Sic Schottky Diodes and Polyphase Buck Converters

Wright State University CORE Scholar

Browse all Theses and Dissertations Theses and Dissertations

2007

SiC Schottky Diodes and Polyphase Buck Converters

Veda Prakash N. Galigekere Wright State University

Follow this and additional works at: https://corescholar.libraries.wright.edu/etd_all

Part of the Electrical and Computer Engineering Commons

Repository Citation Galigekere, Veda Prakash N., "SiC Schottky Diodes and Polyphase Buck Converters" (2007). Browse all Theses and Dissertations. 181. https://corescholar.libraries.wright.edu/etd_all/181

This Thesis is brought to you for free and open access by the Theses and Dissertations at CORE Scholar. It has been accepted for inclusion in Browse all Theses and Dissertations by an authorized administrator of CORE Scholar. For more information, please contact [email protected]. SiC SCHOTTKY DIODES AND POLYPHASE BUCK CONVERTERS

A thesis submitted in partial fulﬁllment of the requirements for the degree of

Master of Science in Engineering

Veda Prakash Galigekere B.E., Visvesvaraya Technological University, Karnataka, India, 2004

2007 Wright State University WRIGHT STATE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

August 27, 2007

I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Veda Prakash Galigekere ENTITLED SiC Schottky Diodes and Polyphase Buck Converters BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in Engineering

Marian K. Kazimierczuk, Ph.D. Thesis Director

Fred D. Garber, Ph.D. Department Chair

Committee on Final Examination

Marian K. Kazimierczuk, Ph.D.

Raymond E. Siferd, Ph.D.

Gary C. Farlow, Ph.D.

Joseph F. Thomas, Jr., Ph.D. Dean, School of Graduate Studies Abstract

Galigekere, Veda Prakash. M.S.E., Department of Electrical Engineering, Wright State University, 2007. SiC Schottky Diodes and Polyphase Buck Converters.

The turn-off characteristics of a SiC Schottky diode are analyzed theoretically, by simulation, and by experiment. The static characteristics of SiC Schottky diodes and Si junction diodes are analyzed for normal and high temperatures. The effects of diffusion capacitance and junction capacitance on the turn-off transition of SiC Schottky diode have been analyzed theoretically. The turn-off transition of a SiC

Schottky barrier diode is analyzed by modeling the metal-semiconductor junction capacitance considering the linear and the non-linear effects. Behavior of the linear and the non-linear metal-semiconductor junction capacitance models are evaluated experimentally. The performance of SiC Schottky diodes is compared to the performance of similarly rated Si junction diodes. The effect of diode reverse-recovery current on the primary switch of a PFC boost converter is analyzed by the aid of PSPICE simulations. A 250 W, PFC boost converter is designed and simulated. In the 250 W PFC boost converter, the performance of SiC Schottky diode and similarly rated Si junction diodes are evaluated. The PSPICE simulation models of a SiC Schottky diode and two Si junction diodes are compared and some important parameters are discussed and their effect on the turn-off transition of the diodes are presented.

The principle and advantages of polyphase operation of buck converters is analyzed. The design equations for a two-phase buck converter operating in CCM are derived. A two-phase 6 V/120 W (PWM) buck converter is designed and simulated using PSPICE. The design equations are veriﬁed by PSPICE simulation results.

iii Contents

1 Introduction 1

1.1 Power Semiconductor Devices and Power Electronic Systems . . . . . 1

1.1.1 Motivation for the Research ...... 2

1.1.2 Thesis Objectives ...... 3

1.2 Eﬀect of Diode Reverse Recovery on PFC Boost Circuit ...... 4 1.2.1 Motivation for the Research ...... 4

1.2.2 Thesis Objectives ...... 5 1.3 Polyphase Buck Converter ...... 6

1.3.1 Motivation for the Research ...... 6

1.3.2 Thesis Objectives ...... 7

2 Silicon Carbide (SiC) Schottky Barrier Diodes 8

2.1 Static Characteristics of SiC Schottky Diodes ...... 11

2.1.1 Forward Characteristics of SiC Schottky and Si Junction Diodes 11 2.1.2 Reverse Characteristics of SiC Schottky and Si Junction Diodes 15

2.2 Switching Characteristics of SiC Schottky Diodes ...... 17 2.2.1 Diﬀusion Capacitance ...... 17

2.2.2 Junction Capacitance ...... 18 2.2.3 Switching Analysis Based on Linear Junction Capacitance . . 22

2.2.4 Switching Analysis Based on Non-Linear Junction Capacitance 26

2.3 Simulation and Experimental Results ...... 31

2.3.1 Behavior of Linear Junction Capacitance Model ...... 31 2.3.2 Behavior of Nonlinear Junction Capacitance Model ...... 35

2.4 Performance of SiC Schottky Diodes and Si Junction Diodes . . . . . 41 2.4.1 Response to Pulsating Input Voltage ...... 41

2.4.2 Response to Sinusoidal Input Voltage ...... 44

iv 2.5 Conclusions ...... 47

3 Eﬀect of Diode Reverse Recovery in Boost Converter 49

3.1 Introduction ...... 49

3.2 Overview of Operation of Boost Converter ...... 51 3.3 Diode Reverse Recovery in Boost Converter ...... 52

3.4 Performance of MUR1560, CSD10060 and MSR860 in PFC Boost Con- verter ...... 55

3.5 Comparison of PSPICE Models of Si Junction Diodes and SiC Schottky

Diodes ...... 57 3.6 Conclusions ...... 62

4 Polyphase Buck PWM DC-DC Converter 63

4.1 Introduction ...... 63 4.2 Steady-State Analysis of Two-Phase PWM Buck Converter ...... 64

4.3 DC Voltage Transfer Function and Design Equations ...... 68 4.4 Design and Simulation ...... 70

4.5 Conclusions ...... 74

Bibliography 75

v List of Figures

1 Structure of a SiC-Al Schottky diode...... 9

2 MATLAB plot of forward VD-ID characteristics of CSD10060 SiC Schot- tky diode obtained by PSPICE simulation...... 12

3 MATLAB plot of forward VD-ID characteristics of MSR860 Si junction diode obtained by PSPICE simulation...... 13

4 MATLAB plots of reverse VD-ID characteristics of CSD10060 SiC Schot- tky diode obtained by PSPICE simulation...... 15

5 MATLAB plot of reverse VD-ID characteristics of MSR860 Si junction diode obtained by PSPICE simulation...... 16

6 CD , CJ , and CJ + CD as functions of vD for CSD10060 SiC Schottky diode...... 18

7 CD , CJ , and CJ + CD as functions of vD for forward-biased CSD10060 SiC Schottky diode...... 19

8 Variation of CD with respect to variation in vD for reverse-biased CSD10060 SiC Schottky diode...... 20

9 Variation of CD with respect to variation in vD for forward-biased CSD10060 SiC Schottky diode...... 21

10 Variation of CJ due to variation of vD for CSD10060 SiC Schottky diode. 21 11 Equivalent circuit of Schottky diode for switching transitions. . . . . 22 12 Voltage and current waveforms during turn-oﬀ and turn-on transition. 23

13 Sinusoidal input voltage with f = 200 kHz and Vm = 9 V...... 27 14 Current through the non-linear junction capacitance at f = 200 kHz. 27

dvD 15 Component of iCJ due to dt ...... 28

dCJ 16 Component of iCJ due to dt ...... 29

17 Component iCJ1 , iCJ2 and iCJ1 + iCJ2 ...... 29

vi 18 Theoretically predicted voltage waveforms for turn-oﬀ and turn-on

transitions of the CSD10060 SiC Schottky diode obtained using MAT- LAB...... 31

19 Voltage waveform for the turn-on transition of CSD10060 SiC Schottky diode. x-axis scale: 50 ns/div. y-axis scale: 2 V/ div...... 32 20 Voltage waveform for the turn-oﬀ transition of CSD10060 SiC Schottky

diode. x-axis scale: 50 ns/div. y-axis scale: 2 V/ div...... 32

21 Diode current waveform for CSD10060 SiC Schottky diode at f = 100 kHz. x-axis scale: 200 µs/div. y-axis scale: 50 mA/ div...... 33

22 Diode current waveform for CSD10060 SiC Schottky diode at f = 1

MHz. x-axis scale: 200 ns/div. y-axis scale: 50 mA/ div...... 34

23 Diode current waveform for CSD10060 SiC Schottky diode at f = 2

MHz. x-axis scale: 100 ns/div. y-axis scale: 50 mA/ div...... 34 24 Diode current waveform for CSD10060 SiC Schottky diode at f = 3

MHz. x-axis scale: 100 ns/div. y-axis scale: 50 mA/ div ...... 35 25 Voltage and current associated with CSD10060 SiC Schottky diode obtained by MATLAB. Top trace- voltage: x-axis scale: 1 µs/div., y-

axis scale: 1 V/ div. Bottom trace- current: x-axis scale: 1 µs/div., y-axis scale: 1 mA/ div...... 36 26 Experimental voltage and current waveform for CSD10060 SiC Schot-

tky diode. Top trace- voltage: x-axis scale: 1 µs/div., y-axis scale: 2 V/ div. Bottom trace- current: x-axis scale: 1 µs/div., y-axis scale: 4

mA/ div...... 36 27 Current through CSD10060 SiC Schottky diode obtained by MATLAB. x-axis scale: 1 µs/div., y-axis scale: 1 mA/ div...... 37

vii 28 Experimental current waveform for CSD10060 SiC Schottky diode. x-

axis scale: 1 µs/div., y-axis scale: 2 mA/ div...... 37

29 iCJ1 through CSD10060 SiC Schottky diode for f = 20 kHz...... 38

30 iCJ2 through CSD10060 SiC Schottky diode for f = 20 kHz...... 38

31 iCJ1 through CSD10060 SiC Schottky diode for f = 200 kHz. . . . . 39

32 iCJ2 through CSD10060 SiC Schottky diode for f = 200 kHz...... 39

33 iCJ1 through CSD10060 SiC Schottky diode for f = 2 MHz...... 40

34 iCJ2 through CSD10060 SiC Schottky diode for f = 2 MHz...... 40 35 Diode reverse-recovery current in MUR1560 ultra fast recovery Si junc-

tion diode at f = 2 MHz...... 42

36 Diode reverse current in CSD10060 SiC Schottky diode at f = 2 MHz. 43 37 Diode reverse-recovery current in MSR860 soft recovery Si junction

diode at f = 2 MHz...... 43 38 Diode current for one time period of CSD10060 SiC Schottky diode

at different temperatures obtained by PSPICE.(The waveforms corresponding to different temperatures are imposed on each other) . . . . 45 39 Diode reverse current in CSD10060 SiC Schottky diode at different

temperatures obtained by PSPICE...... 45 40 Diode current for one time period of MSR860 Si junction soft recovery diode at diﬀerent temperatures obtained by PSPICE...... 46

41 Diode reverse current in MSR860 Si junction soft recovery diode at diﬀerent temperatures obtained by PSPICE...... 46

42 Circuit diagram of PWM dc-dc boost converter...... 51 43 Simulated current through CSD10060 SiC Schottky diode ...... 54

44 Simulated current through IRFBE30 International Rectiﬁer MOSFET. 54

viii 45 Simulated current through CSD10060 SiC Schottky diode during the

diode turn-oﬀ transition...... 56

46 Simulated current through IRFBE30 International Rectiﬁer MOSFET

during the MOSFET turn-on transition...... 57 47 Simulated current through IRFBE30 International Rectiﬁer MOSFET during the MOSFET turn-on transition...... 58

48 Simulated voltage across IRFBE30 International Rectiﬁer MOSFET during the MOSFET turn-on transition...... 58

49 Simulated power loss in IRFBE30 International Rectiﬁer MOSFET

during the MOSFET turn-on transition...... 58

50 Simulated current through IRFBE30 International Rectiﬁer MOSFET during the MOSFET turn-on transition for MUR1560 Si junction ultra

fast recovery diode...... 59 51 Simulated current through IRFBE30 International Rectiﬁer MOSFET

during the MOSFET turn-on transition for MSR860 Si junction soft recovery diode...... 59 52 Simulated current through IRFBE30 International Rectiﬁer MOSFET

during the MOSFET turn-on transition for CSD10060 SiC Schottky diode...... 60 53 Circuit diagram of a two-phase buck PWM DC-DC converter. . . . . 64

54 Equivalent circuit of the two-phase buck converter for (0 ≤ t ≤ DT ) . 65 55 Equivalent circuit of the two-phase buck converter for (DT ≤ t ≤ T ) . 66

56 Theoretically predicted voltages and currents associated with the steady state operation of a two-phase buck converter in CCM...... 67 57 Simulated input and output voltage waveforms of the two-phase buck

converter...... 72

ix 58 Simulated current waveforms through the two inductors of the two-

phase buck converter...... 72

59 Simulated waveforms of the sum of the two inductor currents and the

waveform of the load current...... 73 60 Simulated output voltage and the current waveforms of the two-phase buck converter...... 73

x List of Tables

1. Properties of Silicon and Silicon Carbide at T = 300 K...... 9

2. (VT h) at diﬀerent temperatures for CSD10060...... 12

3. (VT h) at diﬀerent temperatures for MSR860...... 13

4. Simulated average power loss at T = 300 K...... 42

5. Simulated power loss in the MOSFET and overall eﬀeciency of the 250 W boost

converter ...... 56

6. PSPICE parameters of CSD10060, MUR1560, and MSR860 ...... 60

7. Eﬀect of τ on trr and iP for MSR860 ...... 61

8. Eﬀect of CJ0 on trr and iP for MSR860 ...... 61

xi Acknowledgements

I would like to express gratitude to my advisor, Dr. Marian K. Kazimierczuk, for his invaluable support, encouragement, supervision and useful suggestions throughout this research work. I wish to thank Dr. Raymond E. Siferd and Dr. Gary C. Farlow for serving as members of my MS thesis defense committee, giving the constructive criticism and comments.

I would also like to thank the Department of Electrical Engineering and Dr. Fred D. Garber, the Department Chair, for giving me the opportunity to obtain my MS degree at Wright State University.

Finally, I would like to thank my family and friends for their constant encouragement and support.

xii Dedicated to my Family Members and Teachers

xiii 1

1 Introduction

1.1 Power Semiconductor Devices and Power Electronic Sys- tems

Power electronic systems employ one or more passive elements such as inductors or capacitors, and semiconductor devices operating as switches to manipulate certain important parameters associated with electrical power. Power electronic energy converters can be broadly classiﬁed into ac-dc rectiﬁers, dc-ac inverters, ac-ac converters (frequency changer), and dc-dc converters. Power converters are used in a wide range of consumer and industrial applications. Some of the notable consumer applications are: as power supply to lap-top computers, audio and video applications, mobile phones, battery chargers, and electrically operated domestic appliances. In the industry, power electronic energy converters are employed in building power sources for desktop computers, Un-interruptible Power Supplies (UPS), motor drives and traction applications, Power-Factor Corrector (PFC) circuits, and High Voltage DC Systems (HVDC systems). They are also widely used in the automobiles and other automotive applications. The present day and the future electric vehicles largely consist of power electronic converters and associated equipments for their operation.

Diodes, MOSFETs, Insulated Gate Bipolar Transistors (IGBTs), and thyristors are semiconductor devices, which are widely employed as switches in different power electronic circuits and systems. Stringent operating requirements of power electronic systems have resulted in an ever-increasing need for understanding, modeling, and designing superior semiconductor devices. All semiconductor devices currently employed as switches have a semiconductor-semiconductor or a metal-semiconductor junction. The junction properties such as the width of the junction, electric-field intensity in the junction, and resistivity of the junction are modulated by an external signal to regulate the flow of charge carriers through the device. The degree of control 2 over the flow of charge carriers through the semiconductor junction depends on the advance made in semiconductor material research and the control strategy employed.

1.1.1 Motivation for the Research

A diode, even though it is the simplest in construction amongst the semiconductor devices, plays a very important role in majority of power electronic systems. For example, a family of Pulse-Width Modulated (PWM) switched-mode dc-dc converters including buck (step-down), boost (step-up), buck-boost, forward converter and their derivative circuits employ a rectiﬁer diode for their operation. The above mentioned dc-dc converters are employed in a wide range of power and voltage ratings. The demand for high power-density, compact, and high eﬃciency power converters has led to a trend of realizing higher switching frequencies. The present day power diodes are required to operate at high power ratings (> 200 W) and high frequencies (> 500 kHz). The static and the switching characteristics of the power diode are crucial in the performance of power converters employing them. The type of semiconductor material employed and its properties play an important role in determining the characteristics and performance of the power diode. In the present scenario, for operating

◦ junction temperatures TJ < 100 C, Si junction diodes are the most popular type of power diodes employed. With the advent of SiC Schottky diodes in the market, it is necessary to understand the behavior of these diodes and compare their performance with the conventional Si diodes. Papers have been published comparing the performance of SiC Schottky diodes and Si junction diodes in certain speciﬁc power electronic applications such as [4], [9]-[11]. However, a detailed study of the behavior of SiC Schottky diodes considering their static and dynamic behavior at normal and high temperature does not seem to be reported. The present work is focussed on analysis, characterization, and performance of SiC Schottky diodes. 3

1.1.2 Thesis Objectives

In this work, it is proposed:

1. To study the static and dynamic characteristics of SiC Schottky diodes and compare those with the corresponding characteristics of Si diodes.

2. To deduce a circuit model for the switching transitions of a SiC Schottky diode by assuming the metal-semiconductor junction capacitance to be linear in volt-

age and to verify the model with the aid of simulations and experiments.

3. To deduce a circuit model for the switching transitions of a SiC Schottky diode considering the non-linearity of the metal-semiconductor junction capacitance-

voltage and to verify the non-linear model with the aid of simulations and experiments.

4. To compare the performance of SiC Schottky diode with that of a similarly

rated Si junction diode. 4

1.2 Eﬀect of Diode Reverse Recovery on PFC Boost Circuit

The usage of PWM power converters in power engineering is increasing signiﬁcantly since the last ten years. The PFC boost converter is one of the important applications of power electronic systems in power engineering [24],[23]. Diode reverse recovery is a crucial problem in boost converter topology. Diode reverse-recovery current imposes a current spike on the controlled switch in the converter, i.e, the MOSFET. The current spike together with the voltage across the MOSFET lead to considerable power loss in the circuit. This leads to additional thermal management issues. At higher switching frequencies, the current spike hampers the Electromagnetic Compatibility (EMC) of the converter [10]. Employing a Zero-voltage or zero-current switching circuit or a snubber circuit is one of the ways to counter the diode reverse recovery issue, however, the ideal solution would be to employ a power diode with zero or negligible diode reverse recovery [15],[16].

1.2.1 Motivation for the Research

Silicon carbide Schottky power diodes are relatively new in the market and their performance needs to be investigated. This research analyzes the performance of SiC Schottky diode in a PFC boost converter. A lot of work is being carried out ana- lyzing the behavior and performance of SiC Schottky diodes [1], [4]-[9]. Zero-voltage switching or zero-current switching techniques or snubber circuits are the popular methods employed to reduce the effect of diode reverse recovery in PFC boost circuit [15],[16]. The above mentioned methods increase the complexity of the converter topology by increasing the parts count leading to increased cost and reduced reliability. Paper [10] compares the efficiency and conducted electromagnetic interference (EMI) noise of a 300 W, PFC circuit, employing similarly rated Si junction diodes, RURD460 and STTH5R06D, and SiC Schottky diode, Infineon SDP04S60. This research attempts to elaborate on the effects of diode reverse recovery in a typically 5 rated PFC boost converter and evaluates the performance of Si junction ultra fast recovery diode MUR1560, Si junction soft-recovery diode MSR860, and SiC Schottky diode CSD10060. Further an attempt is made to understand the different parameters of the diodes and their effect on the reverse-recovery current.

1.2.2 Thesis Objectives

In this work, it is proposed:

1. To analyze the eﬀects of diode reverse-recovery current on the MOSFET and its eﬀect on the overall performance of the boost converter operated as a power- factor corrector circuit.

2. To evaluate the performance of CSD10060 SiC Schottky diode, MUR1560 Si junction ultra fast recovery diode, and MSR860 Si junction soft recovery diode

operating in a 250W PFC boost converter topology by the aid of PSPICE simulations.

3. To understand the eﬀect of minority carrier life time τ and unbiased junction

capacitance CJ0 on the reverse-recovery current in MSR860 Si junction soft recovery diode. 6

1.3 Polyphase Buck Converter

A buck Pulse-Width Modulated (PWM) dc-dc converter is a step down converter. It is employed for supplying power at specific voltage and current ratings to computers, mobile phones, microprocessors and other electronic applications [17]-[21]. Single phase buck converters require large filter capacitance to reduce the output voltage ripple. This makes the converter bulky and less efficient while meeting dynamic load changes. A polyphase buck converter employs two or more individual buck converters operating in parallel. In parallel operation of the buck converter, the output voltage ripple is reduced due to cancelation of the ripple currents in the inductors. Polyphase converters also increase the output voltage ripple frequency leading to reduced filter capacitance requirement. Polyphase operation may also provide new control strategies. Polyphase buck converters, even though they have a higher parts count, offer features which make them more attractive than their conventional single phase counterparts.

1.3.1 Motivation for the Research

Polyphase buck converters are used extensively to power high end microprocessors [17]. The VRM employed for driving the microprocessors is setting a limitation on the number of components that are fabricated on an Integrated Chip (IC) as the VRM has to deliver power satisfactorily to every component on the IC [21],[22]. Sub- stantial work is being carried out to address specific and complex problems involved in polyphase buck converters [18]-[22]. This research attempts to analyze and design a two-phase buck converter, with a SiC Schottky diode employed as the rectifier, operating in Continuous Conduction Mode. The design and operation of the converter is verified by the aid of PSPICE simulations. 7

1.3.2 Thesis Objectives

In this work it is proposed:

1. To analyze and derive the design equations for a two-phase PWM buck converter operating in CCM and to estimate the stresses on the various components of

the converter.

2. To verify the operation and design procedure by the aid of PSPICE simulations. 8

2 Silicon Carbide (SiC) Schottky Barrier Diodes

A Schottky barrier diode is formed when a metal such as aluminum is placed in direct contact with a suitable semiconductor such as silicon (Si) or silicon carbide (SiC).

Theoretically either a p or an n-type semiconductor can be used, but in practice n-type semiconductor is opted owing to the higher mobility of electrons. Due to the difference in the absolute potential energy of the electrons present in the metal to that of the electrons present in the semiconductor, a depletion region is formed as a result of electrons flowing across the metal-semiconductor interface, with the metal acquiring a negative charge and the semiconductor acquiring a positive charge [5],[6]. The number of electrons drifting from the semiconductor to the metal is greater than the number of electrons drifting from the metal to the semiconductor because of the higher potential energy of the electrons in the semiconductor. The potential barrier grows in magnitude and eventually no electron will be able to cross the barrier and a state of thermal equilibrium is established. The entire process of establishing the junction barrier takes place by the flow of only majority carriers, i.e, the electrons. As a result, Schottky barrier diodes are called majority-carrier devices.

Fig. 1 illustrates the elementary layout of a SiC-Al Schottky diode. The metal- semiconductor interface exhibits rectifying property similar to that of the pn junction in a junction diode [6]. SiC Schottky diodes are relatively new in the market and their characteristics and performance have created a lot of interest in the research and the industry communities. Table I presents the electrical properties of SiC and Si. SiC has a higher band gap energy, EG(SiC ) > 3.00 eV, compared to Si, EG(Si) = 1.12 eV. Band gap energy is the diﬀerence between the energy state of the electrons in conduction band and the energy state of the electrons in the valence band. Due to the higher band gap and lesser intrinsic charge carrier concentration, SiC devices are better immune to electro-magnetic interference (EMI) issues. The breakdown electric ﬁeld of SiC is an 9

Figure 1: Structure of a SiC-Al Schottky diode. order of magnitude higher than that of Si. This is one of the reasons why high voltage power Schottky diodes are viable using SiC. The voltage rating of Si Schottky diodes is

Table I Properties of Silicon and Silicon Carbide at T = 300 k

Parameter Symbol Unit Si SiC

Band gap energy EG eV 1.12 3.26 −19 −19 Band gap energy EG J 1.792 × 10 5.216 × 10 5 6 Break down electric ﬁeld EBD V/cm 2 × 10 2.2 × 10

Dielectric constant ²r - 11.9 9.7 2 Electron mobility µn cm /Vs 1360 900 2 Hole mobility µp cm /Vs 480 120 2 Surface µn µn cm /Vs 600 400 6 7 Sat. electron drift velocity vsat cm/s 8 × 10 2.7 × 10 −3 10 −8 Intrinsic concentration ni cm 1.5 × 10 1.097 × 10 ◦ Max. junction temperature TJmax C 200 600

Thermal conductivity Gth W/cmK 1.5 4.56 10 limited to ≈ 250 V. With regard to the maximum junction temperature and thermal conductivity, SiC is superior to Si. Due to the above mentioned properties, SiC is better suited for high temperature, high-frequency, high-voltage, and high-power applications. SiC also exhibits higher physical strength and chemical inertness as compared to Si. Amongst the diﬀerent polytypes of SiC, 4H-SiC is preferred due to its higher electron mobility [9]. The intrinsic carrier concentration of SiC is signiﬁcantly lesser than that of Si. As a result, the diode reverse current is considerably less in SiC diodes in comparison to that of Si diodes.

In Si junction diodes, the flow of current is by majority and minority charge carriers. This leads to the recombination process of holes and electrons during the turn-off transition leading to the diode reverse-recovery current [8]. SiC Schottky diodes being majority carrier devices do not suffer from reverse-recovery issue. The metal-semiconductor junction in the Schottky diode has an inherent capacitance associated with it. This junction capacitance plays an important role during the turn-on and turn-off transition of the SiC Schottky diode. The overall performance of a power diode can be attributed to its static characteristics and switching or dynamic characteristics. The static characteristics correspond to steady-state behavior and the dynamic characteristics correspond to transient behavior of the diode. In this work, an attempt has been made to analyze and characterize the behavior of SiC Schottky diodes and compare their performance with that of the popular Si junction diodes. 11

2.1 Static Characteristics of SiC Schottky Diodes

The properties of SiC shown in Table I dictate the static characteristics of a SiC

Schottky diode. The variation of diode forward current ID with respect to variation in the voltage across the diode VD at diﬀerent operating temperatures is the forward- biased characteristics of the diode. Similarly, the variation in the reverse current through the diode due to variation in the diode voltage VD when the diode is reverse biased at diﬀerent operating temperatures is the reverse-biased characteristics of the diode. In this section the static characteristics of CSD10060 SiC schottky diode will be presented and compared to the static characteristics of MSR860 Si junction soft recovery diode.

2.1.1 Forward Characteristics of SiC Schottky and Si Junction Diodes

The static forward biased characteristics of CSD10060 SiC Schottky diode obtained by PSPICE simulation at different operating temperatures are shown in Fig. 2. The temperature range selected for simulation is from 300 K - 600 K. The data points corresponding to the results obtained by PSPICE simulation were extracted and the waveforms were obtained using MATLAB. From Fig. 2 it is seen that the diode begins to conduct at lesser diode voltages as the operating temperature increases. The minimum potential difference required for the diode to start conducting is defined as the threshold voltage VT h. Increase in junction temperature leads to higher thermal energy in the electrons and they require reduced electrical energy to jump to conduction band. Table II shows VT h at different temperatures for CSD10060 SiC Schottky diode.

Fig. 3 shows the forward characteristics of MSR860 Si junction soft recovery diode at diﬀerent operating temperatures. The operating temperature range for Si junction diodes are limited as compared to that of SiC Schottky diodes. Comparing Figs. 2 and 3 it is seen that the threshold voltage of MSR860 Si junction diode is lesser than 12

10 T = 300 K 9 T = 400 K T = 500 K 8 T = 600 K

6 (A)

5 D i 4

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 v (V) D

Figure 2: MATLAB plot of forward VD-ID characteristics of CSD10060 SiC Schottky diode obtained by PSPICE simulation.

Table II (VT h) at different temperatures for csd10060 Silicon carbide Schottky diode

T VT h 300 K 0.75 V 400 K 0.65 V 500 K 0.58 V 600 K 0.48 V

that of CSD10060 SiC Schottky diode. Table III shows the threshold voltage VT h at diﬀerent temperatures for MSR860 Si junction soft recovery diode.

Incremental forward voltage drop δvF SiC due to change in operating temperature is deﬁned as the change in voltage drop across the diode for every ◦C change in operating 13

8 T = 300 K T = 320 K 7 T = 340 K T = 360 K 6

5 (A)

4 D i

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 v (V) D

Figure 3: MATLAB plot of forward VD-ID characteristics of MSR860 Si junction diode obtained by PSPICE simulation.

Table III (VT h) at different temperatures for msr860 Si junction Schottky diode

T VT h 300 K 0.35 V 320 K 0.32 V 340 K 0.29 V 360 K 0.26 V temperature at the fully rated diode current. The incremental forward voltage drop for CSD10060 SiC Schottky diode at its rated forward current of 10 A is deduced from Fig. 2. ∆V δ = = −0.7 mV/◦C. (1) vF SiC ∆T 14

The incremental forward voltage drop δvF Si for MSR860 Si junction soft recovery diode at the rated forward current of 8 A is deduced from Fig. 3 and is given by

∆V δ = = −1.7804 mV/◦C. (2) vF Si ∆T

The change in the threshold voltages of CSD10060 SiC Schottky diode and MSR860 Si junction soft recovery diode due to a unit change in the junction temperature is obtained by Figs. 2 and 3, respectively, and given below

∆VT h ◦ δv = = −1 mV/ C (3) T hSiC ∆T and

∆VT h ◦ δv = = −1.33 mV/ C. (4) T hSi ∆T In Figs. 2 and 3, the slope of the current waveform gives the on-state resistance

Ron oﬀered by the diode. From Fig. 2, Ron for CSD10060 SiC Schottky diode at T

= 300 K is 58.8 mΩ and from Fig. 3, Ron at T = 300 K for MSR860 Si junction soft recovery diode is 69.0 mΩ. Ron contributes to the Ohmic loss in the diode when conducting a steady current. Ron of CSD10060 SiC Schottky diode is marginally lower than that of the MSR860 Si junction soft recovery diode, however the forward voltage drop VF is higher ≈ 0.4 V for CSD10060 SiC Schottky diode. 15

2.1.2 Reverse Characteristics of SiC Schottky and Si Junction Diodes

The static reverse biased characteristics for CSD10060 SiC Schottky diode and MSR860 Si junction soft recovery diode are shown in Figs. 4 and 5 respectively. The character- istic waveforms are PSPICE simulation results extracted and plotted using MATLAB.

The incremental reverse current δIRSiC due to change in the operating temperature

−5

−10 (mA)

D i −15

−20 T = 300 K T = 400 K T = 500 K T = 600 K −25 −600 −500 −400 −300 −200 −100 0 v (V) D

Figure 4: MATLAB plots of reverse VD-ID characteristics of CSD10060 SiC Schottky diode obtained by PSPICE simulation. at the rated blocking voltage of the diode is deﬁned as the change in the diode reverse

◦ current for every C change in operating temperature. From Figs. 4 and 5, δIRSiC for

CSD10060 SiC Schottky diode at the rated blocking voltage of −600 V and δIRSi for MSR860 Si junction soft recovery diode at the rated blocking voltage of −600 V is found to be ∆I δ = R = −0.054 mA/◦C. (5) IRSiC ∆T 16

0 T = 300 K T = 320 K T = 340 K −0.2 T = 360 K

−0.4 (A)

−0.6 D i

−0.8

−1

−1.2 −600 −500 −400 −300 −200 −100 0 v (V) D

Figure 5: MATLAB plot of reverse VD-ID characteristics of MSR860 Si junction diode obtained by PSPICE simulation. and ∆I δ = R = −8.9 mA/◦C. (6) IRSi ∆T At an operating temperature T = 300 K, the static performance of MSR860 Si junction diode is marginally better than that corresponding to CSD10060 SiC

Schottky diode. The temperature range for satisfactory operation is limited for Si junction diodes in comparision with SiC Schottky diodes. The maximum operating temperature for MSR860 Si junction diode is 100◦ C. CSD10060 SiC Schottky diode has a higher range of operating temperature upto 300◦ C . From Fig. 2, it is seen that the operation is satisfactory for T upto 300◦ C. Comparing (1) and (5) with (2) and (6), it may be inferred that CSD10060 SiC Schottky diode is strongly preferred over MSR860 Si junction diode for high temperature applications. 17

2.2 Switching Characteristics of SiC Schottky Diodes 2.2.1 Diﬀusion Capacitance

Diﬀusion capacitance is due to the excess minority carriers stored in the neutral regions when the diode is forward biased. The holes injected across the depletion region are stored in the quasi-neutral n region. Similarly the free electrons are stored in the quasi-neutral p region. However, for pn junction diodes the electron current is negligible and the hole carrier charge due to diﬀusion is given by

vD nV QDp ≈ τpiD = τpIS(e T − 1) (7)

where τp is the minority carrier lifetime [6] in the n-type region. Any change in the diode voltage results in a change in the charge stored due to diﬀusion resulting in the incremental diﬀusion capacitance

dQ di τ vD Dp D p nV ∆CD = = τp = ISe T (8) dVD dVD nVT where iD is the diode current, n is the emission coeﬃcient, IS is the reverse saturation current, and VT is the thermal junction potential. For reverse-biased junctions the diﬀusion capacitance is negligible as iD = IS and diD/dt ≈ 0. Fig. 8 shows the variation of CD with respect to variation in vD for CSD10060 SiC Schottky diode

−12 at T = 300 K, τp = 1 × 10 s, and n = 1. For CSD10060 SiC Schottky diode

−20 IS = 1 × 10 A as per the data provided by the manufacturers of the diode. From

Figs. 6 and 7 it is seen that for vD < 1.2 V, CJ is dominant over CD and for vD > 1.2

V, CD is dominant over CJ . Hence the switching transitions of the SiC Schottky diode are primarily inﬂuenced by CJ and its behavior at diﬀerent voltages and frequencies. 18

20 10

15 10

10 10

5 C + C (pF) 10 D J D C J C

+ 0 J 10 C

, C D D −5 C 10 , J C −10 10

−15 10

−20 10 0 0.5 1 1.5 2 v (V) D

Figure 6: CD , CJ , and CJ +CD as functions of vD for CSD10060 SiC Schottky diode.

2.2.2 Junction Capacitance

When the diode is reverse biased the depletion region does not contain free mobile charge carriers for conduction of current and behaves almost like an insulator. The width of the depletion region is directly proportional to the applied reverse voltage. The junction is analogous to a parallel plate capacitor with the boundaries of the depletion region acting as parallel plates and the depletion region acting as the dielectric medium. If the diode voltage changes, the resulting junction capacitance is given by CJ = ∆Q/(−∆vD). As the diode voltage changes, the charge accumu- lated also changes leading to a change in the junction capacitance, hence the junction capacitance is governed by a charge control equation given by v u u2q²r²oND(Vbi − vD) QJn = qNDxnAJ = AJ t (9) 1 + ND NA 19

4 10

C + C D J

3 10 (pF)

D C J C + J C , D C

, 2

J C 10 D C

1 10 1.2 1.225 1.25 1.275 1.3 v (V) D

Figure 7: CD , CJ , and CJ + CD as functions of vD for forward-biased CSD10060 SiC Schottky diode.

where QJn is the charge stored in the junction, ND is the donor ion concentration,

NA is the acceptor ion concentration, xn is the length of the n side of the depletion region, Vbi is the built-in potential, and AJ is the area of the junction. The small signal junction capacitance is deduced below with vD = VD

¯ s dQ ¯ ² ² q C = − Jn ¯ = A r o J ¯vD=VD J 1 1 vD dvD 2Vbi( + )(1 − ) ND NA Vbi

²AJ CJ0 = q for vD ≤ Vbi (10) W 1 − vD Vbi where CJ0 is the junction capacitance at vD = 0.

The relation between CJ and CJ0 for the impurity concentration proﬁle of a step junction is given by (10). But for impurity concentration proﬁles being more gradual 20

−19 x 10

2.5

1.5 (pF) D

C 1

0.5

−1 −0.8 −0.6 −0.4 −0.2 0 v (V) D

Figure 8: Variation of CD with respect to variation in vD for reverse-biased CSD10060 SiC Schottky diode. than a step junction the small signal junction capacitance is given by

CJ0 CJ = ³ ´m for vD ≤ Vbi (11) 1 − vD Vbi

1 1 where m is the grading coeﬃcient. m = 3 for linearly graded junctions and m = 2 for step junctions [6],[23]. 21

15 x 10 2.5

1.5 (pF) D 1 C

0.5

0 0.5 1 1.5 2 v (V) D

Figure 9: Variation of CD with respect to variation in vD for forward-biased CSD10060 SiC Schottky diode.

1800

1600

1400

1200

(pF) 1000 J C

800

600

400

200 −10 −8 −6 −4 −2 0 2 4 6 8 v (V) D

Figure 10: Variation of CJ due to variation of vD for CSD10060 SiC Schottky diode. 22

Figure 11: Equivalent circuit of Schottky diode for switching transitions.

2.2.3 Switching Analysis Based on Linear Junction Capacitance

The transient performance of a SiC Schottky diode under large-signal square wave voltage is analyzed below. The square wave pulsates between an applied forward voltage VH and reverse blocking voltage VR. During the turn-off transition, the voltage across the diode switches from the forward voltage drop VF to VR and the metal- semiconductor junction capacitance is charged during this process. The equivalent circuit for the turn-off transition consists of the metal-semiconductor junction capacitance lumped as the capacitor CJ and the equivalent series resistance R as shown in Fig. 11. In this section the metal-semiconductor junction capacitance is assumed to be linear. The nonlinear effects are considered in Section 2.2.4. For the switching transitions the current through the junction capacitance will be the diode current. The analytically obtained instantaneous diode current, diode voltage and the power dissipated in the diode are shown in Fig. 12.

From circuit analysis the equations for the instantaneous diode current and the voltage are given by

−t iD = IRe τ (12) 23

Figure 12: Voltage and current waveforms during turn-oﬀ and turn-on transition. and

−t vD = VF + (VR − VF )(1 − e τ ). (13) where τ is the time constant of the RCJ network, IR is the reverse saturation current, and VF is the diode forward conduction voltage drop. Typical values of IR and VF for SiC Schottky diodes are 10−7 to 10−9 A and ≈ 1.1 V respectively. Assuming

|VR| >> VF , and considering the equations for instantaneous current and voltage in the diode, the average power loss in the diode during turn-oﬀ transition is given by

Z ∞ Z ∞ 1 IRVR −t −2t PD = pDdt = (e τ − e τ )dt T 0 T 0 I V τ V (V − V )RC = R R = R R F J 2T 2TR f C V 2 ≈ S J R (14) 2

1 where fS = T is the switching frequency. 24

Similarly, during the turn-on transition, the voltage across the diode changes from

VR to VF and the expressions for the instantaneous diode current and the diode voltage are given by

−t iD = IF (1 − e τ ) (15) and

−t −t VD = VF + (VR − VF )e τ ≈ VRe τ . (16)

The expression for instantaneous power in the diode during the turn-on transition is given by

−t −t pD(t) = idvD = IF VRe τ (1 − e τ ) (17)

VF where IF = R is the forward biased diode current. The average power dissipated in the diode during turn-on transition is deduced below. Z ∞ Z ∞ 1 IF VR −t −2t pD = pDdt = (e τ − e τ )dt T 0 T 0 I V τ V (V − V )RC = F R = R H F J 2T 2TR 1 = f C V (V − V ). (18) 2 S J R H F The junction capacitance stores energy when the diode is in the oﬀ state and the stored energy is dissipated during the turn-on transition resulting in the turn-on switching power loss given by

1 P = f C V 2. (19) turn−on 2 S J R Considering (14) and (19), the total switching power loss is given by

2 Pswitch = fSCJ VR . (20) 25

The diode turn-oﬀ and turn-on transition voltage waveforms governed by (13) and

(16) are obtained using MATLAB and presented in Section 2.3.1 along with the waveforms obtained experimentally. 26

2.2.4 Switching Analysis Based on Non-Linear Junction Capacitance

The current through the junction capacitance iCJ is a function of vD and CJ and their derivatives with respect to time. In this section CJ is treated as a nonlinear parameter. The theory of metal-semiconductor junction capacitance CJ is discussed brieﬂy in Section 2.2.2. From (9) we get v u Ã ! u QJn t2q²r²oND Vbi − vD C = = AJ . (21) J(LS) ND 2 vD 1 + v NA D

The current through CJ is the time derivative of the charge stored in the metal- semiconductor junction and is given by

dQJn d(CJ vD) dvD dCJ dvD dCJ dvD iCJ = = = CJ + vD = CJ + vD (22) dt dt dt dt dt dvD dt

By substituting the expression for CJ obtained in terms of CJ0 as given by (10) we get

CJ0 dvD CJ0 vD dvD iCJ = q + 3 vD ³ ´ 1 − dt vD 2 Vbi dt Vbi 2 1 − Vbi      CJ0 CJ0vD  dvD = q + 3 . (23)  vD ³ ´  1 − vD 2 dt Vbi 2Vbi 1 − Vbi

The current through the junction capacitance CJ is a function of vD and CJ , their time derivatives and the interdependence between them. As a result (23) is a highly non-linear equation which is valid for vD << Vbi. For example, if the diode voltage is sinusoidal, when the diode is OFF,

vD = Vmsin ωt for vD < Vbi. (24)

the current through the junction capacitance iCJ is given by    ωC ωC V sin ωt  q J0 J0 m  iCJ = + ³ ´ 3 Vmcos ωt for vD < Vbi (25)  Vmsin ωt  1 − Vmsin ωt 2 Vbi 2Vbi 1 − Vbi 27

(V) 0 D v −2

−4

−6

−8

−10 0 2.5 5 7.5 10 12.5 15 t (µs)

Figure 13: Sinusoidal input voltage with f = 200 kHz and Vm = 9 V.

0 (mA) CJ i

−5

−10

−15 0 2.5 5 7.5 10 12.5 15 t (µs)

Figure 14: Current through the non-linear junction capacitance at f = 200 kHz. 28

(mA) 0 1 CJ i

−2

−4

−6 0 5 10 15 t (µs)

dvD Figure 15: Component of iCJ due to dt .

A sinusoidal voltage with an amplitude of Vm = 9 V at a frequency of f = 200 kHz as shown in Fig. 13 is taken to be driving a SiC Schottky diode. For the considered sinusoidal input, the Schottky diode junction current waveform as per (25) is predicted with CJ0 = 380 pF and Vbi = 9.9900 V. Fig. (14) shows the theoretically predicted iCJ . The values chosen correspond to the values speciﬁed in the PSPICE model of CSD10060 SiC Schottky diode provided by the Manufacturers of the diode.

The current through CJ given by (23) is split into two components, one representing the current due to dvD/dt and the other representing the current due to dCJ /dt.

The individual components are named iCJ1 and iCJ2 and are given by   ωC  J0  iCJ1 = q Vmcos ωt for vD < Vbi (26) 1 − Vmsin ωt Vbi

     ωCJ0Vmsin ωt  iCJ2 =  ³ ´ 3  Vmcos ωt for vD < Vbi (27) Vmsin ωt 2 2Vbi 1 − Vbi 29

(mA) 0 2 CJ i

−5

−10

−15 0 5 10 15 t (µs)

dCJ Figure 16: Component of iCJ due to dt .

15 i CJ 1 12 i CJ 2 i + i 9 CJ CJ 1 2

6 (mA)

2 3 CJ i + 1 0 CJ i , 2 CJ i −3 , 1 CJ i −6

−9

−12

−15 0 3 6 9 12 15 t (µs)

Figure 17: Component iCJ1 , iCJ2 and iCJ1 + iCJ2 . 30

The current waveforms corresponding to (26) and (27) are as shown in Figs. 15

and 16 respectively. Fig. 17 shows iCJ1 , iCJ2 and their sum iCJ1 + iCJ2 . 31

2.3 Simulation and Experimental Results 2.3.1 Behavior of Linear Junction Capacitance Model

The equations governing the voltage transition during the turn-off and the turn-on transition of the diode are given by (13) and (16) respectively. These equations are employed to obtain the theoretical voltage waveforms shown in Fig. 18 for the turn- on and turn-off transition of CSD10060 using MATLAB. In the equation, a forward voltage drop of VF = 1 V has been selected. Obtaining an accurate waveform is dependent upon a proper estimation of τ. From Fig. 18 the 10% to 90% rise time of the diode voltage for the turn-on transition is ≈ 45 ns and the 90% to 10% fall time of the diode voltage equation for the turn-off transition is ≈ 90 ns.

The circuit diagram shown in Fig. 11 is bread boarded with V = ±10 V, CSD10060 Schottky diode, and R = 100 Ω. CSD10060 is a 10 A, 600 V Cree (SiC) Schottky diode recommended for switched-mode power supply, power factor corrector and motor

Figure 18: Theoretically predicted voltage waveforms for turn-oﬀ and turn-on transitions of the CSD10060 SiC Schottky diode obtained using MATLAB. 32

Figure 19: Voltage waveform for the turn-on transition of CSD10060 SiC Schottky diode. x-axis scale: 50 ns/div. y-axis scale: 2 V/ div.

Figure 20: Voltage waveform for the turn-oﬀ transition of CSD10060 SiC Schottky diode. x-axis scale: 50 ns/div. y-axis scale: 2 V/ div. drive applications. Agilent 33120A which has an internal resistance of 50 Ω is the function generator employed. Agilent 54622A is the oscilloscope used to capture the current and the voltage waveforms. Tektronics P6021 AC current probe which has a bandwidth of 120 HZ to 60 MHz is employed to obtain the diode current waveforms. 33

Figs. 19 and 20 show the turn-on and turn oﬀ transition voltages across CSD10060

SiC Schottky diode respectively. The turn-on transition 10% to 90% rise time is 34 ns and the turn-oﬀ transition 90% to 10% fall time is 102 ns respectively. Theoretically predicted waveforms shown in Fig. 18 and the experimentally obtained waveforms shown in Figs. 19 and 20 agree to a good extent. The minor discrepancy can be attributed to the uncertainty in the estimation of τ and unaccounted parasitics present in the experimental setup. Figs 21 - 24 show the diode current waveforms at 100 kHz, 1 MHz, 2 MHz, and 3 MHz respectively. It can be seen that the diode reverse current is satisfactory at a frequency of 100 kHz while for f > 1MHz the diode conducts for a considerable time duration during the oﬀ period.

Figure 21: Diode current waveform for CSD10060 SiC Schottky diode at f = 100 kHz. x-axis scale: 200 µs/div. y-axis scale: 50 mA/ div. 34

Figure 22: Diode current waveform for CSD10060 SiC Schottky diode at f = 1 MHz. x-axis scale: 200 ns/div. y-axis scale: 50 mA/ div.

Figure 23: Diode current waveform for CSD10060 SiC Schottky diode at f = 2 MHz. x-axis scale: 100 ns/div. y-axis scale: 50 mA/ div. 35

Figure 24: Diode current waveform for CSD10060 SiC Schottky diode at f = 3 MHz. x-axis scale: 100 ns/div. y-axis scale: 50 mA/ div

2.3.2 Behavior of Nonlinear Junction Capacitance Model

The current through the nonlinear junction capacitance is given by (23). For a sinusoidal input voltage of amplitude Vm = 9 V at a frequency of 200 kHz, the theoretically predicted current through the junction capacitance of the diode as per (25) is shown in Fig. 25. The experimentally obtained current waveform through the diode is as depicted in Fig. 26. Figs. 27 and 28 present the theoretically predicted and experimentally obtained diode current waveforms respectively. By comparing Figs. 25 and

26, and Figs. 27 and 28 it is seen that the nonlinear junction capacitance model for turn-oﬀ transition is in very good agreement with the actual diode behavior. Equa- tions (26) and (27) give the expressions for the currents through CJ inﬂuenced by

dvD/dt and dCJ /dt respectively, denoted by iCJ1 and iCJ2 . The eﬀect of frequency is analyzed by obtaining plots of iCJ1 and iCJ2 at diﬀerent frequencies. Figs. 29 and 30 give the plots of iCJ1 and iCJ2 at 20 kHz, Figs. 31 and 32 give the plots of iCJ1 and iCJ2 at 200 kHz, and Figs. 33 and 34 give the plots of iCJ1 and iCJ2 at 2 MHz. 36

12 i CJ v 9 D

3 (V) D v 0

(mA) , −3 CJ i

−6

−9

−12

−15 6 7 8 9 10 11 t (µs)

Figure 25: Voltage and current associated with CSD10060 SiC Schottky diode obtained by MATLAB. Top trace- voltage: x-axis scale: 1 µs/div., y-axis scale: 1 V/ div. Bottom trace- current: x-axis scale: 1 µs/div., y-axis scale: 1 mA/ div.

Figure 26: Experimental voltage and current waveform for CSD10060 SiC Schottky diode. Top trace- voltage: x-axis scale: 1 µs/div., y-axis scale: 2 V/ div. Bottom trace- current: x-axis scale: 1 µs/div., y-axis scale: 4 mA/ div. 37

0 (mA) CJ i −3

−6

−9

−12

−15 6 7 8 9 10 11 t (µs)

Figure 27: Current through CSD10060 SiC Schottky diode obtained by MATLAB. x-axis scale: 1 µs/div., y-axis scale: 1 mA/ div.

Figure 28: Experimental current waveform for CSD10060 SiC Schottky diode. x-axis scale: 1 µs/div., y-axis scale: 2 mA/ div. 38

0.6

0.4

0.2

0 (mA) 1 CJ i −0.2

−0.4

−0.6

−0.8 0 20 40 60 80 100 t (µs)

Figure 29: iCJ1 through CSD10060 SiC Schottky diode for f = 20 kHz.

1.5

0.5

(mA) 0 2 CJ i

−0.5

−1

−1.5 0 20 40 60 80 100 t (µs)

Figure 30: iCJ2 through CSD10060 SiC Schottky diode for f = 20 kHz. 39

(mA) 0 1 CJ i

−2

−4

−6 0 2 4 6 8 10 t (µs)

Figure 31: iCJ1 through CSD10060 SiC Schottky diode for f = 200 kHz.

(mA) 0 2 CJ i

−5

−10

−15 0 2 4 6 8 10 t (µs)

Figure 32: iCJ2 through CSD10060 SiC Schottky diode for f = 200 kHz. 40

(mA) 0 1 CJ i

−20

−40

−60 0 0.2 0.4 0.6 0.8 1 t (µs)

Figure 33: iCJ1 through CSD10060 SiC Schottky diode for f = 2 MHz.

150

100

(mA) 0 2 CJ i

−50

−100

−150 0 0.2 0.4 0.6 0.8 1 t (µs)

Figure 34: iCJ2 through CSD10060 SiC Schottky diode for f = 2 MHz. 41

2.4 Performance of SiC Schottky Diodes and Si Junction Diodes 2.4.1 Response to Pulsating Input Voltage

The discussion in Section 2.3.1 considers the response of CSD10060 SiC Schottky diode for an input voltage pulsating between ± 10 V. In Section 2.3.2 a sinusoidal input voltage of amplitude 9 V is considered. In order to obtain a fair performance evaluation, in this section, the performance of CSD10060 SiC Schottky diode is analyzed by driving the diode at the voltage and current ratings of the diode. PSPICE simulations are carried out for the input voltage pulsating between + 20 V and −

500 V. A series resistance of 5 Ω is incorporated in the circuit resulting in a forward current of 4 A. The forward current and the reverse-blocking voltage chosen are based on the typical environment in which the power diodes are commonly operated. The performance of CSD10060 10 A, 600 V, SiC Schottky diode is compared with the performance of MUR1560 15 A, 600 V, Si junction ultra fast recovery diode and MSR860

8 A, 600 V, Si junction soft recovery diode.

Figs. 35-37 present the diode reverse current waveforms for one period of operation for MUR1560 Si junction ultra fast recovery diode, CSD10060 SiC Schottky diode, and MSR860 Si junction soft recovery diode respectively, simulated at a frequency of 2 MHz. Table 2.4.1 presents the average power loss at T = 300 K in the three diodes at diﬀerent frequencies. From Figs. 35 - 37 it is seen that the peak reverse current of

MUR1560 Si junction ultra fast recovery diode is 45 A which is an order of magnitude higher than the corresponding values of the other two diodes. This introduces a current spike in the circuit leading to current stress on the other components of the circuit. From IV its is observed that the average power loss in the diode is comparable in the case of MSR860 Si junction soft recovery diode and CSD10060

SiC Schottky diode. However, the average power loss in MUR1560 Si junction ultra 42

Figure 35: Diode reverse-recovery current in MUR1560 ultra fast recovery Si junction diode at f = 2 MHz. fast recovery diode is signiﬁcantly higher in the frequency range of 1 MHz - 2.5 MHz. This can be attributed to the power switching loss playing a dominant role in MUR1560 Si junction ultra fast recovery diode in the considered frequency range.

The performance of SiC Schottky diode CSD10060 is comparable to the performance of Si soft recovery diode MSR1560, while both CSD10060 and MSR860 outperform MUR1560 Si junction ultra fast recovery diode at an operating temperature of 300

Table IV Simulated Average Power Loss at T = 300 K

Diode 500 kHz 1 MHz 2 MHz 2.5 MHz 3 MHz CSD10060 2.10 W 2.06 W 1.90 W 1.85 W 1.75 W MUR1560 621 mW 3.00 W 9.40 W 4.90 W 2.80 W MSR860 2.09 W 1.90 W 1.51 W 1.31 W 1.09 W 43

Figure 36: Diode reverse current in CSD10060 SiC Schottky diode at f = 2 MHz.

Figure 37: Diode reverse-recovery current in MSR860 soft recovery Si junction diode at f = 2 MHz. 44

2.4.2 Response to Sinusoidal Input Voltage

The performance of CSD10060 SiC Schottky diode and MSR860 Si junction soft recovery diode under a sinusoidal input voltage is analyzed at different operating temperatures by the aid of PSPICE simulations. Power diodes used in full-wave ac- dc rectifiers are subjected to high voltage sinusoidal input. Figs. 38 and 39 show the effect of temperature on the diode reverse current during turn-off transition for

CSD10060 SiC Schottky diode. The waveforms are obtained by PSPICE simulations. The simulations correspond to a sinusoidal voltage source of amplitude 100 V at a frequency of 200 kHz in series with CSD10060 SiC Schottky diode and a resistance of 10 Ω. From Fig. 39 it is seen that the magnitude of the reverse current decreases with increase in temperature for CSD10060 SiC Schottky diode. It is also observed from Fig. 38 that the forward current remains unaﬀected by the change in operating temperature. In 38 the waveforms corresponding to T = 300 K, 400 K, 500 K, and 600 K coincide and are indistinguishable. It shows that CSD10060 operates satisfactorily in the considered temperature range. Figs. 40 and 41 show the diode current for MSR860 Si junction soft recovery diode at diﬀerent temperatures obtained by PSPICE simulations. The simulations correspond to a sinusoidal voltage source of amplitude 100 V at a frequency of 200 kHz in series with the MSR860 Si junction soft recovery diode and a resistance of 10 Ω. It is observed that the diode reverse current increases with increase in temperature. Comparing Figs. 38 and 39 with Figs. 40 and 41 it is observed that CSD10060 SiC Schottky diode has superior performance with respect to operation of MSR860 Si junction soft recovery diode particularly at higher temperatures. 45

Figure 38: Diode current for one time period of CSD10060 SiC Schottky diode at different temperatures obtained by PSPICE.(The waveforms corresponding to diﬀerent temperatures are imposed on each other)

Figure 39: Diode reverse current in CSD10060 SiC Schottky diode at diﬀerent temperatures obtained by PSPICE. 46

Figure 40: Diode current for one time period of MSR860 Si junction soft recovery diode at diﬀerent temperatures obtained by PSPICE.

Figure 41: Diode reverse current in MSR860 Si junction soft recovery diode at diﬀerent temperatures obtained by PSPICE. 47

2.5 Conclusions

The static characteristics, which include the forward-biased and reverse-biased characteristics, of CSD10060 SiC Schottky diode have been studied with the aid of PSPICE for T = 300 K, 400 K, 500 K, and 600 K. The static characteristics of MSR860 Si junction soft recovery diode has been studied for T = 300 K, 320 K, 340 K, and 360 K with the aid of PSPICE simulations. Based on the PSPICE simulation results it can be concluded that at T = 300 K CSD10060 SiC Schottky diode oﬀers a higher forward voltage drop as compared to MSR860 Si junction soft recovery diode. How- ever, as the operating temperature increases the performance of MSR860 Si junction soft recovery diode suﬀers considerably.

With respect to the switching characteristics of the SiC Schottky diode, it was observed that diffusion capacitance CD has a negligible role and the junction capacitance CJ has a dominant role. The circuit model developed based on the assumption of linear junction capacitance CJ is in fair agreement with PSPICE simulation and experimental results. The diode turn-on and turn-off voltage waveforms predicted based on the linear junction capacitance model are in accordance with the PSPICE simulation and experimental results, however a minor discrepancy was observed in predicting the magnitude of the waveforms. The non-linear junction capacitance model developed to predict the junction capacitance current for the turn-off transition of SiC Schottky diode is in very good agreement with the experimental results.

The model also accommodates for obtaining the contribution due to non-linearity in junction capacitance to the overall diode current during turn-off transition. Based on the theoretical analysis, PSPICE simulation, and experimental results it can be concluded that SiC Schottky diodes do suffer from diode reverse recovery, however the reverse-recovery effect is lesser in SiC Schottky diode as compared to that in

Si junction diodes. The reverse recovery in SiC Schottky diodes is due to metal- 48

semiconductor junction capacitance CJ as opposed to Si junction diodes in which the reverse recovery is due to diﬀusion capacitance CD. The reverse-recovery current in SiC Schottky diodes increase in magnitude as the switching frequency increases however it reduces as the temperature increases. 49

3 Eﬀect of Diode Reverse Recovery in Boost Con- verter

3.1 Introduction

Pulse-Width Modulated (PWM) boost converter is a Switched-Mode Power Converter

(SMPC) used extensively in power engineering and automotive applications. The output voltage of the boost converter is always greater than the input voltage. With respect to power engineering, boost converters operating in continuous conduction mode are employed as active Power-Factor Corrector (PFC) circuits at high power ratings (> 200W). The reverse recovery of the power diode employed hampers the satisfactory operation of the PFC boost circuit[14]. Diode reverse-recovery current imposes a current spike on the power MOSFET employed as the controlled switch in the boost converter. This leads to additional power loss and electro-magnetic compatibility issues[12]-[16]. Increased power loss leads to heat-sinks getting bigger and reduction of power density of the boost converter. Higher switching frequencies in PWM converters are favorable as they reduce the value of the passive components required. Reduction in the value of passive components makes the system more compact and improves the dynamic behavior of the system. The eﬀect of diode reverse recovery is limiting the switching frequency employed for the satisfactory operation of the PFC boost converter.

Currently, the most popular methods of overcoming the adverse eﬀect of diode reverse recovery in boost converter are employing zero-voltage or zero-current switching circuits or active snubber circuits [14]-[16]. The above mentioned methods increase the part count of the PFC system making the operation complex. This leads to a reduction in reliability and increase in cost. The introduction of active or passive snubber circuits alters the dynamic response of the boost converter. Selection of an appropriate power diode can mitigate the eﬀect of diode reverse recovery in the boost 50 converter. 51

L D

+ V R I S C −

Figure 42: Circuit diagram of PWM dc-dc boost converter.

3.2 Overview of Operation of Boost Converter

A boost converter consists of two semiconductor switches and an energy transfer element to convert dc voltage from a lower level to dc voltage at a higher level. Fig.

42 shows a boost converter with input voltage source VI , diode D and MOSFET S acting as switches, inductor L acting as the energy transfer element, and the output capacitor C employed for reducing the voltage ripple at the load R. The duty ratio

D of the switch S is defined as the ratio of the switch on-period ton, to the total time period of the gate pulse T . The converter is assumed to be operating in continuous conduction mode (CCM), i.e, the inductor current is non zero for the entire period of operation. The analysis can be divided into two sections depending on the state of the MOSFET and the diode. For the time interval corresponding to the switch being in the on-state and the diode in the off-state (0 < t < DT ), the input voltage source transfers energy to the inductor, which is stored in the electro-magnetic form. When the switch turns off (DT < t < T ), the inductor discharges the stored energy by forcing current through the diode and hence turning it on. During this phase the input voltage source and the energy stored in the inductor supply the load boosting the voltage at the load resistance.

When the switch S begins the turn-on transition in the next cycle the diode

D begins the turn-off transition as the inductor current begins to flow through the 52 switch instead of the diode. During the turn-off transition the diode suffers from the phenomenon of reverse recovery. The reverse-recovery current of the diode flows through the switch S and appears as a current spike in the switch current waveform, as the inductor will not allow for fast current changes. At the instant the current spike appears, the switch is in the process of turning on and a significant part of the input voltage VI is present across it. In boost PFC circuits, the input voltage, typically being more than 100 V, together with the current spike leads to considerable power loss during the diode turn-off and MOSFET turn-on transition.

A 250 W boost converter is designed for operation in CCM. The input voltage,

VI is 150 V, the required output voltage VO is 400 V. A switching frequency of, fS = 500 kHz is selected. The parameters are selected based on the typical voltage, current, and power ratings of a medium-high power PFC circuit. The minimum value of inductance required for CCM was found to be 60 µH. An inductance of 100 µH was opted to ensure CCM operation. A ﬁlter capacitance C = 10 µF was selected.

IRFBE30, 800 V, 4.1 A, International Rectiﬁer MOSFET and CSD10060, 600 V, 10 A, Cree SiC Schottky diode is employed for simulation. The design procedure employed is described in [23]].

3.3 Diode Reverse Recovery in Boost Converter

The diode turn-oﬀ transition and the MOSFET turn-on transition occur simultaneously in the steady state operation of the boost converter. IRFBE30, 800 V, 4.1

A, International Rectiﬁer MOSFET and CSD10060, 600 V, 10 A, Cree SiC Schot- tky diode is employed for simulation. The PSPICE circuit model provided by the Manufacturers of the MOSFET and SiC Schottky diode are employed for simulation.

Figs. 43 - 46 show the simulated current waveforms through CSD10060 SiC Schottky diode and IRFBE30 power MOSFET during the diode turn-off and MOSFET turn- on transitions. As the diode turns off, the diode reverse-recovery current has to flow 53 through the MOSFET and it is reflected in the MOSFET current waveform in Fig.

44. Figs. 47-49 show the simulated voltage, current, and the instantaneous power associated with IRFBE30 power MOSFET during its turn-on transition. From Fig.

49 it can be inferred that the power loss in IRFBE30 power MOSFET is substantial and the overall efficiency of the converter will be affected if diode reverse-recovery effect is not mitigated. Figs. 47 - 49 show the simulated voltage, current, and the instantaneous power associated with the MOSFET during its turn-on transition. From Fig. 49 it can be inferred that the power loss in the MOSFET is substantial and the overall efficiency of the converter will be affected if diode reverse-recovery effect is not mitigated. 54

−1 (A)

D i −2

−3

−4

−5

−6 4.2232 4.2234 4.2236 4.2238 4.224 4.2242 4.2244 4.2246 4.2248 4.225 t (ms)

Figure 43: Simulated current through CSD10060 SiC Schottky diode .

4 (A)

3 S i

−1 4.2232 4.2234 4.2236 4.2238 4.224 4.2242 4.2244 4.2246 4.2248 4.225 t (ms)

Figure 44: Simulated current through IRFBE30 International Rectiﬁer MOSFET. 55

3.4 Performance of MUR1560, CSD10060 and MSR860 in PFC Boost Converter

The diode reverse-recovery current is examined for MUR1560 15 A, 600 V Si junction ultra fast recovery diode, CSD10060 10 A, 600 V SiC Schottky diode, and MSR860, 8 A, 600 V Si junction soft recovery diode operating in the PFC boost converter by the aid of PSPICE simulations. The simulations are carried out at a temperature of 300 K. The PSPICE simulation model provided by the makers of the diodes are incorporated. The boost converter described in Section 3.2 is employed for simulation.

Figs. 50 - 52 show the current through the MOSFET during the turn-on transition for MUR1560 Si junction ultra fast recovery diode, MSR860 Si junction soft recovery diode, and CSD10060 SiC Schottky diode. From Fig. 50 it is seen that MUR1560

Si junction ultra fast recovery diode imposes a current spike of i(p) ≈ 16 A on the MOSFET which is unacceptable for the satisfactory operation of the boost converter.

In comparison CSD10060 SiC Schottky diode results in a current spike of i(p) ≈ 6 A which is relatively better, however, operation of MSR860 Si junction soft recovery diode results in a current spike which is negligible and lesser than the maximum steady state value of the current through the MOSFET. Table V gives the PSPICE simulated average power loss, eﬃciency of the boost converter, reverse-recovery time, and the peak value of the reverse-recovery current for the three considered diodes incorporated in the circuit individually. From V it is observed that the eﬃciency of the converter with the CSD10060 SiC Schottky diode and the converter with MSR860 Si junction soft recovery diode was comparable, even though CSD10060 SiC Schottky diode resulted in a much higher reverse current. With respect to the reverse-recovery time MSR860 Si junction soft recovery diode is considerably faster than MUR1560 Si junction ultra fast recovery diode and CSD10060 SiC Schottky diode. 56

−1

−2 (A)

D i −3

−4

−5

−6 812 812.005 812.01 812.015 812.02 812.025 812.03 812.035 812.04 812.045 t (µs)

Figure 45: Simulated current through CSD10060 SiC Schottky diode during the diode turn-oﬀ transition.

Table V Simulated Power Loss in MOSFET and Overall Efficiency of the 250 W Boost Converter.

Diode MUR1560 MSR860 CSD10060

W(S) (W) 42 22 27 Eﬃciency (%) 73 78 76

trr (ns) 14 7 13

ip (A) 15.8 0.6 6.1 57

3.5 Comparison of PSPICE Models of Si Junction Diodes and SiC Schottky Diodes

The PSPICE simulation models provided by the Manufacturers of the diodes give useful insight regarding the parameters associated with the actual diode. Even though, the principle of operation of junction diodes diﬀer from that of the Schottky diodes, the PSPICE models have a similar features. Table VI shows the parameters associated with the PSPICE models of CSD10060 Cree, SiC, Schottky diode, MUR1560 ON Semiconductor, Si junction ultra fast recovery diode and MSR860 ON Semiconductor

Si junction soft recovery diode. The PSPICE model parameters are provided by the manufacturers of the diodes.

In Table VI , IS the reverse saturation current and τ the transition time is sig- niﬁcantly less for CSD10060 SiC Schottky diode and the junction potential VJ and unbiased junction capacitance CJ0 is signiﬁcantly higher as compared to Si junction diodes MUR1560 and MSR860. Transition time τ is the minority-carrier life time is

3 (A)

S i 2

−1 812 812.005 812.01 812.015 812.02 812.025 812.03 812.035 812.04 812.045 t (µs)

Figure 46: Simulated current through IRFBE30 International Rectiﬁer MOSFET during the MOSFET turn-on transition. 58

3 (A)

S i 2

−1 812 812.005 812.01 812.015 812.02 812.025 812.03 812.035 812.04 812.045 t (µs)

Figure 47: Simulated current through IRFBE30 International Rectiﬁer MOSFET during the MOSFET turn-on transition.

450

400

350

300

250 (V)

v 200

150

100

0 812 812.005 812.01 812.015 812.02 812.025 812.03 812.035 812.04 812.045 t (µs)

Figure 48: Simulated voltage across IRFBE30 International Rectiﬁer MOSFET during the MOSFET turn-on transition.

1.5

1 (kW)

S P 0.5

−0.5 812 812.005 812.01 812.015 812.02 812.025 812.03 812.035 812.04 812.045 t (µs)

Figure 49: Simulated power loss in IRFBE30 International Rectiﬁer MOSFET during the MOSFET turn-on transition. 59

8 (A)

S i 6

−2 4.2232 4.2234 4.2236 4.2238 4.224 4.2242 4.2244 4.2246 4.2248 4.225 t (ms)

Figure 50: Simulated current through IRFBE30 International Rectiﬁer MOSFET during the MOSFET turn-on transition for MUR1560 Si junction ultra fast recovery diode.

2.5

1.5

1 (A)

S i 0.5

−0.5

−1 4.2232 4.2234 4.2236 4.2238 4.224 4.2242 4.2244 4.2246 4.2248 4.225 t (ms)

Figure 51: Simulated current through IRFBE30 International Rectiﬁer MOSFET during the MOSFET turn-on transition for MSR860 Si junction soft recovery diode. 60

4 (A)

3 S i

−1 4.2232 4.2234 4.2236 4.2238 4.224 4.2242 4.2244 4.2246 4.2248 4.225 t (ms)

Figure 52: Simulated current through IRFBE30 International Rectiﬁer MOSFET during the MOSFET turn-on transition for CSD10060 SiC Schottky diode.

Table VI PSPICE Parameters of CSD10060 Silicon carbide Schottky Diode, MUR1560 Silicon Junction Ultra Fast Recovery Diode and MSR860 Silicon Junction soft Recovery Diode

Parameter Units CSD10060 MUR1560 MSR860

−21 −7 −4 IS A 10 × 10 1.2294 × 10 3.7410 × 10 M - 0.63338 0.37348 0.5

−12 −10 −11 CJ0 F 381 × 10 5.432 × 10 1 × 10

VJ V 9.9900 0.4 0.7 τ s 14.474 × 10−12 7.141 × 10−8 1 × 10−9 61 the time duration the minority carriers exist before the recombination process. Dif- fusion capacitance CD is dependent on τ. It is inferred that CD is considerably less for SiC Schottky diode. The unbiased junction capacitance CJ0 is dependent on the width of the junction in the diode which is decided by the current and voltage rating of the diode. MUR1560 Si junction ultra fast recovery diode has a current rating which is higher than that of MSR1560 Si junction soft recovery diode or CSD10060

SiC Schottky diode. From Table VI it is seen that MUR1560 Si junction ultra fast recovery diode has a relatively higher CJ0.

Tables VII and VIII, present the variation in the reverse-recovery time trr and the peak reverse-recover current ip with respect to change in the minority-carrier life time τ and unbiased junction capacitance CJ0 respectively for MSR860 Si junction soft recover diode. Tables 3.5 and 3.5 correspond to the values obtained by the

PSPICE simulation of the boost PFC circuit considered in 3.3.

Table VII Effect of τ on trr and ip for msr860 Silicon Junction Soft Recovery Diode

τ (s) trr (ns) ip (mA) 1 × 10−8 11.2 -33.4 1 × 10−9 11.7 -9.2 1 × 10−10 11.9 -8.6

Table VIII Effect of CJ0 on trr and ip for msr860 Silicon Junction Soft Recovery Diode

CJ0 (s) trr (ns) ip (mA) 1 × 10−10 38.1 -34.9 1 × 10−11 11.7 -9.2 1 × 10−12 9.0 -3.9 62

It is seen from Tables VII and VIII that both τ and CJ0 aﬀect the reverse-recovery time trr and reverse-recovery current ip considerably. The relatively better performance of MSR860 Si junction soft recovery diode can be attributed to a reduced value of CJ0 in comparison to that of MUR1560 Si junction ultra fast recovery diode and CSD10060 SiC Schottky diode.

3.6 Conclusions

The eﬀect of diode reverse recovery on PFC boost converter has been analyzed by the aid of PSPICE simulated waveforms. From Fig. 47-49 it is seen that diode reverse- recovery current leads to considerable power loss in the MOSFET. From Table V it can be inferred that the performance of MSR860 Si junction soft recover diode and CSD10060 SiC Schottky diode is comparable while MUR1560 Si junction ultra fast recovery diode leads to a very lossy operation. The reverse-recovery time of

CSD10060 SiC Schottky diode and MUR1560 Si junction ultra fast recovery diode was comparable, however, the peak value of the reverse-recovery current was more than twice as that of CSD10060 SiC Schottky diode. At the considered conditions, based on PSPICE simulation results it can be concluded that MSR860 Si junction soft recovery diode offers the best performance among the considered diodes. From Table VII it can be inferred that the value of minority carrier life time τ affects the peak value of the reverse-recovery current while it does not harm the reverse-recovery time. The peak value of the reverse-recovery current directly increases with an increase in minority carrier life time. From Table VIII it is inferred that CJ0 critically affects the reverse-recovery time and current of the diode. 63

4 Polyphase Buck PWM DC-DC Converter

4.1 Introduction

Pulse-Width Modulated (PWM) buck converter is a Switched Mode Power Converter which converts dc voltage from a higher value to a lower value. A buck converter employs a MOSFET S and a diode D, an inductor L, and a capacitor C to modulate the input voltage. The output voltage is controlled by controlling the duty ratio of the

MOSFET and hence the name pulse-width modulated buck converter. Conventional buck converters employ a single inductor as the energy transfer element between the input and the load.

The advancements in the microprocessor technology have presented a lot of chal- lenges to the Voltage Regulator Modules (VRM) driving the present day microprocessors. In order to attain higher efficiency, it is advantageous to operate the microprocessors at lower voltages and higher currents as the switching loss in the semiconductor switches is directly proportional to the voltage across it. Currently, the operating point of the microprocessors is around 1.5 V and 100 A [17]-[19]. Further, there is a stringent requirement on the output voltage tolerance. The transient response of the VRM has to be good enough to efficiently meet the dynamic load variations. This imposes restrictions on the values of inductor and the filter capacitor. Under these circumstances, it is not practical to employ a conventional single-phase buck converter as it requires a relatively large filter capacitor. In a polyphase buck converter, two or more single-phase converters are operated in parallel with their drive signals shifted by 180◦. When the individual phases of the converter are switched complimentarily the output voltage ripple reduces considerably due ripple cancelation. If ”n” individual phases are operated in parallel, the frequency of the ripple in output voltage will be n times the ripple frequency of an equivalent single phase converter. Due to reduced magnitude and increased frequency of the output voltage ripple, the filter 64

Figure 53: Circuit diagram of a two-phase buck PWM DC-DC converter. capacitance required reduces signiﬁcantly. Polyphase operation improves the quality of power supplied and enhances the transient response.

4.2 Steady-State Analysis of Two-Phase PWM Buck Con- verter

The circuit diagram of two-phase PWM buck converter is show in Fig. 53 The inductor L1, MOSFET S1 and the diode D1 constitute one phase of the buck converter, similarly, L2, S2 and D2 constitute the second phase of the converter. The MOSFETs

S1 and S2 are switched complimentarily by delaying the gate-drive signal of S2 by 180◦. The diodes are turned on and off depending the state of the current through the inductor in series with it. C is the filter capacitor and RL represents the load. The duty ratio D of the two MOSFETs are considered equal and is equal to 50 (%). The steady-state operation of the converter is divided into two time intervals, i.e, corresponding to S1 and S2 being in the on state or off state complimentarily. I. 0 ≤ t ≤ DT The analysis assumes the converter to be operating in a steady-state condition. In this time interval S1 is on and S2 is off. D1 is reverse biased and D2 is in the on state as the inductor L2 discharges and drives a current through it. The equivalent circuit corresponding to this time instant is shown in Fig. 54. The voltage across the 65

Figure 54: Equivalent circuit of the two-phase buck converter for (0 ≤ t ≤ DT ).

inductor L1 is given by

VL1 = VI − VO. (28)

The potential diﬀerence across L1 results in a current iL1 (T ) which has a rising slope of (VI − VO)/L1. During this period L1 stores energy in the electromagnetic form.

In the next period when S1 is oﬀ, L1 discharges the energy to the load RL through

D1. The switch S2 is in the oﬀ state and L2 discharges the energy stored in it in the previous cycle. The voltage across L2 is a falling voltage given by

VL2 = −VO (29)

resulting in a decreasing current of slope −VO/L to ﬂow through it. The currents in

L1 and L2 due to VL1 and VL2 respectively are given by

1 Z t iL1(t) = (VI − VO)dt + iL1(0) (30) L1 0 1 Z t iL2(t) = (−VO)dt + iL2(T ) (31) L1 0

The currents through L1 and L2 have a rising slope and a falling slope respectively. They exhibit symmetry about the dc load current. As a result, their resultant sum is approximately a constant ripple free dc current. 66

Figure 55: Equivalent circuit of the two-phase buck converter for (DT ≤ t ≤ T ).

II. DT ≤ t ≤ T

In this time interval S2 is on and S1 is oﬀ and D1 is conducting and D2 is reverse biased. The equivalent circuit associated with this time instant is shown in Fig. In comparison to the previous time instant, the MOSFETs S1 and S2 and the diodes D1 and D2 have switched their roles. The voltage and the current associated with L1 are given by

VL1 = −VO (32) and 1 Z t iL1(t) = (−VO)dt + iL1(DT ) (33) L1 DT

Similarly, the voltage and current associated with L2 are given by

VL2 = (VI − VO). (34)

1 Z t iL2(t) = (VI − VO)dt + iL1(DT ) (35) L1 0 Fig. 56 shows the voltage and current waveforms for the steady-state operation of the two-phase buck converter operating in CCM. The waveforms are deduced analytically. 67

Figure 56: Theoretically predicted voltages and currents associated with the steady state operation of a two-phase buck converter in CCM. 68

The filter capacitor establishes a low impedance path for any ac component present in the circuit to flow through it. The current ripple flowing through the capacitor is the sum of the ac components of the currents flowing through the two inductors.

When the current through inductor L1 has a rising slope of (VI − VO)/L1, the current through the inductor L2 has a falling slope of (−V o)/L2 and vice-versa. For D = 0.5 and L1 = L2, the slopes of the two currents are equal and opposite. The individual inductor currents exhibit mirror image like symmetry about the dc load current. This leads to cancelation of current ripple and this is one of the important advantages of two-phase converters over their conventional single-phase counterparts. Since there are two inductors operating in parallel, the frequency of the current ripple is two times the ripple frequency of the equivalent single-phase converter. This reduces the value of the ﬁlter capacitance required. This improves the transient response of the converter and also makes the converter more compact

4.3 DC Voltage Transfer Function and Design Equations

The dc voltage transfer function of the converter gives the relation between the input and the output voltages in terms of the duty ratio D of the MOSFET. Let D1 and D2 be the duty ratios of the MOSFETs S1 and S2 respectively. From the principle of con- servation of energy, the net energy in an inductor over one full cycle of magnetization is zero. By applying the volt-second balance for the inductor L1 we obtain

Z Z D1T T vL1dt = − vL1dt 0 D1T

(VI − VO)D1T = VO(1 − D1)T. (36)

Similarly for L2, we have Z Z T (1−D2)T vL2dt = − vL2dt (1−D2)T 0

(VI − VO)D2T = VO(1 − D2)T. (37) 69

By (36) and (37) we obtain the dc voltage transfer function for a two-phase lossless buck converter V D + D O = 1 2 . (38) VI 2

For D1 = D2 = D, the dc voltage transfer function is VO/VI = D.

In Continuous Conduction Mode the inductor current iL is non zero through out the steady state operation. A minimum value of inductance Lmin is required to keep the converter operation in CCM. If L < Lmin the converter enters the Discontinu- ous Conduction Mode of operation (DCM). At the boundary between CCM/DCM operation, the peak value of the current ripple inductor L1 is given by

(VI − VO)(DT ) ∆iL1 = = iL1(DT ). (39) L1

The average current current ﬂowing through L1 is

∆iL1 (VI − VO) IL1 = . (40) 2 2fSL1 Hence the minimum value of inductance to ensure CCM is given by

(VI − VO) L1min = . (41) 2fSIL1

Similarly, L2min is given by (VI − VO) L2min = . (42) 2fSIL2

If the filter capacitor is sufficiently large, the output voltage ripple Vr, is determined by the ripple voltage across the Equivalent Series Resistance (ESR) of the filter capacitor [class notes]. The ESR of the filter capacitor is determined by the expression

Vr rC = (43) ∆iL The minimum value of the ﬁlter capacitance, beyond which, the output voltage ripple is dependent on the ESR is given by D Cmin = (44) 2frrC 70

where fr is the ripple frequency. For a single-phase converter the ripple frequency is equal to the switching frequency. In a two-phase converter, since there are two inductors operating in parallel the ripple frequency is twice the switching frequency.

For a two-phase buck converter, the expression, in terms of the duty ratio and the switching frequency, for the minimum filter capacitance needed to keep the ripple voltage bellow a specified value is D Cmin = (45) 4fsrC where fs is the switching frequency. The minimum filter capacitor required in a two-phase converter is half of that needed for an equivalent single-phase converter.

This improves the transient response by lowering the corner frequency of the output network of the converter. The component stresses are evaluated based on the idealized voltage and current waveforms of the two-phase buck converter shown in Fig. 56 The voltage and the current stresses on the MOSFETs are

VS1(max) = VS2(max) = VI (46) and I ∆i I = I = O(max) + L(max) (47) S1(max) S1(max) 2 2 respectively. The voltage and the current stresses on the diodes D1 and D2 are the same as that on the MOSFETs.

4.4 Design and Simulation

A two-phase 12 V/ 6 V buck converter with Vr < 60 mV is designed to supply a ﬁxed load of 120 W is designed as per the equations described in Section 4.3. The duty ratios of the two MOSFETs are equal to 50 %. The two inductances are of equal value and a switching frequency of fs = 100 kHz is chosen. The load current is given by

PO IRL = = 20 A. (48) VO 71

The average value of the currents ﬂowing through the inductors are

I I = I = O = 10 A. (49) L1 L2 2

The minimum inductance required to ensure CCM operation is

(VI − VO)D L1(min) = L2(min) = = 1.5 µH. (50) 2fSIL

An inductance of 10 µ H is selected. From (39) we obtain ∆iL1 = 1.5 A. The output voltage ripple is to be less than 1 %, therefore the ESR of the capacitor is

Vr rC = = 40 mΩ. (51) ∆IL

The minimum ﬁlter capacitance required is

D Cmin = = 31.25 µF. (52) 4fSrC

A ﬁlter capacitor of 50 µ F is selected. The two-phase buck converter is simulated using PSPICE with the designed values. IRF6613, International Rectiﬁer power MOS- FET, intended for application in synchronous buck converters and CSD10060 SiC Schottky diode are employed for simulation. The PSPICE simulation model provided by the makers of the MOSFETs and diodes were employed. Fig. 57 shows the simulated input and output voltage of the two-phase buck converter. Fig. 58 shows the inductor currents iL1 and iL2. it is seen that the individual inductor currents are symmetric about IO/2 ≈ 9 A. When the two inductor currents add up, a substantial part of the ripple is canceled as seen in Fig. 59. Fig. 60 shows the simulated load voltage and current for the two-phase buck converter. 72

15 V I V O 12

9 (V) (V)

O , V , I V 6

0 0 50 100 150 200 250 300 t (µs)

Figure 57: Simulated input and output voltage waveforms of the two-phase buck converter.

11 I L 1 10.5 I L 2

9.5 (A)

2 L 9 , I 1 L I 8.5

7.5

7 4.502 4.504 4.506 4.508 4.51 4.512 4.514 4.516 4.518 t (ms)

Figure 58: Simulated current waveforms through the two inductors of the two-phase buck converter. 73

18.1 I + I L L 1 2 I R L 18.05

18 (A)

L R

, I 17.95 2 L + I 1 L I

17.9

17.85

17.8 2.8 2.802 2.804 2.806 2.808 2.81 2.812 2.814 2.816 2.818 2.82 t (ms)

Figure 59: Simulated waveforms of the sum of the two inductor currents and the waveform of the load current.

25 V O 22.5 I O 20

17.5

15 (A)

O I 12.5 (V), (V),

V 10

7.5

2.5

0 0 50 100 150 200 250 300 t (µs)

Figure 60: Simulated output voltage and the current waveforms of the two-phase buck converter. 74

4.5 Conclusions

The operation of a two-phase buck converter was analyzed by the aid of PSPICE simulations. The design equations for a two-phase buck converter operating in CCM were derived and a 12 V-6 V, 120 W, two-phase buck converter was designed and simulated. The design equations were validated by the PSPICE simulation results. Based on the simulation results presented the operation of the 12 V-6 V, 120 W two- phase buck converter was analyzed. The key features such as the reduction in output voltage ripple due to two inductors operating simultaneously were observed. From the simulation results it can be inferred that, even though polyphase operation increases the part count of the system, it oﬀers advantages which are favorable. As an extension of this work, the performance of the converter at D 6= 0.5 can be considered. It will be interesting to see the dynamic behavior of polyphase converters in comparison to single-phase converters. 75

References

[1] Veda Prakash Galigekere and Marian K. Kazimierczuk, “Performance of SiC

Schottky Diodes,” IEEE Midwest Symposium on Circuits and Systems, 2007.

[2] Veda Prakash Galigekere and Marian K. Kazimierczuk, “Eﬀect of SiC Schottky and Si Junction Diode Reverse Recovery on Boost Converter,” Proceedings of

Electrical Manufacturing and Coil Winding Conference, October 22-24, 2007 Nashville, Tennessee, In publication.

[3] Veda Prakash Galigekere and Marian K. Kazimierczuk, “Analysis and Design of a Polyphase Buck Converter,” Proceedings of Electrical Manufacturing and Coil Winding Conference,Proceedings of Electrical Manufacturing and Coil Winding

Conference, Indianapolis, IN, October 23-26, 2005.

[4] A. Elasser, M. H. Kheraluwala, M. Ghezzo, R. L. Steigerwald, N. A. Evers, J.

Kretchmer and T. P. Chow, “A comparative evaluation of new silicon carbide diodes and state-of-the-art silicon diodes for power electronic applications,” IEEE Trans. Ind.Appl., vol. 39, no. 4, pp. 915-921, July/Aug. 2003.

[5] N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics: Converters, Applications, and Design, 3rd Ed., New York: John Wiley & Sons, 2004.

[6] J. G. Kassakian, M. F. Schlecht, and G. C. Verghese, Principles of Power Elec-

tronics, Reading, Mass.: Addison-Wesley, 1991.

[7] A. M. Abou-Alfotouh, A. V. Radun, Hsueh-Rong Chang, and C. Winterhalter,

“A 1-MHz hard-switched silicon carbide dc-dc converter,” IEEE Trans. Power Electronics, vol. 21, no. 4, pp. 880-889, July. 2006.

[8] M. K. Kazimierczuk, “Reverse recovery of power pn junction diodes,” Journal

of Circuits, Systems, and Computers, vol. 5, no. 4, pp. 589-606, July. 1995. 76

[9] K. Shenai, M. Trivedi, and P. G. Neudeck, “Characterization of hard- and soft-

switching performance of high-voltage Si and 4H-SiC PiN diodes,” JIEEE Trans. Electron Devices, vol. 49, no. 9, pp. 1648-1656, July. 1995.

[10] G. Spiazzi, S. Buso, M. Citron, M. Corradin, and R. Pierobon, “Performance evaluation of a Schottky SiC power diode in a boost PFC application,” IEEE Trans. Power Electronics, vol. 18, no. 6, pp. 1249-1253, Nov. 2003.

[11] R. Singh, J. A Cooper, Jr., M. R. Melloch, T. P. Chow, and J. W. Palmour, “SiC power Schottky and PiN diodes,” IEEE Trans. Electron Devices, vol. 49, no. 4, pp. 665-672, Apr. 2002.

[12] Milan M. Jovanovic, Yungtaek Jang, “State-of-the-Art, Single-phase, Ac- tive Power-Factor-Correction Techniques for High-Power Applications - An Overview,” IEEE Trans. Ind. Appl, vol. 52, no. 3, pp. 701-708, June. 2005.

[13] Giorgio Spiazzi, Simone Buso, Massimiliano Citron, Michele Corradin, and Roberto Pierobon, “Performance Evaluation of a Schottky SiC Power Diode

in a Boost PFC Application,” IEEE Trans. Power Electronics, vol. 18, no. 6, pp. 1249-1253, Nov. 2003.

[14] Milan M. Jovanovic, “A Technique for Reducing Rectiﬁer Reverse-Recovery-

Related Losses in High-Power Boost Converters,” IEEE Trans. Power Electron- ics, vol. 13, no. 5, pp. 932-941, Sep. 1998.

[15] Brian T. Irving and Milan M. Jovanovic, “Analysis, Design, and Performance

Evaluation of Flying-Capacitor Passive Lossless Snubber Applied to PFC Boost Converter,” Proceedings of IEEE APEC’02 Conference, 2002, vol. 18, pp. 503- 508, 2002. 77

[16] Milan M. Jovanovic and Yungtaek Jang, “A Novel Active Snubber For High-

Power Boost Converters,” IEEE Trans. Power Electronics, vol. 15, no. 2, pp. 278-284, March 2000.

[17] Xunwei Zhou, Pit Wong, Peng Xu, Fred C. Lee and Alex Q. Huang, “Investi- gation of Candidate VRM Topologies for Future Microprocessors,” IEEE Trans. Power Electronics, pp. 1172-1182, Nov. 2000.

[18] Peng Xu, Jia Wei, Fred C. Lee, “Multiphase Coupled-Buck Converter - A Novel High Eﬃcient 12 V Voltage Regulator Module,” IEEE Trans. Power Electronics, pp. 74-82, No. 2000.

[19] Yuancheng Ren, Ming Xu, Kaiwei Yao, Yu Meng, and Fred C. Lee, “Two - Stage Approach for 12-V VR,” IEEE Trans. Power Electronics, pp. 1498-1505, Nov. 2004.

[20] Kaiwei Yao, Mao Ye, Ming Xu, and Fred C. Lee, “Tapped - Inductor Buck Converter for High - Step - Down DC - DC Conversion,” IEEE Trans. Power

Electronics, pp. 775-780, Nov. 2005.

[21] Jinghai Zhou, Ming Xu, Julu Sun, and Fred C. Lee, “A Self - Driven Soft - Switching Voltage Regulator for Future Microprocessors,” IEEE Trans. Power

Electronics, pp. 806-814, July. 2005.

[22] Yuri Panov, and Milian M. Jovanovi?, “Design Considerations for 12 - V/1.5 - V, 50 - A Voltage Regulator Modules,” IEEE Trans. Power Electronics, pp.

776-783, Nov. 2001.

[23] M. K. Kazimierczuk, Class notes, EE 741-Power Electronics I, Wright State University, Fall 2005. 78

[24] R. D. Middlebrook and S. Cuk, Advances in Switched-Mode Power Conversion,

vols. I, II, and III. Pasadena, CA: TESLAco, 1981.

[25] G. Massobrio and P. Antogetti, Semiconductor Device Modeling with SPICE,

2nd Ed. New York: McGraw-Hill, 1993.

[26] www.irf.com.

[27] www.cree.com.

[28] www.onsemi.com