A Möbius Transformation Impedance Matching Approach for Large Load Region and Multi-Level Power Modulation in High Frequency Switched Mode Power Amplifier

The switched mode power amplifier (PA) is widely used for high frequency high power applications due to its high efficiency. In the switched mode Pas, impedance matching network (IMN) is usually needed to ensure that the varying load impedances can be matched to the target impedances for high efficiency. The existing IMN design methods usually depend on empirical trial and error, load pull simulation, and numerical optimization, which cannot achieve actual region-to-region impedance matching. Therefore, this paper proposed a novel impedance matching design approach for switch mode PAs based on the property of circle preservation in Möbius transformation which guarantee that all the impedance points in a region or trajectory can be precisely transferred to the target region or trajectory. The proposed approach gives the simple and explicit formulas to design the IMN parameters, which helps solve the design challenge of accurate impedance matching for large load region. And the impedance matching design for frequency tuning control is also presented to achieve high efficiency and multi-level power modulation over a large impedance region. For verification, a 500W 13.56MHz GaN-based Class E PA is built and the experiments show that the PA with proposed matching design can achieve 87.2%-95% efficiency over a large load region. And the high speed pulsing (200kHz) and multi-level (25.6kHz) power modulation can be also achieved by frequency tuning with ultra-fast transitions (369ns) and 91% average efficiency by uisng the proposed design.