HIGH-DENSITY MULTIPHASE
DC-DC CONVERTER WITH
INTEGRATED COUPLED INDUCTOR
A Dissertation Presented
By
Wenkang Huang
to
The Department of Electrical and Computer Engineering
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
in the field of
Electrical Engineering
Northeastern University Boston, Massachusetts
May 2017
ii
ABSTRACT
Social media, e-commerce, cloud computing, gaming, and most recently artificial
intelligence all rely more heavily on computing power in data centers, where server
processors, memories and FPGA circuits demand increasing load current with fast slew-
rate and are powered by interleaved multiphase synchronous buck converters. High
efficiency is the most important requirement on power converters in data centers because
of operational cost associated with power consumption and cooling system. Small size is
another critical requirement due to large number of servers packed in the data centers.
Intel processors and semiconductors have been following Moore’s Law for decades, and
therefore, semiconductor devices have shrunk rapidly. However, volume of inductors has
not followed Moore’s Law, and inductors currently dominate power converter size. Both
the mitigation and utilization aspects of inductor coupling are addressed in the
dissertation. Design guidelines are established to minimize unwanted direct inductor
coupling in computer systems based on analysis, magnetic simulation, and experiment.
To utilize the inverse inductor coupling effect, a compact single-turn coupled-inductor
structure is developed to reduce winding loss and makes it possible to utilize ferrite
magnetic material with low core loss. The new inductor structure is suitable for high-
current and fast load slew-rate applications and can be either embedded between PCB
layers of motherboards and POL modules, or co-packaged with loads, such as processors
and FPGAs. Multiphase POL modules are built to demonstrate operation of the new
coupled-inductor structure and to improve power density of the POL modules.
iii
ACKNOWLEDGMENTS
I would like to express my sincere appreciation to my advisor, Prof. Brad Lehman,
for his guidance, patience, motivation, encouragement, and continuous support of my
study and research. His extensive knowledge and creative thinking have been the source
of inspiration for me throughout these years. It was an invaluable learning experience to
be his student.
It is an honor for me to have Professor Vincent Harris and Professor Mahshid
Amirabadi as my committee members. I am truly grateful to them for their insightful
comments and valuable advice.
My sincere thanks also go to graduate student from the CPES, Virginia Tech, Dr.
Yipeng Su for his help and discussions on Maxwell simulation, and to graduate students
and staff at the Power Electronics Group of Northeastern University, Dr. Ting Qian, Dr.
Chung-Ti Hsu, Dr. Qian Sun, and Ms. Lindsay Sorensen for their help and discussions.
I would like to acknowledge the administrative staff at the Department of Electrical
and Computer Engineering of Northeastern University for their countless help.
Finally, I would like to thank my mother, my wife Yixian, and my daughters for
supporting me during my study. I truly appreciate my family, especially my wife, for
encouraging me while I have spent seemingly endless time in research as a part-time
student. Their love, support, and understanding have been extremely important
throughout these years.
iv
TABLE OF CONTENTS
Chapter 1 Introduction …..……………..………………………….………..… 1
1.1 Motivation and Background ……………….……………….…………….… 1
1.2 Power Converters for Computer Processors……….………….…….…….… 4
1.3 Miniaturization of Power Converters ………...…………….……….…….… 8
1.4 Review of Coupled Inductors in Multiphase Converters …….….………… 11
1.5 State-of-the-Art DC-DC Point-of-Load Modules ……….….……...…….… 14
1.6 Dissertation Summary and Outline ……….…………………….……….…. 16
Chapter 2 Analysis, Verification and Mitigation of Inductor
Coupling Effect …………………………………………………... 20
2.1 Existence of Undesired Inductor Coupling Effect in
Commercial Products ………………………………………………………. 21
2.2 Modeling of Coupling Effect in Single-turn Staple-type Inductors ……...… 27
2.3 Consideration of Fringing Flux in Air Gap for Staple-type Inductor
Coupling Effect Modeling ………………………………………….……… 34
2.4 Modeling of Coupling Effect in Multiturn Inductor …………….…………. 37
2.5 Verification of Inductor Coupling Effect …………………………….…….. 41
2.5.1 Verification of Inductor Coupling Effect by Magnetic Simulation ……...… 41
2.5.2 Verification of Inductor Coupling Effect by Experiment ………………..… 46
2.6 Mitigation of Undesired Inductor Coupling …………………….…………. 49
v
2.6.1 Design Guidelines for Inductor Spacing ….…………….……….…………. 49
2.6.2 Alternative Inductors with Minimum Direct Coupling ………….………… 52
2.7 Discussion and Summary ….…………………………….………....…........ 53
Chapter 3 Single-turn Coupled Inductor Structure for Multiphase
DC-DC Converters ……………….………………….……………. 56
3.1 Two-phase Lateral Coupled Inductor …….................................................... 57
3.2 Design and Simulation of Two-phase Coupled Inductor ……..…….……… 62
3.3 Experimental Verification of Single-turn Coupled Inductor Concept …..…. 69
3.4 Extension of Single-turn Coupled Inductor Structure to Multiple Phases .… 75
3.5 Extension of Single-turn Coupled Inductor Structure to Single Phase …….. 78
3.6 Summary ……..………………………………….…….………....……….... 81
Chapter 4 Design Optimization of Single-turn Coupled Inductors ………. 83
4.1 Overview of Lateral Inductor Model ……………..………………………... 84
4.2 Mathematical Model for Single Phase Inductor ………..……………..….... 87
4.3 Mathematical Model Two-Phase Coupled Inductor ….................................. 91
4.4 Design Optimization of Two-phase Coupled Inductor …............................. 96
4.5 Summary …………………………………………………………….......... 103
Chapter 5 Multiphase Point-of-Load Modules ………………………….... 105
5.1 Fabrication and Assembly of Coupled Inductors and
Point-of-Load Modules …………………………………………………… 106
5.2 Point-of-Load Module with Two-phase and Four-phase Single-turn
Coupled Inductors ………..………..…………….……………….……….. 109
5.3 Converter Power Loss Analysis ……………………………………..……. 115
vi
5.4 Summary ………………..………….…………………….………....…...... 116
Chapter 6 Conclusions and Future Work ……………….….……………… 117
6.1 Summary and Conclusions ……………….………………..…………...… 117
6.2 Future Work …………….………….…………………….………....…...... 119
6.2.1 Core Material Investigations ……...………………….….…….…....…...... 119
6.2.2 Power Density Improvement …….…………………….…………...…...... 120
6.2.3 MOSFET RDS(on) Current Sensing …………..………..….………....…...... 120
References …………..………………………………………………………..…... 122
vii
LIST OF TABLES
TABLE 1.1 State-of-the-Art DC-DC Point-of-Load Modules ………………….. 15
TABLE 2.1 Distances and Saturation Current of Inductors in
Four-Phase Converters …………..…..…………………………….. 23
TABLE 2.2 Parameters of 150-nH Inductor Used in Calculation and
Maxwell Simulation ……………..………….…………….……….. 32
TABLE 2.3 Coupling Coefficient of Commonly Used Coupled Inductors …..… 32
TABLE 2.4 Coupling Coefficient of Discrete Multiturn Ferrite Core
Inductor with d = 0 mm ……………………………………….…… 41
TABLE 2.5 Test Conditions in Inductor Coupling Verification Experiment …... 46
TABLE 2.6 Guidelines for Inductor Spacing ………………………………...…. 51
TABLE 2.7 Spacing Recommendations for Different Inductor Values …….…... 51
TABLE 3.1 Dimensions of Two-phase Prototype Coupled Inductors …….…..... 65
TABLE 3.2 Parameters of Two-phase Lateral Coupled Inductors ………..……. 74
TABLE 3.3 Benefits of Interleaved Multiphase Converters …………..…..……. 75
TABLE 4.1 Dimensions of the Optimized Coupled Inductors ………………...... 96
viii
LIST OF FIGURES
Figure 1.1 Activities happened in ONE minute on the internet …….…..…....…. 1
Figure 1.2 Google data center at Lenoir, North Carolina ……...…….....………. 2
Figure 1.3 Power distribution in data center ………………………………....…. 3
Figure 1.4 Moore’s Law and number of transistors in Intel processors .....…..… 4
Figure 1.5 Blade server motherboard …..………………….……..……….....….. 5
Figure 1.6 Block diagram of power converters in a blade server motherboard … 6
Figure 1.7 Two-phase interleaved synchronous buck converter ….…….………. 7
Figure 1.8 Commercial motherboards with small spaces between inductors …... 9
Figure 1.9 Two-phase interleaved synchronous buck converters with
coupled inductor ……………………………………………………. 10
Figure 1.10 PCB layouts that create inductor coupling ………………………..... 11
Figure 1.11 Coupled inductor structures ………………………………………... 12
Figure 1.12 Two-phase lateral coupled inductor structure with LTCC material .. 13
Figure 1.13 Two-phase lateral PCB-embedded coupled inductor
structure with alloy flake composite material ……………….……... 14
Figure 2.1 Misalignment of inductors after reflow in commercially built
multiphase converters …………………………………………….... 23
Figure 2.2 Multiphase converter output voltage waveforms …..…………….... 24
ix
Figure 2.3 Inductor saturation current per phase at different temperatures in
commercially-built multiphase converters ………………………..... 25
Figure 2.4 Switching waveform of one phase coupled to adjacent idle phase … 26
Figure 2.5 Single-turn “Staple” ferrite core inductors ………………….…....... 27
Figure 2.6 Magnetic reluctance model of two single-turn discrete inductors .… 29
Figure 2.7 Calculated coupling coefficient of single-turn inductors …….…….. 31
Figure 2.8 Coupling coefficient of 150-nH inductors from different
reluctance models versus 3-D simulation …………………….…..... 34
Figure 2.9 Fringing flux cross section of air gap …............................................ 35
Figure 2.10 Coupling coefficient of 150-nH inductors from different
reluctance models in the interested d/g range …….……….….…..... 36
Figure 2.11 Structure and placement of multiturn ferrite core inductors ….....…. 37
Figure 2.12 Magnetic reluctance model of two discrete multiturn
ferrite-core inductors …………………………………………......... 39
Figure 2.13 3-D simulation of flux density distribution in two-phase
single-turn ferrite inductors ………………………….….……….… 42
Figure 2.14 Maxwell magnetic transient simulation circuit of two-phase
converter with discrete inductors ………………………….……..… 43
Figure 2.15 Simulated current in two-phase single-turn inductors ………..….… 45
Figure 2.16 Two-phase inductor coupling test boards ……………….…………. 46
Figure 2.17 Measured current waveform in two-phase single-turn inductors .…. 48
Figure 2.18 Two-phase multiturn direct-coupling inductor current
waveforms, L = 360 nH ………………….……………………..….. 49
x
Figure 2.19 New single-turn inductor structure without coupling …………...…. 53
Figure 2.20 Commercial two-phase single-turn non-coupled inductor design …. 54
Figure 3.1 New two-phase single-turn lateral coupled inductor structure ..…... 58
Figure 3.2 PCB layout of two-phase converters with inversely
coupled inductor …………………………………………….…..…. 59
Figure 3.3 Coupling in two-phase single-turn lateral coupled inductor ..….….. 60
Figure 3.4 Front and top views of two-phase embedded coupled
inductor implementations ………….….……………………..….…. 61
Figure 3.5 Exploded perspective view of converter implementation
with two-phase coupled inductor ……….……………………….…. 63
Figure 3.6 Two-phase coupled inductor dimensions and reluctance model …... 64
Figure 3.7 Inductor LB calculation and simulation …………….………..….…. 66
Figure 3.8 3-D simulation of two-phase single-turn ferrite
inductor LB at 40A ……………………………………..…….….…. 67
Figure 3.9 Simulated current in two-phase single-turn inductors with
inverse coupling ……………………………………………………. 68
Figure 3.10 Procedure of building prototype coupled inductor …..………….…. 70
Figure 3.11 Two-phase coupled inductor prototype ………………....…………. 70
Figure 3.12 Current waveform of two-phase inversely-coupled inductor at
1-MHz switching frequency …………………………………….…. 71
Figure 3.13 Measured steady-state inductance LSS and
transient inductance LTR ……………..………………………….…. 73
Figure 3.14 Three-phase single-turn coupled inductor …….………………...…. 76
xi
Figure 3.15 Circuit of three-phase synchronous buck converter with
coupled inductor …….…………………………………………...…. 77
Figure 3.16 Four-phase single-turn coupled inductor …….…………..……...…. 77
Figure 3.17 Circuit of four-phase synchronous buck converter with
coupled inductor …….…………………………………………...…. 78
Figure 3.18 Single-phase single-turn lateral inductor …….…………..……...…. 79
Figure 3.19 Front and top views of single-phase inductor applications …….…... 79
Figure 3.20 Exploded perspective view of converter with
single-phase lateral inductor…………………………….……….…. 80
Figure 4.1 B-H curve of 3F45 magnetic material ……………………………... 85
Figure 4.2 Magnetic field strength of lateral inductor from FEA simulation …. 86
Figure 4.3 Concept of dividing lateral inductor into concentric
circles and ellipses ……………………………..…………………... 87
Figure 4.4 Magnetic field strength of lateral inductor with air gap ………….... 88
Figure 4.5 B-H curve illustrating incremental permeability …………………... 90
Figure 4.6 Inductance variation of single-phase inductor ……….………...…... 92
Figure 4.7 Simulation of magnetic field strength of two-phase
lateral coupled inductor with air gap …….………………….……... 93
Figure 4.8 Magnetic field generated by two conductors in two-phase
coupled inductor …….………………..…………………………..... 95
Figure 4.9 Inductance and coupling coefficient variations with core width …... 97
Figure 4.10 Inductance and coupling coefficient variations with core length ….. 99
Figure 4.11 Inductance and coupling coefficient variations with core height .... 100
xii
Figure 4.12 Inductance and coupling coefficient variations with
distance between conductors …………………..…………….……. 101
Figure 4.13 Magnetic flux and magnetic field density simulation of
inductor LC ……………………………………..…….……..…….. 102
Figure 4.14 Magnetic flux and magnetic field density simulation of
inductor LD …………………………………………….………...... 103
Figure 5.1 Improved procedure of building two-phase prototype
coupled inductor ……………………………….………….………. 107
Figure 5.2 Improved procedure of building four-phase prototype
coupled inductor ……………………………….………….………. 108
Figure 5.3 Stack-up of two-phase and four-phase POL modules from top,
middle to bottom board ……………………………….…..………. 110
Figure 5.4 Circuit of two-phase synchronous buck converter with
closed-loop control ……………………………………….…….…. 111
Figure 5.5 Two-phase synchronous buck converter module and test fixture .... 111
Figure 5.6 Current probing in single-turn coupled inductor …….………….... 112
Figure 5.7 Inductor current waveforms of two-phase synchronous buck
converter module at 1.5 MHz switching frequency …..…….….…. 113
Figure 5.8 Measured steady-state inductance LSS and transient
inductance LTR of inductor LD …………….…………………...…. 114
Figure 5.9 Four-phase POL module with single-turn coupled inductor …...…. 114
Figure 5.10 Power loss distribution at different frequencies in two-phase
synchronous buck module ………………………….……………... 115
xiii
LIST OF SYMBOLS AND ABBREVIATIONS
2-D Two-Dimension
3-D Three-Dimension
AFC Alloy Flake Composite material
A Cross sectional area of inductor core
B Magnetic flux density
CPES Center for Power Electronics System, Virginia Tech
CPU Central Processing Unit
d Distance between two inductors
DBC Direct Bonded Copper
DCR Direct Current Resistance of inductor
DDR Double Data Rate memory
ESR Equivalent Series Resistance of capacitor
FEA Finite Element Analysis
FPGA Field Programmable Gate Array
g Air gap in inductor
GPU Graphics Processing Unit
H Magnetic field strength
l Length of magnetic path
L Self inductance
LTCC Low Temperature Co-fired Ceramic material
xiv
M Coupled inductance
MMF MagnetoMotive Force
N Number of turns in inductor
n Number of phase in multiphase converter
PCB Print Circuit Board
POL Point Of Load
PWM Pulse Width Modulation
R Reluctance of inductor
RDS(on) Drain to Source Resistance in on-state of MOSFET
RMS Root Mean Square
VCCIO Voltage for Input and Output of CPU or GPU
VCORE Core Supply Voltage to CPU or GPU
VDDR Supply Voltage to DDR Memory
VRM Voltage Regulator Module
VSA Voltage for System Agent of CPU or GPU
VTT Termination Tracking Voltage
α Coupling coefficient
ζ MagnetoMotive Force
μ0 Permeability of vacuum
μr Relative permeability
∆γµ Incremental permeability
1
CHAPTER 1 INTRODUCTION
1.1 Motivation and Background
Google search, YouTube, Facebook, Skype, Flickr, Twitter, LinkedIn, Amazon,
Netflix, iCloud, and most recently gaming, such as Pokémon Go, are internet services
that people have increasingly relied upon in recent years. Fig. 1.1 reveals what has
happened in ONE minute on the internet [1], each of which generates internet traffic
volumes and consumes large amount of computing power. Behind all these services stand
data centers around the world. Fig. 1.2(a) shows a Google data center in Lenoir, North
Carolina [2], which houses chassis after chassis of blade servers. Besides the servers in
each data center, there are cooling systems, as shown in Fig. 1.2(b). Cooling accounts for
Figure 1.1. Activities happened in ONE minute on the internet [1].
2
approximately 38% of electricity usage within a well-designed data center, while
thousands of servers and power supplies consume 49% of data center electric power [3],
as shown in Fig. 1.3. The data service providers have been emphasizing high efficiency
in power conversion due to the increasing operational cost, which is mainly for supplying
power consumed by servers and power supplies as well as controlling temperature rise
associated with heat generated by the power loss [4]. Therefore, high efficiency power
conversion has double benefits, lowering the power loss and at the same time reducing
(a) Server chassis
(b) Cooling system
Figure 1.2. Google data center at Lenoir, North Carolina [2].
3
the power required to remove the heat. There is no doubt that high efficiency is a critical
requirement in data centers.
Intel processors have been widely used in central processing unit (CPU), graphics
processing unit (GPU) and double data rate (DDR) memory of servers, storage and
communication systems. A typical server in the data center consists of processors, DDR
and flash memories, memory controller hub, input/output controller hub, and Ethernet
controller, etc. However, most of the power is actually consumed by these Intel
processors, which have been following Moore’s law for more than four decades. The
numbers of transistor inside the Intel processors double every two years [5] and have
increased from 2,300 in the very first generation processor (4004) to 5,560,000,000 in the
latest generation of processor (Xeon Haswell) [6], as shown in Fig. 1.4. The exponential
increases of transistor numbers since 2005 poses serious challenge to converters that
Figure 1.3. Power distribution in data center [3].
4
power these processors, since processor load current is proportional to number of
transistors, although smaller transistor size lowers power loss of unit transistor.
1.2 Power Converters for Computer Processors
Power converters have been developed for different generations of processors, from
low dropout (LDO) regulator powering 15-V, 30-mA load in the early stage, to buck
converter, and most recently to synchronous buck converter. The latest processors have
increasingly challenging power management requirements of up to 300-A load currents at
low voltages of around 1 V and current slew rate as high as 300 A/µs [7]. Very high
efficiency, fast load transient response, reduced space, and low cost are some of the key
demands for these computing systems. In order to meet these requirements, interleaved
multiphase synchronous buck converters have been adopted [8] - [13]. Different
Figure 1.4. Moore’s Law and number of transistors in Intel processors.
0
1,000,000,000
2,000,000,000
3,000,000,000
4,000,000,000
5,000,000,000
6,000,000,000
7,000,000,000
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
Num
ber o
f Tra
nsis
tors
Year
Moore's Law
Number of Transistors
5
techniques, including constant switchovers between power saving modes and phase
shedding, have been used to improve converter efficiency.
The importance of higher efficiency of power supplies, particularly in data center
servers, cannot be understated. To squeeze thousands of servers into chassis in a data
center, small volume is another important specification for the power converters. Fig. 1.5
is one of the blade server motherboards installed in a chassis shown in Fig. 1.2(a), and
Fig. 1.6 shows block diagram of power converters in a server motherboard. Among more
than thirty dc-dc converter rails in the motherboard, two CPUs (VCORE) and four DDR
memories (VDDR) require multiphase Point-Of-Load (POL) dc-dc converters that convert
12-V input voltage to 1.8-V or 1.2-V output voltages respectively. Other important
Figure 1.5. Blade server motherboard.
CPU
CPU
DDR4
DDR4
6
voltage rails include Voltage for System Agent (VSA) of CPUs, Voltage for Input and
Output (VCCIO) of CPUs, and Voltage for Termination Tracking (VTT) of memories.
Figure 1.6. Block diagram of power converters in a blade server motherboard.
7
The focus of this dissertation research is high-density POL converters with integrated
inductor that meet the demanding requirements of small size, high current, fast transient
response, and low voltage.
Fig. 1.7(a) is a two-phase interleaved synchronous buck converter with its switch
node, and inductor waveforms shown in Fig. 1.7(b). The inductor current ripple
(a) Circuit
(b) Waveforms (c) Layout
Figure 1.7. Two-phase interleaved synchronous buck converter.
VOUT
VIN
SW1 IL1
IL2
Q1
Q2
L1
L2
Driv
ers
Q1
Q2
Driv
ers SW2
M1
M2
CIN1
CIN2 COUT12
COUT21 COUT22
COUT11
IL1+IL2
8
cancellation effect shown in the “IL1 + IL2” waveform is due to the phase interleaving
with the two phases conducting 180° out of phase. The phase interleaving makes it
possible to reduce the inductance, and therefore, benefit load transient response. The
power stage in each phase, which consists of two MOSFETs and their driver, can be co-
packaged in a multichip module (M1 or M2) to save space and reduce parasitic
inductance and resistance.
As shown in Fig. 1.7(c), the inductors dictate the size of a high-current multiphase
converter. However, in many ways inductor technology has lagged behind semiconductor
technology development. Inductor size reduction has not followed Moore’s law and is
often the bottleneck to reduce the volume of the switching converters that power the
processors. The intent of this dissertation is to minimize the inductor sizes in power
converters, particularly focusing on target applications that require small size and low
power loss, such as the blade servers in Fig. 1.5.
1.3 Miniaturization of Power Converters
There are different ways to minimize inductor area in the switching converters. The
simplest approach is to place inductors closer to each other while avoiding undesired
inductor coupling. This research discovers that some commercial computer products were
designed with insufficient margins for inductor spacing without recognizing the severity
of inductor coupling. Fig. 1.8 shows multiphase converters in two blade server
motherboards, and the measured spacing between inductors is in the range of 0.279 to
0.457 mm. This research demonstrates that the closeness of inductors causes converter
performance degradation. This issue will be addressed with analysis, simulation,
experiment and recommended layout guidelines in Chapter 2.
9
The second approach of reducing inductor size is to increase switching frequency. A
four-phase integrated voltage regulator is presented in [14], where the regulator runs at
frequency of 233 MHz with surface-mount air-core inductors of 6.8 nH. Even smaller air-
core inductors of 1.8 nH are used in an eight-phase integrated voltage regulator that runs
at 100 MHz [15]. In both cases, the power stages of the converters are implemented in a
90-nm process, and the input voltages are only 1.4 to 2.5 V. A 16-phase voltage regulator
integrated with CPU die in 22-nm process is demonstrated in [16], where the regulator
runs at switching frequency of 140 MHz with air-core inductors implemented with metal
layers. Although small size and proximity of the inductors to load reduce conduction
power loss, the high switching loss is the major reason why the switching frequency in
megahertz range has not been popular in the power converters.
The coupled inductor is another effective approach to reduce inductor area in
converters. Fast load-transient response demands small inductance, since inductor current
slew rate is inversely proportional to inductance in switching converters. However, small
inductance increases steady-state current ripple and therefore MOSFET conduction loss,
(a) Motherboard #1 (b) Motherboard #2
Figure 1.8. Commercial motherboards with small spaces between inductors.
10
which contributes to the lower converter efficiency. To solve the dilemma, coupled
inductors have been proposed [17], [18], [19]. There are two types of inductor couplings,
“direct” coupling in Fig. 1.9(a) and “inverse” coupling in Fig. 1.9(b). The inverse
coupling is an excellent solution, since the inductor is designed so that the equivalent
inductance during transient, LTR, is held at the same value while the steady-state
inductance, LSS, is increased to a larger value to lower conduction loss and improve
efficiency [17]-[33]. The direct coupling, on the contrary, either increases steady-state
(a) Direct coupling
(b) Inverse coupling
Figure 1.9. Two-phase interleaved synchronous buck converters with coupled inductor.
VOUT
VIN
SW1 IL1
IL2
Q1
Q2
L1
L2
Driv
ers
Q1
Q2
Driv
ers SW2
M1
M2
CIN1
CIN2 COUT12
COUT21 COUT22
COUT11
VIN
SW1 IL1
IL2
Q1
Q2
L1
Driv
ers
Q1
Q2
Driv
ers SW2
M1
M2
VOUT
CIN1
CIN2
VOUT
COUT12
COUT22
COUT11
L2
11
current ripple or reduces current slew rate during load transient if the inductance is
increased to keep the same current ripple magnitude [17], [33].
Fig. 1.10 shows printed circuit board (PCB) layouts that may create inductor coupling
between two discrete inductors. The currents of the two inductors in Fig. 1.10(a) are in
the same direction, which has the shortest current paths, and therefore, is commonly used
in the layout of multiphase converter to reduce PCB copper loss. It may introduce
unwanted direct coupling if two inductors are placed close to each other. The currents of
the two inductors in Fig. 1.10(b) are in opposite directions and can create desired inverse
coupling if the distance between inductors is controlled properly.
1.4 Review of Coupled Inductors in Multiphase Converters
The discrete non-coupled inductors are shown in Fig. 1.11(a). Commercial inversely-
coupled inductors are available [34], [35], but the coupled inductor’s “twisted winding”
(a) Direct coupling (b) Inverse coupling
Figure 1.10. PCB layouts that create inductor coupling.
Input Voltage Bus
Input Voltage Bus
Output Voltage Bus
Output Voltage Bus
ModuleM1
Inductor L1
Inductor L2
Module M2
IL1 IL2
Input Voltage Bus, VIN
Output Voltage Bus, VOUT
InductorL1
InductorL2
Module M2
Module M1
IL1 IL2
12
path shown in Fig. 1.11(b) is about three times the winding path length of non-coupled
discrete inductors shown in Fig. 1.11(a). Therefore, the winding loss of coupled inductors
becomes much larger, which limits their applications in high-current regulators.
A special coupled inductor structure with “twisted-core” is proposed in [21], [22],
[23], as shown in Fig. 1.11(c). The winding path is kept straight and short, while the
magnetic core is wrapped around the windings. The twisted-core coupled inductor has a
lower winding loss but a higher core loss. Since the winding loss dominates total inductor
loss in the high-current applications, twisted-core coupled inductor is a better choice in
high-current voltage regulators.
A lateral coupled inductor structure is demonstrated in [27], [28] and [29] to further
reduce the converter size, as shown in Fig. 1.12. The Low Temperature Cofired Ceramic
(LTCC) material with lower permeability is selected for low-profile planar inductor
(a) Non-coupled inductors
(b) Twisted-winding coupled inductor (c) Twisted-core coupled inductor
Figure 1.11. Coupled inductor structures.
13
design and high frequency operation and is embedded between Direct Bonded Copper
(DBC) ceramic substrates. The winding resistance includes silver conductor and silver
traces and can reach 0.6 mΩ in a 40-A POL module design.
The LTCC ferrite material is actually ferrite particles mixed with a ceramic tape
material. Commercial LTCC tape materials with different properties are available from
ESL ElectroScience [36]. The thick-film tape layers can be stacked together, pressed, cut
to desired shapes, and then co-fired in an oven with sintering profile up to 885°C to
create a hard ferrite core. The LTCC ferrite has similar permeability and core loss density
as traditional NiZn ferrite material and has more flexibility in building different shapes of
magnetic cores [37]. The ceramic-based LTCC inductor is suitable for prototyping since
the inductor thickness can be adjusted easily by changing number of the LTCC sheet
layers. However, it has not been widely adopted in industry possibly because of the
relatively higher cost and high temperature involved in the fabrication process of the
material [29].
Magnetic cores of Alloy Flake Composite (AFC) materials have been available
recently. The alloy composite materials are milled to flakes with a high aspect ratio and
(a) Single-turn windings (b) Two-turn windings
Figure 1.12. Two-phase lateral coupled inductor structure with LTCC material (light color indicates conductors on bottom layer).
14
molded to any core shapes. With improvement in alignment and volume ratio of flakes,
the relative permeability of the new material has been increased to several hundred, and
its core loss density is comparable to sintered NiZn ferrites [30] [31]. The advantage of
the soft composite material is the convenience of being cut and drilled with simple
mechanical machines, which is desirable for prototyping.
The alloy flake composite material with low-temperature fabrication process is
chosen to replace the LTCC material [30], [31]. As shown in Fig. 1.13, the inductor is
embedded between PCB layers instead of the more expensive DBC ceramic substrates in
Fig. 1.12. The inductor structure stays the same as in [27], [28] and [29], but the winding
resistance is higher due to the higher resistance of PCB vias and copper traces, which
leads to significant efficiency reduction at heavy loads. Even with PCB vias replaced by
solid pins and thick copper trace of 4 oz, the estimated winding resistance can still be as
high as 1.8 mΩ, which creates large conduction loss in high current POLs [31].
1.5 State-of-the-Art DC-DC Point-of-Load Modules
Table 1.1 shows state-of-the-art dc-dc POL modules from industry and academia. The
three POL modules from 1-A to 10-A output current [38], [39], [40] are monolithic
(a) Single-turn windings (b) Two-turn windings
Figure 1.13. Two-phase lateral PCB-embedded coupled inductor structure with alloy flake composite material (light color indicates conductors on bottom layer).
15
solution with integrated inductors. The switching frequencies are in megahertz range. The
volume is small, and the power density (output power over volume) is higher than 1000
W/in3. As output current of the POLs increases, the switching frequency is lowered to
reduce the power loss. They are co-packaged multichip modules with power devices and
inductor on lead frame [41] or PCB board [42] – [46]. Once the current is above 25 A,
two phases are paralleled and interleaved to enhance the current capacity and reduce the
input and output capacitors. Coupled inductors are used in [27], [31], [44] to take
advantage of the benefits of faster transient response and higher efficiency.
TABLE 1.1 STATE-OF-THE-ART DC-DC POINT-OF-LOAD MODULES
References Input, Output
Voltage (V)
Maximum
Load
Current (A)
Switching
Frequency
(kHz)
Module
Dimensions
(mm)
Inductor
Altera [38] 2.4 - 6.6, 3.3 1 5,000 3 x 3.3 x 1.1 1-phase
Altera [39] 2.4 - 6.6, 3.3 9 4,000 8 x 11 x 1.9 1-phase
Ti [40] 8 - 14, 2.0 10 4,000 9 x 15 x 2.3 1-phase
MPS [41] 4.5 - 18, 3.3 25 1,000 10 x 12 x 4 1-phase
Intersil [42] 4.5 - 20, 3.3 30 500 17 x 17 x 7.5 2-phase, ferrite
Murata [43] 4.5 - 20, 3.3 35 400 25 x 13 x 12 2-phase, ferrite
Intersil [44] 4.5 - 14, 3.3 50 533 18 x 23 x 7.5 2-phase, ferrite,
coupled
Linear Tech [45] 4.7 - 15, 3.3 50 600 16 x 16 x 5 2-phase, ferrite
Delta [46] 8 – 12.8, 3.3 65 450 25 x 13 x 12 2-phase, ferrite
CPES [27] 12, 1.8 40 1,500 12 x 13.2 x 1.8 2-phase, LTCC,
coupled
CPES [31] 12, 1.8 40 2,000 (150 mm2) x
1.8
2-phase, AFC,
coupled
16
The inductor material is ferrite in all two-phase POLs except the two modules with
embedded two-phase coupled-inductors from Center for Power Electronics System
(CPES), Virginia Tech. The power density of the DBC ceramic-based module with
inductor of the LTCC material in Fig. 1.12 is 700 W/in3 [27], while power density of the
PCB based module with inductor of alloy flake composite material in Fig. 1.13 reaches
850 W/in3 [31].
1.6 Dissertation Summary and Outline
The goal of the dissertation research is to achieve higher power density of POL
modules at current of 40 A or higher. Since inductor is the bottleneck that limits
development in switching converters, a compact inductor structure is necessary to
improve current capacity and power density of the POLs. The research involves both
aspects of the inductor coupling in multiphase dc-dc converters, mitigation and
utilization.
1) Mitigation of Unwanted Direct Coupling: The research has demonstrated that the
direct inductor coupling effect exists in commercial multiphase converters and analyzes
quantitatively the coupling coefficient, which is verified by magnetic simulation and
experiment. The guidelines for inductor placement in motherboard designs have been
established to eliminate the undesired direct coupling.
2) Utilization of Inverse Coupling: A new compact coupled inductor structure for
multiphase converters has been proposed so that the inductor can be easily integrated
with power devices and drivers in switching converters and possibly co-packaged with
loads, i.e. processors, Field Programmable Gate Arrays (FPGA), or integrated circuits.
17
The lateral inductor reduces the converter size and at the same time lowers winding and
core losses to increase power capacity.
In summary, inductors dominate the volume of high-current dc-dc converters because
magnetic material technology has not shown size reduction as in semiconductor
technology, which follows Moore’s Law. There are three different approaches to
minimize inductor area in switching converters.
1) Minimizing distance between inductors is the simplest approach for size reduction,
but it creates unwanted direct inductor coupling issues. This is further discussed and
analyzed in Chapter 2.
2) Increasing switching frequency to hundreds of megahertz is effective in reducing
inductor size, but it increases power loss so significantly that it has not been adopted in
high-current high-efficiency converters.
3) Using coupled inductor not only minimizes converter size but also improves
transient response of the converters. A new coupled-inductor structure is presented in
Chapter 3 with design optimized in Chapter 4 and implemented in two-phase and four-
phase POL modules in Chapter 5.
The six chapters of the dissertation are organized as follows.
Chapter 1 presents background and introduction of the research. It then describes the
increasingly stringent requirements of computers on efficiency and size of the power
converters. Different approaches to improve converter efficiency and reduce converter
size are analyzed and compared, which leads to the proposed coupled inductor structure
in this dissertation with improved performance in efficiency, size and transient response.
18
Chapter 2 analyzes and verifies the direct inductor coupling effect in multiphase dc-
dc converters. First, the undesired inductor coupling effect and its impact on performance
in commercial multiphase dc-dc converters is identified and measured, which is followed
by Maxwell transient simulation and experiment to verify the coupling effect through
inductor current waveforms. Then a reluctance model for discrete inductors to calculate
coupling coefficient versus distance between discrete inductors is created and verified by
Maxwell magnetostatic 3-Dimension (3-D) simulation. Based on the simplified model,
design guidelines for inductor placement are established to mitigate the undesired direct
inductor coupling.
Chapter 3 utilizes the inverse inductor coupling effect and develops a new coupled
inductor structure that has small size and lower winding loss for multiphase dc-dc
converters. A two-phase compact inductor structure that addresses the issues of high
inductor winding loss and large size is proposed. A coupled inductor lumped model is
built and verified by magnetic simulation. Following the inductor design procedure
established from the simplified model, two-phase coupled inductors prototype from off-
the-shelf magnetic cores are built for proof of concept in a two-phase converter to
achieve higher power density. In this chapter, the new lateral inductor concept is
extended to single phase where different implementations are investigated to achieve
higher power density in single-phase converters. The two-phase coupled inductor
structure is also extended to multiple phases so that the inverse coupling between phases
is achieved while direct inductor coupling is avoided at the same time.
Chapter 4 optimizes design of the two-phase coupled inductor to achieve better
performance and makes it possible to embed the inductor inside PCB layers of modules
19
and motherboards. A distributed inductor model is created and then used in the
optimization of inductance and coupling coefficient versus length, width, thickness, air
gap, and distance between windings.
Chapter 5 demonstrates the fabrication of single-turn coupled inductors and
implements the PCB-based two-phase and four-phase converters for improvement in
power density and current capacity of POL modules. The designs of two-phase and four-
phase converters are experimentally verified, and current waveforms as well as measured
steady-state and transient inductances of the coupled inductors are shown. This chapter
uses an efficiency tool to predict power loss of MOSFET devices, driver, and inductor
windings in dc-dc converters at different switching frequencies so that an optimum
frequency can be selected.
Chapter 6 provides summary and conclusions of the dissertation and then outlines
proposed future research works.
20
CHAPTER 2 ANALYSIS, VERIFICATION AND
MITIGATION OF INDUCTOR COUPLING EFFECT
This chapter reports (for the first time in [33]), analyzes and verifies the coupling
effect between discrete inductors in multiphase dc-dc converters. The research provides
design guidelines and recommendations on mitigating the undesired direct inductor
coupling effect. The result has been published in [47], and the main research
contributions presented in this chapter are:
1) Identifying Coupling Concerns: Section 2.1 identifies, measures and explains the
qualitative reasons and impact on performance of the inductive coupling effect of the
surface mount inductors in some multiphase commercial dc-dc converters. The issue is
aggravated by manufacturing inaccuracies in inductor placement due to reflow in
soldering process, causing inductors to sometimes become too close to their adjacent
neighboring inductors.
2) Simple Reluctance Models: In Section 2.2, reluctance models are proposed to
calculate coupling coefficient versus distance between discrete inductors and are verified
by Maxwell magnetostatic 3-Dimension (3-D) simulation. The formulas are for single-
turn ferrite core inductor with air gap commonly used in multiphase converters, and the
impact of fringing flux in air gap is also discussed in Section 2.3. It is shown that the
coupling effect exists and the coupling coefficient can reach the value adopted in coupled
inductors. In Section 2.4, the reluctance model for multiphase inductor is presented,
21
which shows that the coupling effect is negligible in this type of inductors. A strength of
this research is that it presents simple models to explain the documented coupling effects
that can be used to create simple design guidelines to avoid the coupling effect.
Fortunately, 3-D simulations models can be accurately approximated with the simple
formula.
3) Verification of the Coupling Effect: In Section 2.5, single-turn inductor current
waveforms from Maxwell transient simulation are presented to demonstrate the coupling
effect of both direct and inverse coupling between adjacent discrete inductors.
Experimental results of basic two-phase synchronous buck converters are also shown to
verify the coupling effect on the shape of current ripple in single-turn and multiturn
inductors.
4) Design Recommendations and Mitigation of the Coupling Effect: Then in Section
2.6.1, design recommendations on mitigating undesired direct coupling are provided. The
simple models from Section 2.2 are used in establishing guidelines for inductor
placement. There is a trade-off between size, spacing, coupling and even inductance
value (gap size) for the designer, and this is fully explained so that the designer can deal
with this real-world problem that has begun to appear in the dc-dc converter industry. In
Section 2.6.2, a new single-turn inductor is proposed as an alternative solution to
eliminate unwanted coupling effect based on analysis of the multiturn inductor. Finally,
in Section 2.7, summary and discussion are presented.
2.1 Existence of Undesired Inductor Coupling Effect in Commercial Products
As described in Chapter 1, the inductor development is much slower than transistor
development in silicon technology, and therefore, inductors are the largest volume
22
components in power switching converters. The spacing between inductors becomes a
limiting factor in reducing the converter size, especially in space-limited applications like
blade servers. The situation becomes even worse in some designs where only small
pockets of space are left for power converters after system signal buses are routed.
Another example is from next generation Intel processors, which require smaller width in
layout of multiphase converters for CPUs so that DDRs can be placed closer to CPUs for
even higher speed communication between them. The distance between inductors has to
be further reduced to fit the converters into the smaller space.
The surface mount soldering aggravates the problem since it is difficult to control the
distance between inductors during reflow process. The inductors may shift during reflow
due to their ability to float on the molten solder, but inductor floating on the surface of
the molten solder is restrained, which creates inductor misalignment. The root causes are
the much heavier weight of inductors than other components and restricted flowing
capability of lead-free solders, which have been introduced in recent years to electronic
product manufacturing.
Fig. 2.1 shows three out of ten commercially built four-phase converter boards that
are tested for this research, each with varied spacing between inductors after the
assembly. The intended spacing between adjacent inductors is around 0.65 mm without
realizing the potential coupling effect by designer, while the actual spacing is measured
by a feeler gauge and shown in Table 2.1. The inductor spacing in Fig. 2.1(a)
corresponding to board #1 is wider than what was designed for because of misalignment
of inductors. Fig. 2.1(b) shows board #3, which represents a typical assembled board.
23
Fig. 2.1(c) shows more uneven spacing in board #5 due to misalignment of inductors,
with one of them even smaller than 0.2 mm.
TABLE 2.1 DISTANCES AND SATURATION CURRENT OF INDUCTORS IN FOUR-PHASE CONVERTERS
Evaluation Boards * Distances between Inductors
(L1 - L4, from left to right in Fig. 2.1) (mm)
Total Saturation
Current at 60 °C (A)
L1 – L2 L2 – L3 L3 – L4
Board #1, Fig. 2.1(a) 0.940 0.940 0.813 238.0
Board #2 1.574 0.533 0.889 229.5
Board #3, Fig. 2.1(b) 1.143 0.584 0.533 227.5
Board #4 0.940 0.406 0.889 225.0
Board #5, Fig. 2.1(c) 2.133 0.381 0.178 199.0
Design Target 1.600 ** 0.650 0.650 250.0
* Test conditions: VIN = 12 V, VOUT = 1.2 V, ROUT = 0.8 mΩ, fSW = 400 kHz, L = 150 nH.
** The extra space is kept for a thermistor used to sense inductor temperature.
(a) Board #1 (b) Board #3
(c) Board #5
Figure 2.1. Misalignment of inductors after reflow in commercially built multiphase converters.
24
An inductor saturation test is conducted on five boards with multiphase Pulse Width
Modulation (PWM) controllers that keep phase interleaving during steady state and load
transients. Since the inductor saturation current changes with temperature, the same
inductor temperatures are maintained in the test of all boards to achieve consistent result.
For each board tested, the following procedure is followed: Apply a dc current load, add
the same 120-A step current with a fixed slew rate of 5 A/μs to the converters, and
increase the dc load until inductor saturation is captured right after the 120-A load step.
The scope probe is attached right to the VOUT side of Inductor L4 for easy detection
of the inductor current spikes. The normal waveform of converter output voltage without
inductor saturation is shown in Fig. 2.2(a). When inductor saturation happens after the
load step on top of the dc load, the inductor current slope increases, which results in
higher peak current within the same duty cycles. As shown in Fig. 2.2(b), the higher
current slope and magnitude generates spikes on output voltage, which is used to trigger
the scope and capture inductor saturation events. During the 120-A load transient
(a) Normal operation. (b) Inductor saturation.
Figure 2.2. Mulphase converter output voltage waveforms.
Vout500 mV/div
Vout500 mV/div
25
response test, the switching frequency is changed slightly but the phase interleaving
relationship is kept by the multiphase PWM controller.
The inductor saturation current decreases with temperature. The saturation current per
phase at different temperatures is shown in Fig. 2.3, while the total inductor saturation
current of each board at 60 °C is recorded in Table 2.1. Each board uses the same
inductor core and value. Board #1 has the highest saturation current due to sufficient
spacing between inductors. Boards #2 to #4 have lower saturation current, which
decreases slightly from Board #2 to #3 to #4 with small reduction in spacing. Board #5 is
the worst case from board assembly and demonstrates a drop of about 10 A/phase in
saturation current comparing to Board #1. The total saturation current variation due to
inductor misalignment in the four-phase converter reaches 39 A, which is more than 15%
of the converter rated output current. This is an indication of direct coupling between
inductors due to insufficient margins for inductor misalignment in assembly and inductor
mechanical dimension (width).
Figure 2.3. Inductor saturation current per phase at different temperatures in
commercially-built multiphase converters.
0
5
10
15
20
25
30
35
40
45
50
55
60
60°C 70°C 80°C
Indu
ctor
Sat
urat
ion
Cur
rent
per
Pha
se (A
)
#1 #2 #3 #4 #5
26
As demonstrated in Section 2.5, the direct coupling changes the shape of inductor
current and increases peak ripple current, which leads to earlier inductor saturation and
jeopardizes MOSFETs in converters. Inductor saturation degrades power converter
performance and computer system reliability in long term.
Besides the reduction of inductor saturation current, the proximity of the inductors
makes it possible to couple switching waveform from an active phase (SW1) to an
adjacent idle phase (SW2) in tri-state, which means that both high-side and low-side
MOSFETs are turned off. Fig. 2.4(b) shows an example of noise coupled to an idle phase
when inductors are very close, while Fig. 2.4(a) is waveform from the converter with
enough space between inductors. The noise spike in Fig. 2.4(b) falsely triggers protection
circuit and creates system issue, since SW2 voltage is the 1.58-V coupled voltage from
SW1 on top of the 1.2-V output voltage, which exceeds the 2.5-V threshold in protection
circuit when inductor distance is less than 0.2 mm.
This is similar to a transformer with secondary winding open when a 12-V input pulse
is applied to primary winding. The coupled output pulse seen on the secondary winding is
(a) Distance = 2 mm. (b) Distance = 0.2 mm.
Figure 2.4. Switching waveform of one phase coupled to adjacent idle phase.
SW14 V/div
SW21 V/div
SW14 V/div
SW21 V/div
2.78 V
1.52 V
27
equal to the input pulse magnitude applied to the primary winding multiplied by the
transformer turns ratio, or coupling coefficient for inductor.
To minimize or eliminate direct coupling between inductors, extra spacing has to be
maintained in the converter designs to ensure enough clearance margin, which wastes
precious area in motherboards and is not practical in some compact designs, e.g. in blade
servers.
2.2 Modeling of Coupling Effect in Single-turn Staple-type Inductors
In the three types of inductors used in multiphase converters, single-turn ferrite core
inductors (the so-called “staple” inductors) are most popular in converters for server
applications because of their lower winding dc resistance and larger saturation current.
The inductance is limited within hundreds of nano-Henries, but the larger current ripple
due to the smaller inductance can be compensated by phase interleaving or higher
switching frequency.
The placement of single-turn type inductors in a two-phase converter is shown in Fig.
2.5 where “d” is the distance between two inductors and “g” represents air gap in the
inductors. To simplify manufacturing process of a series of inductors, the sizes of two
Figure 2.5. Single-turn “Staple” ferrite core inductors.
d, distance between inductors
g, air gap
Upper core
Conductor
Lower core
28
magnetic cores are kept the same while the air gap is adjusted for different inductor
values.
For quick analysis of the inductor coupling effect, a simple lumped inductance model
is derived for approximation of coupling coefficient between discrete inductors. Fig.
2.6(a) shows the equivalent reluctance circuit of discrete inductors L1 and L2 in a two-
phase converter, where ζ1 and ζ2 are MagnetoMotive Force (MMF) sources, and R1, R2,
R3 and R4 are reluctances.
Fig. 2.6(b) shows core structure of discrete inductors L1 and L2 in a two-phase
converter. Each inductor has a single-turn winding. The solid lines represent fluxes
coupled from the winding of one inductor to the winding of other inductor, while the
dashed lines show fluxes that are not coupled.
Equations for self-inductance L, coupled inductance M and coupling coefficient α are
expressed in (2.1), (2.2) and (2.3) respectively, where N is number of turns, which is N =
1 for the staple type inductor:
( )214312
2
//// RRRRRRNL
+++=
))(2(22)])((2[
432
22
1212
2122
1
4321212
12
RRRRRRRRRRRRRRRRRN
+++++++++
= (2.1)
( ) 21
1
21431
1
214312
2
////// RRR
RRRRRR
RRRRRRNM
+⋅
+++⋅
+++=
))(2(22 432
22
1212
2122
1
21
2
RRRRRRRRRRRN
+++++=
(2.2)
))((2 4321212
1
21
RRRRRRRR
LM
++++==α
(2.3)
29
(a) Equivalent magnetic reluctance circuit
(b) Core structure and coupling, front view
(c) Dimensions of magnetic paths, front view
(d) Dimensions of cross section areas, top view (e) Dimensions of cross section areas, side view
Figure 2.6. Magnetic reluctance model of two single-turn discrete inductors.
R3
R2 R1 R1 R2
ζ1 ζ2R4
g
dL1 L2
IL1, L1 Winding IL2, L2 Winding
L2 coupled to L1L1 coupled to L2
d
l2a
l1 l1
l3
g
L1 L2
l4l2b
l2c l2c
l2a
l2b
30
The reluctances R1 and R2 consist of air gap reluctance and magnetic path reluctances,
which are proportional to mean length of magnetic paths l1 and l2 (= l2a + l2b + l2c) shown
in Fig. 2.6(c) and are defined by (2.4) and (2.5). The A1, A2a, A2b, and A2c are cross
sectional areas of inductors corresponding to l1, l2a, l2b, and l2c respectively, as shown in
Fig. 2.6(d) and 2.6(e). The gap reluctance R3 in (2.6) and gap reluctance R4 in (2.7) are
created by the distance between two discrete inductors, while the magnetic path
reluctances in (2.6) and (2.7) are proportional to mean length of magnetic path l3 or l4
and inversely proportional to cross sectional areas A2a or A2b respectively. The μr is
relative permeability of the ferrite core and μ0 is permeability of vacuum.
10
1
101 A
glA
gRrµµµ−
+= (2.4)
br
b
ar
a
cr
c
c Al
Al
Agl
AgR
20
2
20
2
20
2
202 µµµµµµµ
++−
+= (2.5)
ara Adl
AdR
20
3
203 µµµ
−+=
(2.6)
brb Adl
AdR
20
4
204 µµµ
−+=
(2.7)
By using (2.3) - (2.7) of the reluctance model, without considering fringing flux, the
coupling coefficient α versus distance d can be calculated for different inductor values, as
shown in Fig. 2.7(a). The parameters of the 150-nH inductor used in the calculation are
listed in Table 2.2. The coupling coefficient increases with lower inductor value or larger
air gap. When d = 0 mm, i.e. two inductors are placed together, the coupling coefficient
reaches the maximum value of 0.32. This is close to that of coupled inductors commonly
31
used in multiphase converters, as shown in Table 2.3, and therefore, the unwanted
coupling effect should not be ignored in the designs of multiphase converters.
As shown in Fig. 2.7(b), when the distance is normalized relative to air gap, coupling
coefficient curves of all inductors merge, which validates that the ratio of distance to air
gap, d/g, is a better indicator of the coupling effect than either distance or air gap.
(a) Coupling coefficient versus distance
(b) Coupling coefficient versus distance-to-air gap ratio, d/g
Figure 2.7. Calculated coupling coefficient of single-turn inductors.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Cou
plin
g C
oeff
icie
nt
Distance between Inductors (mm)
L=120nH
L=150nH
L=180nH
L=210nH
L=270nH
L=300nH
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 1 2 3 4 5 6 7 8 9 10
Cou
plin
g C
oeff
icie
nt
Distance to Air Gap Ratio
L=120nH
L=150nH
L=180nH
L=210nH
L=270nH
L=300nH
d = g
32
TABLE 2.2 PARAMETERS OF 150-NH INDUCTOR USED IN CALCULATION AND MAXWELL SIMULATION
Parameters Values Unit
Air gap, g 0.12 mm
Relative permeability, µr 1000 --
Length of magnetic paths, l1, l2c 3.97 mm
Length of magnetic paths, l2a,
5.0 mm
Cross sections, A1, A2c 22.5 mm2
Cross section, A2a 27.9 mm2
Cross section, A2b 28.8 mm2
Width, W, W1 7.5, 2.5 mm
Length, LEN 9.0 mm
Height of lower core, HL 3.2 mm
TABLE 2.3 COUPLING COEFFICIENT OF COMMONLY USED COUPLED INDUCTORS
References Inverse Coupling Coefficient Conditions
Wong [17] 0.33 VIN = 5 V, VOUT = 2 V
Zhu [24] 0.622 VIN = 12 V, VOUT = 1.15 V
Su [29] 0.35, 0.6 VIN = 12 V, VOUT = 1.2 V
Wibowo [26] 0.2 VIN = 5 V, VOUT = 1.2 V
For quick evaluation of the coupling effect between discrete inductors, a simple
model is derived. Since µr >> 1, R1 and R2 are dominated by the first terms in (2.4) and
(2.5), and therefore, can be approximated as
101 A
gRµ
≈ (2.8)
11020
2 RA
gAgR
c
==≈µµ
(2.9)
Using R1 ≈ R2, the coupling coefficient in (2.3) can be simplified as
)(23 431
1
RRRR
++=α
(2.10)
33
In normal cases, the approximation that R1 ≈ R2 is reasonable, since A2c = A1 due to
symmetry in the staple-type inductor geometry shown in Fig. 2.6(d). Therefore, for any
staple-type ferrite core inductor, the accurate model without modeling fringing, (2.3) -
(2.7), can be approximated by ‘simplified model’ (2.10) with reasonable accuracy.
Since µr >> 1, R1, R3 and R4 are dominated by the first terms in (2.4), (2.6) and (2.7)
respectively, and therefore, the coupling coefficient in (2.10) can be further simplified as
)11(23
1
221
ba AAA
gd
++=α (2.11)
When distance d between two discrete inductors is equal to air gap g of the inductors,
i.e. d = g, the coupling coefficient becomes 1/7 (≈ 0.14) assuming A1 = A2a = A2b. It
should be noted that the approximation that A2a = A2b is normally reasonable, but there is
a little error for staple-type inductors to approximate A1 to be this value. An interesting
qualitative design formula, however, can be derived by letting A1 = A2a = A2b in (2.11).
gd43
1
+≈α (2.12)
which gives qualitative insight into the influence of the d/g ratio on the coupling between
two staple-type inductors. The simplified equation (2.11) will be used in Section 2.6.1 in
establishing design guidelines on spacing of inductors used in multiphase converters for
high current applications.
The comparison of the accurate coupling coefficient model (2.3) - (2.7) with the
simplified model (2.11) is shown in Fig. 2.8. The flux fringing effect at the air gaps is
also added to the accurate model (2.3) - (2.7) for completeness, as shown in Fig. 2.8, and
34
the analysis is detailed in Section 2.3. The analysis proves that the fringing flux does
increase the inductance based on the reluctance model, but its effect on inductor coupling
coefficient is insignificant when the distance-to-gap ratio, d/g, is small. Therefore, the
reluctance model of (2.3) - (2.7) without modeling fringing effect is sufficient for
inductor coupling calculation.
2.3 Consideration of Fringing Flux in Air Gap for Staple-type Inductor
Coupling Effect Modeling
The discussion in Section 2.2 does not model the 3-D fringing flux of air gaps, g and
d in staple-type inductors. This fringing flux has minimal influence on the coupling
coefficient for the d/g ratios being discussed in this dissertation. This section explains in
more detail the reasons why the fringing flux can be ignored. Specifically, the fringing
flux cross section of the air gaps can be modeled by three separate areas, gap, face and
corner [23], [48], as shown in Fig. 2.9. The overall gap reluctance with fringing flux
Figure 2.8. Coupling coefficient of 150-nH inductors from different reluctance models
versus 3-D simulation.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Cou
plin
g C
oeff
icie
nt
Distance to Air Gap Ratio, d/g
Calculation with Fringing added to (2.3) - (2.7)
Calculation without Fringing, (2.3) - (2.7)
Simplified Calculation without Fringing (2.11)
3-D Simulation
35
considered is equal to gap, face and corner reluctances in parallel, as calculated as in
(2.13) - (2.15).
4//
2//
2// 21
1021
CORNERFACEFACEgg
RRRA
gRRµ
== (2.13)
4//
2//
2// 21
201
CORNERFACEFACE
ad
RRRAdR
µ= (2.14)
4//
2//
2// 21
202
CORNERFACEFACE
bd
RRRAdR
µ= (2.15)
Gap reluctances, the first terms in (2.13) - (2.15), are the same as when fringing flux
of inductor gap is not considered; the face reluctances for air gap g are calculated by
using (2.16) - (2.18), which are derived in [23], [48]; the corner reluctance for air gap, g,
is calculated by following the approximation given in (2.19) for air gap g [23], [49].
The face and corner reluctance equations for air gap d are similar to (2.16) - (2.19) for
air gap g. Replacing the first terms in (2.4) and (2.5), (2.6), and (2.7) by (2.13), (2.14),
and (2.15) respectively, the reluctance model with fringing flux considered is obtained.
Figure 2.9. Fringing flux cross section of air gap.
36
)]1)2(ln(614.0[
22
01
1
++=
gHMW
RL
FACE
µ
π
(2.16)
)]1)2(ln(614.0[
22
0
2
++=
gHML
RL
EN
FACE
µ
π
(2.17)
where
2)21(42
1)21(4
)2( 22
−+++=gH
gH
gHM LLL ππ
(2.18)
4077.0
10
0L
CORNER HgR µµ +
= (2.19)
Fig. 2.10 shows calculation result when the model is applied to the 150-nH inductors
with all the parameters defined in Fig. 2.6 and Table 2.2. The coupling coefficient
calculated with fringing flux is closer to the 3-D simulation than that calculated without
fringing flux when d/g is smaller than 1.2, which is the area where the coupling is more
Figure 2.10. Coupling coefficient of 150-nH inductors from different reluctance models in the interested d/g range.
37
relevant to the analysis in this dissertation. When d/g is larger than 1.2, there is more
discrepancy, although small, from calculation with fringing flux. This is caused by
inaccuracy in RFACE equations at large values of air-gap, d, between two inductors [48].
However, this is the region where the inductor coupling is already very small.
In summary, the effect of fringing flux on inductor coupling coefficient is
insignificant when the distance-to-gap ratio d/g is small, and therefore, the reluctance
model of (2.3) - (2.7) without modeling fringing effect is sufficient for inductor coupling
calculation.
2.4 Modeling of Coupling Effect in Multiturn Inductors
Multiturn ferrite core inductors are used mostly in desktop computer applications,
where low switching frequency, large inductance and low cost are preferred. This section
demonstrates that the coupling effect on this type of inductors is inconsequential and can
be ignored, unlike the staple inductors.
In multiturn ferrite core inductors, the air gap of the ferrite core is fixed, while
different winding turns are built to generate various inductor values. As shown in Fig.
2.11, there are two possible orientations of multiturn ferrite core inductor placement, two
windings in parallel shown in Fig. 2.11(a) or two windings in series shown in Fig.
2.11(b).
(a) Windings in parallell (b) Windings in series
Figure 2.11. Structure and placement of multiturn ferrite core inductors.
38
Fig. 2.12 shows core structure and equivalent magnetic reluctance circuit of multiturn
ferrite core inductors in a two-phase converter. Each inductor has a two-turn winding in
parallel with the other inductor, as shown in Fig. 2.11(a). The solid lines in Fig. 2.12(a)
represent fluxes coupled from winding of one inductor to winding of other inductor,
while the dashed lines show fluxes that are not coupled. Fig. 2.12(b) shows reluctance
circuit, where ζ1 and ζ2 are MMF sources, and R1, R2, R2a, R2b and Rd are reluctances.
Equations for self-inductance L, coupled inductance M and coupling coefficient α are
written in (2.20) - (2.22), where N is number of turns.
)))//2//(2//(2//( 21222221
22
RRRRRRRRRN
RNL
abdba ++++==
(2.20)
.))//2//(2//(2 2122222
22
RRRRRRRRR
RNM
abdba ++++⋅=
21
2
2122
2
21222
2
//2)//2//(2 RRR
RRRRR
RRRRRRR
ab
b
abdb
b
+⋅
++⋅
+++
(2.21)
LM
=α (2.22)
The reluctance R1, R2a, R2b and Rd are proportional to mean length of the magnetic
paths, l1, l2a, l2b and ld, shown in Fig. 2.12(c) and are determined by (2.23) - (2.27). The
cross sectional areas of inductors, A1, A2a, and A2b, are corresponding to l1, l2a (and ld),
and l2b respectively, as shown in Fig. 2.12(d) and 2.12(e). The μr is relative permeability
of the core, and μ0 is permeability of vacuum. Only reluctance R1 involves air gap, g, in
the inductors, while reluctance Rd is controlled by distance, d, between inductors. Similar
to before, various magnetic reluctances can be derived and then used in the calculation.
39
g
d
IL1
g
IL2
g g
(a) Core structure and coupling, top view.
Rd
R2b
ζ1
R2 R1
R2a
R2a Rd
R2b
R2a
R2a
ζ2
R1 R2
(b) Equivalent magnetic reluctance circuit.
(c) Magnetic paths, top view.
(d) Cross sectional areas, front view. (e) Cross sectional areas, side view.
Figure 2.12. Magnetic reluctance model of two discrete multiturn ferrite-core inductors.
40
1010
11
22Ag
AglR
r µµµ+
−=
(2.23)
ba RRR 222 2 += (2.24)
ar
aa A
lR20
22 µµ
= (2.25)
br
bb A
lR20
22 µµ
= (2.26)
aar
dd A
dAdlR
2020 µµµ+
−=
(2.27)
Combining (2.20) - (2.27), the coupling coefficient of two discrete inductors with
windings in parallel can be calculated for different distances. As an example, the
equations are used in computing the coupling coefficient of two 360-nH ferrite core
inductors with windings in parallel. The coupling coefficient is the highest when two
inductors are placed together (d = 0 mm) but is only 0.0020 from the above reluctance
model, as shown in Table 2.4. The same analysis is applied to ferrite-core discrete
multiturn inductors with two windings in series shown in Fig. 2.11(b), and the coupling
coefficient is even smaller, as shown in Table 2.4.
The Maxwell Magnetostatic simulation result of two 360-nH inductors shown in
Table 2.4 confirms that coupling coefficient is very small whether the two multiturn
ferrite-core inductor windings are in parallel or series. As shown in Fig. 2.12(b), instead
of being coupled to the other inductor winding, the fluxes from ζ1 or ζ2 is bypassed by R2
and R2a + R2b + R2a paths, since neither path involves any air gap, and therefore, has
41
very small reluctance. The conclusion is that the coupling effect in multiturn ferrite-core
inductors can be ignored.
TABLE 2.4 COUPLING COEFFICIENT OF DISCRETE MULTITURN FERRITE CORE INDUCTORS WITH D = 0 MM
Ferrite Core Inductors Calculation Maxwell Simulation
360 nH, windings in parallel 0.0020 0.0023
360 nH, windings in series 0.0005 0.0005
2.5 Verification of Inductor Coupling Effect
The verification of the inductor coupling effect includes magnetic simulation and
experiment.
2.5.1 Verification of Inductor Coupling Effect by Magnetic Simulation
The Ansys Maxwell software is used to verify the inductor coupling effect in
multiphase converters. The parameters and dimensions of the inductor used in the
simulations are given in Table 2.2. Flux-density distribution of two typical 150-nH
inductors with direct coupling is obtained from Maxwell “Magnetostatic” analysis, as
shown in Fig. 2.13. The 3-D simulation is run under 5-A dc current condition, since the
coupling coefficient change with inductor dc current is negligible.
The flux density distribution changes with distance between two inductors. When the
distance is 3 mm (distance-to-gap ratio, d/g = 25), there is minimum interaction between
two inductors, as shown in Fig. 2.13(a). The coupling effect starts to become noticeable
when the distance is reduced to 0.5 mm (d/g = 4.2) in Fig. 2.13(b) and to 0.25 mm (d/g =
2.1) in Fig. 2.13(c). When the distance is close to air gap value, the coupling effect
42
(a) Distance d = 3 mm, d/g = 25.
(b) Distance d = 0.5 mm, d/g = 4.2.
(c) Distance d = 0.25 mm, d/g = 2.1.
(d) Distance d = 0.12 mm, d/g = 1.
(e) Distance d = 0 mm, d/g = 0.
Figure 2.13 3-D simulation of flux density distribution in two-phase single-turn ferrite inductors.
43
becomes more obvious, as shown in Fig. 2.13(d) for d = 0.12 mm (d/g = 1) and Fig.
2.13(e) for d = 0 mm (d/g = 0).
The coupling coefficient is also generated from the same “Magnetostatic” simulation
and added to Fig. 2.8 and Fig. 2.10. The direct coupling coefficient increases dramatically
when the distance is smaller than twice the air gap and reaches 0.35 when two inductors
are placed together (d = 0 mm). The simulation matches very well with calculated results
from the reluctance model (2.3) - (2.7). Therefore, for this specific application, it seems
not necessary to use 3-D simulation packages or partial differential equation analysis.
The Maxwell “Transient” analysis is used to simulate inductor current waveforms to
evaluate the impact of inductor coupling on inductor ripple current. The schematic of a
simulation circuit is shown in Fig. 2.14. The circuit includes all the components in Fig.
1.7(a), but the MOSFET pairs are replaced by pulse voltage sources that reproduce the
SW1 and SW2 switch node voltage waveforms. The netlist of the circuit is loaded to the
Figure 2.14. Maxwell magnetic transient simulation circuit of two-phase converter with discrete inductors.
44
simulation tool, and the initial conditions of inductor current are preset. After the
simulation is completed, the output data is used to generate the inductor current
waveform in Fig. 2.15.
Fig. 2.15 shows steady-state inductor current in two single-turn ferrite core inductors
with all the parameters shown in Table 2.2. As shown in Fig. 2.15(a), the coupling effect
is hardly seen in the 150-nH inductor current waveform when the inductor distance is 3
mm with distance-to-gap ratio, d/g = 25.
Fig. 2.15(b) shows current in two inductors with direct coupling and placed close
together (d = 0.25 mm, d/g ≈ 2.1). As shown in Table 2.1, the two inductors may become
this close due to the soldering reflow process for the surface mount staple-type inductors
in multiphase applications. During discharge period of one inductor, its down slope is
abruptly increased immediately after the other phase is turned ON but recovers after the
other phase is turned OFF. This slope change during the other phase ON period results in
the increase of current ripple magnitude from 14.9 A to 15.6 A (+4.5%), which generates
higher MOSFET conduction loss, and therefore, lowers converter efficiency. To keep
inductor current ripple and conduction loss unchanged, the inductance has to be
increased, which may result in slower load transient response.
Fig. 2.15(c) shows current in two inductors with inverse coupling and close to
each other (d = 0.25 mm, d/g ≈ 2.1). During discharge period of one inductor, its down
slope is decreased during the period when other phase is turned ON, which reduces the
current ripple magnitude from 14.9 A to 13.5 A (-9.4%). Therefore, the inverse coupling
either lowers power loss by decreasing current ripple or speeds up load transient response
if the inductance is reduced to keep current ripple magnitude the same.
45
(a) Direct coupling, distance d = 3 mm
(b) Direct coupling, distance d = 0.25 mm
(c) Inverse coupling, distance d = 0.25 mm
Figure 2.15. Simulated current in two-phase single-turn inductors.
-10.0
-7.5
-5.0
-2.5
0.0
2.5
5.0
7.5
10.0
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0
Indu
ctor
Cur
rent
(A)
Time (us)
-10.0
-7.5
-5.0
-2.5
0.0
2.5
5.0
7.5
10.0
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0
Indu
ctor
Cur
rent
(A)
Time (us)
-10.0
-7.5
-5.0
-2.5
0.0
2.5
5.0
7.5
10.0
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0
Indu
ctor
Cur
rent
(A)
Time (us)
46
2.5.2 Verification of Inductor Coupling Effect by Experiment
Several evaluation boards of two-phase synchronous buck converter are built to
verify the analysis and simulation. Fig. 2.16(a) shows an evaluation board for testing the
coupling effect between single-turn ferrite inductors with different distances. Fig. 2.16(b)
is an evaluation board for multiturn ferrite-core inductors with either direct or inverse
couplings. The evaluation boards are tested under the conditions listed in Table 2.5.
TABLE 2.5 TEST CONDITIONS IN INDUCTOR COUPLING VERIFICATION EXPERIMENT
Parameters Values
Input voltage 12 V
Output voltage 1.2 V
Switching frequency 400 kHz
Inductance, single-turn ferrite core 150 nH
Inductance, multiturn ferrite core 360 nH
Load current 0 A or 40 A
Fig. 2.17(a) shows switch node waveform and current in two single-turn inductors
with direct coupling and d = 3 mm. No coupling effect is observed in the inductor current
(a) Single-turn ferrite core inductors (b) Multiturn ferrite core inductors
Figure 2.16. Two-phase inductor coupling test boards.
Two 120nH inductors,d = 3mm
Two 150nH inductors,
d = 0.25mm
2-phase Power Stages with
Drivers
2-phase Power Stages with
Drivers
Two 360nH inductors
2-phase Power Stages with
Drivers
47
waveform. The ripple current magnitude is about 14 A, which is slightly smaller than that
from the simulation shown in Fig. 2.15(a). This is due to the extra small loops (about 40
mm long) inserted for inductor current probing, which adds parasitic inductance in series
with the inductors, and therefore, reduces the inductor current ripple magnitude.
Since each single-turn inductor consists of two pieces of magnetic cores, which
creates uneven surface on the inductors, it is impossible to move two inductors close
enough to run test at d = 0 mm. So the inductor current waveform at d = 0.25 mm is
measured instead. Fig. 2.17(b) shows current waveform of inductors with direct coupling
at d = 0.25 mm, which confirms the direct coupling effect from simulation shown in Fig.
2.15(b). The inductor current ripple is increased to 14.8 A with direct coupling from 14 A
without inductor coupling. Fig. 2.17(c) shows current waveform of inductors with inverse
coupling at d = 0.25 mm, which verifies the inverse coupling effect shown in Fig.
2.15(c). The inductor current ripple is decreased to 13 A with inverse coupling from 14 A
without inductor coupling.
The same switching test is also conducted on multiturn ferrite-core inductors. Fig.
2.18 shows current ripple and switch node waveforms of the converter with two 360-nH
inductors. When the two inductors are close together (d = 0 mm), no inductor coupling
effect is noticeable whether two inductor windings are in parallel or in series. This
supports the analysis in Section 2.4 that multiturn ferrite core inductors will not exhibit
the noticeable coupling effect.
48
(a) Direct coupling, distance d = 3 mm
(b) Direct coupling, distance d = 0.25 mm
(c) Inverse coupling, distance d = 0.25 mm
Figure 2.17. Measured current waveform in two-phase single-turn inductors.
IL15A/div
IL25A/div
Time, 400ns/div
SW110V/div
SW210V/div
Time, 400ns/div
IL15A/div
IL25A/div
SW110/div
SW210V/div
IL15A/div
IL25A/div
Time, 400ns/div
SW210V/div
SW110V/div
49
2.6 Mitigation of Undesired Inductor Coupling
This section presents two approaches to mitigate the undesired inductor coupling.
Section 2.6.1 establishes design guidelines that can be used to minimize direct coupling
by ensuring enough space between inductors. Section 2.6.2 describes alternative inductor
designs that have minimum coupling between inductors placed together.
2.6.1 Design Guidelines for Inductor Spacing
Based on modeling, simulation and test of single-turn inductors with various
dimensions and air gaps as well as multiturn ferrite-core inductors with different
orientations, design guidelines on spacing of these inductors are established.
The simplified model (2.12) is a practical tool and can be used for quick evaluation of
the coupling coefficient of single-turn staple-type discrete inductors. The more accurate
model (2.11) is used here to establish the guidelines. The minimum d/g = 6 is selected
Figure 2.18. Two-phase multiturn direct-coupling inductor current waveforms, L = 360 nH.
IL12.5A/div
IL22.5A/div
Time, 400ns/div
SW110V/div
SW210V/div
50
since it corresponds to coupling coefficient of around 0.05, as shown in Fig. 2.8. Thus,
the coupling effects would just begin to get noticed.
Margins for board assembly and inductor mechanical dimension (width) should be
added. For example, suppose there is a space limitation, the d/g ≥ 6 is recommended for
staple inductors. In the 150-nH examples of this dissertation where the gap of the staple
core is 0.12 mm, then this indicates that the inductors should be placed at least 6 x 0.12
mm = 0.72 mm apart. However, this must include margins for the assembly and inductor
width. As shown in Table 2.1, the spacing variation due to the reflow process for the two
staple inductors might be as large as 0.47 mm. Therefore, depending on the tolerance of
the assembly house, the inductors should have been designed to be up to 1.19 mm (= 0.72
mm + 0.47 mm) apart for these 150-nH inductors, as shown in Table 2.7. However, this
answer depends, also, on the inductance value. For different inductance values and same
core size, the gap is adjusted. Therefore, lower inductance values would need higher
board spacing. For example, the staple inductor with 90 nH on the same core would have
approximate gap of 0.21 mm. In this case, to keep d/g ≥ 6, the distance between the
inductors should be kept 1.26 mm apart. Assuming the same 0.47 mm possible error from
the soldering reflow, then this would lead to a design distance, d ≥ 1.73 mm. This, in fact,
is a design constraint that is sometimes difficult to keep in space saving applications. On
the other hand, if a larger 300-nH inductor is used, then the d/g ≥ 6 may lead to a value,
including manufacturing tolerances, to be as low as d ≥ 0.77 mm.
As examples, Table 2.7 gives specific recommended spacing for more single-turn
inductors with added margins to assembly and width. The air gap corresponding to
different inductor values are also included in Table 2.7.
51
TABLE 2.6 GUIDELINES FOR INDUCTOR SPACING
Inductors Distance-to-gap ratio Comments
Single-turn ferrite
d/g ≥ 15 plus margins for inductor
width and assembly. Minimum coupling. Recommended.
6 ≤ d/g < 15 plus margins for
inductor width and assembly.
Some coupling. Only recommended
for space limited applications.
Multiturn ferrite No limit. No limit on orientation.
TABLE 2.7 SPACING RECOMMENDATIONS FOR DIFFERENT INDUCTOR VALUES
Inductor Parameters
Inductor Air Gap and Recommended Inductor Spacing (mm)
90 nH 120 nH 150 nH 210 nH 300 nH
Indutor air gap 0.21 0.16 0.12 0.08 0.05
Inductor d/g ≥ 15
(with margins for assembly and width)
3.15
(3.62)
2.40
(2.87)
1.80
(2.27)
1.20
(1.67)
0.75
(1.22)
Inductor d/g ≥6
(with margins for assembly and width)
1.26
(1.73)
0.96
(1.43)
0.72
(1.19)
0.48
(0.95)
0.30
(0.77)
In summary, the proposed method in this paper uses simplified formula combined
with manufacturing tolerance to evaluate inductor placement of converters in
motherboards. There are design tradeoffs between coupling, inductance values, current
ripple, and board space. The single-turn inductor models in Section 2.2 and plots of Fig.
2.8 should give flexibility to the designer in understanding the space versus coupling
decisions that must be made. For the multiturn ferrite-core inductors, there is no
restriction on the distance and orientation of the inductor placement since the inductor
coupling effect is negligible.
52
2.6.2 Alternative Inductors with Minimum Direct Coupling
Based on analysis of the multiturn inductors in Section 2.4 and experiment in Section
2.5.2, it is possible that the inductor coupling is minimized even when two discrete
inductors are placed next to each other. It can be explained by the flux distribution of the
two multiturn inductors in Fig. 2.12(a). The solid lines represent fluxes coupled from the
winding of one inductor to the winding of other inductor, while the dashed lines show
fluxes that are not coupled. The flux paths including air gaps have higher reluctances, so
fluxes tend to flow along paths with lower reluctance (no air gap). In Fig. 2.12(b), the two
R1 paths have higher reluctance due to the air gaps, and the two R2 paths and two R2a +
R2b + R2a paths have lower reluctance and bypass the fluxes that create coupling between
windings. Therefore, the inductor coupling in this structure is minimized.
A similar structure can be derived for single-turn inductors that can minimize
inductor coupling even when two inductors are close. Fig. 2.19(a) shows the inductors
proposed, where the air gap in one leg of each inductor is eliminated, while the air gap in
the other leg is kept to adjust the inductor values. The remaining air gap is twice that in
Fig. 2.6(b) to maintain the same inductor value.
Fig. 2.19(b) shows flux distribution in two discrete inductors, where the coupling flux
is bypassed through the two center legs without air gap. This inductor structure is a
perfect solution to applications with stringent space requirement and can replace the
popular single-turn inductor structure shown in Fig. 2.6. The idea can be further refined
for a non-coupled two-phase inductor design, as shown in Fig. 2.20(a). The coupling flux
is bypassed through the center leg without air gap, as shown in Fig. 2.20(b).
53
2.7 Discussion and Summary
The research result in this chapter on undesired inductor coupling can be applied to
motherboard design verification in different ways. For completed PCB designs, different
switching frequencies or inductors can be selected through firmware or Bill of Material
changes to mitigate inductor coupling that causes degradation in performance and
reliability of converters in motherboards. For space-limited designs, a feasibility study
using the approaches in this chapter can be conducted by determining minimum space
(a) Front view
(b) Flux distribution of two inductors
Figure 2.19. New single-turn inductor structure without coupling.
2g 2g
2g
L1 L2
IL1, L1 Winding IL2, L2 Winding
2g
54
required for each inductor. Efficiency may be sacrificed by choosing different inductors
that demand smaller sizes and space, or tradeoff may be made between efficiency,
reliability, and other performance by using different inductor structures that have less or
no coupling issues. For all other motherboard designs, the proposed method provides
guidelines on inductor spacing.
As package sizes shrink and circuit component integration continues to advance,
parasitic inductance will reduce steadily. However, the package miniaturization creates
(a) Front view
(b) Flux distribution of two-phase inductor
Figure 2.20. Commercial two-phase single-turn non-coupled inductor design.
2g 2g
L1 L2
IL1, L1 Winding IL2, L2 Winding
2g 2g
55
new problems due to closeness of components. There are instances in computer
motherboards that have exhibited inductor coupling through magnetic field or noise
coupling through heat sink and PCB traces because of the proximity of components
including inductors, MOSFETs, drivers and controllers. This poses a challenge when
computer systems demand higher current, smaller space, lower cost, and especially
higher di/dt. This chapter demonstrates that technology is reaching a critical point, where
the leakage and stray coupling starts affecting the power converter, and its influence on
system performance cannot be ignored by industry anymore.
In summary, there are several ways to mitigate the negative effect of coupling before
reaching physical limitations on the magnetic components. This chapter has covered the
following first two solutions, and Chapter 3 focuses on the third one.
(1) Minimize distance between components: Follow the design guidelines established
in Section 2.6.1 while keeping enough margins based on analysis in Sections 2.2 and 2.4
and verification in Section 2.5.
(2) Design new inductor structures: Mitigate the coupling while keeping low inductor
resistance and small size using inductor structure similar to the multiturn ferrite inductor
in Fig. 2.12. A special inductor design with minimum direct coupling is presented in
Section 2.6.2.
(3) Create new coupling inductor structures: Achieve inverse coupling so that the
coupling effect can be utilized instead of being mitigated, which is the main topic in
Chapter 3.
56
CHAPTER 3 SINGLE-TURN COUPLED INDUCTOR
STRUCTURE FOR MULTIPHASE DC-DC CONVERTERS
In this chapter, a compact lateral coupled inductor structure with very low winding
resistance is proposed and has been published in [50]. The structure is suitable for both
multiphase and single-phase converters. It can be either embedded in PCB layers of
motherboards and POL modules, or co-packaged with loads, i.e. processors, FPGAs, or
integrated circuits. Specifically, this chapter presents the following research
contributions:
1) New Compact Coupled Inductor with Different Implementations: Section 3.1
presents a single-turn lateral inductor structure with commonly used ferrite material. The
high permeability core material makes it possible to use only single-turn windings instead
of two-turn or three-turn windings. The combination of single-turn windings and lateral
structure reduces the winding resistance to one tenth of a milliohm from the several
milliohms in state-of-the-art coupled inductors, which is critical in low-voltage high-
current dc-dc converters. Five different implementations with inverse coupling are
presented for two-phase converters embedded in motherboards or POL modules to
demonstrate the feasibility in the applications.
2) Coupled Inductor Model, Simulation and Design Procedure: In Section 3.2, a
simplified lumped model and Maxwell simulation demonstrate the inductance and
coupling coefficient relationships with air gap and distance between windings. The model
57
reveals independence of two control parameters of the coupled inductor, so the distance
between windings can be used to control coupling coefficient while the air gap is for
adjusting the inductance. The coupled inductor design procedure is established based on
the simple model and magnetic simulation.
3) Proof of Concept of the Coupled Inductor: In Section 3.3, concept and operation
of the compact coupled inductor are experimentally verified in a basic two-phase
synchronous buck converter. Magnetic core pieces from off-the-shelf inductor cores have
been selected to build the inductors at lab, although the inductor dimensions are not
optimized especially the width and thickness. The inductor current waveforms, steady-
state inductance, and transient inductances are shown. The measured inductance and
coupling coefficient are compared against the design target established in Section 3.2.
4) Extension of the Single-turn Coupled Inductor Structure to Multiple Phases and
Single Phase: In Section 3.4, the lateral single-turn coupled inductor structure is extended
to both three and four phases for higher-current embedded module applications. The
special issue of the multiphase coupled inductors is addressed to maintain inverse
coupling while minimizing direct coupling between any phases. Then in Section 3.5, the
inductor structure is also extended to single phase for portable electronics applications,
where size is more critical but the load current is small. Finally, in Section 3.6, summary
and discussion are presented.
3.1 Two-phase Lateral Coupled Inductor
In the low-voltage, high-current applications, the RDS(on) of low-side MOSFETs, Q2 of
M1 and M2 modules in Fig. 1.7(a), is usually in milliohm range due to the high efficiency
requirement. Any inductor winding resistance higher than a few milliohms contributes to
58
significant power loss increase and therefore efficiency reduction. For POL modules with
small volume and limited thermal capacity, the extra power loss means reduced current
capacity and lower power density.
In high-current, low-voltage dc-dc converters, the length of inductor windings has to
be reduced to lower the winding power loss. Reducing the number of turns by using high
permeability core material is most effective, and the winding length can be further
reduced by changing the inductor structure from vertical to lateral [27].
Fig. 3.1 shows a new lateral coupled inductor proposed for an embedded two-phase
dc-dc converter module shown in Fig. 3.2(a), which is actually an extension to a three-
dimension (3-D) coupled-inductor converter from the two-dimension (2-D) converter
with inverse coupling proposed in the early stages of this research and presented in the
conference paper [33, Fig. 15], as shown in Fig. 1.10(b). As a comparison, the layout of
the 2-D converter is shown in Fig. 3.2(b). The 3-D converter in Fig. 3.2(a) decreases the
inductor power loss by replacing PCB traces by short low-resistance inductor windings.
The ferrite core material used in this coupled inductor has higher permeability than the
LTCC and alloy flake composite materials [27] - [31], which makes it possible to further
decrease the winding loss by reducing number of turns from two or three to only one. The
air gap, g, next to the windings 1 and 2 in Fig. 3.1 is used to adjust the inductance. The
Figure 3.1. New two-phase single-turn lateral coupled inductor structure.
59
lateral inductor in Fig. 3.2(a) is placed close to the power stages to save space and at the
same time eliminate power loss of the extra PCB traces in Fig. 3.2(b).
The relative current direction in windings 1 and 2 in Fig. 3.3 determines the inductor
coupling. Fig. 3.3(a) shows direct coupling since the currents in two windings are in the
same direction [17], [33]. Fig. 3.3(b) shows inverse coupling since the currents are in
(a) 3-D converter with lateral inductor
(b) 2-D converter with discrete inductors
Figure 3.2. PCB layout of two-phase converters with inversely coupled inductor.
60
reverse directions. As demonstrated in [18] and [19], the inverse coupling is necessary for
the improvement of transient response and converter efficiency in applications that
require fast current slew-rate and high efficiency. To achieve inverse coupling in the
proposed inductor structure, several implementations of a two-phase converter are
created. Fig. 3.4 shows front and top views of five proposed implementations of the
inversely coupled inductor in a two-phase converter, where dashed lines represent
components on the bottom side.
Two implementations for POL modules are shown in Fig. 3.4(a) and (b), where the
inductor is sandwiched by two PCB layers with one pair of MOSFETs on top side and
another pair on bottom side. The input voltage, output voltage and control signals of the
module can be connected to the motherboard either laterally or vertically, as shown in
Fig. 3.4(a) and 3.4(b) respectively.
Fig. 3.4(c) shows a converter with the coupled inductor embedded between
motherboard PCB layers. One pair of MOSFETs is on top side of the motherboard, while
the second pair is on bottom side. This layout is similar to those in Fig. 3.4(a) and (b), but
the power loss from connectors between the module and motherboard is eliminated.
(b) Direct coupling (c) Inverse coupling
Figure 3.3. Coupling in two-phase single-turn lateral coupled inductor.
61
(a) In horizontal module (b) In vertical module
(c) In motherboard (d) In horizontal module on motherboard
(e) In horizontal module with one phase in motherboard
Figure 3.4. Front and top views of two-phase embedded coupled inductor implementations.
Module
M1
M2
CIN1
CIN2 COUT12
COUT21
L
M1 CIN1CIN2
COUT11
M2
COUT22
COUT11
COUT21 COUT22
Module
Module
Motherboard
Motherboard
Module
Motherboard
Motherboard
CIN1CIN2
COUT11
M2
COUT21 COUT22
M1
L
MotherboardMotherboard
Module
Motherboard
Motherboard Module
M1
M2
CIN1
CIN2 COUT12
COUT21 COUT22
COUT11
M1
M2
CIN1COUT21 COUT22
CIN1CIN2
COUT11
M2
COUT21 COUT22
M1
CIN1CIN2
COUT11
M2
COUT21 COUT22
M1
CIN2
COUT12 COUT11
L L
Motherboard
Module
Motherboard
Module
CIN1CIN2
COUT11
M2
COUT21 COUT22
M1
M1
M2
CIN1
CIN2 COUT12
COUT21 COUT22
COUT11
L
62
Therefore, the efficiency and thermal performance are improved at the expense of
motherboard area and extra cost associated with inductor embedding process in
motherboard.
Fig. 3.4(d) shows a module with co-packaged coupled inductor and one pair of
MOSFETs, which can be placed onto the motherboard as one component. The second
pair of MOSFETs is placed on top of the motherboard. Fig. 3.4(e) uses the same module
with co-packaged coupled inductor and one pair of MOSFETs as in Fig. 3.4(d), while the
second pair of MOSFETs is embedded inside the motherboard PCB layers, which is
similar to the chip embedded package [51].
Fig. 3.5 is the exploded perspective view of converter implementation with two-phase
coupled inductor shown in Fig. 3.4(a) or (c), where copper traces on the PCB layers are
used for electrical connections of power stage, coupled inductors, input power and
converter output shown in Fig 1.7(a). The four red circles represent Rogowski coils used
in Section 5.2 for inductor current probing. The arrows indicate current directions in
conductors of the two-phase coupled inductor. The current of phase 1 flows from input
VIN on top side to power stage M1, then through inductor L1 winding in the direction
indicated by the arrows, and finally to converter output VOUT on bottom side. The current
of phase 2 flows from input VIN to power stage M2 on bottom side, then through inductor
L2 winding in the direction indicated by the arrows, and finally to output VOUT on top
side. The current in the two phases are in opposite directions to achieve inverse coupling.
3.2 Design and Simulation of Two-phase Coupled Inductor
In this section, a lumped model is derived for relationships of inductance and
coupling coefficient with air gap and distance between windings. The simplified model
63
provides basis for establishing design procedure for coupled inductor and is verified by
magnetic simulations of two-phase coupled inductors.
For quick design of the coupled inductor, a basic reluctance model is created. Fig.
3.6(a) and (b) show the dimensions and equivalent magnetic reluctance circuit of a two-
phase coupled inductor respectively, where ζ1 and ζ2 are MMF sources, R1, and R2 are
reluctances, and l1, and l2 are mean length of magnetic paths. The inductance values and
coupling coefficient are derived in (3.1) – (3.3), where L, M, and α are self-inductance,
Figure 3.5. Exploded perspetive view of converter implementation with two-phase coupled inductor.
64
coupled inductance, and coupling coefficient respectively. The N is number of turns,
which is N = 1 for this single-turn coupled inductor. Since µr >> 1, R1 and R2 are
dominated and can be approximated by the first term in (3.4) and (3.5) respectively. Then
the L and α can be approximated and simplified in (3.1) and (3.3) respectively.
)2
1(2
)(// 21
2202
212
2
212
212
2
ddd
ghdN
RRRRRN
RRRNL
+−⋅≈
++
=+
=µ
(3.1)
212
2
12
21
1
212
2
2// RRRRN
RRR
RRRNM
+⋅
=+
⋅+
= (3.2)
21
2
21
1
ddd
RRR
LM
+≈
+==α (3.3)
hdg
hdgl
hdgR
r 1010
1
101 µµµµ
≈−
+= (3.4)
hdg
hdgl
hdgR
r 2020
2
202 µµµµ
≈−
+= (3.5)
cddl 22 21 ++= (3.6)
(a) Top and front views (b) Equivalent magnetic reluctance circuit
Figure 3.6 Two-phase coupled inductor dimensions and reluctance model.
65
The dimensions of two coupled inductors are shown in Table 3.1. For inductor LB, the
calculated steady-state inductance versus air gap g from the model is shown in Fig.
3.7(a), and the calculated coupling coefficient versus distance d1 between windings from
the model is shown in Fig. 3.7(b), where the negative coupling coefficient represents
inverse coupling. As apparent from (3.3) and Fig. 3.7(b), the coupling coefficient
magnitude reduces with increasing distance between winding but does not change with
air gap g. Therefore, the air gap is an independent control parameter that can be used to
adjust the inductance, while the distances d1 is used to control coupling coefficient of the
inductor.
TABLE 3.1 DIMENSIONS OF TWO-PHASE PROTOTYPE COUPLED INDUCTORS
Dimensions (mm) Inductor, LA Inductor, LB
Length, l 9.0 10.0
Width, w 7.0 + 4.0 7.5 + 6.5
Thickness, h 1.9 3.1
Winding Diameter, c 1.2 1.2
Distance between Winding, d1 2.8 2.8
Distance to Edges, d2 1.9 2.4
Mean Length of Magnetic Path, l1 3.1 3.6
Mean Length of Magnetic Path, l2 8.9 9.7
Air Gap, g 0.08 0.08
The Ansys Maxwell magnetic software is used to verify the model for inductance and
coupling coefficient of the inductor. The “Magnetostatic” simulation runs at 10-A dc
current, i.e. 5 A per phase. The simulated steady-state inductance versus air gap g and
coupling coefficient α versus distance d1 are added to Fig. 3.7(a) and (b) respectively for
comparison. There are some discrepancies between simulation and the simplified
calculation, but they are reasonable for proof of concept development. The calculated
66
inductance is lower than the simulation by 4% to 14%, while the calculated coupling
coefficient is higher than the simulation only by 0.2% to 7%. Therefore, the calculations
from the simplified model (3.1) - (3.5) shown in Fig. 3.7(a) and (b) seem sufficient for
intitial coupled inductor designs.
The flux density and magnetic field of the two-phase coupled inductor are obtained
from the same magnetostatic simulation. Fig. 3.8(a) and (b) show the flux density and
(a) Steady-state inductance versus air gap
(b) Coupling coeficient versus distance between windings
Figure 3.7. Inductor LB calculation and simulation.
0
40
80
120
160
200
0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11
Stea
dy-s
tate
Indu
ctan
ce (n
H)
Air Gap, g (mm)
Simulation, d1 =2.8mm
Calculation, d1 = 2.8mm
Design Target
Experiment
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
Cou
plin
g C
oeffi
cien
t
Distance between Windings, d1 (mm)
Experiment
Design Target
Simulation, g=0.102mm
Simulation, g = 0.076mm
Simulation, g = 0.051mm
Calculation, g = 0.102mm
Calculation, g = 0.076mm
Calculation, g = 0.051mm
2.5 3.0 3.5 4.0 4.5 5.0
67
magnetic field of the inductor respectively at 40 A, i.e. 20 A per phase. The flux density
reaches 0.25 Tesla, while the maximum magnetic field is less than 100 A/m.
The Maxwell “Transient” analysis with simulation circuit in Fig. 2.14 is used to
simulate inductor current waveforms to evaluate the effect of inverse coupling on
inductor ripple current. Fig. 3.9 shows steady-state inductor current in the single-turn
ferrite-core coupled inductor, which demonstrates the inverse coupling effect on inductor
current ripple.
(a) Flux density
(b) Magnetic field
Figure 3.8. 3-D simulation of two-phase single-turn ferrite inductor LB at 40A.
68
Based on the simplified model and simulation, the following procedure is established
for the coupled inductor designs:
1. Preselect the core length l and width w based on the available area for the
converter. Preselect the thickness h based on layers and thickness of motherboard or
module PCB, inside which the inductor is to be embedded. There are limited standard
PCB thickness options to choose from, ranging from 0.8 mm to 3.2 mm.
2. Select winding diameter c per current rating of each phase. The holes are for
winding conductors of the two phases, and the current capacity of each winding should
be higher than one half of the converter load.
3. Decide the distance between windings d1 and distance to edges d2 for the required
coupling coefficient α. As indicated by (3.3), the coupling coefficient is directly
dependent on the distance d1. The distances d1 and d2 are determined by (3.3) and (3.6)
with preselected core length l.
Figure 3.9. Simulated current in two-phase single-turn inductors with inverse coupling.
-40
-30
-20
-10
0
10
20
30
40
6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0
Indu
ctan
ce C
urre
nt (A
)
Time (uS)
L1L2
69
4. Determine air gap g for the desired inductance. As shown in (3.1), the inductance is
related to core thickness h, gap g, and distances d1 and d2. Since the h, d1 and d2 have
already been selected in Steps 1 and 3, the g is the only variable left to determine the
inductance.
5. Recalculate and finalize the core length l from distance d1, distance d2 and winding
diameter c from (3.6).
Two inductors with different thicknesses, LA and LB, are designed following the
procedure, and the target inductance and coupling coefficient of inductor LB are marked
by two dots in Fig. 3.7(a) and (b), where d1 = 2.8 mm and g = 0.08 mm.
3.3 Experimental Verification of Single-Turn Coupled Inductor Concept
Several two-phase coupled inductor samples are built to verify feasibility and
applications in two-phase synchronous buck converter. For inexpensive prototyping and
proof of concept, magnetic core pieces from off-the-shelf inductor cores have been
selected to build the inductors at lab. The inductor dimensions are not optimized
especially width w and thickness h.
Fig. 3.10 illustrates the procedure of building a prototype coupled inductor at lab.
1) Choose two pieces of magnetic cores with sizes close to the design target.
2) Then on the first piece of core, drill two holes with diameter of 1.2 mm, where the
distance between the holes is determined by coupling coefficient. As shown in Fig.
3.7(b), the target coupling coefficient is about -0.46 with distance d1 = 0.28 mm. The
holes are drilled with at least 1 mm off the edge to avoid breaking the drill bit.
3) File and sand the first piece of core to expose the two holes at the edge.
70
4) Use Cyanoacrylate adhesive to glue the second piece to the first piece of core
having exposed holes. The air gap between the two pieces is controlled by inserting small
pieces of paper that has the desired sheet thickness. The thickness of 3 mil (about 0.08
mm) gives steady-state inductance of about 80 nH, as shown by the dot in Fig. 3.7(a).
Fig. 3.11(a) and (b) show two different sizes of coupled inductors, LA and LB, which
are built following the procedure described in Fig. 3.10. The inductors are not
Figure 3.10. Procedure of building prototype coupled inductor.
21
4 3
(a) LA inductor sample (b) LB inductor sample
Figure 3.11. Two-phase coupled inductor prototype.
71
symmetrical in the width dimension after one piece of core is filed, which is not critical
since the extra width in the other piece of core contributes little to the inductance. All
dimensions of the two prototype inductors are listed in Table 3.1. The LA core material is
DMR50B [52], which is equivalent to the 3F35 material from Ferroxcube [53].
The two-phase converter is run under the conditions of 12-V input voltage, 1.2-V or
1.8-V output voltage, 1-MHz switching frequency, and 0-A to 50-A loads. Fig. 3.12(a)
(a) Inductor LA, 1.2-V output voltage
(b) Inductor LB, 1.8-V output voltage
Figure 3.12. Current waveform of two-phase inversely-coupled inductor at 1-MHz switching frequency.
SW2
10 V/div
SW1
10 V/div
IL1
10 A/div
SW2
10 V/div
SW1
10 V/div
IL1
10 A/div
T2
T1
IPP2IPP1
72
and (b) show switch node waveform, SW1 and SW2, and inductor ripple current of one
phase, IL1, of inductors LA and LB respectively. The inverse coupling effect is shown on
the inductor waveform, which helps enhance converter transient response while keeping
the same efficiency, or improve efficiency while keeping the same transient response.
The inductor current ripple, IPP1 and IPP2, and conduction time, T1 and T2, are
measured in Fig. 3.12(b) and repeated for different loads. Based on measurements, the
steady-state inductance LSS, transient inductance LTR, and coupling coefficient α are
calculated by using equations (3.7) - (3.9) [17], [31], where VIN and VOUT are input
voltage and output voltage of the converter.
1
1)(
PP
outinss I
TVVL ⋅−= (3.7)
2
2
PP
outtr I
TVL ⋅= (3.8)
)()1(2
1
TT
LL
LL
ss
tr
ss
tr +−=α (3.9)
The steady-state inductance and transient inductance of inductors LA and LB are
shown in Fig. 3.13(a) and (b) respectively. The LA inductances stay flat at light loads and
start decreasing when the load is higher than 20 A. The reduction of inductance LSS at full
load is less than 7%, which is small for ferrite core inductors with air gap. The LB
inductances start decreasing at lower load (12 A) and at a faster rate. However, the
reduction of inductance LSS is within 22% at full load, which is smaller than the typical
30% for ferrite core inductors with air gap.
The steady-state inductance and coupling coefficient of inductor LB at 10 A are 87 nH
and -0.48 respectively and are marked by two diamonds in Fig. 3.7 (a) and (b). They are
73
close to both the 3-D simulation results (93 nH and -0.47) and the design targets
calculated from the model (80 nH and -0.46) indicated by two dots, which confirms that
the simplified coupled inductor model provides reasonable accuracy.
The steady-state inductance, coupling coefficient, and measured inductor winding
resistances of the two inductors are also shown in Table 3.2 for comparison with other
(a) Inductor LA
(b) Inductor LB
Figure 3.13. Measured steady-state inductance LSS and transient inductance LTR.
0
20
40
60
80
100
0 10 20 30 40
Indu
ctan
ce (n
H)
Load Current (A)
Steady State Inductance
Transient Inductance
0
20
40
60
80
100
0 10 20 30 40 50
Indu
ctan
ce (n
H)
Load Current (A)
Steady State Inductance
Transient Inductance
74
lateral inductors. The LSS inductances are selected for operation at 1 MHz switching
frequency and are smaller than those in [27] [31] due to the reduced turn of windings
from two to one. The higher inductance can be achieved by reducing air gap g while
keeping enough margins for inductor saturation current, which is studied in inductor
design optimization in Chapter 4.
The decrease of winding resistance from milliohms to one tenth of a milliohm is
significant for high-current dc-dc converters with MOSFET RDS(on) in milliohm range.
For example, a reduction from 0.6 mΩ to 0.1 mΩ for a 40-A converter leads to reduced
power loss of only 0.4 W, however, a reduction from 2.0 mΩ to 0.1 mΩ in a 40-A
converter lowers the power loss by 1.5 W, which is equivalent to 3.2% of the total output
power. In a 50-A converter, a reduction from 2.0 mΩ to 0.16 mΩ lowers the power loss
by 2.3 W, i.e. 4.6% of the total output power, since the power loss is proportional to
square of the current through each winding.
TABLE 3.2 PARAMETERS OF TWO-PHASE LATERAL COUPLED INDUCTORS
Parameters Inductance
(nH)
Number
of Turns
Winding
Resistance
(mΩ)
Inductor
Thickness
(mm)
Core Material
Li [27], DBC-based, 40 A 80 2 0.6 1.8 LTCC
Su [31], 40 A, Nonembedded 85 2 2.0 1.2 Alloy Flake Composite
Su [31], 40 A, PCB-embedded 195 2 4.3 1.8 Alloy Flake Composite
Su [31], 40 A, Improved
PCB-embedded 195 2 1.8 1.8 Alloy Flake Composite
Inductor Sample, LA, 40 A 56 1 0.1 1.9 Ferrite
Inductor Sample, LB, 50 A 87 1 0.16 3.1 Ferrite
75
3.4 Extension of Single-turn Coupled Inductor Structure to Multiple Phases
For high-current applications, more than two phases are required to meet the load
current and slew rate requirements [8], [10]. The multiphase converter with paralleled
phases has the advantage of more even thermal distribution. Once the n paralleled phases
are interleaved with phase delay of 360 °/n, the converter has even more benefits, as
listed in Table 3.3. The smaller input Root-Mean-Square (RMS) current reduces number
of input capacitors and their Equivalent Series Resistance (ESR) power loss. The load
transient response is faster, since response delay time is reduced. The output voltage
ripple is also lowered, making it possible to save output capacitors and the space. Smaller
inductance can be selected owing to the benefit of inductor current ripple cancellation, so
inductor size is reduced and inductor slew rate is faster, which further improves transient
response.
TABLE 3.3 BENEFITS OF INTERLEAVED MULTIPHASE CONVERTERS
Converters Single Phase Interleaved Multiphase Benefits
Switching Frequency per Phase fsw fsw Same frequency per phase
Input Capacitor Ripple Frequency fsw n * fsw Higher frequency reduces input
RMS current.
Input RMS Current Iin_rms Iin_rms / n Smaller input RMS current reduces number of input capacitors.
Output Capacitor Ripple Frequency fsw n * fsw Higher frequency reduces output
voltage ripple.
Output Voltage Ripple Vout_ripple Vout_ripple / n Smaller output voltage ripple reduces number of output capacitors.
Transient Response Delay Time T_delay T_delay / n Shorter delay improves transient
response.
Inductance L L / n Smaller inductance can be selected, reducing size and improving transient response.
Inductor Slew Rate di/dt n * di/dt Faster inductor current slew rate improves transient response.
Total Energy Stored in Inductor(s) E_ind E_ind / n
Smaller stored energy reduces output voltage overshoot and undershoot.
76
Therefore, in this section, the two-phase coupled inductor structure is extended to
multiple phases including odd and even phase numbers to take advantage of the benefits
of interleaving phases.
Fig. 3.14(a) shows a proposed three-phase coupled inductor. The three small air gaps
control inductance and coupling between windings 1 and 2 as well as windings between 2
and 3, as shown in Fig. 3.14(b) by the solid ellipses, while a larger air gap between
winding 1 and winding 3 is added to eliminate direct coupling between these two
windings, as shown in Fig. 3.14(b) by the dashed ellipse.
Fig. 3.15 is the schematic of a three-phase synchronous buck converter with the
proposed three-phase coupled inductor, where the dots and arcs indicate inductor
coupling between phases 1 and 2 as well as between phases 2 and 3.
Fig. 3.16(a) shows a proposed four-phase coupled inductor. There is strong inverse
coupling between winding 1 and winding 2 as well as between winding 3 and winding 4,
as shown in Fig. 3.16(b) by the solid ellipses. However, the direct couplings between
windings 1 and 3, as well as between windings 2 and 4, is weaker due to the two extra air
(a) Coupled inductor (b) Top view, coupling paths
Figure 3.14. Three-phase single-turn coupled inductor.
77
gaps along flux coupling paths indicated by the dashed ellipses. With this arrangement,
the inverse coupling is achieved while the direct coupling is minimized.
Fig. 3.17 is the schematic of a four-phase synchronous buck converter with the
proposed four-phase coupled inductor, where the dots and arcs indicate inductor coupling
between phases 1 and 2 as well as between phases 3 and 4.
Figure 3.15. Circuit of three-phase synchronous buck converter with coupled inductor.
VIN
SW1 IL1
IL2
Q1
Q2
L
Driv
ers
Q1
Q2
Driv
ers SW2
M1
M2
VOUT
CIN1
CIN2
VOUT
COUT12
COUT22
COUT11
SW3
IL3
Q1
Q2
Driv
ers
M3CIN3
COUT32
COUT31
(a) The coupled inductor (b) Top view, coupling paths
Figure 3.16. Four-phase single-turn coupled inductor.
78
3.5 Extension of Single-turn Coupled Inductor Structure to Single Phase
In the portable electronics applications, the converter size is one of the most
important specifications although load current is much smaller. The new lateral inductor
structure is a good candidate for reducing size in the converter. The lateral coupled
inductor structure is simplified to a single-phase inductor, as shown in Fig. 3.18.
In Fig. 3.19, the lateral inductor is then employed in dc-dc converters in three
different ways. Fig. 3.19(a) shows an inductor on top of the power stage, which saves
space in height dimension. Fig. 3.19(b) is an inductor embedded between module PCB
layers and connected to a motherboard, which reduces winding length and lowers power
Figure 3.17. Circuit of four-phase synchronous buck converter with coupled inductor.
VIN
SW1 IL1
IL2
Q1
Q2
L
Driv
ers
Q1
Q2
Driv
ers SW2
M1
M2
VOUT
CIN1
CIN2
VOUT
COUT12
COUT22
COUT11
SW3
IL3
IL4
Q1
Q2
Driv
ers
Q1
Q2
Driv
ers SW4
M3
M4
CIN3
CIN4 COUT32
COUT42
COUT31
COUT41
79
(a) Inductor on top (b) Inductor embedded in module
(c) Inductor embedded in motherboard
Figure 3.19. Front and top views of single-phase inductor applications.
M1
CIN1COUT11L
LCIN1
COUT11
COUT12
COUT12
Motherboard
Motherboard
M1 CIN1
COUT11L
CIN1
COUT11
COUT12
COUT12
Module
Motherboard
Motherboard
SW1
M1
M1 CIN1
COUT11
L
COUT11
COUT12
COUT12
Motherboard
SW1
L
CIN1M1
(a) Single-phase inductor (b) Top view
Figure 3.18. Single-phase single-turn lateral inductor.
80
loss. The input power and control signals are connected to the module from the
motherboard through connectors. Fig. 3.19(c) shows an inductor embedded between PCB
layers in a motherboard, where connectors between the module and the motherboard are
eliminated to further reduce power loss.
Fig. 3.20 is the exploded perspective view of a converter with the single-phase
inductor implementation shown in Fig. 3.19(c). The current flow is from power supply to
converter input VIN, then to power stage M1, through inductor L1 winding in the direction
indicated by the arrows, to load through output VOUT, and finally back to the power
supply ground.
Figure 3.20. Exploded perspetive view of converter with single-phase lateral inductor.
81
3.6 Summary
Inductor always dominates the volume of high-current dc-dc switching converters.
This chapter explains how the proposed coupled inductor with inverse coupling not only
minimizes the inductor size for space-limited applications but also reduces the transient
inductance, which improves the transient response in the multiphase dc-dc converters for
fast current slew-rate applications. The research in this chapter includes:
1) The combination of single-turn windings and lateral structure lowers the winding
resistance from up to several milliohms to one tenth of a milliohm range, which is critical
in low-voltage high-current dc-dc converters. Five different implementations of two-
phase coupled inductor embedded in motherboards or POL modules are illustrated to
demonstrate the feasibility in applications.
2) The simple lumped inductance model reveals the independence of two control
parameters of the coupled inductor, distance d1 between windings for controlling
coupling coefficient and air gap g for adjusting the steady-state inductance. The coupled
inductor design procedure is established based on the simplified model and used in the
coupled-inductor prototype designs.
3) The concept and operation of the compact coupled inductor are experimentally
verified by a basic two-phase synchronous buck converter with inductor built from off-
the-shelf magnetic cores. The measured winding resistance, inductance and coupling
coefficient of the single-turn coupled inductor compare favorably with state-of-the-art
coupled inductors using different core materials and two-turn or three-turn windings.
4) The lateral single-turn coupled inductor structure has been extended not only to
multiple phases to meet the higher current and fast transient-response requirements but
82
also to single phase to satisfy the smaller size demands in portable electronics
applications. Single-turn coupled inductors of one-phase, three-phase, and four-phase are
presented.
83
CHAPTER 4 DESIGN OPTIMIZATION OF SINGLE-
TURN COUPLED INDUCTORS
This chapter presents a mathematical distributed inductor model developed for
optimization of the two-phase coupled inductor design. It is more accurate than the
lumped inductor model developed in Section 3.2 and provides a faster inductor design
tool than the Finite Element Analysis (FEA) magnetic simulation. Specifically, the
research contributions in this chapter include:
1) Overview of Distributed Lateral Inductor Model: Section 4.1 presents an
overview of FEA simulation and analytic models for low-profile lateral inductor. The
FEA simulation is time consuming, so analytic distributed model is used to address the
issue of non-uniform flux distribution in the lateral core.
2) Distributed Mathematical Inductor Model: Section 4.2 develops a mathematical
distributed model for single-phase inductor with air gap. When a core is divided into
large enough number of circles, the flux inside each circle is uniform. The total inductance
is the sum of inductance from each circle.
3) Distributed Mathematical Coupled Inductor Model: Applying similar methods
used in Section 4.2, Section 4.3 introduces a distributed model for the coupled inductor
with air gap. The magnetic core is divided into several sections to calculate inductance
and coupling coefficient. The distributed model is used to replace the tedious magnetic
simulation and expedite design optimization process.
84
4) Optimization of Two-phase Single-turn Coupled Inductors: Based on the derived
models, Section 4.4 presents optimization of the two-phase coupled inductor to improve
performance of the prototype inductors demonstrated in Chapter 3, where the inductors
are designed only for proof of concept but not optimized due to limitation in available
materials and manufacturing process. The inductor parameters, including length, width,
thickness, air gap, and distance between conductors are optimized to reduce inductor size,
lower inductor core loss, and push the power density and current capacity to higher
levels. Finally, in Section 4.5, summary is presented.
4.1 Overview of Lateral Inductor Models
Computer aided design tools have been widely adopted in the magnetic component
design, and the FEA simulation has become one of the most frequently used methods for
solving electromagnetic problems. Ansys Maxwell is an electromagnetic field simulation
software for designing and analyzing 3-D and 2-D electromagnetic devices. It uses the
accurate finite element method to solve static, frequency-domain and time-varying
electromagnetic fields. Once the geometry and material properties are specified, Maxwell
will automatically generate an appropriate and accurate mesh for solving the problem.
This automatic adaptive meshing process and accuracy of the numerical technique have
already been proved [54].
The FEA has been successfully used in inductor design and predictions. Several
authors [55] [56] report consistent results of the FEA simulation verified by experimental
measurements. The FEA models based on Maxwell 3-D simulation for the lateral
inductors will be used as baseline for the analytic inductor models in this chapter.
85
Fig. 4.1 is the typical curve of magnetic flux density, B, versus magnetic field
strength, H, of magnetic material 3F45 from Ferroxcube [57] used in the FEA simulation.
The DMR51 [58] is another material used in the research and is equivalent to the 3F45.
Fig. 4.2 displays the FEA simulation of magnetic field strength distribution in a single-
phase lateral inductor. From the simulation, it is evident that the field strength is unevenly
distributed, which is different from the assumptions of the lumped inductor model
developed in Section 3.2.
The FEA inductor models provide results that are more precise but is time consuming
in inductor design, especially in design optimization when repeated simulations are run
with multiple parameters varied. The lumped model in Section 3.2 is simple and easy to
use, but it has inaccuracies and might only be used for initial estimation of inductor
design. To achieve design accuracy and expedite design optimization at the same time, a
more accurate analytic model is favored to replace the time-consuming FEA simulation.
Figure 4.1. B-H curve of 3F45 magnetic material.
0
50
100
150
200
250
300
350
400
450
0 100 200 300 400 500 600 700 800 900 1000
B (m
T)
H (A/m)
86
Using the FEA simulation, it is possible to observe that the flux lines around the
conductor can be approximated by circles or ellipses. Based on this approximation,
methods were proposed in [27], [59], [60], and [61] to create analytic models for the
planar inductors with non-uniform flux and permeability. With this method, the planar
inductor is divided into multiple small concentric circles for round conductor [27] [59] or
ellipses for rectangular conductor [27] [60], as shown in Fig. 4.3. It assumes that flux inside
each circle or ellipse is uniform, and therefore, inductance can be calculated for each circle or
ellipse based on equations used in the lumped model. If the number of circles or ellipses is
infinite or large enough, the sum of inductance of all the circles or ellipses can give accurate
total inductance of the planar inductor.
Figure 4.2. Magnetic field strength of lateral inductor from FEA simulation.
87
4.2 Mathematical Model for Single Phase Inductor
In the past analytic models for the lateral inductors [27], [59], [60], [61], no air gap is
involved. Fig. 4.4 shows the flux distribution of a lateral inductor with air gap from FEA
simulation, which indicates that the flux is still not uniform with the added air gap.
(a) Circles for round conductor
(b) Ellipses for rectangular conductor
Figure 4.3. Concept of dividing lateral inductor into concentric circles and ellipses.
88
Although the approximation method with circles still applies, modifications to the past
models are required to include impact of the air gap. The flux lines are not exactly circles
especially in the areas near the conductor. However, the flux lines are very close to round
rings, so they are still approximated by circles in the model and have been verified that
there is reasonable accuracy. The other effects of the air gap on the modeling include
reduced magnetic field strength and incremental permeability, which are considered in
the following equations.
For lateral inductor without air gap, when current through the conductor is IDC, the
magnetic field strength HDC of each circle can be calculated according to Amperes Law,
)(2 C
DCDC rr
INH−⋅
⋅=
π (4.1)
where N is the number of inductor turns, which is N = 1 for single-turn inductor, and rc is
radius of the conductor and r is radius of the circle in a magnetic core, as shown in Fig.
4.3(a).
Figure 4.4. Magnetic field strength of lateral inductor with air gap.
89
After adding air gap to the core, the field strength in the core has been changed
according to Ampere Law and continuity of magnetic flux. Following procedure in
Section 9.7 in [62], the field strength is derived for common inductors.
g
CrC
DCDC
AAgl
INH⋅
⋅⋅+
⋅=
0
0
µµµ (4.2)
where g, Ag, and µ0 are length, cross sectional area and permeability of the air gap
respectively, and lC, AC, and µr are length, cross sectional area and relative permeability
of the core respectively.
For single-turn lateral inductor with air gap, (4.2) can be simplified to (4.3) since N =
1, AC = Ag, and lC = 2π ( r- rC) when field density distribution is approximated by circles.
rC
DCDC grr
IHµπ ⋅+−⋅
=)(2
(4.3)
Equations (4.4) – (4.7) are used to derive the effective permeability of magnetic core
with air gap [63]. The equivalent inductance of the common inductor with air gap is,
gCr
C
gCr
Ce
Ag
Al
N
Ag
Al
NL+
⋅
⋅=
⋅+
⋅⋅
=
µ
µ
µµµ
20
00
2 (4.4)
For lateral inductor, AC = Ag, so (4.4) can be simplified to (4.5).
glANL
r
C
Ce
+
⋅⋅=
µ
µ 20 (4.5)
The equivalent inductance of an inductor with air gap can also be written as follows,
where µe is the effective permeability.
90
e
C
C
Ce
Ce l
AN
AlNL
µ
µ
µµ
⋅⋅=
⋅⋅
=2
0
0
2
(4.6)
Comparing (4.6) with (4.5), we obtain the effective permeability of inductor with air
gap.
gll
r
C
Ce
+=
µ
µ (4.7)
Incremental permeability, µr∆, is defined as gradient of the flux density to
magnetizing force (B/H) curve, i.e. µr∆ = ∆B/∆H. This represents the
effective permeability for a small alternating field superimposed on a larger steady field.
The incremental permeability of a magnetic material without air gap can be obtained
from the curve provided in the datasheet by manufacturers, as shown in Fig. 4.5. Curve-
fitting is used to determine the relationship between incremental permeability µr∆ and
HDC. As an example, the incremental permeability of the 3F45 material is as follows.
Figure 4.5. B-H curve illustrating incremental permeability.
0
50
100
150
200
250
300
350
400
450
0 100 200 300 400 500 600 700 800 900 1000
B (m
T)
H (A/m)
∆H∆B
∆B
∆H
91
2538411 1043.71054.71077.2)( DCDCDCDC HHHH ⋅⋅+⋅⋅−⋅⋅= −−−
∆γµ
93.41015.3 2 +⋅⋅+ −DCH (4.8)
When air gap is included in a core, the equivalent incremental permeability is
determined as in (4.7), where lC = 2π (r- rC) for lateral inductor when field density
distribution is approximated by circles.
gH
rrrr
gHl
lH
DC
C
C
DC
C
CDCe
+−⋅
−⋅=
+=
∆∆
∆
)()(2
)(2
)(
)(
γγ
γ
µπ
π
µ
µ (4.9)
The inductance of each circle is calculated as,
)(2)(
C
DCeUNIT rr
NhHL
−⋅⋅⋅
= ∆
πµ γ (4.10)
where h is height of the core. The total inductance is integration of the inductance from
every circle, with the integration from edge of the conductor hole, rc, to edge of the
magnetic core, re.
∫ −⋅⋅⋅
= ∆e
C
r
r C
DCe drrr
NhHL
)(2)(
πµ γ (4.11)
Using (4.3), (4.5), (4.8), (4.9) and (4.11), inductance of a lateral inductor with
different heights and widths is calculated, as shown in Fig. 4.6(a) and (b), which indicates
that the inductance is proportional to height and width.
4.3 Mathematical Model for Two-phase Coupled Inductor
The lumped model of the two-phase lateral coupled inductor is employed in Section
3.2 for preliminary inductor design although there is insufficient accuracy. As in the
92
single phase inductor, optimization of the coupled inductor design requires an analytic
distributed model to expedite design process.
(a) Variation with core height
(b) Variation with core width
Figure 4.6. Inductance variation of single-phase inductor.
0
10
20
30
40
50
60
70
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Indu
ctan
ce (n
H)
Core Height (mm)
Gap = 0.06 mm
Gap = 0.08 mm
Gap = 0.1 mm
0
10
20
30
40
50
60
70
3 4 5 6 7 8 9
Indu
ctan
ce (n
H)
Core Width (mm)
Gap = 0.06 mm
Gap = 0.08 mm
Gap = 0.1 mm
93
The FEA is used to simulate magnetic field strength of the coupled inductor, as
shown in Fig. 4.7. The simulation shows that the flux lines are close to circular shape in
some areas and to elliptical shape in other areas. The simulation also displays non-
uniform distribution of magnetic field. To apply the approximation method used in the
modeling of single-phase lateral inductor to the two-phase coupled inductor,
simplification needs to be made.
Assuming only Phase 1 conducts current while the current in Phase 2 is zero, the
magnetic field is similar to single phase. However, the magnetic field distribution is
different due to the asymmetry of conductor position in the core. Fig. 4.8(a) illustrates the
magnetic field generated when a current flows through conductor of Phase 1 only. The
core is divided into five sections. The magnetic field in each section is approximated by
circles with different diameters and then multiplied by a factor that is percentage of each
sectional area to the total core area. Inductance is calculated in each section and then
Figure 4.7. Simulationm of magnetic field strength of two-phase lateral coupled inductor with air gap.
94
summed to obtain total inductance contributed from Phase 1. The same method is
repeated for Phase 2, as shown in Fig. 4.8(b).
The inductance of each section is calculated in a similar method presented for single-
phase inductor in Section 4.2. The inductances of the five areas are marked L11, L12, L13,
L14, and L15, as shown in Fig. 4.8(a) and L21, L22, L23, L24, and L25 in Fig. 4.8(b). Each
inductance is calculated following the procedure in Section 4.2 before (4.12) - (4.15) are
applied, where the arctan function is used to determine percentage of each triangle
sectional area relative to the whole rectangular core area.
ππµ γ 1)arctan(
)(2)(
12111
1
⋅⋅−⋅
⋅⋅== ∫ ∆
lwdr
rrNhH
LLl
r C
DCe
C
(4.12)
ππµ γ 1)
2arctan(
)(2)( 21
2
23221312 ⋅+
⋅−⋅
⋅⋅==== ∫ ∆
wlldr
rrNhH
LLLLw
r C
DCe
C
(4.13)
ππµ γ 1)arctan(
)(2)(
22414 ⋅⋅
−⋅⋅⋅
== ∫−
∆
lwdr
rrNhH
LLC
C
rd
r C
DCe (4.14)
ππµ γ 1)arctan(
)(2)(
22515
2
⋅⋅−⋅
⋅⋅== ∫
+
∆
lwdr
rrNhH
LLl
rd C
DCe
C
(4.15)
After inductance from each phase is calculated, superposition theorem is applied to
find self inductance and mutual inductance of the two-phase coupled inductor.
15141312111 LLLLLL ++++= (4.16)
25242322212 LLLLLL ++++= (4.17)
1513121112 LLLLM +++= (4.18)
2523222121 LLLLM +++= (4.19)
The coupling coefficient is the ratio of mutual inductance over self inductance.
95
1
1212 L
M=α (4.20)
2
2121 L
M=α (4.21)
(a) Magnetic field generated by current in Conductor 1
(b) Magnetic field generated by current in Conductor 2
Figure 4.8. Magnetic field generated by two conductors in two-phase coupled inductor.
96
where 12α and 21α are equal due to the symmetry in structure of the two-phase coupled
inductor.
4.4 Design Optimization of Two-phase Coupled Inductor
The two-phase single-turn coupled inductors presented in Chapter 3 are for proof-of-
concept, and some dimensions are not optimized, especially the core width and thickness.
The objective of this section is to design a two-phase coupled inductor, which are to be
embedded in the PCB based POL modules. The design optimization is necessary for
integration with other components in the modules, and the dimensions to be optimized
include core width, length, thickness, distance between conductors, and air gap. After
going through the optimization process, the parameters in Table 4.1 are obtained for
inductors LC and LD. Different coupling coefficients from these two inductor options
provide flexibility in meeting transient response requirements. How these parameters are
determined will be demonstrated and explained in rest of this section.
TABLE 4.1 DIMENSIONS OF THE OPTIMIZED COUPLED INDUCTORS
Dimensions (mm) Inductor, LC Inductor, LD
Length, l 14.0 14.0
Width, w 8.0 10.0
Thickness, h 1.3 1.5
Winding Diameter, c 1.2 1.2
Distance between Winding, d1 5.4 4.0
Distance to Edges, d2 4.3 5.0
Air Gap, g 0.08 0.08
97
The core width w is optimized first to meet the size requirement. The core width in
the prototype in Chapter 3 is too large and should be reduced for integration with other
components in the POL modules. Fig. 4.9(a) shows inductance variation with the width.
It is counterintuitive that the inductance does not drop significantly when the width is
reduced from 12 mm to 5 mm.
(a) Inductance versus core width
(b) Coupling coefficient versus core width
Figure 4.9. Inductance and coupling coefficient variations with core width, w.
0
10
20
30
40
50
60
70
80
4 5 6 7 8 9 10 11 12
Indu
ctan
ce (n
H)
Core Width (mm)
h=1.5mm
h=1.3mm
4 5 6 7 8 9 10 11 12
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
Cou
plin
g C
oeffi
cien
t
Core Width (mm)
h = 1.5 mm
h = 1.3 mm
98
Examining Fig. 4.7, the air gap, which dominantly affects the inductance, is along
direction of the core length instead of the width. When the width is reduced, the
reluctance change is smaller than when the air gap is included. Therefore, the impact of
the width reduction on inductance is small. Fig. 4.9(b) shows coupling coefficient
variation with the width, which reveals the same trend as the inductance. Since increasing
the width above certain value does not have the benefit of proportionally increased
inductance, this analysis can be used to determine the minimum width, which is valuable
for inductor size reduction.
The core length l is equally important as width w in optimizing inductor size. Fig.
4.10(a) shows inductance variation with the length, which is expected considering that
the air gap is along direction of core length. Trade-off has to be made between inductance
and the size. Fig. 4.10(b) shows coupling coefficient variation with the length. When the
length is reduced while keeping the same distance d1 between conductors, the flux
coupling path lengths between the two phases decreases and hence the coupling
coefficient magnitude also decreases.
99
The core height h has to be minimized to fit inductor between standard PCB layers.
Thinner inductor core is preferred for integration but tends to reduce the steady-state
inductance. Therefore, trade-off has to be made between inductance and the thickness.
Fig. 11(a) and (b) show inductance and coupling coefficient variation with height.
(a) Inductance versus with core length
(b) Coupling Coefficient versus with core length
Figure 4.10. Inductance and coupling coefficient variations with core length, l
0
10
20
30
40
50
60
70
80
9 10 11 12 13 14 15 16
Indu
ctan
ce (n
H)
Core Length (mm)
h=1.5mm, w=10mm
h=1.3mm, w=8mm
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
Cou
plin
g C
oeffi
cien
t
Core Length (mm)
h = 1.5mm, w=10mm
h = 1.3 mm, w=8mm
9 10 11 12 13 14 15 16
100
The coupling coefficient determines the transient inductance Ltr, which affects the
transient response of the multiphase converter. Distance d1 controls the coupling
coefficient, as shown in Fig. 4.12(b), and also affects the inductance, as shown in Fig.
4.12(a).
(a) Inductance versus core height
(b) Coupling coefficient versus core height
Figure 4.11. Inductance and coupling coefficient variations with core height, h.
0
20
40
60
80
100
120
140
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Indu
ctan
ce (n
H)
Core Height (mm)
g = 0.08 mm
g = 0.1 mm
0.0 0.5 1.0 1.5 2.0 2.5 3.0
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
Cou
plin
g C
oeffi
cien
t
Core Height (mm)
g = 0.08mm
g = 0.1mm
101
Air gap g affects the steady-state inductance, as shown in Fig. 4.11 and Fig. 4.12.
Smaller gap increases the steady-state inductance for higher efficiency but reduces the
inductor saturation current, and therefore, a trade-off has to be made to ensure that higher
(a) Inductance versus distance between conductors
(b) Coupling coefficient versus distance between conductors
Figure 4.12. Inductance and coupling coefficient variations with distance between conductors, d1.
0
10
20
30
40
50
60
70
80
4.0 4.5 5.0 5.5 6.0
Indu
ctan
ce (n
H)
Distance between Conductors (mm)
g = 0.08mm
g = 0.1mm
4 .0 4.5 5.0 5.5 6.0
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
Cou
plin
g C
oeffi
cien
t
Distance between Conductors (mm)
g = 0.08mm
g = 0.1mm
102
inductance can be obtained while enough margins for inductor saturation current are
maintained.
The parameters of final inductor designs of inductors LC and LD are shown in Table
4.1. They are verified by magnetic simulation, as shown in Fig. 4.13 and Fig. 4.14, and
implemented in Section 5.2.
Fig. 4.13 and Fig. 4.14 show magnetic flux and magnetic field density at 40-A current
(20 A per phase) from the simulation of inductor LC and LD respectively.
(a) Magnetic flux
(b) Magnetic field strength
Figure 4.13. Magnetic flux and magnetic field strength simulation of inductor LC .
103
4.5 Summary
In this chapter, an analytic model for coupled-inductor with air gap is developed to
replace the FEA simulation in optimization of two-phase lateral coupled inductor design.
The distributed model runs much faster than the FEA simulation and is more accurate
than the lumped inductor model developed in Section 3.2. The research involves both
model development and its application in design optimization.
(a) Magnetic flux
(b) Magnetic field strength
Figure 4.14. Magnetic flux and magnetic field strength simulation of inductor LD .
104
1) Model Development. Accuracy and simulation speed of lumped inductor model,
distributed model and FEA simulation are compared in this chapter, and the distributed
analytic model is preferred due to its speed and accuracy. To expedite inductor design
process and achieve more accurate result, distributed models for single-phase inductor
and coupled inductor with air gap are created. The inductor cores are divided into
multiple circles or ellipses, where the flux is uniform. The inductance of each circle or
ellipse is calculated using standard formula for inductor with air gap, and then inductance
of all circles or ellipses is summed to obtain total inductance of both single-phase
inductor and two-phase coupled inductor. The coupling coefficient is also obtained for
the coupled inductor.
2) Design Optimization. The analytic distributed inductor model is used in the
optimization of the two-phase coupled inductor design. Trade-offs have been made to
minimize inductor size, ensure enough inductance, select right coupling coefficient for
transient response, and improve current capacity of the POL modules while avoiding
inductor saturation. The optimized designs are verified by FEA simulation before being
applied to the design of two-phase and four-phase dc-dc synchronous buck converters in
Chapter 5.
105
CHAPTER 5 MULTIPHASE POINT-OF-LOAD
MODULES
This chapter demonstrates fabrication of single-turn inductors and then presents
assembly process and performance of two-phase and four-phase POL modules. It
presents power loss analysis of a multiphase converter including power loss from the
coupled inductor with ferrite core and air gap at different switching frequencies.
Specifically, the researches include:
1) Coupled Inductor Fabrication and POL Module Assembly: Section 5.1 first
presents the procedure of building single-turn coupled inductor. The fabrication and
assembly process has been improved over that used in building the prototype inductors in
Section 3.3. Then several PCB board layers of the POL modules are assembled with the
coupled inductor embedded between the layers.
2) Two-phase and Four-phase POL Modules with Single-turn Coupled Inductors:
Section 5.2 presents implementation of two-phase single-turn inductor design in a
synchronous buck POL module followed by implementation of four-phase single-turn
inductor design in a higher-current synchronous buck POL module. The inductor current
waveforms as well as measured steady-state and transient inductances from the
experiment are shown.
3) Power Loss Analysis for Converter with Coupled Inductor: Section 5.3
demonstrates the power loss increase with switching frequency and the importance of an
106
efficiency tool to the optimization of switching frequency of converter modules. Finally,
in Section 5.4, summary is presented.
5.1 Fabrication and Assembly of Coupled Inductors and Point-of-Load Modules
The prototype inductors built in Section 3.3 are not optimized in some dimensions.
The edge surfaces of the magnetic cores for air gapping are not smooth, and the air gap is
not controlled accurately. These factors affect precise control of inductance and coupling
coefficient as well as performance of the coupled inductors. Therefore, the fabrication
and assembly processes need improvement.
Fig. 5.1 demonstrates improved procedure of building a two-phase prototype coupled
inductor.
1) After the optimized dimensions are finalized, select the available standard cores
that are either the same as or close to the target dimensions.
2) If the standard core is not available, use a machine to grind the cores to the desired
dimensions (width in this example). Grind any surfaces except the edge used for air
gapping and keep the original surface of this edge untouched to ensure a smooth surface.
3) Instead of drilling the holes on one piece as in Section 3.3, grind two half-holes on
one edge of both core pieces that face each other. The distance between the two half-
holes determines the coupling coefficient of the inductors.
4) Use Cyanoacrylate adhesive to glue the two pieces. The air gap between the two
cores is controlled by inserting small pieces of Grafix Dura-Lar film with sheet thickness
of 3 mil (0.076 mm) for LC and LD, There are other sheet thicknesses of the film available
for different air gap options, for example, 2 mil (0.051 mm), 4 mil (0.102 mm) and 5 mil
(0.127 mm).
107
5) Insert copper pins and use them as conductors of the coupled inductor.
The procedure of building a four-phase coupled inductor is similar to that for two-
phase inductor, as shown in Fig. 5.2, which starts with standard cores. There are three
pieces of core and two air gaps. Eight half-holes are ground before the three pieces are
glued together with desired air gaps.
The cost of fabricating nonstandard magnetic cores for the prototype is much higher
than that of standard cores. Once the nonstandard core design is finalized, it is feasible to
build molds for the required dimensions. Then the cores can be manufactured in large
volume to lower the cost considerably.
Fig. 5.1 Improved procedure of building two-phase prototype coupled inductor.
1
4
21
3
5
108
The cores of two-phase coupled inductor LC is manufactured by a contractor through
grinding the standard cores to the target dimensions with the two half-holes on each piece
ground at the same time. The two edges for air gapping are not ground so that original
even surfaces can be maintained. The core material is DMR51 [58], which is similar to
3F45 [57].
The cores of two-phase coupled inductor LD are standard cores from Ferroxcube [64].
No grinding is needed for core dimensions, and only two half-holes on each core are
ground at the lab before the two pieces are glued together. The core material is 3F45 [57].
Fig. 5.2 Improved procedure of building four-phase prototype coupled inductor.
1
4
21
3
109
The dimensions of both two-phase coupled inductors are listed in Table 4.1, which
are much smaller than prototype inductors LA and LB shown in Table 3.1 and Section 3.3.
The size of core pieces of the four-phase inductor is the same as the core pieces of two-
phase inductor LD. The smooth surfaces of the core pieces ensure more accurate control
of inductance and coupling coefficient.
5.2 Point-of-Load Modules with Two-phase and Four-phase Single-turn Coupled
Inductors
After the inductor fabrication has been completed, the inductor is then assembled
with PCB boards and connectors to build the POL modules. Fig. 5.3(a) and (b) show the
PCB board layer stack-up of the two-phase and four-phase converter modules
respectively with the coupled inductors built in Section 5.1.
In the two-phase module in Fig. 5.3(a), power stage of the first phase is placed on top
side of the upper board, while power stage of the second phase is placed on bottom side
of the lower board. The two-phase coupled inductor is embedded between these two
boards, and the middle board fills the space not occupied by the inductor so that power
connections and thermal performance are improved.
In the four-phase module in Fig. 5.3(b), power stage of the first phase and third phase
are placed on top side of the upper board, while power stage of the second phase and
fourth phase are placed on bottom side of the lower board. The four-phase coupled
inductor is embedded between these two boards and surrounded by the middle board to
enhance power connections and reduce thermal resistance.
110
Fig. 5.4 shows the schematic of a two-phase synchronous buck converter with the
added circuitry to Fig. 1.7(a) for inductor Direct Current Resistance (DCR) current
sensing [65], voltage loop regulation and current sharing between phases. The two-phase
coupled inductor is from the design in Section 4.4.
Based on the procedure described in Fig. 5.3(a), a two-phase POL module is built, as
shown in Fig. 5.5 with its test fixture, which is used to evaluate steady-state inductance,
transient inductance, coupling coefficient, power loss, and current capacity of the
module.
(a) Two-phase module (b) Four-phase module
Fig. 5.3 Stack-up of two-phase and four-phase POL modules from top, middle to bottom board.
111
Figure 5.4 Circuit of two-phase synchronous buck converter with closed-loop control.
Module
VOUT
VIN
Q1
Q2
L1
L2
Driv
ers
Q1
Q2
Driv
ers
M1
M2
CIN1
CIN2 COUT12
COUT21
COUT22
COUT11
Controller
CS1CS2PWM1PWM2
Vout Sense
Figure 5.5 Two-phase synchronous buck converter module and test fixture.
112
The waveform of current ripple has been taken using Rogowski current waveform
transducer, which has an extremely thin, clip-around Rogowski coil of 1.6mm cross-
section. Such a thin coil enables currents to be measured in the most difficult to reach
areas of the module with negligible disruption to the circuit under test. It only measures
AC portion (ripple) of the current signal but does not display the DC portion. Since there
is only single-turn straight conductors in the new couple inductor, the only way to
measure inductor current is to insert Rogowski coil between the PCB board and the
inductor, as shown by the four circles in Fig 3.5. Fig. 5.6(a) shows the module built
specifically for measuring the inductor current waveform, and Fig 5.6(b) is the Rogowski
current waveform transducer with a 50 mV/A current-to-voltage signal gain.
(a) Module for current measurment (b) Rogowski current waveform transducer
Figure 5.6 Current probing in single-turn coupled inductor.
113
The inductor ripple current and switch node waveforms of inductors LC and LD at 1.5
MHz switching frequency are shown in Fig. 5.7(a) and (b) respectively. Similar to
Section 3.3, the steady-state inductance and transient inductance of inductor LD are
calculated based on measurement on waveforms in Fig. 5.7(b) and shown in Fig. 5.8.
(a) Inductor LC , 12-V input voltage, 1.2-V output voltage, 0-A current
(b) Inductor LD, 12-V input voltage, 1.8-V output voltage, 40-A current
Figure 5.7 Inductor current waveforms of two-phase synchronous buck converter module at 1.5 MHz switching frequency.
IL1
4 A/div
SW1
10 V/div
IL2
4 A/div
IL1
4 A/div
SW1
10 V/div
IL2
4 A/div
114
To meet the higher-current and fast load slew-rate requirement, a four-phase
synchronous buck converter with the single-turn coupled inductor is implemented in the
POL module. Fig. 5.9 is a four-phase POL module based on schematic in Fig. 3.17 with
some added circuitry for inductor DCR current sensing and close loop control of output
voltage, which is similar to that in two-phase POL module in Fig. 5.4.
Figure 5.9. Four-phase Point-of-Load module with single-turn coupled inductor.
Figure 5.8. Measured steady-state inductance LSS and transient inductance LTR of inductor LD.
0
10
20
30
40
50
60
70
80
0 5 10 15 20 25 30 35 40
Indu
ctan
ce (n
H)
Load Current (A)
Steady State Inductance
Transient Inductance
115
5.3 Converter Power Loss Analysis
The power density is the amount of power delivered per unit volume. To improve
power density of the POL modules, it is important to reduce the power loss of the
converter, which consists of MOSFET power loss, inductor loss, and PCB loss, etc.
Fig. 5.10 shows power loss pie charts of the two-phase synchronous buck converter
module at three different switching frequencies, 1 MHz, 1.5 MHz and 2 MHz. The
MOSFET loss dominates the total converter loss and includes switching loss, conduction
loss and driver loss. As frequency increases, the MOSFET switching loss and driver loss
increase, while the conduction loss decreases due to the smaller inductor current ripple
(a) 1 MHz
(b) 1.5 MHz (b) 2 MHz
Figure 5.10. Power loss distribution at different frequencies in two-phase synchronous buck module.
Top FET Conduction
Top FET Switching
Bottom FET Conduction
Bottom FET Switching
Inductor Winding
Inductor Core
PCB Copper
Driver Loss
116
with the same inductance. Therefore, the percentage of switching loss of both top and
bottom MOSFETs as well as driver loss increases with switching frequency.
Although the MOSFET switching loss and inductor core loss is relatively small at 1
MHz (41%), as shown in Fig. 5.10(a), it becomes a larger portion at higher switching
frequencies. As shown in Fig. 5.10(b) and (c), the switching loss of both MOSFETs plus
the inductor core loss is 50% of the total converter loss at 1.5 MHz and further increases
to 55% at 2 MHz. When higher frequency is selected to improve power density of the
POL modules, it is important to manage the power losses proportional to switching
frequency. Based on tradeoff between size and power loss, 1.5 MHz frequency is selected
for the POL modules.
5.4 Summary
In this chapter, the fabrication process of the new single-turn coupled inductors has
been improved to ensure accurate inductance and coupling coefficient. The processes of
building both two-phase and four-phase inductors have been described in details. The
inductors are then sandwiched by PCB boards and assembled with other devices in the
POL modules. The two-phase synchronous buck converter module is evaluated with test
fixture. Inductor current waveforms as well as measured steady-state and transient
inductances from the experiment are shown.
The power loss analysis of the coupled inductors with ferrite core and air gap is
conducted so that optimized switching frequency can be selected to minimize the size and
lower power loss of the POL modules, which leads to improved power density of the
modules. The power loss analyzed through the efficiency tool includes inductor core loss
and winding loss, MOSFET and driver loss, and PCB loss in the modules.
117
CHAPTER 6 CONCLUSIONS AND FUTURE WORK
The final chapter summaries research in the dissertation and presents future work
involving different core materials, power density improvement, and current sensing in the
POL modules.
6.1 Summary and Conclusions
More and more internet services, such as social media, e-commerce, cloud
computing, gaming, and most recently artificial intelligence, rely more heavily on
computing power in data centers. To reduce operational cost in data centers, dc-dc
converters that power the processors, memories, and other integrated circuits on server
motherboards are required to provide higher current with fast transient response, higher
conversion efficiency, and smaller size.
High current with fast transient is achieved by interleaving multiple synchronous
buck converters, where smaller inductors can be used to increase the current slew rate.
The current capacity is also enhanced in the multiphase converter, which is proportional
to number of converters paralleled.
To achieve size reduction in multiphase dc-dc converters, three options have been
evaluated, i.e. high switching frequency, reduced space between inductors that are the
biggest components in dc-dc converters, and coupled inductor. Solutions at switching
frequency as high as hundreds of megahertz are available, but higher switching frequency
increases converter power loss, which contradicts the high efficiency requirement.
118
Reduced space between inductors creates unwanted coupling between inductors and
degrades performance of converters and computer systems. This leaves coupled inductors
as the best suitable option.
This dissertation research involves both the mitigation and utilization aspects of the
inductor coupling in multiphase dc-dc converters. The dissertation starts with mitigation
of inductor coupling in multiphase dc-dc converters after it is verified that the unwanted
direct coupling does exist in commercial computer motherboards. Experiment reveals
that inductor saturation current is reduced when the space between inductors is too small,
and magnetic simulation demonstrates that root cause of inductor performance
degradation is the increased inductor ripple current due to direct inductor coupling.
Quantitative analysis in the dissertation provides a simple formula for coupling
coefficient calculation that is used in establishing guidelines of inductor placement in
motherboards to mitigate the undesired direct coupling. Based on the analysis of inductor
coupling, an alternative inductor design is presented with minimal coupling between
inductors placed together.
The second aspect of the research is to utilize the inductor coupling effect to benefit
multiphase converter design. By creating a new coupled-inductor structure, the inverse
coupling is realized to improve transient response or converter efficiency or both. The
single-turn lateral coupled inductor structure for multiphase converters presented in this
dissertation makes it possible to integrate the inductor with power devices and drivers in
switching converters and co-package with loads, i.e. processors, FPGAs, or integrated
circuits. The lateral inductor reduces the converter size and core loss, and the single-turn
structure lowers winding loss to increase power capacity of the power modules.
119
The coupled inductor structure is extended not only to multiple phases for high-
current loads but also to single phase for small-size low-current applications. Different
implementations of the coupled inductors are illustrated in 2-D and 3-D drawings for
integration in the POL modules or motherboards.
To optimize design of the coupled inductor so that better performance can be
achieved, an analytic inductor model is created and applied to inductor optimization of
inductance and coupling coefficient versus length, width, thickness, air gap, and distance
between windings. The inductor designs are verified by the FEA magnetic simulation
before they are used in the POL modules.
6.2 Future Work
Future work of this research involves investigations of more core materials and
improvement of power density and current sensing in the dc-dc POL modules.
6.2.1 Core Material Investigations
In this dissertation research, ferrite core materials with air gap is analyzed so that
enough inductance is available from the single-turn coupled inductor structure. There are
other options for the magnetic core material. The relative permeability of the latest alloy
flake composite material reaches several hundred, and its core loss density in multi-
megahertz range is comparable with that of the sintered NiZn ferrite material. It would be
interesting in future studies to make more detailed comparisons about how this new
material performs with the new single-turn coupled inductor structure.
Several MnZn ferrite core materials, DMR50B, DMR51, and 3F45, with air gap have
been used in this research, which is suitable for switching frequencies around 1 MHz.
120
Other ferrite materials with lower core loss at higher switching frequency, especially
NiZn ferrite material, are worth investigation. The switching frequency can be pushed
even higher to further reduce the inductor size.
6.2.2 Power Density Improvement
The prototype of both two-phase and four-phase POL modules is optimized in
inductor design but is not optimized in some other areas, and therefore, the power density
can be further improved by reducing size of the module. For example, a quick update of
the POL module is to replace the through-hole connectors, which occupy extra space, by
much smaller surface-mount connectors.
In the current POL module, three PCB boards are manufactured and then manually
stacked together after the coupled inductor is inserted, as shown in Fig. 5.3. There is no
direct thermal bonding between the three PCB boards, which increases thermal resistance
of the POL module and deteriorates its thermal performance. In the future study, the
coupled inductor can be embedded between layers during the PCB manufacturing process
to enhance thermal performance, and it thus improves the power density and current
capacity of the POL modules.
6.2.3 MOSFET RDS(on) Current Sensing
In the POL modules with the coupled inductor, the simple inductor DCR current
sensing scheme is used. A resistor-capacitor (RC) circuit in parallel with the inductor L is
added to retrieve the current information, which is then amplified by a current sense
amplifier inside controller of the dc-dc converter. The temperature coefficient of the
inductor winding material (copper) is well defined, which makes it easy to compensate
121
for the inductor DCR variation with temperature. The disadvantage of the inductor DCR
sensing is the large percentage of variation due to very small DCR value, which is in
milliohm range. Moreover, the inductor DCR sensing relies on equivalent time constants
to provide accurate load current signal where ideally R * C = L / DCR, but the fixed R*C
time constant cannot track the inductor L / DCR due to the inductor DCR increase with
temperature and inductance decrease with load current.
Therefore, the investigation of more accurate current sensing scheme, such as
MOSFET RDS(on) sensing, is another future research topic. In the co-packaged power
stage, the known MOSFETs are paired with an intelligent driver containing a current
sense amplifier. It is possible to accurately trim offset and gain of the current sense
amplifier circuits corresponding to the RDS(on) of a specific pairs of MOSFETs at certain
temperatures. The tolerance of the integrated current sensing system is trimmed to within
2% at a given system environment, which is much lower than the inductor DCR tolerance
of 5% to 7% plus current sense amplifier tolerance. The temperature and drive voltage
compensation for MOSFET RDS(on) variation are inside the intelligent driver, which is in
the same package with known MOSFET characteristics and local temperature
information. Accurate current sensing scheme like MOSFET RDS(on) sensing improves
current sharing between phases and enhances current capacity of the multiphase
converters.
122
REFERENCES
[1] Victoria Woollaston, “Revealed, what happens in just ONE minute on the internet,”
[Online]. Available: http://www.dailymail.co.uk/sciencetech/article-2381188
[2] Web Odysseum, “Visit the Google’s data center,” [Online]. Available:
http://webodysseum.com/technologyscience/visit-the-googles-data-centers
[3] Clarke Energy, “Data center combined heat and power or cogeneration,” [Online].
Available: https://www.clarke-energy.com/natural-gas/data-centre-chp-trigeneration
[4] John Judge, Jack Pouchet, Anand Ekbote, and Sachin Dixit, “Reducing data center
energy consumption,” [Online]. Available: http://ashraephilly.org/images/downloads/
CTTC_Articles/1503_cttc.pdf
[5] Gordon E. Moore, “Cramming more components onto integrated circuits,” Electronics,
pp. 114-117, April 19, 1965.
[6] Wikipedia, “Transistor count,” Available: https://en. wikipedia.org/wiki/Transistor_count
[7] Intel, “Voltage regulator module (VRM) and enterprise voltage regulator-down (EVRD)
11.1 design guidelines,” September 2009. Available: http://www.intel.com.
[8] Xunwei Zhou, Pit-Leong Wong, Peng Xu, Fred C. Lee, and Alex Q. Huang,
“Investigation of candidate VRM topologies for future microprocessors,” IEEE
Transactions on Power Electronics, vol. 15, no. 6, pp. 1172-1182, November 2000.
123
[9] Wenkang Huang, “A new control for multiphase-phase buck converter with fast transient
response,” in Proceedings of IEEE Applied Power Electronics Conference, March 2001,
pp. 273-279.
[10] Wenkang Huang, George Schuellein, and Danny Clavette, “A scalable multiphase buck
converter with average current share bus,” in Proceedings of IEEE Applied Power
Electronics Conference, Feburary 2003, pp. 438-443.
[11] Wenkang Huang, "The design of a high-frequency multiphase voltage regulator with
adaptive voltage positioning and all ceramic capacitors," in Proceedings of IEEE Applied
Power Electronics Conference, March 2005, pp. 270-275.
[12] Wenkang Huang, Danny Clavette, George Schuellein, Mark Crowther, and John Wallace,
“System accuracy analysis of the multiphase voltage regulator module,” IEEE
Transactions Power Electronics, vol. 22, no. 3, pp. 1019-1026, May 2007.
[13] Jen-Ta Su, and Chih-Wen Liu, “A novel phase-shedding control scheme for improved
light load efficiency of multiphase interleaved DC-DC converters,” IEEE Transactions
on Power Electronics, vol. 28, no.10, pp.4742-4752, October 2013.
[14] Peter Hazucha, Gerhard Schrom, Jaehong Hahn, et al., “A 233-MHz 80%–87% efficient
four-phase DC–DC converter utilizing air-core inductors on package,” IEEE Journal on
Solid-State Circuits, vol. 40, no.4, pp.838-845, April 2005.
[15] Gerhard Schrom, Peter Hazchua, Fabrice Paillet, et al., “A 100MHz eight-phase buck
converter delivering 12A in 25mm2 using air-core inductors,” in Proceedings of IEEE
Applied Power Electronics Conference, February 2007, pp.727-730.
124
[16] Edward Burton, Gerhard Schrom, Fabrice Paillet, et al., “FIVR – Fully integrated voltage
regulators on 4th generation Intel® Core™ SoCs,” in Proceedings of IEEE Applied
Power Electronics Conference, March. 2014, pp. 432-439.
[17] Pit-Leong Wong, “Performance improvements of multi-channel interleaving voltage
regulator modules with integrated coupling inductors,” PhD dissertation, Virginia
Polytechnic Institute and State University, Blacksburg, VA, USA, March, 2001.
[18] Pit-Leong Wong, Peng Xu, Bo Yang, and Fred C. Lee, “Performance improvements of
interleaving VRMs with coupling inductors,” IEEE Transactions on Power Electronics,
vol. 16, no. 4, pp. 499-507, July 2001.
[19] Jieli. Li, Charles Sullivan, and Aaron Schultz, “Coupled-inductor design optimization for
fast-response low-voltage DC-DC converters,” in Proceedings of IEEE Applied Power
Electronics Conference, March 2002, pp. 817-823.
[20] Jieli. Li, A. Stratakos, A. Schultz, and C. R. Sullivan, “Using coupled inductors to
enhance transient performance of multi-phase buck converters,” in Proceedings of IEEE
Applied Power Electronics Conference, February 2004, pp. 1289–1293.
[21] Yan Dong, Jinghai. Zhou, Fred C. Lee, Ming Xu, and Shuo Wang, “Twisted core coupled
inductors for microprocessor voltage regulators,” IEEE Transactions on Power
Electronics, vol. 23, no. 5, pp. 2536-2545, September 2008.
[22] Yan Dong, Fred C. Lee, and Ming Xu, “Evaluation of coupled inductor voltage
regulators,” in Proceedings of IEEE Applied Power Electronics Conference, February
2008, pp. 831-837.
125
[23] Yan Dong, “Investigation of multiphase coupled-inductor Buck converters in point-of-
load applications,” PhD dissertation, Virginia Polytechnic Institute and State University,
Blacksburg, VA, USA, July 2009.
[24] Guangyong Zhu, Brent McDonald, and Kunrong Wang, “Modeling and analysis of
coupled inductors in power converters,” IEEE Transactions on Power Electronics, vol.
26, no. 5, pp. 1355-1363, May 2011.
[25] Ming Xu, Yucheng Ying, Qiang Li, and Fred C. Lee, “Novel coupled-inductor multi-
phase VRs,” in Proceedings of IEEE Applied Power Electronics Conference, February
2007, pp. 113-119.
[26] Santhos Wibowo, Zhang Ting, Masashi Kono, Tetsuya Taura, Yasunori Kobori, and
Haruo Kobayashi, “Analysis of coupled inductors for low-ripple fast-response buck
converter,” in Proceedings of IEEE Asia Pacific Conference on Circuits and Systems,
November 2008, pp.1860-1863.
[27] Qiang Li, “Low-profile magnetic integration for high-frequency point-of-load
converters,” PhD dissertation, Virginia Polytechnic Institute and State University,
Blacksburg, VA, USA, August 2011.
[28] Qiang Li, Yan. Dong, Fred C. Lee, and David. Gilham, “High-density low-profile
coupled inductor design for integrated point-of-load converters,” IEEE Transactions on
Power Electronics, vol.28, no.1, pp. 547-554, January 2013.
[29] Yipeng Su, Qiang Li, and Fred C. Lee, “Design and evaluation of a high-frequency
LTCC inductor substrate for a three-dimensional integrated DC/DC converter,” IEEE
Transactions on Power Electronics, vol.28, no.9, pp. 4354-4364, September 2013.
126
[30] Yipeng Su, Wenli Zhang, Qiang Li, Fred C. Lee and Mingkai Mu, “High frequency
integrated Point-of-Load (POL) module with PCB embedded inductor substrate,” in
Proceedings of IEEE Energy Conversion Congress & Exposition, September 2013,
pp.1243-1250.
[31] Yipeng Su, “High frequency, high current 3D integrated point-of-load module,” PhD
dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA,
October 2014.
[32] Dongbin Hou, Yipeng Su, Qiang Li, and Fred C. Lee, “Improving the efficiency and
dynamics of 3D integrated POL,” in Proceedings of IEEE Applied Power Electronics
Conference, March 2015, pp. 140-145.
[33] Wenkang Huang and Brad Lehman, “Mitigation and utilization of the inductor coupling
effect in interleaved multiphase DC/DC converters,” in Proceedings of IEEE Energy
Conversion Congress & Exposition, September 2013, pp. 1822-1829.
[34] Charles Sullivan, Aaron Schultz, Anthony Stratakos, and Jieli Li, “Method for making
magnetic components with N-Phase coupling, and related inductor structures,” Patent,
US7498920, March 2009.
[35] Pulse Electronics Corporation. Power beads - PA131xAHL series coupled inductors.
[Online]. Available: http://productfinder.pulseeng.com/products/datasheets/P685.pdf
[36] ESL ElectroScience, “Low-Temperature Co-Fired Ceramic (LTCC) tape,” [Online].
Available: http://www.electroscience.com/taxonomy/term/59/3
127
[37] Mingkai Mu, Yipeng Su, Qiang Li, and Fred C. Lee, “Magnetic characterization of low
temperature co-fired ceramic (LTCC) ferrite materials for high frequency power
converters”, in Proceedings of IEEE Energy Conversion Congress & Exposition,
September 2011, pp. 2133-2138.
[38] Altera, “EP53A7LQI/EP53A7HQI 1A PowerSoC light load mode buck regulator with
integrated inductor,” [Online]. Available: www.altera.com/enpirion
[39] Altera, “EN5394QI 9A PowerSoC voltage mode synchronous buck PWM DC-DC
converter with integrated inductor,” [Online]. Available: www.altera.com/enpirion
[40] Texas Instruments, “TPSM84A22, 8-V to 14-V input, 1.2-V to 2.05-V output, 10-A
SWIFT™ power module,” [Online]. Available: www.ti.com/PowerModules
[41] Monolithic Power Systems, “MPM3695-25 16V, 25A, scalable, DC/DC power module
with PMBus,” [Online]. Available: https://www.monolithicpower.com/Products/Power-
Modules
[42] Intersil, “Dual 15A / single 30A step-down power module,” [Online]. Available:
http://www.intersil.com/content/intersil/en/products/power-management/power-
modules.html
[43] Murata, “OKLP-X/60-W12A-C 60A power block non-isolated DC-DC converter,”
[Online]. Available: http://www.murata-ps.com
[44] Intersil, “ISL8272M 50A digital DC/DC PMBus power module,” [Online]. Available:
http://www.intersil.com/content/intersil/en/products/power-management/power-
modules.html
128
[45] Linear Technology, “LTM4650-1 dual 25A or single 50A μModule regulator with 0.8%
DC and 3% transient accuracy,” [Online]. Available: http://www.linear.com/products/umodule_regulators
[46] Delta, “D12S1R8100D non-isolated power block DC/DC power modules,” [Online].
Available: http://www.deltaww.com/dcdc [47] Wenkang Huang and Brad Lehman, “Analysis and verification of the inductor coupling
effect in interleaved multiphase DC-DC converters,” IEEE Transactions Power
Electronics, vol. 31, no. 7, pp. 5004-5017, July 2016.
[48] A. Balakrishnan, W. T. Joines, and T. G. Wilson, “Air-gap reluctance and inductance
calculations for magnetic circuits using a Schwarz-Christoffel transformation,” IEEE
Transactions Power Electronics, vol.12, no.4, pp. 654-663, July 1997.
[49] Herbert C. Roters, Electromagnetic Devices. New York, NY, USA: Wiley, 1941,
pp.130−143.
[50] Wenkang Huang and Brad Lehman, “A compact coupled inductor for interleaved
multiphase DC-DC converters,” IEEE Transactions Power Electronics, vol. 31, no. 10,
pp. 6770-6775, October 2016.
[51] Wolfgang Peinhopf, “Chip-Embedded Packaging Contributes to New Performance
Benchmark for DrMOS, ” March 2013. [Online]. Available,
http://powerelectronics.com/power-electronics-systems/chip-embedded-packaging-
contributes-new-performance-benchmark-drmos
[52] DMEGC Magnetics, “DMR50B Material Characteristics,” [Online]. Available:
http://www.chinadmegc.com/en/products_list.php?2/16.
129
[53] Ferroxcube, “3F35 Material Specification,” September 2008. [Online]. Available:
http://www.elnamagnetics.com/wp-content/uploads/library/Ferroxcube-
Materials/3F35_Material_Specification.pdf
[54] Ansys, “Maxwell 15.0 3D User’s Guide,” [Online]. Available,
http://register.ansys.com.cn/ansyschina/minisite/201411_em/motordesign/electromagneti
sm/material/CompleteMaxwell3D_V15.pdf
[55] Andrew F. Goldberg, John G. Kassakian, and Martin F. Schlecht, “Finite-element
analysis of copper loss in 1–10 MHz transformers,” IEEE Transactions Power
Electronics, vol. 4, pp. 157–167, March 1989.
[56] Qiang Li and Fred C. Lee, “Winding AC resistance of low temperature co-fired ceramic
inductor,” in Proceedings of IEEE Applied Power Electronics Conference, February
2012, pp. 1790-1796.
[57] Ferroxcube, “3F45 Material Specification,” September 2008. [Online]. Available:
http://www.ferroxcube.com/FerroxcubeCorporateReception/datasheet/3f45.pdf
[58] DMEGC Magnetics, “DMR51 Material Characteristics,” [Online]. Available:
http://www.chinadmegc.com/en/products_list.php?2/16.
[59] E. Osegueda, K. D. T. Ngo, W. Polivka, M. Walters, “Perforrated - Plate Magnetics. Part
I: Mode - 1 Inductor/Transformer,” IEEE Transactions on Aerospace and Electronic
System, vol. 31, no. 3, pp. 968 – 976, July 1995.
[60] M. J. Prieto, A. M. Pernia, J. M. Lopera, J. A. Martin, F. Nuno, "Design and analysis of
thick-film integrated inductors for power converters," IEEE Transactions Industry
Applications, Volume 38, no. 2, pp. 543 - 552, March 2002.
130
[61] Michele H. Lim, J. D. van Wyk, K. D. T. Ngo, “Modeling of an LTCC Inductor Capable
of Improving Converter Light-Load Efficiency,” in Proceedings of IEEE Applied Power
Electronics Conference, February 2007, pp.85 – 89.
[62] MIT, Electromagnetism. Section 9.7, Magnetic Circuits, [Online]. Available:
http://web.mit.edu/6.013_book/www/book.html
[63] Di Xu, and K. D. T. Ngo. "Optimal constant-flux-inductor design for a 5 kW boost
converter," in Proceedings of IEEE Applied Power Electronics Conference, March 2013,
pp. 2436-2443.
[64] Ferroxcube, “E14/3.5/5 planar E cores and accessories,” September 2008. [Online].
Available:
http://www.ferroxcube.com/FerroxcubeCorporateReception/datasheet/e14355r.pdf
[65] Wenkang Huang, John Clarkin, Peter Cheng, and George Schuellein, “Analysis of loss-
less current sensing and sharing in multi-phase high-current DC/DC converters, “ in
Proceeding of High Frequency Power Conversion Conference, September 2001, pp. 322-
327.
![A Unified Approach to Reliability Assessment of Multiphase Dc-Dc …people.ece.umn.edu/~sdhople/Journals/TPEL_2012... · 2013-05-25 · 2 [25]-[27] has renewed focus on the reliability](https://static.documents.pub/doc/80x56/5f15e2d150642602aa363985/a-unified-approach-to-reliability-assessment-of-multiphase-dc-dc-sdhoplejournalstpel2012.jpg)
