As wireless cellular communication keeps expanding toward higher bandwidth, multiband signals, and high frequencies of operation, the design of power efficient radio frequency power amplifiers (PAs) for cellular phone basestations is submitted to more stringent requirements. This paper discusses the promising technique of nonlinear embedding , which may help stream line the design of such PAs. To this order, the design of a GaN radio frequency PA from device modeling to circuit design is presented. The large signal modeling of GaN high-electron-mobility transistors including thermal and trapping memory effects is discussed first. The nonlinear embedding device model is then introduced using the concept of an anti-circuit transfer network. This embedding device model is then applied to the design of a Chireix amplifier. New Chireix design equations are developed to work with the memoryless inner core of the embedding device model, and their validity is confirmed in circuit simulations. The Chireix amplifier is then designed using the multi-harmonic impedance terminations predicted by the embedding device model for the package reference planes. Finally, the resulting Chireix amplifier is implemented in a circuit simulator with the original GaN high-electron-mobility transistors device model and verified in simulations to have a performance approaching that of the originally targeted Chireix at the current reference planes. These theoretical and simulation results demonstrate the potential of the nonlinear embedding PA design technique in the design of Chireix power amplifiers.