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In this brief, a continuum of novel closed-form solutions is derived for class-E power amplifiers (PAs). It is analytically proven that the class-E zero voltage/zero voltage derivative switching conditions can be satisfied for an arbitrarily selected reactive second harmonic switch impedance (Z2S). The higher order harmonic currents are terminated capacitively. The conventional class-E, class- E/F2, and class-EF2 modes are thus subsets of the continuum. The arbitrary selection of Z2S enables robust waveform engineering for performance optimization in specific applications. Furthermore, the theoretical derivation provides important possibilities for wideband class-E PA synthesis.