A Methodology for Practical Design and Optimization of Class-E DC-DC Resonant Converters

Abstract

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.

A Comparison between Class-E DC-DC Design Methodologies for Wireless Power Transfer

“…Due to this, the standard sinusoidal approximation cannot be used for its design. We rely its design on an innovative procedure first proposed in [12] and improved in [13] that is based on the exact analysis of the differential equations regulating the converter evolution, and possibly due to the low number of reactive elements in the circuit. Note that, being this analysis exact, it allows a much more accurate design with respect to the previously considered approximated one.…”

“…The last available degree of freedom for the class-E design is the duty cycle D of the main clock. According to [13] and [15], D = 30% has been chosen in order to reduce the voltage stress V DS (t) across the main switch. The lower peak value of the V DS (t) can be clearly appreciated in Figure 3.…”

“…By putting the latter data into the model developed in [13], the desired design is achieved for C inv = 32.9 nF, C rec = 36.3 nF and L p = L s = 688.7 nH. A screenshot of the voltage V DS (t), taken from the Spice simulation, is shown in Figure 3(b) where it can be clearly seen that for k = 0.1 the voltage exactly reaches the zero voltage level just before the MOS turn-ON instant (ZVS).…”

“…A screenshot of the voltage V DS (t), taken from the Spice simulation, is shown in Figure 3(b) where it can be clearly seen that for k = 0.1 the voltage exactly reaches the zero voltage level just before the MOS turn-ON instant (ZVS). As described in [13], if k is too low, it is not possible to satisfy both ZVS and ZVDS unless we add an additional inductance. It is worth noting that the beneficial effects deriving from ZVDS are less relevant than the negative consequences deriving from the addition of an extra passive component in terms of power loss, size, and cost.…”

“…In the much simpler topology of Figure 2, no circuital elements are introduced to make the sinusoidal approximation reasonable. Therefore, we use the completely different approach proposed in [12], [13] that is based on an exact analysis of the circuit behavior.…”