# Active Source Management to Maintain High Efficiency in Resonant Conversion over Wide Load Range

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High-frequency and large amplitude current is a driving requirement for applications such as induction heating, wireless power transfer, power amplifier for magnetic resonant imaging, electronic ballasts, and ozone generators. Voltage-fed resonant inverters are normally employed, however, current-fed (CF) resonant inverters are a competitive alternative when the quality factor of the load is significantly high. The input current of a CF resonant inverter is considerably smaller than the output current, which benefits efficiency. A simple, parallel resonant tank is sufficient to create a high-power sinusoidal signal at the output. Additionally, input current is limited at the no-load condition, providing safe operation of the system. Drawbacks of the CF resonant inverter are associated with the implementation of the equivalent current source. A large input inductor is required to create an equivalent dc current source, to reduce power density and the bandwidth of the system. For safety, a switching stage is implemented using bidirectional voltage-blocking switches, which consist of a series connection of a diode and a transistor. The series diode experiences significant conduction loss because of large on-state voltage. The control of the output current amplitude for constant-frequency inverters requires a pre-regulation stage, typically implemented as a cascaded hard-switched dc/dc buck converter. The pre-regulation also reduces the efficiency.

In this dissertation, a variety of CF resonant inverters with two input inductors and two grounded switches are investigated for an inductive-load driver with loaded quality factor larger than ten, constant and high-frequency (~500 kHz) operation, high reactive output power (~14 kVA), high bandwidth (~100 kHz), and high efficiency (over 95 %). The implementation of such system required to question the fundamental operation of the CF resonant inverter. The input inductance is reduced by around an order of magnitude, ensuring sufficient bandwidth, and allowing rich harmonic content in the input current. Of particular importance are fundamental and second harmonic components since they influence synchronization of the zero-crossing of the output voltage and the turn-on of the switches. The synchronization occurs at a particular frequency, termed synchronous frequency, and it allows for zero switching loss in the switches, which greatly boosts efficiency. The synchronous conditions were not know prior this work, and the dependence among circuit parameters, input current harmonics, and synchronous frequency are derived for the first time. The series diode of the bidirectional switch can reduce the efficiency of the system to below 90 %, and has to be removed from the system. The detrimental current-spikes can occur if the inverter is not operated in synchronous condition, such as in transients, or during parametric variations of the load coil. The resistance of the load coil has a wide variance, five times or more, while the inductance changes as well by a few percent. To accommodate for non-synchronous conditions, a low-loss current snubber is proposed as a safety measure to replace lossy diodes. The center-piece of the dissertation is the proposal of a two-phase zero-voltage switching buck pre-regulator, as it enables fixed frequency and synchronous operation of the inverter under wide parametric variations of the load. The synchronous operation is controlled by phase-shifting the switching functions of the pre-regulator and inverter. The pre-regulator reduces the dc current in the input inductors, which is a main contributor to current stress and conduction losses in the inverter switches. Total loss of the inverter switches is minimized since no switching loss is present and minimal conduction losses are allowed. The dc current in the input inductors, once seen as a means to transfer power to load, is now contradictory perceived as parasitic, and the power is transferred to the load using a fundamental frequency harmonic! The input current to the resonant tank, previously designed to be a square-wave, now resembles a sine-wave with very rich harmonic content. Additionally, the efficiency of the pre-regulator at heavy-load condition is improved by ensuring ZVS for with an additional inductive tank.

The dissertation includes five chapters. The first chapter is an introduction to current-fed resonant inverters, applications, and state-of-the-art means to ensure constant frequency operation under load's parametric variations. The second chapter is dedicated to the optimization of the CF resonant inverter topology with a dc input voltage, two input inductors, and two MOSFETs. The topology is termed as a boost amplifier. If the amplifier operates away from the synchronous frequency, detrimental current spikes will flow though the switches since the series diodes are eliminated. Current spikes reduce the efficiency up to few percent and can create false functioning of the system. Operation at the synchronous frequency is achieved with large, bulky, input inductors, typically around 1-2 mH or higher, when the synchronous frequency follows the resonant frequency of the tank at 500 kHz. The input inductance cannot be reduced arbitrarily to meet the system bandwidth requirement, since the synchronous frequency is increased based on the inductance value. The relationship between the two (input inductance and the synchronous frequency) was unknown prior this work. The synchronous frequency is determined to be a complicated mathematical function of harmonic currents through the input inductors, and it is found using the harmonic decomposition method. As a safety feature, a current snubber is implemented in series with the resonant tank. Snubber utilizes a series inductance of cable connection between the tank and the switching stage, and it is more efficient than the previously employed series diodes. Topology optimization and detailed design procedure are provided with respect to efficiency and system dynamics. The mathematics is verified by a prototype rated at 14 kVA and 1.25 kW. The input inductance is reduced by around an order of magnitude, with the synchronous frequency increase of 2 %. The efficiency of the power amplifier reached 98.5 % and might be improved further with additional optimization. Silicon carbide MOSFETs are employed for their capability to operate efficiently at high frequency, and high temperature.

The third chapter is dedicated to the development of the boost amplifier's large signal model using the Generalized State-space Averaging (GSSA) method. The model accurately predicts amplifier's transient and steady-state operation for any type of input voltage source (dc, dc with sinusoidal ripple, pulse-width modulated), and for either synchronous or non-synchronous operating frequency. It overcomes the limitation of the low-frequency model, which works well only for dc voltage-source input and at synchronous frequency. As the measure of accuracy, the zero-crossing of the resonant voltage is predicted with an error less than 2° over a period of synchronous operation, and for a range of interest for input inductance (25 μH – 1000 μH) and loaded-quality factor (10 – 50). The model is validated both in simulation and hardware for start-up transient and steady-state operation. It is then used in the synthesis of modulated output waveforms, including Hann-function and trapezoidal-function envelopes of the output voltage/current.

In the fourth chapter, the GSSA model is employed in development of the PWM compensation method that ensures synchronous operation at constant frequency for the wide variation of the load. The boost amplifier is extended with a cascaded pre-regulator whose main purpose is to control the output resonant voltage. The pre-regulator is implemented as two switching half-bridges with same duty-cycle and phase-shift of 180°. The behavior of the cascaded structure is the same as of the buck converter, so the half-bridges are named buck pre-regulators. ZVS operation is ensured by putting an inductive tank between the half-bridges. Each output of half-bridges is connected to each of input inductors of the boost to provide the PWM excitation. Using the GSSA model, the synchronous condition and control laws are derived for the amplifier. Properties of the current harmonics in the input inductors are well examined. It is discovered that the dc harmonic, once used to transfer power, is unwanted (parasitic) since it increases conduction loss in switches of the boost. A better idea is to use the fundamental harmonic for power transfer, since it does not create loss in the switches. Complete elimination of the dc current is not feasible for constant frequency operation of the amplifier since the dc current depends on the load coil's resistance. However, significant mitigation of around 55 % is easily achievable. The proposed method improves significantly the efficiency of both the buck pre-regulator and the boost. Synchronous operation is demonstrated in hardware for fixed switching frequency of 480 kHz, power level up to 750 W, input voltage change from 300 V to 600 V, load coil's resistance change of three times, and load coil's inductance change of 3.5 %. Measured efficiency is around 95 %, with a great room for improvements. Chapter five summarizes key contributions and concludes the dissertation.