Novel Inductor‐less Conversion Strategy Based on Multiphase Transformer‐Coupled Converters: Analysis, Design and Applications

There are many the requirements that modern power converters should fulfill. Most of the applications where these converters are used, demand smaller converters with high efficiency, improved power density and a fast dynamic response. For instance, loads like microprocessors demand aggressive current steps with very high slew rates (100A/mus and higher); besides, during these load steps, the supply voltage of the microprocessor should be kept within tight limits in order to ensure its correct performance. The accomplishment of these requirements is not an easy task; complex solutions like advanced topologies - such as multiphase converters- as well as advanced control strategies are often needed. Besides, it is also necessary to operate the converter at high switching frequencies and to use capacitors with high capacitance and low ESR. Improving the dynamic response of power converters does not rely only on the control strategy but also the power topology should be suited to enable a fast dynamic response. Moreover, in later years, a fast dynamic response does not only mean accomplishing fast load steps but output voltage steps are gaining importance as well. At least, two applications that require fast voltage changes can be named: Low power microprocessors. In these devices, the voltage supply is changed according to the workload and the operating frequency of the microprocessor is changed at the same time. An important reduction in voltage dependent losses can be achieved with such changes. This technique is known as Dynamic Voltage Scaling (DVS). Another application where important energy savings can be achieved by means of changing the supply voltage are Radio Frequency Power Amplifiers. For example, RF architectures based on ‘Envelope Tracking’ and ‘Envelope Elimination and Restoration’ techniques can take advantage of voltage supply modulation and accomplish important energy savings in the power amplifier. However, in order to achieve these efficiency improvements, a power converter with high efficiency and high enough bandwidth (hundreds of kHz or even tens of MHz) is necessary in order to ensure an adequate supply voltage. The main objective of this Thesis is to improve the dynamic response of DC-DC converters from the point of view of the power topology. And the term dynamic response refers both to the load steps and the voltage steps; it is also interesting to modulate the output voltage of the converter with a specific bandwidth. In order to accomplish this, the question of what is it that limits the dynamic response of power converters should be answered. Analyzing this question leads to the conclusion that the dynamic response is limited by the power topology and specifically, by the filter inductance of the converter which is found in series between the input and the output of the converter. The series inductance is the one that determines the gain of the converter and provides the regulation capability. Although the energy stored in the filter inductance enables the regulation and the capability of filtering the output voltage, it imposes a limitation which is the concern of this Thesis. The series inductance stores energy and prevents the current from changing in a fast way, limiting the slew rate of the current through this inductor. Different solutions are proposed in the literature in order to reduce the limit imposed by the filter inductor. Many publications proposing new topologies and improvements to known topologies can be found in the literature. Also, complex control strategies are proposed with the objective of improving the dynamic response in power converters. In the proposed topologies, the energy stored in the series inductor is reduced; examples of these topologies are Multiphase converters, Buck converter operating at very high frequency or adding a low impedance path in parallel with the series inductance. Control techniques proposed in the literature, focus on adjusting the output voltage as fast as allowed by the power stage; examples of these control techniques are: hysteresis control, V 2 control, and minimum time control. In some of the proposed topologies, a reduction in the value of the series inductance is achieved and with this, the energy stored in this magnetic element is reduced; less stored energy means a faster dynamic response. However, in some cases (as in the high frequency Buck converter), the dynamic response is improved at the cost of worsening the efficiency. In this Thesis, a drastic solution is proposed: to completely eliminate the series inductance of the converter. This is a more radical solution when compared to those proposed in the literature. If the series inductance is eliminated, the regulation capability of the converter is limited which can make it difficult to use the topology in one-converter solutions; however, this topology is suitable for power architectures where the energy conversion is done by more than one converter. When the series inductor is eliminated from the converter, the current slew rate is no longer limited and it can be said that the dynamic response of the converter is independent from the switching frequency. This is the main advantage of eliminating the series inductor. The main objective, is to propose an energy conversion strategy that is done without series inductance. Without series inductance, no energy is stored between the input and the output of the converter and the dynamic response would be instantaneous if all the devices were ideal. If the energy transfer from the input to the output of the converter is done instantaneously when a load step occurs, conceptually it would not be necessary to store energy at the output of the converter (no output capacitor COUT would be needed) and if the input source is ideal, the input capacitor CIN would not be necessary. This last feature (no CIN with ideal VIN) is common to all power converters. However, when the concept is actually implemented, parasitic inductances such as leakage inductance of the transformer and the parasitic inductance of the PCB, cannot be avoided because they are inherent to the implementation of the converter. These parasitic elements do not affect significantly to the proposed concept. In this Thesis, it is proposed to operate the converter without series inductance in order to improve the dynamic response of the converter; however, on the other side, the continuous regulation capability of the converter is lost. It is said continuous because, as it will be explained throughout the Thesis, it is indeed possible to achieve discrete regulation; a converter without filter inductance and without energy stored in the magnetic element, is capable to achieve a limited number of output voltages. The changes between these output voltage levels are achieved in a fast way. The proposed energy conversion strategy is implemented by means of a multiphase converter where the coupling of the phases is done by discrete two-winding transformers instead of coupledinductors since transformers are, ideally, no energy storing elements. This idea is the main contribution of this Thesis. The feasibility of this energy conversion strategy is first analyzed and then verified by simulation and by the implementation of experimental prototypes. Once the strategy is proved valid, different options to implement the magnetic structure are analyzed. Three different discrete transformer arrangements are studied and implemented. A converter based on this energy conversion strategy would be designed with a different approach than the one used to design classic converters since an additional design degree of freedom is available. The switching frequency can be chosen according to the design specifications without penalizing the dynamic response or the efficiency. Low operating frequencies can be chosen in order to favor the efficiency; on the other hand, high operating frequencies (MHz) can be chosen in order to favor the size of the converter. For this reason, a particular design procedure is proposed for the ‘inductorless’ conversion strategy. Finally, applications where the features of the proposed conversion strategy (high efficiency with fast dynamic response) are advantageus, are proposed. For example, in two-stage power architectures where a high efficiency converter is needed as the first stage and there is a second stage that provides the fine regulation. Another example are RF power amplifiers where the voltage is modulated following an envelope reference in order to save power; in this application, a high efficiency converter, capable of achieving fast voltage steps is required. The main contributions of this Thesis are the following: The proposal of a conversion strategy that is done, ideally, without storing energy in the magnetic element. The validation and the implementation of the proposed energy conversion strategy. The study of different magnetic structures based on discrete transformers for the implementation of the proposed energy conversion strategy. To elaborate and validate a design procedure. To identify and validate applications for the proposed energy conversion strategy. It is important to remark that this work is done in collaboration with Intel. The particular features of the proposed conversion strategy enable the possibility of solving the problems related to microprocessor powering in a different way. For example, the high efficiency achieved with the proposed conversion strategy enables it as a good candidate to be used for power conditioning, as a first stage in a two-stage power architecture for powering microprocessors.

Advanced Control for Very Fast DC-DC Converters Based on Hysteresis of the C-out Current

The bandwidth achievable by using voltage mode control or current mode control in switch-mode power supply is limited by the switching frequency. Fast transient response requires high switching frequency, although lower switching frequencies could be more suitable for higher efficiency. This paper proposes the use of hysteretic control of the output capacitor $(C_{out})$ current to improve the dynamic response of the buck converter. An external voltage loop is required to accurately regulate the output voltage. The design of the hysteretic loop and the voltage loop are presented. Besides, it is presented a non-invasive current sensor that allows measuring the current in the capacitor. This strategy has been applied for DVS (dynamic voltage scaling) on a 5 MHz buck converter. Experimental results validate the proposed control technique and show fast transient response from 1.5 V to 2.5 V in 2 $mu{rm s}$.

Magnetic Attitude Control System for a Small Satellite. Impact on the Thermal Performance

El principal objetivo de la tesis es estudiar el acoplamiento entre los subsistemas de control de actitud y de control térmico de un pequeño satélite, con el fin de buscar la solución a los problemas relacionados con la determinación de los parámetros de diseño. Se considera la evolución de la actitud y de las temperaturas del satélite bajo la influencia de dos estrategias de orientación diferentes: 1) estabilización magnética pasiva de la orientación (PMAS, passive magnetic attitude stabilization), y 2) control de actitud magnético activo (AMAC, active magnetic attitude control). En primer lugar se presenta el modelo matemático del problema, que incluye la dinámica rotacional y el modelo térmico. En el problema térmico se considera un satélite cúbico modelizado por medio de siete nodos (seis externos y uno interno) aplicando la ecuación del balance térmico. Una vez establecido el modelo matemático del problema, se estudia la evolución que corresponde a las dos estrategias mencionadas. La estrategia PMAS se ha seleccionado por su simplicidad, fiabilidad, bajo coste, ahorrando consumo de potencia, masa coste y complejidad, comparado con otras estrategias. Se ha considerado otra estrategia de control que consigue que el satélite gire a una velocidad requerida alrededor de un eje deseado de giro, pudiendo controlar su dirección en un sistema inercial de referencia, ya que frecuentemente el subsistema térmico establece requisitos de giro alrededor de un eje del satélite orientado en una dirección perpendicular a la radiación solar incidente. En relación con el problema térmico, para estudiar la influencia de la velocidad de giro en la evolución de las temperaturas en diversos puntos del satélite, se ha empleado un modelo térmico linealizado, obtenido a partir de la formulación no lineal aplicando un método de perturbaciones. El resultado del estudio muestra que el tiempo de estabilización de la temperatura y la influencia de las cargas periódicas externas disminuye cuando aumenta la velocidad de giro. Los cambios de temperatura se reducen hasta ser muy pequeños para velocidades de rotación altas. En relación con la estrategia PMAC se ha observado que a pesar de su uso extendido entre los micro y nano satélites todavía presenta problemas que resolver. Estos problemas están relacionados con el dimensionamiento de los parámetros del sistema y la predicción del funcionamiento en órbita. Los problemas aparecen debido a la dificultad en la determinación de las características magnéticas de los cuerpos ferromagnéticos (varillas de histéresis) que se utilizan como amortiguadores de oscilaciones en los satélites. Para estudiar este problema se presenta un modelo analítico que permite estimar la eficiencia del amortiguamiento, y que se ha aplicado al estudio del comportamiento en vuelo de varios satélites, y que se ha empleado para comparar los resultados del modelo con los obtenidos en vuelo, observándose que el modelo permite explicar satisfactoriamente el comportamiento registrado. ABSTRACT The main objective of this thesis is to study the coupling between the attitude control and thermal control subsystems of a small satellite, and address the solution to some existing issues concerning the determination of their parameters. Through the thesis the attitude and temperature evolution of the satellite is studied under the influence of two independent attitude stabilization and control strategies: (1) passive magnetic attitude stabilization (PMAS), and (2) active magnetic attitude control (AMAC). In this regard the mathematical model of the problem is explained and presented. The mathematical model includes both the rotational dynamics and the thermal model. The thermal model is derived for a cubic satellite by solving the heat balance equation for 6 external and 1 internal nodes. Once established the mathematical model of the problem, the above mentioned attitude strategies were applied to the system and the temperature evolution of the 7 nodes of the satellite was studied. The PMAS technique has been selected to be studied due to its prevalent use, simplicity, reliability, and cost, as this strategy significantly saves the overall power, weight, cost, and reduces the complexity of the system compared to other attitude control strategies. In addition to that, another control law that provides the satellite with a desired spin rate along a desired axis of the satellite, whose direction can be controlled with respect to the inertial reference frame is considered, as the thermal subsystem of a satellite usually demands a spin requirement around an axis of the satellite which is positioned perpendicular to the direction of the coming solar radiation. Concerning the thermal problem, to study the influence of spin rate on temperature evolution of the satellite a linear approach of the thermal model is used, which is based on perturbation theory applied to the nonlinear differential equations of the thermal model of a spacecraft moving in a closed orbit. The results of this study showed that the temperature stabilization time and the periodic influence of the external thermal loads decreases by increasing the spin rate. However, the changes become insignificant for higher values of spin rate. Concerning the PMAS strategy, it was observed that in spite of its extended application to micro and nano satellites, still there are some issues to be solved regarding this strategy. These issues are related to the sizing of its system parameters and predicting the in-orbit performance. The problems were found to be rooted in the difficulties that exist in determining the magnetic characteristics of the ferromagnetic bodies (hysteresis rods) that are applied as damping devices on-board satellites. To address these issues an analytic model for estimating their damping efficiency is proposed and applied to several existing satellites in order to compare the results with their respective in-flight data. This model can explain the behavior showed by these satellites.