Mathieu Equation-Based Analysis and Suppression Approach of Subharmonic Oscillations in High-Frequency Switched-Mode Power Amplifiers

Switched-Mode Power Amplifiers (SMPAs) are preferable in high-power applications due to their advantage of high efficiency. Whereas the undesirable effects of parasitics in the switches and circuits highly affect their applications at higher frequencies. Though the parasitic effects (e.g., natural ringing down and self-sustained oscillations) have been explicitly investigated, subharmonic oscillations (which cause high-voltage pressure and significant subharmonic distortion) have not received adequate study in SMPAs. Therefore, this paper presents a detailed analysis to reveal the mechanism of subharmonic oscillations in SMPAs. According to the analysis, unlike the linear PAs, the non-linear output capacitance (C_oss) of MOSFETs was found to be the main contributor to the subharmonic oscillations in SMPAs. Furthermore, the load branch plays a damping role, and the simplification to describe the damping effect of load parameters, such as load resistance and quality factor, is discussed. Since the C_oss current is difficult to solve explicitly due to the nonlinear differential equations, a Mathieu Equation-based approach is proposed to describe the variation tendency of the current and evaluate the operation stability of SMPAs. Based on the above analysis, the design-oriented and damping tank-based suppression methods are presented to mitigate the subharmonic oscillations. The proposed analysis and design approach is experimentally validated through a 13.56MHz Class E PA, and the experimental and simulated results match well with the analysis. With the proposed suppression methods, the subharmonic oscillations can be eliminated over the whole voltage modulation range.