Duty and Phase Control of a Self-Synchronized Class E Rectifier for High-Frequency Wireless Power Transfer System

This article proposes a high-frequency (HF) wireless power transfer (WPT) system using duty and phase control of a self-synchronized class E rectifier considering the nonlinear internal capacitance of field-effect transistors (FETs). In HF WPT systems (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&gt;$</tex-math></inline-formula><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \text{13.56}\,\text{MHz}$</tex-math></inline-formula>), the self-synchronized class E rectifier provides a precise gate signal by compensating for the propagation delay. However, when controlling the output power of the HF WPT system, the nonlinear capacitance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{\text{oss}}$</tex-math></inline-formula> of FETs distorts the shape of the drain-voltage waveform, which reduces the efficiency due to nonzero-voltage switching or partial diode operation. To mitigate this issue, we propose an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> (=duty ratio) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> (=phase delay) control method for a self-synchronized class E rectifier while considering the nonlinear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{\text{oss}}$</tex-math></inline-formula> of FET. To achieve robust control and performance of the HF WPT system, we employed a regression method to estimate the value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{\text{oss}}$</tex-math></inline-formula> more accurately. Specifically, considering the impact of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{\text{oss}}$</tex-math></inline-formula> on the performance of the HF WPT system, we selected two optimized control points <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P_{\text{max}}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P_{\text{min}}$</tex-math></inline-formula> and developed a first–order polynomial equation representing the relationship between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula>. Following the determined <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula><inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> relationship, the output power of the WPT was adjusted by hysteresis control while maintaining the highest efficiency. In the experimental validation, the proposed WPT system achieved a conversion efficiency of 82% to 76% in the 160–90 W output power range. Finally, the effectiveness of the proposed control method was also verified in closed-loop control during dynamic operation from 160 to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$100\,\mathrm{W}$</tex-math></inline-formula>, with a minimal ripple (1.7%) in the output power.