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A new methodology for designing and implementing high-efficiency broadband Class-E power amplifiers (PAs) using high-order low-pass filter-prototype is proposed in this paper. A GaN transistor is used in this work, which is carefully modeled and characterized to prescribe the optimal output impedance for the broadband Class-E operation. A sixth-order low-pass filter-matching network is designed and implemented for the output matching, which provides optimized fundamental and harmonic impedances within an octave bandwidth (L-band). Simulation and experimental results show that an optimal Class-E PA is realized from 1.2 to 2 GHz (50%) with a measured efficiency of 80%-89%, which is the highest reported today for such a bandwidth. An overall PA bandwidth of 0.9-2.2 GHz (84%) is measured with 10-20-W output power, 10-13-dB gain, and 63%-89% efficiency throughout the band. Furthermore, the Class-E PA is characterized through measurements using constant-envelop global system for mobile communications signals, indicating a favorable adjacent channel power ratio from -40 to -50 dBc within the entire bandwidth.