In recently published papers, an innovative analytical approach for the design of a class-E resonant dc-dc converter has been first proposed and further extended to many other class-E converter topologies. Its peculiarity is to be dimensionless and based on the exact solution of the system of differential equations regulating the behavior of the circuit, ensuring very high precision and reliability with respect to all methodologies previously proposed by the state-of-the-art and based on the so-called sinusoidal approximation. Here, we review this methodology and improve it in a twofold way. On the one hand, we propose alternative modeling for some devices (in particular the transformer), increasing both flexibility and generality, with the possibility to extend the application to more topologies and more working points. On the other hand, a new normalization is proposed, showing that the actual dimension of the design workspace is 2, and not 3 as assumed in the previous works. This has important consequences. As an example, the solution existence condition can be represented on a simple 2D plot, with the possibility to immediately check whether the optimal class-E condition can be ensured or not. Furthermore, we can completely and conveniently explore the entire design space to investigate properties such as the stress on the switching devices or the root-mean-square currents, allowing further optimization of the converter design. INDEX TERMSCircuit theory, class-E converters, dc-dc converters, resonant converters. I. INTRODUCTIONResonant dc-dc converters have been introduced to operate at high switching frequencies and so increase system power density [1]-[8], with advantages also in terms of dynamic performance [2] and EMI [8], [9]. Frequencies up to the VHF range 30 − 300 MHz are possible [6], [7] by lowering switching losses thanks to techniques used in radio-frequency (RF) power amplifiers [1], [2], [10], thus overcoming the main drawback of conventional switching topologies given by the frequency-dependent losses.We focus here on the class-E approach [2], [5], featuring the so-called soft-switching technique in opposition to the hard-switching of class-D converters. It was first proposedThe associate editor coordinating the review of this manuscript and approving it for publication was Yuh-Shyan Hwang.

In this paper, the design of a wireless power transfer system (WPT) targeting biomedical implants is considered. The novelty of the approach is to propose a co-design of the transmitter and receiver side based on the design of class-E isolated DC-DC converters. The solution, along with the simple introduction of a shunt regulator at the receiver, allows us to solve the problem of ensuring optimal efficiency in the WPT link. In conventional solutions, in order to cope with coupling factor and load variations, information from the receiver is needed, which is usually relayed back onto the transmitter by means of telemetry. With the proposed approach, a very simple minimum power point tracking (mPPT) algorithm can be used to maximize the WPT efficiency based on the information already available at the transmitter side. This reduces the complexity of the circuitry of the implant and thereby its power overhead and possibly its size, both being crucial constraints of a biomedical implant.

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We consider the design of Wireless Power Transfer (WPT) systems based on inductive links and focus on recent works where the whole WPT system (i.e. both energy transmitter and energy receiver) is designed as an isolated resonant class-E DC-DC converter characterized by a loosely-coupled transformer. The aim of this work is to compare the classic WPT design approach with a novel one, which allows achieving the same performance with a significant reduction in the number of reactive components of the circuit, with beneficial effects in terms of system complexity, size, and cost. We will also show that such a reduction in the number of reactive components leads to improved performance robustness to variations in the inductive link coupling factor.

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