This study proposes an approach to obtain maximum power via wireless power transfer using a single primary-side capacitor. It is shown that higher power is achieved when compared to the common wireless power transfer circuit under resonance with dual (primary- and secondary-side) capacitors. This approach is divided into three phases. By choosing the capacitor and frequency as freely assignable variables, we symbolically obtain a formula that allows us to determine the optimized capacitance and frequency for maximum power. To verify our method, we used a numerical analysis and compared it with an electronic circuit simulation. The symbolic formula is able to maintain maximum power despite changes in load or in the coupling coefficients.

In this note, the novel representation is proposed for a linear periodic continuous-time system with T-periodic real-valued coefficients. We prove that a T-periodic real-valued factor and two real-valued matrix exponential functions can be extracted from a state transition matrix, while, in the well-known Floquet representation theorem, a 2T-periodic real-valued factor and a real-valued matrix exponential function are extracted from the state transition matrix. Then we also proved that any T-periodic system can be transformed to a system with T-periodic real-valued trigonometric coefficients using a T-periodic real-valued coordinate transformation, while, in the well-known Lyapunov reducibility theorem, a 2T-periodic real-valued coordinate transformation is utilized to transform the given periodic system into a time-invariant system with real coefficients. This new information can be useful for designing a T-periodic control law.