By multiplying with the continuous factor (CF), the conventional Class- F / F - 1 , Class-J power amplifier (PA) can be expanded to their corresponding continuous modes, resulting in a great degree of freedom for broadband design. However, this method can hardly apply to other types of PAs. In view of this problem, the continuous mode is deeply analyzed from the perspective of equation solving for the first time, and a general theory for high-efficiency broadband continuous PA design is proposed. In this theory, the continuous impedance space does not rely on a mapping relationship achieved by multiplying with the CF, but on a direct solution of the high-efficiency equations to obtain the broadband design space. This approach is simpler and has the potential to provide greater design space. As a validation, this theory is used for the analysis of Class-E PAs and a new continuous Class-E (NC-E) PA is presented. With knee-point voltage and finite harmonics taken into account, this type of PA greatly expands the broadband design space of Class-E PAs, and also has the advantage of harmonic matching. The NC-E PA is designed and manufactured using GaN HEMT CGH40010F, which achieves 40.6∼41.6dBm output power and 66.2%∼74.2% drain efficiency (DE) in the frequency band of 2.5-3.8GHz.