Nonlinear Three-Port Representation of PAs for Embedded Self-Calibration of Envelope-Dependent Dynamic Biasing Implementations

This paper proposes a three-port power amplifier (PA) representation based on distinct sets of nonlinear complex polynomials that describe a combiner, a nonlinear baseband-to-RF converter and a nonlinear RF amplifying function, for processing the PA's input modulated signal and any envelope-dependent dynamic biasing signal. This novel representation of PA nonlinearities simplifies computation and renders possible analytical formulations to describe a 3-port PA system. It allows accurate prediction of the PA's output distortion components as a function of an input multi-tone excitation and a multi-tone dynamic biasing signal. The representation is intended for a context proposed, to the best of the authors' knowledge for the first time, and envisioned as promising for future mobile communication equipment - the automatic optimization of linearity performance in Radio Frequency Integrated Circuit (RFIC) PAs under any modulated excitation and employing envelope-dependent biasing, through implementation of embedded self-calibration within the transmitter front-ends. In this context, the representation introduced here compares favorably in terms of accuracy with respect to Volterra-based approaches and allows a simpler characterization, while the literature often points to the complexity inherent to Volterra-based approaches. The proposed representation allows the optimization of the PA's dynamic biasing for linearity improvement from one mobile unit to another through embedded self-calibration starting from quasi-static measurements alone of the PA's input/output power. Its applicability is highlighted through benchmarking against experimental results demonstrating accurate PA characterization for multiple PA platforms under different dynamic biasing techniques. In one implementation using an industry-designed GaAs PA, it accurately predicts the dynamic biasing adjustments to achieve more than 4dB reduction in the output intermodulation distortion (IMD3). In another implementation using the recently introduced positive envelope feedback linearization scheme, the proposed representation allows, for the first time, analytically predicting the condition of closed-loop stability and the requirements for the feedback components with experimental verification.