Multiphase interleaving buck converters are widely used in today's industrial point-of-load (POL) converters, especially the microprocessor voltage regulators (VRs). The issue of today's multiphase interleaving buck converters is the conflict between the high efficiency and the fast transient in the phase inductor design. In 2000, P. Wong proposed the multiphase coupledinductor buck converter to solve this issue. With the phase inductors coupled together, the coupled-inductor worked as a nonlinear inductor due to the phase-shifted switching network, and the coupled-inductor has different equivalent inductances during steady-state and transient. One the one hand, the steady state inductance is increased due to coupling and the efficiency of the multiphase coupled-inductor buck converter is increased; on the other hand, the transient inductance is reduced and the transient performance of the multiphase coupled-inductor buck is improved. After that, many researches have investigated the multiphase coupled-inductor buck converters in different aspects. However, there are still many challenges in this area: the comprehensive analysis of the converter, the alternative coupled inductor structures with the good performance, the current sensing of converter and the light-load efficiency improvement. They are investigated in this dissertation. The comprehensive analysis of the multiphase coupled-inductor buck converter is investigated. The n-phase (n>2) coupled-inductor buck converter with the duty cycle D>1/n hasn't been analyzed before. In this dissertation, the multiphase coupled-inductor buck converter is systematically analyzed for any phase number and any duty cycle condition. The asymmetric multiphase coupled-inductor buck converter is also analyzed. The existing coupled-inductor has a long winding path issue. In low-voltage, high-current applications, the short winding path is preferred because the winding loss dominates the inductor total loss and a short winding path can greatly reduce the winding loss. To solve this long winding path issue, several twisted-core coupled-inductors are proposed. The twisted-core coupled-inductor has such a severe 3D fringing effect that the conventional reluctance modeling method gives a poor result, unacceptable from the design point of view. By applying and extending Sullivan's space cutting method to the twisted core coupled inductor, a precise reluctance model of the twisted-core coupled-inductor is proposed. The reluctance model gives designers the intuition of the twisted-core coupled-inductors and facilitates the design of the twisted-core coupled-inductors. The design using this reluctance model shows good correlation between the design requirement and the design result. The developed space cutting method can also be used in other complex magnetic structures with the strong fringing effect. Today, more and more POL converters are integrated and the bottleneck of the integrated POL converters is the large inductor size. Different coupled-inductor structures are proposed to reduce the large inductor size and to improve the power density of the integrated POL converter. The investigation is based on the low temperature co-fire ceramic (LTCC) process. It is found that the side-by-side-winding coupled-inductor structure achieves a smaller footprint and size. With the two-segment B-H curve approximation, the proposed coupled-inductor structure can be easily modeled and designed. The designed coupled-inductor prototype reduces the magnetic size by half. Accordingly, the LTCC integrated coupled-inductor POL converter doubles the power density compared to its non-coupled-inductor POL counterpart and an amazing 500W/in³ power density is achieved. In a multiphase coupled-inductor converter, there are several coupled-inductor setups. For example, for a six-phase coupled-inductor converter, three two-phase coupled inductors, two three-phase coupled-inductors and one six-phase coupled inductors can be used. Different coupled-inductor setups are investigated and it is found that there is a diminishing return effect for both the steady-state efficiency improvement and the transient performance improvement when the coupling phase number increases. The conventional DCR current sensing method is a very popular current sensing method for today's multiphase non-coupled-inductor buck converters. Unfortunately, this current sensing method doesn't work for the multiphase coupled-inductor buck converter. To solve this issue, two novel DCR current sensing methods are proposed for the multiphase coupled-inductor buck converter. Although the multiphase coupled-inductor buck converters have shown a lot of benefits, they have a low efficiency under light-load working in DCM. Since the DCM operation of the multiphase coupled-inductor buck converter has never been investigated, they are analyzed in detail and the reason for the low efficiency is identified. It is found that there are more-than-one DCM modes for the multiphase coupled-inductor buck converter: DCM1, DCM2 …, and DCMn. In the DCM2, DCM3 …, and DCMn modes, the phase-currents reach zero-current more-than-once during one switching period, which causes the low efficiency of the multiphase coupledinductor buck converter in the light load. With the understanding of the low efficiency issue, the burst-in-DCM1-mode control method is proposed to improve the light load efficiency of the multiphase coupled-inductor buck converter. Experimental results prove the proposed solution. / Ph. D.

The future of microprocessors is unknown. Over the past 40 years, their historical trend has been for adopting smaller and more powerful designs that drive the world that we live in today. The state of the microprocessor business today faces a crossroad, wishing to continue on the historical trend of doubling the number of transistors on a chip every 18 months (Moore’s Law) but also facing the realistic task of needing to power these sophisticated devices. With the low voltages and high currents that are required for these microprocessors to operate, it poses a difficult task for the future designers of the voltage regulators that are used to power these microprocessors. The technique that has been widely adopted as the preferred method to power these devices is called a multiphase buck converter, or multiphase voltage regulator. This thesis is a continuation of and is aimed to improve previous work done by two former Cal Poly students, Kay Ohn and Ian Waters. A new design that uses an interleaving control scheme, careful component selection, an input LC filter, and a reduction in board size seeks to improve the efficiency, input current noise, and increase the current density of the original design. Research was first conducted to determine how to best make such improvements. The design phase ensued, which used design calculations and simulations to test if the proposed multiphase topology was plausible. Once the theory was fully proven, a real hardware circuit was created and tested to confirm the results. The results yield a multiphase design with improved input noise filtering, greater efficiency, more equal current sharing, and higher current density as compared to previous topologies in this field. Parameters such as output voltage ripple, load and line regulation, and transient response remained excellent, as they were with the previous work.

abstract: Efficiency of components is an ever increasing area of importance to portable applications, where a finite battery means finite operating time. Higher efficiency devices need to be designed that don't compromise on the performance that the consumer has come to expect. Class D amplifiers deliver on the goal of increased efficiency, but at the cost of distortion. Class AB amplifiers have low efficiency, but high linearity. By modulating the supply voltage of a Class AB amplifier to make a Class H amplifier, the efficiency can increase while still maintaining the Class AB level of linearity. A 92dB Power Supply Rejection Ratio (PSRR) Class AB amplifier and a Class H amplifier were designed in a 0.24um process for portable audio applications. Using a multiphase buck converter increased the efficiency of the Class H amplifier while still maintaining a fast response time to respond to audio frequencies. The Class H amplifier had an efficiency above the Class AB amplifier by 5-7% from 5-30mW of output power without affecting the total harmonic distortion (THD) at the design specifications. The Class H amplifier design met all design specifications and showed performance comparable to the designed Class AB amplifier across 1kHz-20kHz and 0.01mW-30mW. The Class H design was able to output 30mW into 16Ohms without any increase in THD. This design shows that Class H amplifiers merit more research into their potential for increasing efficiency of audio amplifiers and that even simple designs can give significant increases in efficiency without compromising linearity. / Dissertation/Thesis / M.S. Electrical Engineering 2013

As a scalable, high-efficiency, and simple converter topology, an interleaved, multiphase buck converter has been widely used to power microprocessors in information industry. As modern microprocessors continuously advance, the required current for high-performance microprocessors used in data center applications could be several hundreds of amperes with a current slew rate larger than 1000 A/μs. This poses great challenges for a high-efficiency, high-power-density voltage regulator design with a fast transient response. On the other hand, the design challenges of voltage regulators in mobile applications are also increasing due to the stringent requirement on the device thickness and the battery life. In a multiphase buck converter, discrete inductors are widely used as energy storage elements. However, this solution has a limited transient response with a large size of magnetic components. To overcome these issues, coupled inductor is proposed to realize a small steady-state current ripple, a fast transient response, and a small inductor size at the same time. Although lots of studies have been conducted in the topic of the coupled inductor, there are still several challenges unsolved in this area. These challenges are addressed through a comprehensive study in this dissertation. First, a comprehensive analysis of different coupled inductor structures is crucial to identify the benefits and limitations of each inductor structure and provide design guidance under different application requirements. Based on the coupling mechanism, different coupled inductor structures are categorized as a direct-coupled inductor (DCL), an indirect-coupled inductor (ICL) or a hybrid-coupled inductor (HCL) in this work. The performance of these three types of coupled inductors is analyzed in detail through the equivalent inductance analysis and the magnetic flux analysis. For the applications that require a small phase number, a DCL can achieve the smallest inductor size with a given inductance requirement. As the phase number increases, it is beneficial to use an ICL and an HCL due to their symmetrical, simple, and scalable inductor structures. As compared to an ICL, an HCL can achieve a smaller inductor size due to the flux-cancellation effect. The difference between a DCL, an ICL and an HCL are revealed quantitively with several design examples through this study. Second, the steady-state inductance (Lss) and the transient inductance (Ltr) are two key design parameters for coupled inductors. A large Lss and a small Ltr are preferred from the circuit performance point of view. However, there is a design conflict in an ICL and an HCL under the inductor size constraint, where reducing Ltr also results in a smaller Lss. A variable coupling coefficient concept is proposed to overcome this issue. With the same Lss, the proposed method can achieve a smaller Ltr during load transients as compared with the conventional method. This concept is realized by applying a nonlinear inductor in the additional winding loop with the current in this loop as the control source. Compared with the conventional structure, the proposed structure can achieve a great output voltage spike reduction and output capacitance reduction. Third, although an ICL and an HCL are promising candidates for multiphase coupled inductors, an extra inductor is required in the additional winding loop to adjust the coupling coefficient. This additional inductor occupies extra space. To shrink the total inductor size, several improved magnetic core structures are proposed to achieve the controllable coupling through the magnetic integration for an ICL and an HCL. Furthermore, the thickness of the core plate can be significantly reduced by the improved core structure for an HCL. Overall, it is demonstrated that the inductor footprint is greatly reduced by the proposed core structure, as compared with the conventional solution. Lastly, a novel PCB-embedded coupled inductor structure is proposed for a 20MHz integrated voltage regulator (IVR) for mobile applications. To achieve a small inductor footprint and a low profile, the inductor structure with a lateral flux pattern and direct coupling is adopted. Compared with the state-of-the-art solution, the proposed structure can adjust the coupling in a simple core structure by changing the inductor winding pattern. The proposed structure integrates multiple inductors into one magnetic core and is embedded into PCB with a total thickness of 0.54 mm. In contrast to prior arts, the proposed inductor structure features a large inductance density and quality factor with a much smaller DC resistance (DCR), thus is seen as a promising candidate for IVR applications. / Doctor of Philosophy / As modern microprocessors continuously advance in the information industry, the required current for high-performance microprocessors used in data center applications could be several hundreds of amperes with a current slew rate larger than 1000 A/μs. This poses great challenges for the power converter design. On the other hand, the design challenges of power converters in mobile applications are also increasing due to the stringent requirement on the device thickness and the battery life. As a scalable, high-efficiency, and simple converter topology, an interleaved, multiphase buck converter has been widely used to power these processors. In a multiphase buck converter, discrete inductors are widely used as energy storage elements. However, this solution has a limited transient response with a large size of magnetic components. To overcome these issues, coupled inductor is proposed to realize a small steady-state current ripple, a fast transient response, and a small inductor size at the same time. Although lots of studies have been conducted in the topic of the coupled inductor, there are still several challenges unsolved in this area. These challenges are addressed through a comprehensive study in this dissertation. First, a comprehensive analysis and comparison of different coupled inductor structures is crucial to identify the benefits and limitations of each inductor structure and provide design guidance under different application requirements. Based on the coupling mechanism, different coupled inductor structures are categorized as a direct-coupled inductor (DCL), an indirect-coupled inductor (ICL) or a hybrid-coupled inductor (HCL) in this work. The performance of these three types of coupled inductors is analyzed in detail through the equivalent inductance analysis and the magnetic flux analysis. The difference between a DCL, an ICL and an HCL are revealed quantitively with several design examples through this study. Second, the steady-state inductance (Lss) and the transient inductance (Ltr) are two key design parameters for coupled inductors. A large Lss and a small Ltr are preferred from the circuit performance point of view. However, there is a design conflict in an ICL and an HCL under the inductor size constraint, where reducing Ltr also results in a smaller Lss. A variable coupling coefficient concept is proposed to overcome this issue. This concept is realized by applying a nonlinear inductor in the conventional structure. Compared with the conventional structure, the proposed structure can achieve a great output voltage spike reduction and output capacitance reduction. Third, although an ICL and an HCL are promising candidates for multiphase coupled inductors, an extra inductor is required in the additional winding loop to adjust the coupling coefficient. This additional inductor occupies extra space. To shrink the total inductor size, several improved magnetic core structures are proposed to achieve the controllable coupling through the magnetic integration for an ICL and an HCL. Lastly, a novel PCB-embedded coupled inductor structure is proposed for a 20MHz integrated voltage regulator (IVR) for mobile applications. Compared with the state-of-the-art solution, the proposed structure can adjust the coupling in a simple core structure by changing the inductor winding pattern. In contrast to prior arts, the proposed inductor structure features a large inductance density and quality factor with a much smaller DC resistance (DCR), thus is seen as a promising candidate for IVR applications.

The trend in isolated DC/DC bus converters is to increase the output power in the same brick form factors that have been used in the past. Traditional intermediate bus converters (IBCs) use silicon power metal oxide semiconductor field effect transistors (MOSFETs), which recently have reached the limit in terms of turn on resistance (RDSON) and switching frequency. In order to make the IBCs smaller, the switching frequency needs to be pushed higher, which will in turn shrink the magnetics, lowering the converter size, but increase the switching related losses, lowering the overall efficiency of the converter. Wide-bandgap semiconductor devices are becoming more popular in commercial products and gallium nitride (GaN) devices are able to push the switching frequency higher without sacrificing efficiency. GaN devices can shrink the size of the converter and provide better efficiency than its silicon counterpart provides. A survey of current IBCs was conducted in order to find a design point for efficiency and power density. A two-stage converter topology was explored, with a multiphase buck converter as the front end, followed by an LLC resonant converter. The multiphase buck converter provides regulation, while the LLC provides isolation. With the buck converter providing regulation, the switching frequency of the entire converter will be constant. A constant switching frequency allows for better electromagnetic interference (EMI) mitigation. This work includes the details to design and implement a hard-switched multiphase buck converter with planar magnetics using GaN devices. The efficiency includes both the buck efficiency and the overall efficiency of the two-stage converter including the LLC. The buck converter operates with 40V - 60V input, nominally 48V, and outputs 36V at 1 kW, which is the input to the LLC regulating 36V – 12V. Both open and closed loop was measured for the buck and the full converter. EMI performance was not measured or addressed in this work. / Master of Science / Traditional silicon devices are widely used in all power electronics applications today, however they have reached their limit in terms of size and performance. With the introduction of gallium nitride (GaN) field effect transistors (FETs), the limits of silicon can now be passed with GaN providing better performance. GaN devices can be switched at higher switching frequencies than silicon, which allows for the magnetics of power converters to be smaller. GaN devices can also achieve higher efficiency than silicon, so increasing the switching frequency will not hurt the overall efficiency of the power converter. GaN devices can handle higher switching frequencies and larger currents while maintaining the same or better efficiencies over their silicon counterparts. This work illustrates the design and implementation of GaN devices into a multiphase buck converter. This converter is the front end of a two-stage converter, where the buck will provide regulation and the second stage will provide isolation. With the use of higher switching frequencies, the magnetics can be decreased in size, meaning planar magnetics can be used in the power converter. Planar magnetics can be placed directly inside of the printing circuit board (PCB), which allows for higher power densities and easy manufacturing of the magnetics and overall converter. Finally, the open and closed loop were verified and compared to the current converters that are on the market in the 48V – 12V area of intermediate bus converters (IBCs).