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This paper presents the operation principle of Class-J power amplifiers (PAs) with linear and nonlinear output capacitors (Couts). The efficiency of a Class-J amplifier is enhanced by the nonlinear capacitance because of the harmonic generation from the nonlinear Cout, especially the second-harmonic voltage component. This harmonic voltage allows the reduction of the phase difference between the fundamental voltage and current components from 45° to less than 45° while maintaining a half-sinusoidal shape. Therefore, a Class-J amplifier with the nonlinear Cout can deliver larger output power and higher efficiency than with a linear Cout. As a further optimized structure of the Class-J amplifier, the saturated PA, a recently-reported amplifier in our group, is presented. The phase difference of the proposed PA is zero. Like the Class-J amplifier, the PA uses a nonlinear Cout to shape the voltage waveform with a purely resistive fundamental load impedance at the current source, which enhances the output power and efficiency. The PA is favorably compared to the Class-J amplifier in terms of the waveform, load impedance, output power, and efficiency. These operations are described using both the ideal and real models of the transistor in Agilent Advanced Design System. A highly efficient amplifier based on the saturated PA is designed by using a Cree GaN HEMT CGH40010 device at 2.14 GHz. It provides a power-added efficiency of 77.3% at a saturated power of 40.6 dBm (11.5 W).