Numerical Optimization for High-frequency Class-E Switching Circuits
Wenqi ZHU
February 2022
High-frequency power converter circuits are desired because the resonant inductance andelectromagnetic interference (EMI) filter become small. However, the switching losses increase
proportionally as the switching frequency increases, resulting in power conversion efficiency
degradation and the requirement for a large cooling system. Therefore, at megahertz-range
operations, it is mandatory to achieve soft switching. For achieving high-frequency power
converter, the class-E families, such as class-E, class-DE, class-EF, and class-Phi inverters, are thesuitable candidates with only one MOSFET. Additionally, the source terminal of the MOSFET isconnected to the ground. Therefore, there is no need for high-side drivers. By applying the ZVS tothe class-E2 converter for both turn-on and turn-off switching, the switching loss can be reducedeffectively.
Nevertheless, the decision of circuit components of the class-E inverter family is challenging due tothe complicated working principle. The circuit component, including the output resonant filter andshunt capacitance, have a complicated effect on the circuit operation. These component values
should be found to satisfy the class-E ZVS and ZDS conditions simultaneously. There are two kindsof component-derivation methods in general, including analytical-based derivation procedures andnumerical-calculation-based ones. The analysis of class E circuits allows the values of circuitcomponents to be explicitly expressed as functions of circuit parameters. Early papers on theanalysis of class E amplifiers are based on some several ideal conditions. Subsequently, the initialassumptions were gradually relaxed. Nevertheless, it requires knowledge and experiment to perform
circuit analysis, which is time-consuming.
For the real applications of the power converter, the conditions such as load devices are everchanging, which may lead to the variation of system output. Therefore, control methods are usuallyapplied to the power converter. For example, regulated output voltage and power factor correction
control are usually applied for the AC-DC converter. For that reason, the circuit works in thetransient states due to the ac input-line voltage and controlled parameters. To achieve high powerconversion efficiency, it is necessary to ensure the achievement of soft-switching conditions overthe entire range of input line-voltage periods. However, there is no numerical design method for theclass-E AC-DC converter which can achieve ZVS for the entire line-voltage period.
In this thesis, a numerical design method based on the Newton-Raphson method is presented inthis thesis for the designing of novel AC-DC converters based on class-E2 topology at MHzoperation. Taking advantage of the class-E switching circuits, a single-switch structure can beachieved. Additionally, a frequency modulation (FM) controller is presented in this section todecrease total harmonic distortion. However, traditional analysis-based design is unpracticalbecause circuit analysis is difficult considering switching frequency variation. For solving thisproblem, a numerical design procedure is proposed in this section. By visualization of switch

voltage patterns, circuit parameters that can achieve ZVS for the entire input line-voltage cycle
can be selected. By conducting the circuit experiment, the validity of the design method
introduced in this section was proven.
Secondly, the comprehensive numerical design method for the class-E switching circuits isproposed. The proposed design method can be applied to a variety of class-E inverters, including
the class-E, class-EF, and class-phi inverters. Unlike the previous equation-solving-based designmethods, there is no limitation on the number of design parameters. It is unnecessary to find theinitial parameters or partial differential equations. The Particle Swarm Optimization (PSO)
algorithm is adopted for optimization. Additionally, only by modifying the PSO algorithm, we
also develop the design method, which provides the parameter sets of different operation modes in
the identical circuit topology simultaneously, such as the class-E amplifier and the frequency
multipliers. Additionally, by evaluating only the system power loss, we can automatically obtain
the parameter set for satisfying the class-E ZVS/ZDS conditions.
Thirdly, a numerical design method for achieving load-independent condition for class-E
switching circuits are proposed in this thesis. As one of the drawbacks of the traditional class-E
switching circuits, the output voltage, current, and ZVS achievement are highly sensitive to loadvariation. For solving this problem, load-independent technology was proposed.
In this research, evaluation functions for achieving load-independent conditions are proposed. By
applying the PSO algorithm, the circuit parameters for achieving the class-E load-independentconditions can be derived.