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`New' Class-E solutions are proposed by varying three different design parameters which are introduced in the voltage and current equations in order to extend the Class-E `design space', of which the `new' solutions can apply to optimal and suboptimal operation. The design procedure of suboptimal Class-E power amplifier (PA) is analysed in details and then a suboptimal Class-E PA based on GaN HEMT CGH40010F is designed to prove the correctness of the `new' solutions. The measured maximum output power of 39.6 dB, power-added-efficiency of 74.7% and drain efficiency of 78.9% were obtained at 2.6 GHz with a 28 dBm input power. These measurement results show that a similar or better level of efficiency and output power that are reported for optimal Class-E PAs at lower frequencies using the same transistor, and the presented `new' solutions extend the `design space' of Class-E PA. This paper give engineers more degrees of freedom to design Class-E PA.