Analysis of Envelope-Tracking Power Amplifier Using Mathematical Modeling

This paper describes analysis of an envelope-tracking power amplifier (ET PA) to show its operational behavior. The RF PA is modeled by sweeping the input power and supply voltage. The RF PA model is composed of three 2-D lookup tables including the amplitude-to-amplitude modulation, amplitude-to-phase modulation, and amplitude-to-efficiency modulation. The hybrid switching supply modulator is also modeled using an ideal op-amp, ideal switches, and other assisting blocks. Based on the mathematical models of the RF PA and supply modulator, the ET PA can be analyzed with a fast calculation speed and a good accuracy to find the optimum ET operation point. A power control strategy is presented for the optimal ET operation over a broad output power range. The effect of the delay mismatch on the characteristics of the ET PA is also described to assist the time alignment algorithm. For a 10-MHz long-term evolution signal with a 7.44-dB PAPR, the implemented ET PA at 1.71 GHz delivers a PAE of 44.3%, a gain of 29 dB, an evolved universal terrestrial radio access adjacent channel leakage ratio of -35.1 dBc, and an error vector magnitude of 2.91% at an average output power of 28 dBm.