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This paper presents a comprehensive analysis of the intrinsic losses in hybrid envelope tracking power supply modulators used in envelope tracking power amplifier systems. The losses are computed entirely symbolically in terms of system parameters and a single design parameter. Resulting formulations are used to provide design insight into optimum biasing to minimize losses in a hybrid configuration, and establish the theoretical upper bound of achievable efficiency. To illustrate the value of this analysis, a Rayleigh distributed waveform is used to evaluate the performance of the hybrid modulator to describe OFDM and other complex modulation schemes. This paper demonstrates that the common convention of biasing the linear converter’s output stage to have zero average current is generally suboptimal from a loss perspective, and establishes how efficiency can be improved without modifying the underlying circuit topology. These findings are validated with a series of simulations modeling a hybrid modulator implemented in a 180-nm CMOS process. This paper derives for the first time, the intrinsic theoretical losses in the hybrid envelope modulator configuration.

Analysis of Systematic Losses in Hybrid Envelope Tracking Modulators