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A new analysis of a class E power amplifier is presented and a fully analytic design approach is developed. Using our analysis, all of the circuit currents and voltages and, hence, the power dissipation in each component is calculated as a function of a key design parameter, denoted by x. This parameter is the ratio of the resonance frequency of the shunt inductor and shunt capacitor to the operating frequency. We have shown that there is a limited continues range for this parameter, in which class E operation with realizable circuit is achieved. Three conventional design methods, namely infinite dc feed, parallel circuit, and even harmonic design methods are the special cases, corresponding to a certain value of x. Our analysis explains the power efficiency, the power capability, and other characteristics of the class E power amplifier circuit as a function of the parameter x. We have developed new design formulas that give the values of the circuit components for each value of x. These equations enable the designer to analytically optimize the circuit for a desired performance measure, such as power efficiency or power capability. To obtain the optimum design, the shunt inductor quality factor and the switch on-state resistance must be given. Then, one can find the value of x corresponding to the optimum value of the given performance measure. The analysis results show that the power efficiency is better a optimization measure than power capability. To assess the analysis results and to compare the new design method with the conventional methods, we have used the foundry design kit for STMicroelectronics 90-nm global-purpose CMOS process. For this purpose, we have designed four identical class E power amplifiers, one using the parallel-circuit method, another with the even-harmonic method, and two others with the proposed design method. One of the latter has been optimized for maximum power capability and the other for maximum po- - wer efficiency. The designed power amplifiers have been simulated in the foundry design kit and the simulation results prove the accuracy of the analysis and reveal the usefulness of our design method.