current Mode HFET : Heterojunction Field-Effect Transistors HEMT : High Electron Mobility Transistors IC : Integrated Circuit

IDE : Integrated Development Environment IGBT : Insulated Gate Bipolar Transistor I2ACM : I2 Average Current Mode

LDE : Linear Difference Equation

MOSFET : Metal Oxide Semiconductor Field Effect Transistor MLFC : Multi-Level Flying Capacitor

PCB : Printed Circuit Board PCM : Peak Current Mode

PDPCM : Predictive Digital Peak Current Mode PFC : Power Factor Correction

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PWM : Pulse Width Modulation

Si : Silicon

SiC : Silicon Carbide

SR : Set-Reset

SMPS : Switch Mode Power Supply VCM : Valley Current Mode VMC : Voltage Mode Control VRM : Voltage Regulator Module WBG : Wide Band Gap

ZOH : Zero Order Hold

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SYMBOLS

C : Capacitance

Co : Output capacitance

Cfly : Flying capacitor

D : Duty cycle Fv : Feedback gain Fm : Modulator gain fx : Crossover frequency fsw : Switching frequency Fg : Feedforward gain Gvg : Input-to-output voltage Gig : Input-to-inductor current Gvd : Control-to-output voltage Gid : Control-to-inductor current

Gic : Current control-to-output loop transfer function

Gvc : Voltage control-to-output transfer function

Gci : Current loop compensator

Gcv : Voltage loop compensator

Gcfly : Flying capacitor balancing loop compensator

He : Sampling gain

is : Sampled current

ic : Control objective

iL : Inductor current

Io : Output current

ifly : Flying capacitor current

ID : Drain current

L : Inductance

Rs : Sense resistance

Pcond : Conduction loss

Psw : Switching loss

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PCOSS : Output capacitance loss

PDT : Dead-time loss

PD : Diode loss

PInd : Inductor loss

QG : Gate charge

Qrr : Reverse recovery charge

RthJC : Junction-to-case thermal resistivity

RDS(on) : On resistance

resr : Capacitor parasitic resistance

rL : Inductor parasitic resistance

Se : Slope of the compensator

Td : Dead-time

ton : On-time

Tsw : Switching period

TJ : Junction temperature

Tiloop : Current loop gain

Tvloop : Voltage loop gain

Tuloop : Uncompensated loop transfer function

Vpp : Peak-to-peak oscillator voltage

VDS : Drain-to-source voltage

VSD : Reverse conduction voltage

Vin : Input voltage

Vo : Output voltage

Vsw : Switching node voltage

Vfly : Flying capacitor voltage

Zfilter : Filter transfer function

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LIST OF TABLES

Page Table 2.1 : Specifications of the converter for comparison of the analog current

mode control methods. ... 23

Table 2.2 : Specifications of compensator for comparison of analog current mode control methods. ... 24

Table 2.3 : Specifications of the analog synchronous buck converter prototype. ... 27

Table 3.1 : Comparison of the GaN and SI based switching devices. ... 30

Table 3.2 : Specifications of the designed converters. ... 34

Table 3.3 : Estimated efficiency for GaN-based synchronous buck converter. ... 35

Table 3.4 : Experimental results for GaN-based synch. buck converter. ... 37

Table 3.5 : Experimental results for GaN-based synch. buck converter. ... 37

Table 4.1 : Specifications of the synchronous buck converter. ... 46

Table 4.2 : Compensator design parameters for DPCM control. ... 46

Table 4.3 : Compensator design parameters for DACM control. ... 53

Table 5.1 : Compensator design parameters for DHCM control. ... 67

Table 6.1 : Specifications of the 3LFC buck converter... 89

Table 6.2 : Components of the 3LFC buck converter. ... 89

Table 6.3 : Current loop compensator parameters of DHCM control for 3LFC buck prototype... 94

Table 6.4 : Flying capacitor balancing loop compensator parameters for 3LFC buck prototype... 94

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LIST OF FIGURES

Page

Figure 1.1 : Comparison of Si, SiC, GaN for power electronics [36]. ... 7

Figure 1.2 : Normally off cascode GaN device [36]. ... 8

Figure 1.3 : p-Doped e-mode GaN HFET [46]. ... 8

Figure 2.1 : Buck converter... 15

Figure 2.2 : Buck converter inductor voltage vL and current iL. ... 16

Figure 2.3 : Analog PCM controlled buck converter. ... 17

Figure 2.4 : Analog PCM waveforms. ... 17

Figure 2.5 : Small-signal model of a PWM buck converter. ... 17

Figure 2.6 : PCM small-signal block diagram [2]. ... 18

Figure 2.7 : Analog ACM controlled buck converter. ... 20

Figure 2.8 : ACM small-signal block diagram. ... 20

Figure 2.9 : Analog I2ACM controlled buck converter. ... 21

Figure 2.10 : I2ACM small signal block diagram. ... 22

Figure 2.11 : (a) I2ACM slow loop compensator, (b) typical waveforms. ... 22

Figure 2.12 : Typical gain curve of PI compensator. ... 23

Figure 2.13 : Current loop transfer functions of PCM, ACM and I2ACM. ... 24

Figure 2.14 : Comparison of analog PCM, ACM and I2ACM to the ref. signal change. ... 25

Figure 2.15 : Comparison of analog PCM, ACM and I2ACM to the load changes. . 26

Figure 2.16 : Comparison of analog ACM and I2ACM to the input changes. ... 26

Figure 2.17 : Analog synchronous buck prototype, top (left), bottom (right). ... 27

Figure 2.18 : Efficiency measurement of the analog synchronous buck prototype. . 28

Figure 3.1 : Typical synchronous buck converter. ... 29

Figure 3.2 : Switching transition of a typical MOSFET during turn-on. ... 32

Figure 3.3 : Si-based synchronous buck converter estimated loss distribution. ... 34

Figure 3.4 : GaN-based sync. buck converter est. loss distribution (Td = 20 ns). .... 35

Figure 3.5 : GaN-based sync. buck converter est. loss distribution (Td = 10 ns). .... 35

Figure 3.6 : Si (Top) and GaN (Bottom) synchronous buck converter prototypes. .. 36

Figure 3.7 : Experimental setup for Si and GaN evaluation. ... 36

Figure 3.8 : Comparison of measured and calculated efficiency for GaN-based synchronous buck converter with 20 ns dead-time. ... 37

Figure 3.9 : Comparison of measured and calculated efficiency for GaN-based synchronous buck converter with 10 ns dead-time. ... 38

Figure 4.1 : Block diagram of a typical digitally controlled DC-DC converter. ... 40

Figure 4.2 : Architecture of a PDPCM controlled synchronous buck converter. ... 42

Figure 4.3 : Inductor current waveform for PDPCM controlled buck converter. ... 42

Figure 4.4 : Architecture of a mixed-signal based DPCM controlled synchronous buck converter. ... 43

Figure 4.5 : Model of the continuous-time DPCM control loop. ... 44

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Figure 4.7 : Timing scheme of DPCM. ... 48 Figure 4.8 : DPCM voltage loop transfer function: mathematical model, simulation

and experimental results. ... 49 Figure 4.9 : Architecture of a DACM controlled synchronous buck converter. ... 50 Figure 4.10 : Model of continuous-time DACM control loop. ... 51 Figure 4.11 : DACM control current loop Bode plots. ... 54 Figure 4.12 : DACM control voltage loop Bode plots. ... 54 Figure 4.13 : Timing scheme of DACM. ... 55 Figure 4.14 : DACM model, simulation and experimental results for inner loop. ... 56 Figure 4.15 : DACM model, simulation and experimental results for outer loop. ... 56 Figure 4.16 : Measurements of the inductor current and output voltage of the DACM

controlled sync. buck converter (voltage loop is open). a) control signal changes from 55% to 100% (output current: 1 A to 1.85 A) b) load changes from 55% to 100% (load resistance: 1.8 Ω to 3.3 Ω). ... 59 Figure 4.17 : Measurements of the inductor current and output voltage of the DACM

controlled sync. buck converter (voltage loop is closed). a) control signal changes from 55% to 100% (output current: 1A to 1.85 A) b) load changes from 55% to 100% (load resistance: 1.8 Ω to 3.3 Ω). ... 60 Figure 5.1 : Architecture of a mixed-signal based DHCM controlled synchronous

buck converter. ... 63 Figure 5.2 : Continuous-time model of the DHCM control loop. ... 64 Figure 5.3 : Perturbed inductor current waveforms a) control b) current perturbation.

... 65 Figure 5.4 : Discrete-time model of the DHCM control loop. ... 65 Figure 5.5 : Flowchart of the compensator design algorithm for DHCM. ... 66 Figure 5.6 : DHCM control current loop Bode plots. ... 68 Figure 5.7 : DHCM control voltage loop Bode plots. ... 68 Figure 5.8 : Timing scheme of the DHCM control. ... 70 Figure 5.9 : Simulation schematic of DHCM controlled buck sync. converter. ... 71 Figure 5.10 : Experimental setup for DHCM controlled buck sync. converter. ... 72 Figure 5.11 : DHCM model, simulation and experimental results for the inner loop.

... 72 Figure 5.12 : DHCM model, simulation and experimental results for the outer loop.

... 73 Figure 5.13 : Measurements of the inductor current and output voltage of the DHCM

controlled sync. buck converter (voltage loop open). a) control signal changes from 55% to 100% (output current: 1 A to 1.85 A) b) load changes from 55% to 100% (load resistance: 1.8 Ω to 3.3 Ω). ... 74 Figure 5.14 : Measurements of the inductor current and output voltage of the DHCM

controlled sync. buck converter (voltage loop closed). a) control signal changes from 55% to 100% (output current: 1.8 V to 3.3 V) b) load changes from 55% to 100% (load resistance: 1.8 Ω to 3.3 Ω). ... 76 Figure 6.1 : Flying capacitor buck converter. ... 80 Figure 6.2 : 3LFC buck converter operation D<0.5. ... 81 Figure 6.3 : 3LFC buck converter operation D>0.5. ... 82 Figure 6.4 : 3LFC buck converter operation waveforms a) D < 0.5, b) D > 0.5... 83 Figure 6.5 : Inductor current ripple comparison. ... 84 Figure 6.6 : Architecture of DHCM control with ASC for a 3LFC buck converter. 85 Figure 6.7 : Waveforms of the DHCM control with ASC for a 3LFC buck converter. ... 86

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Figure 6.8 : Output current Io vs. Δse (A/μs) for v̂fly = -10%Vfly and k = 1%. ... 88 Figure 6.9 : Prototype of the 3LFC buck converter with on-board microcontroller. 90 Figure 6.10 : Gate drive scheme of the 3LFC buck converter prototype... 92 Figure 6.11 : Sensor interface of the 3LFC buck converter prototype. ... 92 Figure 6.12 : Timing scheme for DHCM controlled 3LFC buck converter. ... 93 Figure 6.13 : Flying capacitor voltage change over time for -0.8 < Δse (A/μs) < 0.8

with v̂fly = -10%Vfly a) Iout = 3.2 A b) Iout = 6 A ... 95 Figure 6.14 : Simulation schematic of the DHCM control with ASC for 3LFC buck

converter. ... 96 Figure 6.15 : Simulation results of a digital HCM controlled 3LFC buck converter a)

control command changes from 3.2 A to 6 A, b) zoom in 3.2 A

operation c) zoom in 6 A operation. ... 98 Figure 6.16 : Simulation results of a digital HCM controlled 3LFC buck converter a)

with flying capacitor perturbation v̂fly = -10%Vfly and 6 A current command b) zoom in to (a) at steady-state operation. ... 99 Figure 6.17 : GUI developed for the 3LFC buck prototype control and monitoring.

... 100 Figure 6.18 : Experimental setup for 3LFC buck converter prototype. ... 100 Figure 6.19 : Experimental results of DHCM with ASC for 3LFC buck converter a)

control command changes from 3.2 A to 6 A b) zoom in 3.2 A

operation c) zoom in 6 A operation. ... 102 Figure 6.20 : Progression of the thesis. ... 103

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DIGITALLY CONTROLLED BUCK CONVERTERS FOR CURRENT REGULATED APPLICATIONS

SUMMARY

In this thesis, digitally controlled DC-DC buck converters for current regulated applications are studied. As it is known, the digital control methods are widely used in high power systems. In recent years, the digital control started to replace the analog control in low power applications, due to increasing needs and developing technology. The studies in the literature carried out up to date are generally focused on the regulation of the output voltage. However, various applications such as LEDs, laser diode drivers, battery charging systems require current regulation. Studies in this thesis aim to provide digital solution for such applications. Traditional buck converter is one of the most suitable circuit topologies for current regulated applications due to filter inductor at the output; therefore, the studies are focused on the development of digital control for buck converters.

In order to implement digital control, it is essential to understand the analog control methods. Therefore, at the beginning of the thesis, peak current mode (PCM), average current mode (ACM) and I2 average current mode control (I2ACM) which combines these two control techniques are investigated. Using the small-signal models existing in the literature, the loop transfer functions are compared. It is observed that the control loop transfer function of I2ACM control has high DC gain as in ACM and high bandwidth as in PCM, which makes it the most suitable control technique for DC-DC converters. The studies are further supported with simulations and transient response comparison to load, input voltage and control signal changes. One of the main goals of this thesis is to obtain a new generation step-down DC-DC converter. As a result, the GaN-based transistors are examined for the feasibility in low-power DC-DC converters. The studies on this subject include the efficiency and loss analysis of the synchronous buck converter and comparison of GaN and Si-based converter efficiencies, which are supported by experimental studies. The effectiveness of the GaN transistors for DC-DC buck converters are shown in terms of improving the efficiency and switching frequency.

The digital control studies are conducted in two parts. In the first one, the basic properties of digital control are investigated. For PCM and ACM, digital control loop models are obtained and verified with simulations and experimental studies. Moreover, the transient response of the ACM control is examined which is later used to compare with the the proposed control technique. In the other part of the digital control studies, a novel digital hybrid current control (DHCM) method that combines the digital PCM and ACM is proposed. The proposed DHCM control method is a mixed signal technique consisting two current control loops; an inner current loop, which is applied in analog, and an outer current loop, which is in digital. For the control method both continuous and discrete-time models are built and verified with simulations and experiments. Furthermore, a compensator design algorithm, which

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provides an exact design for a specific gain and phase margin, is proposed. Using a synchronous buck prototype, the transient responses of the systems are analyzed. When the outer voltage loop is open, 30% faster dynamic response is measured by the digital HCM method as compared to digital ACM. Moreover, by adding a third loop for voltage compensation, comparable dynamic response on the output voltage is achieved without inductor current overshooting by the digital HCM control.

In the last part of the thesis, the three-level flying capacitor (3LFC) buck converter, which is emerged recently as an alternative to traditional buck converters, is examined. Due to high effective frequency and reduced voltage stress on the switching devices, the 3LFC buck converter has potential to provide better efficiency and higher power density as compared to the traditional buck converter. However, the control implementation is challenging a result of flying capacitor instability issues. Therefore, the digital HCM control method is modified and implemented to 3LFC buck converter. Flying capacitor balancing is achieved by adjusting the slope compensation of the two switching pairs asymmetrically that is named as Asymmetric Slope Compensation (ASC) control. The effectiveness of the proposed ASC control method is verified with simulations. Moreover, within the scope of the study, a prototype hardware is developed and the proposed digital HCM control with ASC method is applied. The overall control method was verified by applying to the on-board mixed-signal microprocessor of the prototype. As the control methods developed in this thesis are microprocessor based, they also provide cost effective digital solution for the industry.

In conlusion, the studies in this thesis include comprehensive studies about microcontroller based digital control techniques, three-level flying capacitor buck converters and new generation wide bandgap semiconductor switches to contribute to the literature for current regulated DC-DC applications.

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AKIM REGÜLASYONLU UYGULAMALAR İÇİN SAYISAL KONTROLLÜ ALÇALTICI ÇEVİRİCİLER

ÖZET

Bu tez çalışmasında, akım regülasyonlu uygulamalar için sayısal kontrollü DA-DA alçaltıcı çeviriciler incelenmiştir. Bilindiği gibi sayısal kontrol yöntemleri yüksek güç isteyen sistemlerde yaygın olarak kullanılmaktadır. Son dönemde gelişen teknoloji ve artan ihtiyaçlar neticesinde, düşük güçteki sistemlerde de sayısal kontrol uygulamaları yaygınlaşmaya başlamıştır. Bugüne kadar yapılan çalışmalar genellikle çıkış geriliminin regülasyonu üzerine gerçekleşmiştir. Ancak endüstrideki LED sürücü, lazer diyot sürücü, batarya şarj sistemleri gibi çeşitli uygulamalar, akım regülasyonuna ihtiyaç duymaktadır. Bu tezde yapılan çalışmalar, bu tip uygulamalar için çözüm getirmek üzerine yoğunlaşmıştır. Klasik alçaltıcı tip çevirici, filtre bobini sayesinde çıkışta kesintisiz akım sağlayabilmektedir. Bu bağlamda sabit akım regülasyonu için en uygun devre topojilerinden biridir. Çalışma kapsamında yeni nesil alçaltıcı bir sistem elde etmek amaçlanmıştır. Bu sebeple, sayısal kontrol çalışmalarına ek olarak endüstride uygulamaları gittikçe yaygınlaşmakta olan Gallium Nitride (GaN) tabanlı yeni nesil yarı iletkenler incelenmiş ve uygulanmıştır. Ek olarak, son dönemde klasik alçaltıcı çeviricilere alternatif olarak ortaya atılan üç seviyeli uçan kapasitörlü alçaltıcı çevirici yapısı incelenmiş, sayısal kontrol uygulaması gerçekleştirilmiştir.

Sayısal kontrol yöntemlerini anlamak, geliştirmek ve DA-DA çeviricilerde uygulamak için öncelikli olarak analog kontrol yöntemlerinin incelenmesi gereklidir. DA-DA çeviriciler için kontrol yöntemleri biri değişken diğeri sabit frekans olmak iki kategoride değerlendirilebilir. Her iki yaklaşımın da kendine has avantajları olmakla birlikte, özellikle komponent seçimi ve tasarımı kolaylığı açısında sabit frekans daha çok tercih edilebilir durumdadır. Sabit frekans için analog tabanlı iki temel kontrol yaklaşımı bulunmaktadır; bunlardan biri gerilim mod kontrol metodu diğeri ise akım mod kontrol metodudur. Akım modu kontrol metodu, özellikle daha hızlı tepki vermesi ve geri besleme döngüsü transfer fonksiyonunu sadeleştirerek kontrolcü tasarımını kolaylaştırması sebepleriyle tercih edilmektedir. Akım modu kontrol yöntemleri tepe, ortalama ve vadi olmak üzere üç kategoride sınıflandırılmaktadır. DA-DA alçaltıcı çeviriciler için, ortalama bobin akımı aynı zamanda çıkış akımının da kontrol edilmesini sağlamaktadır. Bu sebeple özellikle akım regülasyonuna ihtiyaç duyan LED uygulamalarında ortalama akım kontrollü DA-DA topolojisi için piyasada pek çok entegre bulunmaktadır. Öte yandan tepe akım kontrolü hızlı tepki verebilmesi, doğal yüksek akım koruması sağlaması gibi sebeplerden dolayı anahtarlamalı güç kaynaklarında kullanımı yaygınlaşmıştır. Son dönemde, bu iki akım kontrol yöntemini birleştiren I2ACM kontrol tekniği ortaya

atılmıştır. I2ACM kontrolü iç içe iki akım kontrol döngüsünden oluşmaktadır; içteki

döngü tepe akım kontrolü gibi iken dıştaki döngü ortalama akımı kontrol etmektedir. Bu sebeple akım regülasyonlu uygulamalar için optimum çözüm olarak ortaya

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atılmıştır. Tez çalışmasının ilk kısmında tepe, ortalama ve I2ACM analog akım mod

kontrol yöntemleri incelenmiştir. Literatürde varolan kontrol döngüsü modelleri kullanılarak küçük-sinyal modelleri ve transfer fonksiyonları karşılaştırılmıştır. Bu çalışmalar neticesinde I2ACM kontrol yönteminin düşük frekansta tepe, yüksek

frekansta ise ortalama akım mod kontrol gibi davranış gösterdiği belirlenmiştir. Yapılan benzetişim çalışmalarıyla, kontrol sinyali, yük değişimi ve giriş gerilimi değişimlerinde geçiş tepkisinin ortalama akıma göre daha iyi olduğu tespit edilmiştir. Bu sebeple akım regülasyonlu uygulamalar için oldukça uygun olduğu belirlenmiştir. Çalışmanın üçüncü bölümü, GaN transistorlerinin senkron DA-DA alçaltıcı çeviriciler için fizibilitesine ayrılmıştır. Bu bölümde senkron alçaltıcı çeviricilerin kayıp ve verim analizi yapılarak GaN ve Si tabanlı çeviriciler için verim karşılaştırması yapılmıştır. Yapılan çalışmalar; deneysel çalışmalar ile desteklenmiş teorik değerler ile kıyaslanmıştır. Bu çalışmalar neticesinde GaN-tabanlı DA-DA alçaltıcı çeviricilerin Si-tabanlı olanlara kıyasla verim açısından daha avantajlı olduğu gösterilmiştir.

Tez çalışmasının dördüncü bölümünde ise sayısal kontrol yöntemleri incelenmektedir. Sayısal kontrol ile analog kontrol ile yapılması mümkün olmayan optimal kontrol, otomatik ayarlama ve yapay sinir ağları gibi gelişmiş kontrol yöntemleri uygulanabilmektedir. Bununla birlikte önemli bir yaklaşım sayısal kontrolün; teorisi ve etkinliği kanıtlanmış analog kontrol yöntemlerinin emülasyonu şeklinde yapılmasıdır. Bu tez çalışmasında da bu tip bir yöntem benimsenmiştir. Bilindiği üzere; analog kontrolde kontrol işareti veya darbe genişliği döngüden-döngüye güncellenmektedir. Sayısal kontrolün çalışması da benzer şekildedir ancak ek olarak zaman kayıpları kontrol döngüsünde yer almaktadır. Bu kayıplar; örnekleme zamanı ve tipi, kontrol işaretinin hesaplanması ve sayısal darbe-modülasyon genişliği üretimi ile ilgili olmak üzere üç kategoride değerlendirilebilir. Kontrolcü tasarımı bu etmenler göz önüne alınarak tasarlanmalıdır. Çalışmanın bu kısmında; analog kontrol yönteminde olduğu gibi tepe ve ortalama akım mod kontrol yöntemlerinin sayısal uygulamaları incelenmiştir. Tepe akım yöntemi için kontrol döngüsü modeli çıkarılmış; benzetişim ve bir senkron alçaltıcı çevirici prototipi üzerinde gerçekleştirilen deneysel çalışmalar ile doğrulanmıştır. Sonrasında benzer bir çalışma ortalama akım mod yöntemi için gerçekleştirilmiştir. Ortalama akım yöntemi için de kontrol döngüsü modeli elde edilmiş; yapılan benzetişim ve deneysel çalışmalar ile doğrulanmıştır. Ortalama akım için; yük ve kontrol işareti değişimlerinde geçiş karateristikleri incelenmiş ve sonuçları değerlendirilmiştir. Ortalama akım modu için deneysel çalışmalar bir sonraki bölümde ortaya konulan yeni kontrol yöntemi için karşılaştırma açısından referans olmaktadır.

Tez çalışmasının en önemli çıktısı olarak, akım regülasyonlu uygulamalarda kullanılabilecek DA-DA çeviriciler için yeni bir kontrol yöntemi ortaya konulmuştur. Yapılan bu çalışmalar; tezin beşinci kısmında detaylı olarak ele alınmaktadır. Ortaya konan sayısal hibrit akım mod kontrol metodu; sayısal tepe akım ve ortalama akım mod kontrol yöntemlerini birleştirmektedir. Bu kısımda kontrol döngüsü modeli çıkarılmış; benzetim ve deneysel çalışmalar ile doğrulanmıştır. Ortaya konan kontrol metodu için bir kontrolcü tasarım algoritması geliştirilmiş ve bu sayede önceden belirlenmiş kazanç ve faz payı için isabetli bir tasarım yapılabilmiştir.

Özetle belirtmek gerekirse ortaya konan sayısal hibrit akım mod kontrolü I2ACM

kontrol yönteminde olduğu gibi iç içe iki kontrol döngüsünden oluşmaktadır. İçteki döngü analog karşılaştırıcı ile analog tepe akım kontrolünde olduğu gibi anlık bobin

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akımı ile işaret sinyalini karşılaştırmaktadır. İşaret sinyali ise referans akım değeri ile ortalama akım değerinin farkından oluşan hata değerinin kontrolcü tarafından işlenmesiyle elde edilmektedir. Bu sebeple dıştaki akım döngüsü ortalama akım kontrolü sağlamaktadır. Ortalama akımı ise döngü başında örneklenen akım değeri ile bir önceki işaret sinyali yani tepe akım değerinin yarısına eşittir. Bu sebeple ortaya konan kontrol metodu her anahtarlama döngüsünde sadece bir kere akım örneklemesine ihtiyaç duymaktadır. Ek olarak en dışa bir gerilim döngüsü eklenerek gerilim regülasyonu da elde edilebilmektedir. Sayısal akım yöntemi ile karşılaştırıldığı durumda ortaya konan sayısal hibrit akım mod kontrol yöntemi kontrol sinyali ve yük değişimlerine %30 daha hızlı tepki verdiği ölçümlenmiştir. Tezi son kısmında, son dönemde klasik alçaltıcı çeviricilere alternatif olarak ortaya atılan üç seviyeli uçan kapasitör alçaltıcı çevirici incelenmiş; önerilen yeni sayısal hibrit akım mod kontrol yöntemi uygulanarak sonuçları tartışılmıştır. Üç seviyeli uçan kapasitör çeviriciler bobin üzerindeki efektif frekans değerini ikiye katlaması ve anahtarlar üzerindeki gerilim stresini yarıya düşürmesi sebebiyle klasik çeviricilere göre daha kompakt, yüksek güç yoğunluklu ve daha verimli olmakla birlikte; uçan kapasitörün gerilim dengesizliğinden dolayı kontrol açısından bazı zorluklar barındırmaktadır. Özellikle tepe akım mod kontrolünün doğal olarak gerilim kaçmasına neden olduğu literatürde yer almaktadır. Ortaya konan sayısal hibrit kontrol yöntemi de tepe akım modu kontrol yöntemine benzer bir karaktere sahiptir. Bu sebeple üç seviyeli uçan kapasitör alçaltıcı çeviriciler için asimetrik eğim kompanzasyonu şeklinde adlandırılan yeni bir kontrol mekanizması geliştirilmiştir. Geliştirilen asimetrik eğim kompanzasyonu yöntemi, sayısal hibrit kontrol yöntemi ile birlikte üç seviyeli uçan kapasitör alçaltıcı çeviriciye uygulaması benzetişim çalışmaları ile doğrulanmıştır. Yine bu kapsamda deneysel çalışmalar için dahili mikroişlemci içeren yarı-endüstriyel bir prototip geliştirilmiş; ve tez kapsamında detayları verilmiştir. Geliştirilen kontrol yöntemi bu prototip ile değişen kontrol sinyaline rağmen uçan kapasitör gerilimini giriş geriliminin yarısında dengede tutabildiği doğrulanarak sonuçları ortaya konulmuştur.

Özetle, bu tez çalışmasında; akım regülasyonuna ihtiyaç duyan sistemler için sayısal, yeni-nesil alçaltıcı tip DA-DA çeviricileri incelenmektedir. Çalışmada, yeni bir sayısal hibrit akım mod kontrol yöntemi ortaya konmuş ve yeni bir kontrolcü tasarım algoritması sunulmuştur. Geliştirilen kontrol yönteminin ortalama akım modu kontrol metoduna göre üstünlüğü gösterilmiştir. GaN tabanlı anahtarlama aygıtları incelenmiş ve uygulanmıştır. Çalışma kapsamında yarı-endüstriyel üç-seviyeli uçan kapasitör alçaltıcı çevirici bir prototip donanım geliştirilmiş ve geliştirilen kontrol yöntemi uygulanmıştır. Bu kapsamda; uçan kapasitör gerilim dengelemesi için yeni bir asimetrik eğim kompanzasyon yöntemi geliştirilerek ortaya konan sayısal hibrit kontrol yöntemine eklenmiştir. Geliştirilen kapsayıcı kontrol yöntemi, prototip üzerindeki dahili karışık-sinyal mikroişlemciye uygulanarak doğrulanmıştır. Geliştirilen kontrol yöntemleri mikroişlemci tabanlı olması sebebiyle aynı zamanda maliyet etkinliği sağlamaktadır. Yapılan çalışmalar, gerek yarı-iletken anahtarlar, gerek sayısal kontrol ve gerekse gelişmiş DA-DA devre topolojileri açısından kapsayıcı çalışmalar içermekte ve literatüre katkı sağlamaktadır.

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INTRODUCTION

This thesis is focused on the microcontroller based digital control of buck converters. Until recently, the analog control is the usual method in low-to-medium power electronics applications, whereas the digital control is preferred for high-power levels. In high-power applications, usually complex control methods and protection techniques are required. The switching frequency of the converters are low, therefore high controller bandwidth is not necessary. In addition, the digital controller cost is relatively low as compared to the price of the other components especially the high-power semiconductor devices. As a result, digital control method is advantages for high power applications due to economical and technical reasons. In low power, the switching frequencies of the converters are high, and high-speed dynamic response is required. The controller cost is relatively high, when compared to the other components therefore; the cheaper solution is preferred. Moreover, the analog control methods are highly mature in power electronics in terms of modeling, design and implementation. Therefore, analog control was considered as advantages over the digital one in low power. However lately, due to recent advances in digital control and decreasing prices of the controllers [1], the digital control techniques start to take attention of the researchers for low-power applications.

The DC-DC converters are usually required for step-up or down voltage conversion; therefore the output voltage is regulated. However, in some applications such as LED/Laser diode drivers, battery chargers or power factor correction (PFC) rectifiers, current regulation is required. This thesis investigates the digital power electronics solutions for these systems. The buck converter, which is one of the basic non-isolated DC-DC converter topologies, is particularly convenient for constant current applications since the output current is not chopped because of the filter inductor at the output. For this reason, the digital control for DC-DC buck converter is studied in this thesis.

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Literature Review

1.1.1 Analog control methods

The analog control is the traditional method for the control of power electronic converters. Mainly there are two types of analog control techniques: voltage mode control (VMC) [1]-[3] and current mode control (CMC) [1]-[4]. The voltage mode control is based on a single voltage path in which the output voltage is compared with the reference voltage. Single loop structure provides simplicity in design and analysis. In addition, VMC is advantages due to good noise immunity. However, due to the double poles of the output filter, the compensator design is ratherly difficult. In addition, current limiting should be done seperately. Moreover, the VMC has slow response since any load or line change is sensed from the output voltage. On the other hand, CMC eliminates the disadvantages of the VMC. Unlike the VMC, the turn-off/turn-on of the switches are controlled by comparison of the inductor current with a threshold control signal in CMC. Since the inductor current is a function of input and output voltages, any change can be immediately sensed which results in faster response compared to VMC. Furthermore, the compensator design is relatively simpler since the output filter provides a single pole feedback loop. In addition, it is possible to limit current inherently cycle-by-cycle. The major drawbacks of the CMC are that CMC could be highly susceptible to switching noise, controller requires more than one loop for voltage regulation, and the control loop can be unstable over 50% duty cycle.

Three basic types of CMC techniques are reported in the literature [5]: hysteretic, constant on/off time and constant frequency. In hysteretic control, the peak and valley current are pre-determined by the controller; therefore, both the switching frequency and duty cycle are variable. In constant time control, the switch on-time is fixed whereas the switch turn-off on-time is regulated with the valley current control signal. Alternatively, in constant off-time contol the switch-off time is constant while the switch-on time is determined by the peak current control signal. Although several advantages of these control methods are reported in literature [6], [7], since switching frequency is not constant it is difficult the optimize circuit components values. Therefore, constant frequency current-mode control techniques are usually preferred in DC-DC converter applications.

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On the other hand, the constant frequency CMC methods can be categorized into three types: Peak Current Mode (PCM) [8], Average Current Mode (ACM) [9]-[10], and Valley Current Mode control (VCM) [12]. In PCM control, the inductor current is compared with a threshold control signal by using an analog comparator that terminates the on-time PWM signal. The voltage loop controller determines the threshold level. VCM control has a similar operation principle that is the inductor current compared with threshold control signal to turn-on the switching PWM signal. The ACM control is however, has a different type of operation, which is in ACM control an error amplifier is included into the current loop [9]. The PCM control is highly susceptible to noise, unstable without slope compensation over 50% duty cycle and the current is not controlled precisely. These problems can be eliminated with ACM control technique. Nevertheless, the major drawback of ACM control is slow response time to load and line voltage changes.

Recently a new type of current-mode control method, which named as I2 Average Current Mode (I2ACM) is introduced. I2ACM combines the ACM and PCM control methods to be benefited from their advantages such as accurate current control, overcurrent protection, and fast response [13]. Basically in I2ACM, there are two

current loops; one is the fast current feedback loop similar to PCM which provides the inductor current to the comparator and the other one is slow current feedback current loop that is employed to provide accurate current control as in ACM. Unlike to PCM, the threshold level is not the output of the voltage controller; instead, it is generated by a slow integral current feedback loop. The reference value for the slow loop is provided from the outer voltage loop if the converter is operated in voltage regulated mode, otherwise in current regulated mode it is given as the control signal of the average inductor current. The method is initially proposed for constant on-time control, but fixed frequency is applicable as well [14]. Several studies conducted in [15]-[18] to understand the dynamics and characteristics of the I2ACM control technique show that it is very promising for DC-DC converters.

1.1.2 Digital control methods

Although the analog control techniques are quite mature and applied succesfully to power electronic systems for decades, the digital control has always been appealing

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to the researchers due to several advantages compared to the analog one. These advantages can be listed as below:

 The digital control has immunity to the component tolerances, noise and ageing. In analog control, the compensator poles and zeros are located with passive components that are capacitors and resistors. These passive components are subject to temperature drifting during the operation and value tolerances due the manufacturing process. In digital control, the compensator design can be done with more precision as these component value variations does not exist. In addition, using auto-tuning methods it is possible to compensate other circuit components variations such as inductors, filter capacitors, etc. as well.

 The digital control is highly flexible. It is possible to modify parameters or control strategy without altering the hardware. The compensator can be modified by changing the parameters in the software. Therefore, development phase can be done rapidly. In addition, the compensator can easily be implemented to other converters at different power levels with little effort.  Today many power electronic applications require an embedded

microcontroller for several purposes, such as communication, data logging, user interface, etc. Therefore, the digital control can be implemented along with the other high-level tasks without adding any extra cost to the systems.  The digital control makes it possible to apply advanced control techniques

such as non-linear methods, fuzzy control, neural networks, learning algorithms, auto-tuning methods etc. Obviously, the application of these kind of methods are highly difficult with analog control methods.

The digital control has already been used high power and low frequency applications for a long time. However recently, due to the advances in digital technology, the digital control has started to be considered for high-frequency and low-power applications by power management vendors and researchers [19]. For digital implementation tecnhniques there are basically two groups: one is the software-based controllers such as microcontrollers and DSPs and the other one is hardware-based solutions such as FPGAs and custom-designed ICs [1],[20]-[22]. The major disadvantage of the digital control over the analog one is that the loop bandwidth and

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switching frequency is limited. Applying FPGAs provide fast switching and high-speed controller processing although they are expensive and difficult to learn and implement. The custom digital ICs are advantages in terms of cost and it is possible to operate with high switching frequency. However, the available products are not versatile and it is not possible to use advanced digital control techniques. Microcontrollers are on the other hand, easy to use, versatile for many topologies and applications as well as flexible for many type control techniques. The main disadvantages of the general-purpose microcontrollers are instruction set based operation, which limits the controller processing speed and the limited capability of the digital PWM blocks. However, many chipmakers are started to provide mixed-signal microcontroller products which are equiped with integrated control peripherals optimized for motor control and power applications [23],[24] such as high resolution digital PWM units, integrated analog comparator, floating point processor, compare-capture units and high resolution DAC/ADC blocks. Therefore, microcontrollers is a cost-effective and high-bandwidth solution for next-generation low-power digitally controlled power electronic systems.

In terms of control techniques, the digital control methods can be categorized mainly in two classes : Conventional control methods and Non-linear control methods. The conventional control methods adopt the widely known analog control techniques for digital control. In these methods the traditional PI, PID controllers are implemented in the compensators to regulate the output of the converters. Traditional voltage mode and current mode control techniques such as PCM, ACM or VMC are reported in the literature [25],[26].

As it has been stated, the digital controllers suffer from the time delay that reduces the controller bandwidth. Therefore, several techniques are studied by researchers to reduce this effect. One of the most prominent of these studies is done by C. Jingquan in [26], which introduced the predictive digital control based on the circuit variables such as input/output voltage and inductance value. The predictive control law is provided for PCM, ACM and Valley Current Mode (VCM) for buck, boost and buck-boost converters. The major drawback of this technique is that the prediction is based on the inductor value that might be subject to temperature drift and component tolerances. Another interesting study is proposed in [27] by M. Hallworth that propose a hybrid control scheme for PCM in which the inner current loop is

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implemented in analog domain by means of the internal comparator of the microcontroller. In the hybrid PCM control the need for computation power is reduced and controller does not depend on the circuit variables. The main disadvantage of this method is time-delays are not included into compensator design. Although it will be studied in detail in the next chapters, the digital control techniques that are studied and proposed in this thesis are based on the hybrid control scheme as it combines the advantages of analog and digital control.

On the other hand, there are other non-linear digital control approaches, which are examined in the literature as well. Although it is neither possible nor required to investigate all of these studies since in this thesis, the focus is on the conventional control methods; it is beneficial to mention some notable ones. One of the most distinguished techniques among the non-conventional digital control methods is the time-optimal control [28],[29] in which during a large transient condition an algorithm takes place of the conventional compensator to achieve the best transient dynamics. Another interesting method is digital auto-tuning [30] in which a perturbation is provided to the system and the compensator is tuned based on the response of the system at the output. Several types of auto-tuning methods are reported in the literature, the most interesting ones are system-identification based method [31] and relay-feedback auto-tuning [32]. Other interesting non-conventional digital control approaches can be noted as digital hysteretic control [33] and sensorless optimization for DC-DC converters [34].

It is important to mention that to describe the physical behaviour of a system mathematical modeling is necessary. A proper mathematical model should include all the dominant dynamics of the system while neglecting the insignificant ones. DC-DC converters operating in CCM are usually modelled by neglecting the switching ripples, and considering only the low frequency AC variations. The two most well known AC modeling method are circuit averaging and state-space averaging [2]. Moreover, recently a new technique in [35] is presented based on describing function method to model current mode controls for the DC-DC converters. Nevertheless, through out this study the classical average switch modeling is adopted for both analog and digital control method studies due to simplicity and maturity.

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1.1.3 GaN-based switching devices for power electronic circuits

The wide band-gap devices (WBG) such as Silicon Carbide (SiC) and Gallium Nitride (GaN) are considered to replace the conventional Silicon (Si) based ones due to the favorable material properties (Figure 1.1) which results in lower on-resistance, lower switching losses; as well as provides higher voltage, current and operating temperature capabilities [36]. SiC technology is in competition with IGBT technology for medium and high power applications due to its good thermal performance and high breakdown ratings whereas the GaN-transistors are replacing the Si-MOSFETs in low-to-medium power levels in highly efficient, high-frequency applications [37]. Especially, the effectiveness of the GaN-based swithing devices is confirmed in the competition that is known as Google Little Box Challenge in 2015 [38]. Furthermore, several converters with GaN-based devices are reported with high frequency and power density [39]-[43] recently. Therefore currently, GaN-based devices especially take demand from automotive and infomation industry specifically from the companies such as Google, BMW and Delta Electronics [44]. Today many suppliers including Panasonic, Transphorm, EPC and GaN Systems provide GaN-based switching devices for these industries.

Figure 1.1 : Comparison of Si, SiC, GaN for power electronics [36].

The technical aspects of the internal structure, material characteristics and technological status of the GaN transistors are out of scope of this thesis. However it is beneficial to make a short review based on products available on the market.

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Although there are advances on the development of vertical GaN devices, today’s commercially available GaN transistors are lateral Heterojunction Field-Effect Transistors (HFETs) or known as High Electron Mobility Transistors (HEMTs). The HFET is a fundamentally normally-on device, which is not desired in power electronic converters due to reliability concerns [45]. To obtain a normally-off device several methods exist in literature. Two notable methods which are commercially available are cascode type GaN-transistor by Transphorm and enhancement type transistors by EPC, GaN Systems and Panasonic. The cascode devices are made of a depletion-mode GaN-HFET that is driven by a Enhancement Mode (e-mode) Si-MOSFET as shown in Figure 1.2. On the other hand, the enhancement mode devices are obtained by modifying the gate to shift the threshold voltage positively such as using a p-doped layer beneath the gate as shown in Figure 1.3 [46]. One of the important aspects of the e-mode GaN-transistors is that unlike the Si-MOSFETs there is not a body diode; instead a reverse conduction channel occur to provide the similiar behaviour. Therefore, often a reverse conduction diode is not necessary [47].

Figure 1.2 : Normally off cascode GaN device [36].

Figure 1.3 : p-Doped e-mode GaN HFET [46].

GaN-based converter design also has some challenges. Although the gate driver concept is similar to Si-MOSFETs, the driver requirements is very tight due to low threshold voltage that is around 1-2 V, low allowable gate voltage that is around 7 V and dv/dt and di/dt constraints [48]. Therefore, optimization of gate resistance,

dead-Depletion-mode GaN HFET E-mode Si-MOSFET

G

S

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time [49] and gate circuit layout [50] are necessary. Considering these, a special care is taken to the gate drive to obtain the best performance in this thesis.

1.1.4 Multi-level flying capacitor converters

For low-power step-down DC-DC conversion, many alternative topologies are investigated instead of traditional buck converter such as soft switching [51],[52], multiphase/interleaved [53]-[57] and multilevel topologies [58],[60]. The main motivations for these studies can be listed as higher power density, higher efficiency, higher step-down conversion ratio, lower output ripple, reduced filter size, faster response and reduced cost compared to the conventional buck converter. Among these topologies multi-phase or interleaved buck converters have gained a significant attention lately due to the simple structure and low ripple characteristics especially for applications where high step-down conversion is required such as Voltage Regulator Modules (VRMs) [53]. However, in the conventional interleaved buck converter, although the inductor ripple is reduced, the switching devices are subject to input voltage; as a result, devices with high voltage rating are required which results in high loss and cost. Consequently, several soft switching interleaved buck converters are proposed as solution [55]-[57]. On the other hand, another type of converter which is multi-level flying capacitor (MLFC) buck converter gained an interest more recently which is superior to conventional buck and multi-phase converters as it reduces the switching voltage on the semiconductors, increases the effective frequency and decreases the inductor and output ripple. In other words, flying capacitor multi-level topology enables high power density and efficiency for step-down conversion without using the complicated soft switching techniques, or advanced interleaved buck topologies.

The multi-level flying capacitor converter is initially proposed by T. Meynard [61] for high-power applications to reduce the voltage stresses on the switching components. Later, it had gained an interest in low-power high-frequency applications following the publications of V. Yousefzadeh about the envelope tracking applications [58],[60]. The most appealing benefits of the flying capacitor multi-level DC-DC converters can be listed as follows:

 In MLFC DC-DC converter, the voltage stress over the switching devices is reduced. As a result, swithing devices with lower ratings can be employed

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which decreases the cost. Moreover, the switching losses are decreased which improves the efficiency.

 The MLFC DC-DC converter increases the effective switching frequency; consequently, the inductor size can be decreased. The output ripple is less, compared to the traditional converters; as a result, the output capacitor volume can be reduced.

In other words, with multi-level flying capacitor topology, higher efficiency and power density is achievable compared to the traditional converters, which draw the attention of the researchers. On the other hand, the flying capacitor adds one more circuit state variable, therefore the circuit dynamics are difficult to handle. Moreover, the cost of the multi-level buck converter could be higher compared to the conventional buck due to the higher number of switches and gate driver constraints although reduced voltage stress over the switching devices decreases the cost since components with lower ratings become applicable. Considering these, the three-level flying capacitor (3LFC) buck converter is investigated in this study to achieve both good performance and low cost although higher-level topologies are applicable. The control methods in the literature will be studied in detail in Chapter 6. Nevertheless, a summary will be done in here to get an overview about MLFC and 3LFC buck converter. One of the important problems of the multi-level converters is that some kind of voltage balancing method for the flying capacitors is necessary to obtain the necessary intermediate voltage levels [62]. There are two types of balancing mechanism exist for MLFC converters: active balancing and natural balancing. The natural balancing is achieved with phase shifted pulse width modulation (PSPWM) scheme in which any capacitor inbalance is eliminated with incremental charge or discharge toward the nominal voltage [62]-[64]. However, relying on a self-balancing mechanism is not favorable due to these methods are offen not reliable for big disturbances. On the other hand, the traditional control methods such as voltage-mode and current-mode techniques are usually inherently unstable unless an active balancing scheme is implemented which requires measurement of variables such as flying capacitor, input and output voltages or the inductor current. Several control traditional methods and solutions of the flying capacitor voltage balancing issue for 3LFC converters can be found in [65]-[71].

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Purpose of the Thesis

The main objective of the research conducted in this thesis is to develop a novel digital control method for current regulated applications such as LED/Laser diode drivers or battery chargers. The DC-DC buck converters are considered as the target power electronics topologies. Development of a near-industrial prototype with GaN-based new generation semiconductors and implementation of the proposed control technique to an advanced topology, specifically the three-level flying capacitor buck converter are the other purposes of this research.

Contributions of the Thesis

The digital control has been widely investigated, researched and implemented to DC-DC converters in low-power applications up to 1 kW since the beginning of 2000s. One of the limitations of the digital control is the computation and processing delays, which results in a reduced controller bandwidth. This research aims to provide a fast control method for DC-DC converters, which is based on a mixed-signal approach. The digital implementation research efforts are significantly focused on hardware based processors such as FPGAs. Unlike the most of the studies, in this thesis a microcontroller-based control strategy is adopted which provides a cost effective solution for low-power power electronics applications.

One of the main goals of this thesis is to provide a current regulated step-down converter, which could be used in the applications such as LED/Laser diode drivers, battery chargers and power factor correction circuits. Usually the research efforts for the control of DC-DC converters are focused on the output voltage regulation, therefore the output regulation case is usually disregarded. The study in this research offers reasonable control methods and solutions for these kinds of applications. In this research, a new digital hybrid current mode (DHCM) control technique is introduced. The proposed DHCM control method combines the PCM and ACM control techniques; therefore, it is fast and accurately control the inductor current. Due to the accurate inductor current control, the method provides output current regulation inherently. Moreover, the effectiveness of the method is shown experimentally with low-cost mixed-signal microcontrollers, therefore is applicable in the industry where cost is a matter.

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Although the topology investigation is considered as a mature area in power electronics, the studies to achieve high power density and high efficiency still can be regarded a hot topic. In this study, the proposed digital control method is applied to the one of the emerging topologies, which is known as three-level flying capacitor buck converter. The study provides a prescription how the proposed control method can be implemented to the three-level buck converter and proposes a solution to the one of the significant problems of this topology, which is flying capacitor voltage balancing. The proposed solution named as Asymmetric Slope Compensation (ASC) in which the two-compensator slope of the switching pairs are modified asymmetrically.

Lastly, in this study one of the emerging power electronic switching devices namely GaN transistors are examined and implemented for the three-level flying capacitor buck converter. The merits of the GaN transistors are investigated.

Overall, in this study a step-down converter is developed which posseses the latest state-of-art power electronics including the topology, switching devices and control.

Thesis Outline

The outline of the thesis as follows:

In Chapter 2, the analog control methods are studied. In this chapter, using the well-known existing methods in the literature, the small-signal models of the current mode control methods PCM, ACM and I2ACM for a synchronous buck converter are

investigated and compared. Moreover, the transient response of these control techniques are compared using simulations.

In Chapter 3, GaN-based synchronous buck converter is studied. The loss analysis for a synchronous buck converter is conducted. In addition, a Si-based and a GaN-based prototype are prepared. The efficiency of these prototypes are examined; the experimental results are compared with the theoretical results.

In Chapter 4, the digital current mode control methods are examined. The basic properties of the digital control techniques are investigated. For DPCM control, a mathematical model is provided based on the mixed-signal control approach. For implementation, timing scheme and compensator design are examined. Using a synchronous buck prototype, the models are compared with the experimental

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measurements. Similarly, the DACM control method is investigated. A continuous-time model is constructed. For implementation, timing scheme and compensator design are examined. Using the prototype circuit, the models are compared with the experimental results. Moreover, the transient characteristics of DACM control is investigated to the control signal and load changes for further comparison with the DHCM control, which is proposed in Chapter 5.

In Chapter 5, a new digital hybrid current mode control method, which combines the PCM and ACM control methods, is presented. The continuous-time and discrete-time models are provided. A simulation model is prepared. The control method is implemented with a mixed-signal microcontroller. For this purpose, the timing scheme and compensator design are studied. Using the synchronous buck converter prototype the model, simulation and experimental measurements are compared. In addition, the transient characteristics of the buck converter with DHCM control is investigated. The results are compared with the ones in Chapter 5, and the effectiveness of the DHCM control is demonstrated.

In Chapter 6, the implementation of DHCM to a 3LFC buck converter is investigated. A modification to DHCM control, which is named as asymmetric slope compensation, is proposed for the well-known flying capacitor voltage unbalancing problem. The ASC control is analyzed mathematically and in simulations. In addition, a simulation model for the DHCM with ASC controlled 3LFC buck converter is constructed. The transient characteristics to control signal changes and flying capacitor voltage perturbation are investigated, and the effectiveness of the ASC technique is demonstrated. Furthermore, a 3LFC buck converter prototype is designed with on-board microcontroller. A proper timing scheme is provided. The proposed DHCM control method with ASC technique is implemented and experimentally verified.

In Chapter 7, the conclusion is given. In this chapter, the results of the research and the contributions are discussed. Moreover, in the light of the conducted studies possible future work are provided for the readers.

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ANALOG CURRENT MODE CONTROL FOR BUCK CONVERTER

In this chapter, the analog controlled buck converter is investigated. In Section 2.1, the basics of the buck converter is studied. Several control methods exist in literature are discussed. In Section 2.2, current mode control methods are examined. In this section, the two most common analog current mode control which are Peak Current Mode (PCM) and Average Current Mode (ACM) control methods are studied. In addition, the I2 average current mode control method, which combines the PCM and ACM techniques, is investigated. Moreover, the control methods are simulated; current loop transfer functions and transient characteristics are compared.

An Overview to Buck Converter

In Figure 2.1, the non-synchronous buck converter circuit is given. In continuous-conduction mode of operation, the inductor current flows continuously as shown in Figure 2.2. Then, at steady-state the step-down ratio can be calculated using small ripple approximation as (𝑉𝑖𝑛− 𝑉𝑜)𝑡𝑜𝑛= 𝑉𝑜(𝑇𝑠𝑤− 𝑡𝑜𝑛) (2.1) 𝑉𝑜 𝑉𝑖𝑛 = 𝑡𝑜𝑛 𝑇𝑠𝑤 = 𝐷 (𝑑𝑢𝑡𝑦 𝑟𝑎𝑡𝑖𝑜) (2.2)

where Vin is input voltage, Vo is the output voltage, ton is the conduction time of switch and Tsw is the switching time.

Figure 2.1 : Buck converter.

Vin M iL -Vo + R L Co + v -L D Low-pass filter

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